The origin of comets

Our large article about the origin of comets has finally been published! I and my 47 co-authors from Rosetta’s OSIRIS team have made a thorough summary of what we have learned from the spacecraft’s exploration of comet 67P/Churyumov-Gerasimenko, combined with information from other spacecraft and observations of the outer solar system from ground, with the purpose of clarifying which of the previously proposed theories of comet formation that is closest to the truth, and what relation comets have to other types of bodies in the outer solar system. During that process we have realized that none of the earlier theories are fully satisfactory and we propose a new hybrid model that combines elements from earlier hypotheses in a unique manner.

The article has been published in the international scientific journal Astronomy & Astrophysics and can be downloaded here. The European Space Agency ESA, which led the construction of Rosetta and is responsible for the daily operations of the spacecraft and its orbital maneuvers, have also made a short popular summary of the article in their blog, where text and graphics have been produced in collaboration with me.

I will write several blog posts that describes various aspects of this paper. This is the first one which briefly describes earlier theories and our new scenario, step by step. Later posts will focus on different topics: what observations we used; why we consider certain theories inconsistent with those observations; why we were forced to introduce new concepts – and perhaps most important of all – what are the consequences of this new work regarding our understanding of early solar system history?

It has long been known that the interstellar medium, from which new stars and planetary system are made, contains a very large number of dust grains consisting of silicates, sulfides, metals, organic substances, and ice, whose diameters are less than a micrometer (i.e., one part in one thousand of a millimeter). It was also known that the newly formed protosun surrounded itself by a flattened and extensive disk of gas and dust known as the solar nebula, however, the processes that were responsible for transforming this smoke to a planetary system have been less understood. What is really going on when myriads of little grains merge to form large planets like Earth, or beasts like Jupiter? Over the years a number of theories have been proposed, where gravitational instabilities, hierarchical agglomeration (also known as hierarchical coagulation), and streaming instabilities played particularly important roles. They all aim at explaining how planetesimals are formed – small bodies with diameters ranging from a few hundred meters to a thousand kilometers that gradually merge into large planets.

Gravitational instability

This is the oldest model in modern times, that dominated our thinking in the 1960’s. According to this model a sedimentation process occurred in the solar nebula – the small dust grains gradually sunk towards the midplane. The gas disk was rather thick while the dust formed a thinner slab with an ever decreasing thickness. Because of this the density of the dust disk grew large over time, when all grains tried to fit within a comparably small volume. The reason why individual grains moved toward the midplane is the force of gravity emanating from all other grains. However, the dust disk cannot become arbitrarily thin and dense. Calculations of the strength and direction of the gravity field within the dust disk showed that it would break up into a large number of smaller isolated plates once a certain critical density was reached. It was this sudden breakup of the disk into smaller plates that constituted the instability. Under the influence of gravity the plates then collapsed to form spherical planetesimals with sizes of hundreds of kilometers. In this model gravity was therefore solely responsible for transforming the rocky smoke to a planetary system.

Hierarchical agglomeration

Toward the end of the 1970’s people started to question this type of gravitational instability. The solar nebula gas is denser and warmer close to the protosun, but thins out and gets colder at larger distances from it. For this reason a pressure forms in the gas that slightly counters the force of gravity. The result is that the gas disk orbits the protosun at somewhat lower velocity than what a planet at a corresponding distance would have done. We say that the gas has a sub-keplerian motion, while a planet has keplerian motion. However, the dust grains that accumulate in a thinner disk near the midplane does not feel this pressure, which is why the dust moves in a keplerian manner and also forces the gas in its immediate vicinity to do the same. For this reason a layer of dust and gas emerges near the midplane that moves around the protosun with a higher velocity than the gas under and above the midplane. The consequence is well known for those who have seen a wind blow over a calm lake – if the wind is weak nothing happens but if the wind velocity exceeds a critical value ripples form on the surface of the water. The ripples are examples of the Kelvin-Helmholtz instability that arises when two media with different density has sufficiently fast relative shearing velocity. People realized that the Kelvin-Helmholtz instability near the midplane would make the gas there turbulent and that this turbulence prevented the dust disk from becoming sufficiently thin and dense for the gravitational instability to occur. Gravity was simply incapable of forming planetesimals because the turbulence was too strong. It was necessary to search for other mechanisms that did not rely on gravity.

It was realized that the so called van der Waals force could be the solution to the problem. Small dust grains that collide tend to stick together, due to a weak attractive force that arises between molecules in the grain surface layers when in physical contact. If grains merged to ever larger units then planetesimals would grow gradually without the assistance of gravity, at least initially. The process of grain sticking in collisions is called agglomeration and since large planetesimals are formed by mergers between smaller ones their structure forms a hierarchy – the model is therefore often referred to as hierarchical agglomeration.

This model dominated the thinking about planetesimal formation during the 1980’s and 1990’s. Very advanced computer codes were designed to figure out exactly how the hierarchical agglomeration behaved in the complex environment of the solar nebula, where turbulence, gas drag forces (similar to air resistance), material forces and gravity caused the piles of grains to collide, fragment, bounce, and merge on their winding road leading from the solar nebula to a planetary system. On ground, in space shuttles, and in space stations a large number of laboratory experiments were performed aimed at measuring the outcome of collisions between different types of grain clusters at different speeds, so that the computer codes could be fed with data with increasing quality and realism.

The theoretical studies of hierarchical agglomeration showed that the process was very promising – many computer simulations showed that it was possible to form planetesimals in this manner, and that they would have properties that resembled those observed for the asteroids in the belt between Mars and Jupiter, and seen among the large transneptunians in the Edgeworth-Kuiper belt beyond Neptune. However, the experiences were not exclusively positive. One problem was that the process was very slow: the cores of Jupiter, Saturn, Uranus, and Neptune need to reach a certain size before the gas dissipates in the solar nebula when it reaches an age of about 3 million years – otherwise they do not have time to accrete the gas from the solar nebula that they largely consist of. Hierarchical agglomeration did not seem to manage, except during certain conditions. Some imagined that the solar nebula may have contained very large amounts of dust, so that the hierarchical agglomeration proceeded sufficiently fast. That means that a large number of planetesimals remain once the planets have formed – far too many compared to the observed number of asteroids and transneptunians. Possibly this problem could be solved if the planetesimals collided violently with each other at a later stage so that the excess was ground down to sand. This idea was reasonable since the planets gradually changes the orbits of the planetesimals in such a manner that their collisions become increasingly violent. Therefore, it was generally assumed that only the largest bodies in the asteroid belt and the Edgeworth-Kuiper belt had survived more or less intact since the early solar system, while most smaller bodies had formed gradually by the grinding process. Such collision cascades have been studied thoroughly to understand how they function.

Other problems are known as the drift barrier and the bouncing barrier. The drift barrier is a result of the drag forces that act when a small planetesimal try to move at keplerian velocity through the slower sub-keplerian gas and therefore feels a constant air resistance. These drag forces makes the planetesimal spiral toward the protosun. The speed during this sunward drift can reach very high values for bodies with sizes around a meter, while bodies that are either much smaller or substantially larger than this have a significantly slower drift speed. Under certain conditions the meter-sized bodies can drift so fast that the solar nebula quickly looses all its rock, that is completely engulfed by the protosun. The drift barrier means that planets cannot form at all since the construction material disappear completely from the solar nebula early on. Subsequent research has shown that the drift barrier may be breached if the small planetesimals are very porous. Early work on hierarchical agglomeration did not take porosity into account, which is why the drift barrier problem may have been exaggerated. Later laboratory experiment have shown that the mergers of grains at low velocity creates extremely porous bodies. If this is accounted for the drift barrier seems less problematic – there are paths to gradual growth that Nature may have treaded 4.6 billion years ago.

The bouncing barrier is a problem that was discovered during laboratory experiments with dust balls consisting of small silica grains. Those are sufficiently sticky (due to the van der Waals force) that micrometer-sized grains can merge to extremely porous pebbles with diameters ranging millimeters to centimeters. However, at that point the growth grinds to a halt. When the porous pebbles collide with each other they do not merge into larger bodies but just bounce. The planet formation stops at a very early stage if the bouncing barrier is a reality. However, also in this case there seems to be ways around the problem.

Computer simulations are often so extremely complex and time consuming that it is practically necessary to make simplifications to make any kind of progress. However, some of these simplifications may turn out to be fatal. For example, it has often been assumed that the collision between two pebbles (say one with 1 millimeter diameter and another with 2 millimeter diameter) always occur at a certain velocity that is regulated by the dynamics of the two pebbles as determined by the local gravity field and drag forces according to local turbulent conditions. But Nature is never that simple, and it is more likely that such collisions take place with different velocities according to some statistical probability – perhaps 60% of the collisions take place at 1 meter per second, but in 2% of the cases the speed is perhaps just 0.1 meter per second by chance. If one erroneously assume that all collisions are exactly at 1 meter per second – motivated by the majority of cases – this may lead to a bottleneck, or in the worst case, a dead end. But if one allows for a natural spread in collision velocities, it is possible that the unusually low velocities actually allows for a limited growth, that later leads to dramatic consequences for how the entire collective of grains, pebbles, and boulders behave – there is a way around the bottleneck and the planet formation process continues.

Another aspect is that laboratory experiments based on silica grains may be a very realistic analogue for material in the warm inner solar system, but not necessarily for the cold outer solar system. Beyond Jupiter’s orbit it is so cold that the rocky grains are covered by organic substances, ordinary crystalline water ice, and a type of structure in frozen water that only arise when it is formed at extremely low temperature – amorphous water ice. Organic substances and crystalline ice is much stickier than silica grains, and amorphous ice is stickier still. It is extremely difficult to make realistic laboratory experiments with such material. Only in recent years there have been published results from laboratory experiment were icy grains with the right dimensions where produced in a controlled way, and investigations of how their hierarchical growth differs from that of silica has begun. Experiments with organic species are also very few and as far as I know agglomeration experiments with amorphous ice have never been done. Preliminary results indicates that the bouncing barrier may not have existed in the cold region where comets were born.

For these reasons hierarchical agglomerations remains being a viable model, even though there is a healthy dose of skepticism in parts of the scientist community who doubt that agglomeration is the answer to all questions, everywhere. In hierarchical agglomeration is the the van der Waals force that primarily is responsible for turning the solar nebula dust into a planetary system.

Streaming instabilities

In 2005 a theoretical work was presented that showed that gas and pebbles possibly could collaborate in a previously unforeseen way, with the consequence that large dense swarms of pebbles formed in the solar nebula – as soon as such a swarm formed it grew rapidly thanks to the streaming instability. At some point the swarm became so large that its self-gravity managed to collapse the swarm into a large planetesimal. Ten years earlier it would have been impossible to test the theory in a large-scale computer simulation, but at this time the computers were sufficiently fast for such a test to be feasible. In 2007 the first successful test was presented, which was greeted with a lot of curiosity and enthusiasm by the science community – and with quite much relief. Finally a model that seemed to answer all questions, and that was not troubled by a lot of annoying barriers!

In this model hierarchical agglomeration is responsible of building pebbles with diameters ranging 1-10 centimeters. If the number of pebbles is sufficiently large compared to the amount of gas the streaming instability will form large swarms of pebbles, if not only the gas is allowed to modify the pebble’s dynamics, but the pebbles are allowed to change the gas motion as well – this mutual interaction is the key to the streaming instability. This process is very fast – forming a swarm sufficiently large to produce an asteroid as large as Ceres (an object with a 1000 kilometer diameter) takes about 10 revolutions around the protosun. That corresponds to about 50 years in the asteroid belt and about 3000 years in the Edgeworth-Kuiper belt. The gravitational collapse takes just 100 years. Considering that the solar nebula had an expected lifetime of about 3 million years, we understand that planetesimals form very fast. This solves one of the most difficult problems with hierarchical agglomeration – that process is too slow to build planet-sized bodies on a reasonable timescale.

Apart from the short planetesimal formation time this model is also characterized by another property – there is no hierarchical procedure where bodies are built gradually, but they jump directly from one centimeter to 100 or 1000 kilometers, depending on the size of the swarm. In this model van der Waals forces, gas drag, and gravity are all involved in planetesimal formation, but at different stages.

Earlier theories about the origin of comets

I have previously described what a comet nucleus is in a blog post. There has never been a single commonly accepted view on comet formation in the scientist community. Instead, a handful of theories have coexisted, each supported by a number of theoretical works and observations. It has not been possible to single out a specific model for the simple reason that there was not a sufficient amount of observations of real comets to be able to exclude all models except one, that remains the final winner. That is one of the reasons why humans build spacecraft that explore comets in situ. We need more information to advance our understanding of comets and their role in a larger context – the formation, evolution, and history of the outer solar system.

There are two main lines of thought that have dominated during the last decades:

  1. Comets are primitive bodies that formed in their current state 4.6 billion years ago, and they have not been modified much. They are called primordial rubble piles.
  1. Comets consist of material that originally were parts of larger bodies. When these bodies collided violently with each other a huge amount of rubble was formed. Gravity gathered some pebbles into a loosely bound aggregate. Such an aggregate is called a collisional rubble pile. Such collisions occurred in the early solar system and they still happen today. A given comet nucleus could therefore have formed either as recently as one million years ago, or 4.6 billion years ago.

The scientist that consider comets to be primordial rubble piles imagine at least two birth processes, depending on which planetesimal formation scenario they prefer.

1a) Some scientist claim that hierarchical agglomeration dominated planetesial formation. If they are correct the comets we see today are leftovers from that process – the comets consist of smaller planetesimals (usually called cometesimals) that merged at low velocity in the solar nebula. In that sense they are a pile of rubble. A 2 kilometer diameter comet primarily consists of cometesimals with sizes of a few hundred meters, that in turn are built by 10-meter cometesimals, and so on, down to the original small grains. Most of the kilometer-sized objects were consumed by large transneptunians during their growth. However, a few of them managed to avoid being eaten, and we see them today as comets.

1b) Other scientist thing that streaming instabilities mainly are responsible of forming comets. Since the comet is supposed to be primordial it is then necessary that the solar nebula had capacity to form some swarms sufficiently small to form objects with 1-10 kilometer diameter, that managed to go through a gravitational collapse. They are also primordial rubble piles, with the difference that the ”rubble” is dominated by objects with a diameter around a centimeter.

Regardless how the primordial rubble pile formed these scientist agree that the number of objects (small comets and large transneptunians) were so few that violent collisions were rare. Therefore, no collision fragments form that could mix with the primordial rubble piles. These scientist think that the amount of mass in the solar nebula was rather small and the environment was dynamically cold, which means that bodies rarely collide at high speed.

Not all scientist support this view – they refer to other observations or theoretical difficulties that suggest that the solar nebula was massive and dynamically hot. In such an environment comet are inevitably collision rubble piles. However, these scientists do not agree on what took place before the violent collisions.

2a) Some scientist think that hierarchical agglomeration was responsible of building the large transneptunians (like Pluto and Eris). They were the largest objects in a population were all sizes were represented, from the 2300 kilometers of Pluto and Eris, down to objects just being a few hundred kilometers in size. They think that most transneptunians with sizes above 100 kilometers are primordial bodies that have survived since solar system childhood, while bodies in the 50-100 kilometer range have collided efficiently with each other and that the majority of the present small bodies – including comets – are collisional rubble piles. In other words, there has been an efficient collisional cascade. Although some comets may be primordial rubble piles, they are completely outnumbered by collisional rubble piles.

2b) Other scientist think that the first generation planetesimals all were 100-1000 km-class objects, formed through streaming instabilities. Therefore all small objects, including comets with typical diameters of 1-10 kilometers must be collisional rubble piles, formed in a collisional cascade.

It is difficult to tell which of these alternatives that may be considered most popular today. There are no popularity votes or polls among scientists. However, the opinions of individual scientists on a controversial topic does not matter much, not even the opinions among a certain generation of scientists. After all, there is a single objective historical truth – Nature chose a specific route and comets have formed in a specific way. Beliefs and opinions are meaningless – our task is to recover the truth that always been out there. We know by experience that time corrects all mistakes. One hundred years ago, in 1916, Albert Einstein had just published his general theory of relativity and it was motivated to have opinions about the correctness of the theory. There was room for opinions since there were few measurements that could prove or disprove the theory. But during these one hundred years a large number of measurements have been performed in earthly observatories and in space, and it has been possible to make observations of extreme astrophysical object that their behavior has been documented in detail. The technology that made these experiments and observations possible did not exist in 1916. They were developed over time, and over and over Einstein was proven right. Nowadays no serious scientist doubt that Einstein’s general theory of relatively tells us something profound about the properties of Nature, and no-one questions its capability of quantitatively reproducing observed phenomenon with extremely high precision. The doubters of 1916 have been silenced by history. In the same way astronomers 100 years form now – after a number of spacecraft missions to comets that are similar or superior to Rosetta – will look back at the controversies among the scientists of our time with (as always is the case in retrospect) with a faint smile on their lips because they cannot understand how we could be so primitive and childish in our opinions.

Nevertheless, if one tries to select a dominating line of thought, that primarily has reached its status based on the theoretical works that often constitutes the basis of our world view in the absence of concrete observational evidence, I’d say it would be 2b – that comet nuclei are collisional rubble piles and that their parent bodies formed through streaming instabilities. The first reason is that streaming instabilities currently probably should be considered being a more popular scenario than hierarchical agglomeration. Streaming instabilities is an elegant way of avoiding several of the perceived or real bottlenecks and the slowlyness for which the hierarchical agglomeration often has been criticized. The second reason is that the Nice model is very popular today. It states that the giant planets formed rather close to the Sun and that the outer solar system was dominated by a large number of planetesimals gathered in a structure called the primordial disk. The giant planets acquired their current orbits by strong mutual gravitational perturbations that spread the primordial disk planetesimals all over the solar system – some bombarded the Moon (an may explain the presence of the large and comparatively lately formed dark spots that can be seen by the naked eye), others formed the Trojan swarms that share Jupiter’s orbit or were captured as giant planet satellites (which explains the strange orbits for some of these satellites), while yet others formed the Edgeworth-Kuiper belt (which explains its strange structure in detail). The Nice model, in its basic form, hypothesize that the number of planetesimals in the primordial disk was very large – it would be possible to build 35 earths out of that material. With so much mass in an environment that additionally considered to be dynamically hot a collisional cascade is unavoidable.

This is the reason that we chose to use 2b in the ESA press release (see Figure 1) as a representative of ”earlier” comet theories.

Figure 1: The left column of images shows how we often have imagined comet formation before Rosetta. Hierarchical agglomeration first builds pebbles with sizes around a centimeter. Streaming instabilities in the solar nebula then form gigantic swarms of pebbles that merge through gravity to large transneptunians with typical diameters in the range 100-400 kilometers. These then collide with each other – to begin with rather gently so that some of them merge to objects as large as Pluto (2300 km) or the Neptune satellite Triton (2700km) that was captured from the primordial disk. However, collision velocities increase over time and cease to be constructive (in which two smaller objects merge into a large one) and start to become destructive (two smaller objects pulverize each other). In some cases the collision fragments are joined into loosely bound lumps – many scientists see comets as such collision rubble piles. Our new scenario is seen to the right, with one column for large transneptunians and another for small comets. In our opinion the transneptunians form first through streaming instabilities. Remaining material then grows through hierarchical agglomeration to form comets. The growth rate of the comets is so slow that they have time to dissipate the heat generated internally by radioactive decay – therefore they remain very cold and porous. Due to their slow growth much of it takes place after the solar nebula gas has dissipated. In our opinion this gives comets some unique properties – their outer parts are dominated by concentric shells, and they often merge two by two. If comets form in this manner we demonstrate that they are so few in number that they do not collide violently with each other at later times. Comet nuclei are therefore surviving primordial rubble piles that are 4.6 billion years old.

Figure 1: The left column of images shows how we often have imagined comet formation before Rosetta. Hierarchical agglomeration first builds pebbles with sizes around a centimeter. Streaming instabilities in the solar nebula then form gigantic swarms of pebbles that merge through gravity to large transneptunians with typical diameters in the range 100-400 kilometers. These then collide with each other – to begin with rather gently so that some of them merge to objects as large as Pluto (2300 km) or the Neptune satellite Triton (2700km) that was captured from the primordial disk. However, collision velocities increase over time and cease to be constructive (in which two smaller objects merge into a large one) and start to become destructive (two smaller objects pulverize each other). In some cases the collision fragments are joined into loosely bound lumps – many scientists see comets as such collision rubble piles. Our new scenario is seen to the right, with one column for large transneptunians and another for small comets. In our opinion the transneptunians form first through streaming instabilities. Remaining material then grows through hierarchical agglomeration to form comets. The growth rate of the comets is so slow that they have time to dissipate the heat generated internally by radioactive decay – therefore they remain very cold and porous. Due to their slow growth much of it takes place after the solar nebula gas has dissipated. In our opinion this gives comets some unique properties – their outer parts are dominated by concentric shells, and they often merge two by two. If comets form in this manner we demonstrate that they are so few in number that they do not collide violently with each other at later times. Comet nuclei are therefore surviving primordial rubble piles that are 4.6 billion years old.

 

Our new model of comet origins

In our scenario we assume that the primordial disk had a substantially lower mass than in the nominal version of the Nice model. We start off with the lowest mass – about 15 Earth masses – that still is consistent with the overall properties of the Nice model. Therefore, we do not reject the Nice model, but we feel forced to revise the assumption regarding the amount of mass. The reason for this is that we need to avoid an collisional cascade, since we think that the observations by Rosetta excludes that such a process took place. In our opinion 67P/Churyumov-Gerasimenko is a primordial rubble pile.

We demonstrate that the solar nebula initially had such properties that streaming instabilities should have been active. We therefore think that large transneptunians formed very early and we have reasons to claim that their diameters typically were in the range 50-400 kilometers. Since pebbles continuously are consumed in order to build large planetesimals they eventually become too few, compared to the amount of gas, for streaming instabilities to form new pebble swarms. We estimate that this happens when about 13 earth masses have been consumed.

At that point, about 2 earth masses remain in the form of centimeter-sized pebbles. The question is – what happens to those? We claim that this remaining material eventually form comet nuclei. We think that these pebbles start merging to increasingly large units, that is to say, a hierarchical agglomeration process takes place. As previously mentioned, this is a very slow form of growth. In our case it is even slower than in previous works since we start out with an unusually small amount of dust, furthermore, it is only a small fraction of this dust that grows through hierarchical agglomeration. The extremely slow growth is a problem if one want to form planets – but if one wants to form comets it is a necessity.

The thing is that the small pebbles contained a radioactive element called aluminum-26. When this radioactive substance decays heat is being generated. The large transneptunians will therefore experience strong heating and suffer structural, chemical, and mineralogical changes that we think can be seen among those bodies today. However, the comets must be kept extremely cold at all times since only extreme cold can explain why they still are so rich in very volatiles species, and how they managed to maintain an extremely high porosity.

It is much easier for small bodies to dissipate the heat produced (it escapes to space as infrared radiation), than for large bodies. It is therefore good that these cometesimals grew very slowly, since that gives them the chance to cool off.

We estimate that the cometesimals only had reached diameters between 100 meters and 1 kilometer when the solar system reached an age of 3 million years. A few bodies had grown as large as 5-6 kilometers. When the gas in the solar nebula started to dissipate, most comets had therefore not yet grown to their full final size.

The cometesimals that formed in this manner are extremely porous. They have systematically been built by the merger of smaller objects into bigger ones. Meetings between similarly-sized objects were very rare. Instead, meetings between a comparatively large body and a much smaller one have dominated. That affects the shape of the growing objects – they do not look like 67P/Churyumov-Gerasimenko at this stage, that consists of two large lumps (lobes) that attached to each other. These cometesimals are much more spherical, and look more like the individual lobes.

When the gas goes away the conditions for continued growth change completely. The presence of large transneptunians and the absence of drag forces gives rise to a phenomenon called ”viscous stirring”. The practical consequence is that cometesimals now collide with each other at ever increasing velocity (it increases from 0.1 meter per second to tens of meters per second). The rate of change is very slow, but it changes the appearance of the cometesimals.

The somewhat more violent collisions lead to the formation of a shell around the extremely porous cores, that are somewhat less porous. Layer upon layer of compressed material create a stratified outer shell on the cometesimals that resembles the layers in an onion. Another consequence of the viscous stirring is that cometesimals of similar size for the first time collide frequently in space. It is in these type of collisions that objects similar to 67P/Churyumov-Gerasimenko have formed. The collisions take place at sufficiently low velocity that the lobes do not destroy each other, they just gently attach.

We calculate in detail how the viscous stirring changes the collision velocities over time and estimate the number of large transneptunians and comets that collide within their groups and with each other at any given moment. Therefore, we can estimate how the number of objects and their sizes evolve over time. Previous work has shown that the primordial disk existed for about 400 million years. We show that about 350 transneptunians manage to grow to the size of Triton (2700 km) in this time. We also show that the growth phase of comets primarily is over once 20-25 million years have passed. The largest comet-sized objects have diameters of at least 50 kilometers, thus we claim that large comets like Hale-Bopp reached their full size when the solar system was about 25 million years old.

Due to low-velocity mergers and collisions with transneptunians that number of comet nuclei had been heavily reduced at this time. The fact is that they are so few that they do not manage to collide with each other when the viscous stirring has created such high relative velocities that collisions would have been destructive, if they occurred. This is good, because the primordial rubble piles therefore can survive throughout the solar system lifetime so that we can see them as comets.

When 400 million years have passed the giant planets will enter into the primordial disk and destroy it. We calculate in detail how many comets and large transneptunians that are places into the Edgeworth-Kuiper belt and into another population further from the sun called the scattered disk. The scattered disk is considered being the source region of the comets that currently manage to find their way into the inner solar system so that we can see them (67P/Churyumov-Gerasimenko is one of those).

There are several new things in our scenario. The primordial disk has an unusually small mass and is dynamically cold. We have completely separated the comets from the large transneptunians – the comets are not the precursors of transneptunians (as in classical hierarchical agglomeration) and the transneptunians are not the parents of comets (as in a collisional cascade). Instead we view the large transneptunians and the comets as two entirely different populations that formed out of the same building blocks (the centimeter-sized pebbles) but that evolve in different directions due to two completely different processes – in the case of transneptunians through streaming instabilities and in the case of comets through hierarchical agglomeration. It’s not a matter of ”either one or the other” – we believe in a hybrid where both mechanisms are active simultaneously.

Another novelty is that the number of comets may be much smaller than previously thought. Our model has about 100 times fewer comets in the primordial disk compared with previous estimates – we claim there were ”only” about three billion comets with diameters above 2 kilometers. The earlier estimates are based on the number of currently observed comets, combined with a large number of assumptions that lead backward from the inner solar system to the scattered disk, then backward to the days of the primordial disk. Although these estimates have been done ”by the book” we are not fully convinced of their correctness. If our estimate of a substantially lower number of comets is correct, it is easier to understand certain observational studies of the scattered disk, as well as the number of craters on the Moon.

If we are right it also means that rather few comets hit Earth in its childhood. They may have brought less water and organics to our planet than previously assumed. This does not necessarily mean that we need to exclude that comets played a part in the emergence of life on Earth – but we may have to think more in terms of quality rather than quantity.

More about that another time!

Literature

Davidsson, B. J. R., H. Sierks, C. Güttler, F. Marzari, M. Pajola, H. Rickman, M. F. A’Hearn, A.-T. Auger, M. R. El-Maarry, S. Fornasier, P. J. Gutiérrez, H. U. Keller, M. Massironi, C. Snodgrass, J.-B. Vincent, C. Barbieri, P. L. Lamy, R. Rodrigo, D. Koschny, M. A. Barucci, J.-L. Bertaux, I. Bertini, G. Cremonese, V. Da Deppo, S. Debei, M. De Cecco, C. Feller, M. Fulle, O. Groussin, S. F. Hviid, S. Höfner, W.-H. Ip, L. Jorda, J. Knollenberg, G. Kovacs, J.-R. Kramm, E. Kührt, M. Küppers, F. La Forgia, L. M. Lara, M. Lazzarin, J. J. Lopez Moreno, R. Moissl-Fraund, S. Mottola, G. Naletto, N. Oklay, N. Thomas, and C. Tubiana (2016). The primordial nucleus of comet 67P/Churyumov-Gerasimenko. Astronomy & Astrophysics, 592, A63.

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OSIRIS on Rosetta has imaged Comet 67P/Churyumov-Gerasimenko!

As a member of the OSIRIS Science Team I am happy to announce that our camera OSIRIS, that flies on ESA’s spacecraft Rosetta, now has imaged the target of its ten year long journey – Comet 67P/Churyumov-Gerasimenko!

WACv3_box

Comet 67P/Churyumov-Gerasimenko in constellation Ophiuchus. This image taken with the Wide Angle Camera on March 20 shows a wide field 25 times larger than the diameter of the full moon. The color composite shows a background of hydrogen gas and dust clouds in the constellation Ophiuchus. The white box indicates the position of the close-up taken with the Narrow Angle Camera (below). The images were taken from about 0.03 AU distance to the comet. Rosetta was at a distance of approx. 4.4 AU from Earth. Image credit: ESA ©2014 MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

Rosetta was launched in March 2004. The purpose of the spacecraft is to explore, in situ, what happens to a comet nucleus when it approaches the Sun from a very large distance, gradually is heated and therefore becomes active. Therefore, Rosetta first had to get very far out in the Solar System. The spacecraft swung by Earth three times, and Mars on one occasion, so that the gravitational perturbations from these planets gradually could make Rosetta’s orbit around the Sun wider. On its way, the spacecraft also passed near to two asteroids – (2867) Steins in September 2008 and (21) Lutetia in July 2010. I June the following year, Rosetta had come so far from the Sun that its solar panels no longer managed to generate the electric power necessary to keep the entire spacecraft up and running. Therefore, Rosetta was put in hibernation and all available power was used to heat the instruments to prevent them from break by freezing. The ground control had no contact with Rosetta at all.

In October 2012 Rosetta was farthest from the Sun, no less than 5.3 AU (one astronomical unit, 1 AU, is the mean distance between Sun and Earth, and corresponds to 150 million kilometers). It means that Rosetta was beyond the orbit of Jupiter, that is located 5.2 AU from the Sun. Two and a half years after Rosetta entered hibernation, on January 20, 2014 to be precise, it was time for the spacecraft to wake up. It was an enormous relief when the signals from Rosetta reached the ground control! After the wake-up, careful checks were made to make sure Rosetta was feeling well after its long sleep. We are now at a stage where the scientific instruments are switched on one by one, to see how they have coped with the hibernation. OSIRIS was switched on last week, and has now taken its first images of the comet – the camera works beautifully! We will therefore be ready when Rosetta reaches the comet in August this year, at a distance of about 4.5 AU from the Sun.

OSIRIS WAC

OSIRIS is the camera system on Rosetta. It actually consists of two different telescopes. One of them is called the Wide Angle Camera (WAC) and has a rather large field of view since it will be used to image the comet coma, the cloud of gas and dust that the comet nucleus surrounds itself with (see a previous post on comets). The camera has 14 different filters – glass plates with a special composition and surface coating that makes them transparent to light only at specific wavelengths. These filters are manufactured in Sweden and is the Swedish hardware contribution to OSIRIS. Seven of these filters are so-called narrowband filters – they are transparent only at very strict wavelength regions corresponding to the wavelength were seven different molecular fragments (radicals) emit light when they are illuminated by the Sun. These radicals are CS (a compound consisting of carbon and sulphur), the hydroxyle radical OH and the oxygen atom O (these are formed when the ultraviolet light of the Sun break down water molecules), NH and NH2 (compounds of nitrogen and hydrogen), CN (the cyano radical, consisting of carbon and nitrogen), and the sodium atom (Na), that can be outgassed by dust grains that are strongly heated by sunlight.

The dust grains in the comet coma will reflect sunlight, and some of this light will find its way through the narrowband filters. This is not good, since we will use the intensity of the light to calculate the abundances of radicals and atoms in the coma. Since the dust grains contribute with light, that does not originate from within the gas at all, the risk is that we overestimate the abundance of gas. Therefore, the WAC also has seven filters that is transparent to light just next to the wavelength regions of the narrowband filters. In this way, the contribution of the dust grains to the measured light can be estimated, and compensated for when determining the gas abundance. Four of these filters are transparent in the ultraviolet wavelength region (for example, a filter called UV375), while the others are located in the green, yellow and red wavelength regions.

The image above is really three different WAC images, taken through different filters. The red filter was used during an exposure that lasted one minute. The green filter was used during an equally long exposure. Finally, the UV375 filter was used three times with a total exposure time of nine minutes. By combining these images, the color photo above could be constructed.

OSIRIS NAC

The second camera is called the Narrow Angle Camera (NAC). It has a smaller field of view than the WAC, but is capable of resolving objects that are five times smaller than the ones the WAC manages to resolve. This camera will primarily be used to study the comet nucleus. This camera also has Swedish filters, but with quite different properties – a mixture of broadband filters in different parts of the visible wavelength region to make a rough characterization of the comet spectrum, and a number of filters that will be used to search for specific minerals, like pyroxene, hematite and hydrated silicates.

The figure below shows a picture taken with the NAC, and corresponds to the white square in the picture above. The strongly magnified picture shows a globular cluster called Messier 107 (or M107), as well as the comet nucleus within the small circle. It is still far too distant to be seen in detail, and is only a dot in the sky. But day by day Rosetta is closing in on the comet and soon we will be able to see how it looks like up close!

 

NAC-median-zoom-cometcircled

Comet 67P/Churyumov-Gerasimenko in constellation Ophiuchus. A zoom into an image taken with the Narrow Angle Camera on March 21. The comet is indicated by the small circle, next to the bright globular star cluster M107. The images were taken from about 0.03 AU distance to the comet. Rosetta was at a distance of approx. 4.4 AU from Earth. Image credit: ESA ©2014 MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

For ESAs press release click here.

Why are comet nuclei dark and red?

A comet nucleus is a few kilometers in diameter and consists of a very porous mixture of ice, organics and a fine rocky powder. They often move on a highly elliptic orbit around the Sun, which means that they spend most of their time in extreme cold at large distances from the Sun. The ice is then so cold that it is stable, even when it is directly illuminated by the Sun and exposed to the vacuum of space. But periodically the comet passes its perihelion, its smallest possible distance to the Sun, and on its way there, the surface layer of the comet is heated sufficiently to vaporize the ice. The gases rush out from the comet nucleus, drags dust grains along and form the coma, a vast temporary atmosphere, along with two tails consisting of gas and dust, respectively. The basic properties of comets have been described in an earlier post.

Hale_Bopp

Comet C/1995 O1 (Hale-Bopp) photographed in april 1997. The dust tail is yellow-white since it consists of small dust particles that reflect the light of the Sun. The plasma tail is blue since light with this color is emitted by ionized carbon monoxide in the tail.
Copyright: E. Kolmhofer, H. Raab; Johannes-Kepler-Observatory, Linz, Austria
Original image: http://en.wikipedia.org/wiki/File:Comet_Hale-Bopp_1995O1.jpg

But how close does a comet nucleus need to get to the Sun, in order to send gas and dust into space? How do the production rates of gas and dust vary with the distance to the Sun? Are all parts of the comet nucleus emitting the same amount of gas and dust, or are some regions more productive than others? In order to answer questions of this type astronomers use a tool called thermophysical modeling. The purpose of this modeling is to calculate the temperature of the comet nucleus at different depths below the surface, and how these temperatures are changing with time, as the Sun rises and sets in the sky as seen from a specific point on the comet surface, due to the rotation of the nucleus. These temperatures are depending on a number of different things, like the intensity of solar light, the capability of the surface material to absorb solar radiation, its heat conductivity, its porosity, the abundance of ice, and the physical properties of water as a chemical species. The final product of these calculations is an estimate of the number of water molecules that leaves a square meter of comet surface every second. By adding contributions from different parts of the comet nucleus, that are illuminated by the Sun in different ways at any given moment, it is possible to calculate the total production of gas of the nucleus.

My research has focused on thermophysical modeling for many years, and in a number of posts I will describe the thermophysical model I developed together with Dr. Yuri Skorov, a Russian scientist who presently works at Technische Universität Braunschweig in Germany. The model has several parts that are joined to form a whole – I here describe the first part, that deals with the way the surface material of comet nuclei absorb sunlight. Such research can provide clues as to why comets are so dark – they reflect merely a few percent of the sunlight – and why they are so red. As a fact, they reflect red light much more efficiently than blue light.

What happens to the solar radiation at the surface of the comet?

In order to describe the outgassing of a comet one needs to solve several sub-problems. One of these deals with the sunlight as it hits the surface of the comet. What fraction of this radiation is reflected back into space? What fraction of the radiation is absorbed, so that its energy can be used to vaporize ice? Where does this absorption take place – how deep are the solar rays penetrating?

When I started my PhD studies at Uppsala university in 1998, most thermophysical models used by scientists worldwide, assumed that solar radiation was absorbed at the very surface of the comet, within an infinitely thin layer. The reason for this assumption was very practical – there are so many other things to take into account, that the details of solar light absorption were overlooked in favor of other mechanisms considered more important. However, we envision the comet surface material as very porous – the material consists of loosely bound grains of ice and rock, surrounded by cavities and empty spaces since the gravitational force of the little nucleus is incapable of compacting the material. The solar radiation should be able to penetrate fairly deep into such a porous structure before being absorbed, especially since many of the grains consist of ice, which is rather transparent. Since ice at a depth of a few millimeters or centimeters below the surface therefore may be illuminated directly by sunlight, and if large amounts of vapor therefore are produced at depth, the outgassing of a comet would perhaps behave differently, compared to an object were all solar energy indeed is absorbed within the uppermost layer of tiny grains.

On a related note – the space probe Voyager 2 had flown by Jupiter in July 1979, and observed its ice-rich satellite Europa with an infrared spectrometer, that measures the heat radiated from the surface of Europa. Based on these measurements it is possible to calculate the temperature that prevails on different parts of the surface of Europa. When these temperatures, valid at different local times (night, early morning, noon), were compared to calculations, it was found that thermophysical models failed to reproduce the observations if they assumed that all radiation was absorbed at the very surface. Only when the model allowed radiation to be absorbed gradually within a thicker layer of ice near the surface was it possible to match the calculations with the measurements.

If all radiation is absorbed at the very surface, a sunlit spot on the dayside of Europa will have its highest temperature at the very surface, and the temperature decreases with depth below the surface. However, if the solar radiation is absorbed gradually within a thicker layer, the surface becomes rather cold. Now the temperature increases with depth and reaches a maximum a few millimeters or centimeters below the surface, and is then falling at even larger depths. This phenomena is called a solid-state greenhouse effect and is due to the fact that radiation easily can enter, but has difficulties getting back out. This is because sunlight primarily consists of visible light, and at such wavelengths ice is rather transparent. But the heated ice below the surface tries to get rid of this heat by emitting infrared radiation, at wavelengths where ice no longer is transparent. The energy cannot get out, but accumulates – this causes the temperature peak just below the surface – and it can only be removed by heat conduction or by consumption through ice sublimation.

Nobody had seriously considered solid-state greenhouse effects for comet nuclei, and since I needed a relatively poorly studied topic for my doctoral thesis, I thought I could work on this problem. But where to start?

Comet grains

First one needs to have an idea of how the grains look like in the surface region of the comet – what is the grain size, what minerals and substances are present, how are these materials arranged within the grains, how much void space surrounds the grains, and are the grains homogeneously distributed or lumped together into little clusters?

We know that comets contain grains consisting of silicates, sulfides and metals, typically having a size of a tenth of a micrometer, that is to say, ten thousand times smaller than a millimeter. This is because oxygen, silicon, magnesium, iron and sulphur are some of the most common chemical elements in the interstellar medium from which the Solar System formed (see the post about Voyager 1 and the interstellar medium), and since these elements team up to form silicates, sulfides, and metals – the mixture we call rock. We know that most of the grains have a size of a micrometer or smaller, because they are expelled in large numbers by active comets to form their huge dust tails. The sizes of these grains can be inferred from their motion – the dynamics is determined by the gravity and radiation pressure of the Sun, in a way that makes it possible to estimate the sizes of the grains.

PIA02190_modest

A grain from Comet 81P/Wild 2, captured by the NASA spacecraft Stardust and brought back to Earth. The grain consists of the mineral forsterite, a silicate belonging to the olivine family, consisting of two magnesium atoms (Mg) and four oxygen atoms (O) for each silicon atom (Si); Mg2SiO4. The particle is about 2 micrometers across.
Image Credit: NASA/JPL-Caltech/University of Washington
Original image: http://photojournal.jpl.nasa.gov/catalog/PIA02190

It is likely that such small cores of rock are covered by a mantle of organic substances. This is because carbon is even more common in the interstellar medium than the previously mentioned elements, and it must be present in the comet in one form or another. This is because organic substances have a much lower condensation temperature than silicates, sulfides and metals, and require very cold environments to solidify from the gas phase. Therefore, organic species are rare in the inner Solar System (for Mercury, Venus, Earth, Mars and the inner parts of the asteroid belt), but much more common in the outer Solar System – for example in the comets. The inner Solar System was too warm for organic species to condense in large numbers, but in the outer Solar System this process could proceed undisturbed. In this way, mantles of organics likely formed on the pre-existing grains of rock. Such a grain can be seen in panel A in the figure below.

grains

Drawings of the grain types discussed in this post.

Another species that was present in huge quantities was water – which has an even lower condensation temperature than the organic species. Therefore, essentially all water in the inner Solar System was in the form of vapor, while the substance gradually could condense and freeze in the outer parts of the Solar System. Thus thick crusts of ice were formed on the grains, on top of the layer of organics. This ice could either be rather pure (panel B) or possibly mixed with organic substances and rather dirty (panel C).

About 4.57 billion years ago such free-flying grains started to stick to each other as they collided at low speed, and with time this fluffy ball of rock, organics and ice grew to a size of several kilometers – this is the comet nucleus. We have reasons to believe that these grains are not strongly compressed within the nucleus, but form a loosely bound structure where grains barely touch, and where cavities of different sizes surrounds threads or membranes of loosely bound grains, which makes the material very porous and fragile. The force of gravity is too weak to squeeze the material into a more compact dirty snowball – it may have a structure resembling cotton sugar. We often see that comet nuclei fragment, split or are pulverized completely, which means that they are extremely fragile. We know that comets have a very low density and high porosity since we can measure their masses and volumes. Their masses are very low compared to what we could expect, given their volumes. It is necessary to take this very high porosity into account when trying to calculate the penetration depth of the solar radiation.

fragb_73p_hst_c

Comet 73P/Schwassmann-Wachmann 3 imaged by the Hubble Space Telescope in April 2006. The comet nucleus is fragmenting. At the upper right is one of the largest fragments, “fragment B”, which in turn has ejected three dozens of smaller pieces that drift outward in its tail. Many of these smaller fragments have tails of their own due to outgassing and expulsion of dust grains.
Image Credit: NASA, ESA, H. Weaver (JHU / APL), M. Mutchler and Z. Levay (STScI)
Original image: http://apod.nasa.gov/apod/ap060504.html

We do not know if the grains are homogeneously distributed, or if they form lumps here and there – something we call clusters. Panels D and E show examples of such clusters – in the former case the cluster consists of type A grains (they only contain rock and organics), while clusters of type E consist of type B grains (containing ice in addition to rock and organics). We can also imagine that ice evaporates but that the vapor freezes anew. If this happens over and over again, larger chunks of more compact ice could form, where particles of rock and organics (type A grains) are finely distributed within the chunk – such a dirty ice particle is seen in panel F.

The interaction of sunlight with single grains and clusters

Light, also called electromagnetic radiation, consists of an electrical field and a magnetic field that oscillate about each other. When light from the Sun penetrates the surface layer of the comet, these electric and magnetic fields start to interact with the electrically charged particles – atomic nuclei and electrons – that the grains consist of. As a result of such interaction some of the solar energy is absorbed – this gives the atoms higher vibration speed since they have absorbed the energy of the light. The parameter we call “temperature” is a direct measure of these vibration velocities, so the absorption of sunlight of the grains simply increase their temperature. But a part of the radiation will not be absorbed, but re-emitted by the grain in various directions – we say that the radiation is being scattered.

If we want to know how solar radiation behaves as it enters the surface layer of the comet we therefore first need to understand how the solar radiation interacts with a single grain, or a cluster of such grains. Exactly how much radiation is absorbed and how much is scattered? Exactly how much radiation is scattered into a specific direction, for example, perpendicularly to the original direction of propagation of the light? How do these things depend on the particle size, its chemical composition, and internal structure? How are these dependencies changing depending on the wavelength of the radiation?

There is a whole branch of science dealing with questions of this sort – light scattering theory. The first step was therefore to use techniques that had been developed in this research field. For the simplest grains (type A, B, and C), consisting of spheres or concentric shells with different composition, it is possible to use Mie theory. Mie theory is based on Maxwell’s equations – a group of equations that describe the properties of the electric and magnetic fields that light consists of. By using the Maxwell equations, Mie theory calculates exactly what happens to the electromagnetic wave as it encounters a spherical particle. The result is an analytical solution – a mathematical formula were one can enter the particle size, the thickness of the different layers, the wavelength of the radiation, and parameters that describes the optical properties of the materials (these differ strongly between various types of silicates, sulfides, organics and ice and are measured in the laboratory). The analytical solution then tells us how much radiation is being absorbed or scattered, and in what way.

However, it is not possible to apply Mie theory for the clusters seen in panels D and E. These grains have an extremely complex geometry – matter with very different optical properties are mixed in an elaborated manner, and there are a lot of cavities and spaces where radiation may bounce around and change direction. If a ray of light falls on such a complex particle, how much is absorbed and how much is scattered?

There are many techniques available to calculate the behavior of the electromagnetic wave when it interacts with such a strange grain. In our work, we used a technique called the Discrete Dipole Approximation or DDA. A dipole consists of a particle with positive electrical charge and a particle with negative electrical charge, separated by some distance. If the dipole is illuminated, the electrical and magnetic fields of the light will set the charged particles in motion. An oscillation takes place, so that the distance between the two parts of the dipole periodically is decreasing and increasing. Electrical charges that perform acceleration and deceleration will emit light themselves, into completely different directions compared to the light that initially set the dipole in motion. The energy theft of the dipole is the very reason for the light absorption of the material, while its emission is the source of the scattering phenomenon.

In DDA, the grains are represented by tens of thousands of individual dipoles, that each have their specific position. The dipoles located in a region consisting of silicates are given properties that are typical of silicate. The dipoles located in a region consisting of organics or ice are given properties consistent with those substances. Cavities between grains are not given any dipoles at all. A computer code then calculates what happens to every single dipole, when it is exposed to the combination of sunlight and radiation produced by all other dipoles within the grain. In this way, DDA can calculate very accurately how much sunlight is being absorbed or scattered by the cluster as a whole.

For grains of type F we used a third technique called geometrical optics. That is the type of physics used when calculating what happens to radiation when it passes through large objects like lenses (in telescopes, glasses, etc) or large drops of water. Geometrical optics assumes that the objects is much larger than the wavelength of the light. It is possible to calculate how much radiation that is reflected at the surface of the grain, and how much that enters the grain. For the transmitted radiation, the gradual absorption can be calculated, as well as the scattering, especially considering the presence of small particles of rock and organics that are baked into the grain. This calculation provides the same type of information as Mie theory and DDA – how much radiation is absorbed, how much is scattered, into what directions is the scattered radiation going, and how does these things depend on the size of the chunk and its content of type A grains?

Radiative transport

Thanks to these calculations we had come quite a way. We now had a fairly good idea of how individual grains, or clusters of such grains, interact with sunlight. The next step was to figure out how an entire medium of such grains behave – that is to say, large quantities of such grains or clusters that are spread out within a volume, with empty space between them in a porous yet coherent structure. Basically – what happens to sunlight as it shines on a dirty and very fluffy snowball consisting of millions of little grains?

The first step was to cut out small cubes of material and figure out how such cubes would absorb and scatter radiation, accounting for the fact that only a fraction of their interior consisted of grains or clusters, while most of their volumes were empty space. Through this calculation we could account for the porosity of the comet surface material.

The next problem was far more complicated. The surface region of the comet will consist of an entire network of such cubes. Each cube will receive some radiation from the Sun, keep some for itself, and pass on the rest into different directions. But since each cube is emitting radiation like this, it means that the Sun is not the only source of light. In reality, each cube will be illuminated both by the Sun and by all other cubes, and it is this combined radiation field each cube needs to deal with. Luckily it is possible to describe this complex network of interdependencies of cubes with the aid of a powerful mathematical tool – the so called equation of radiative transfer.

In fact, all of our work had aimed at realistically describing the terms for absorption, degree of scattering and type of scattering that need to be known before one even can attempt to solve this equation. However, the equation of radiative transfer is far too complex to be solved analytically, why we used the computers again. By doing so we obtained numerical solutions that finally allowed us to achieve our goal. We could tell, in a fairly realistic manner, what happens when the Sun shines on a comet nucleus.

Reflectivity and color

By observing comet nuclei we know that they are very dark – they reflect only a few percent of the sunlight that illuminates them. For example, Comet 1P/Halley only reflects 4% of the sunlight. We also know that they are rather red, in the sense that they reflect light at long wavelengths (red) more efficiently than light at short wavelengths (blue). We also know that most comets produce very little water vapor compared to the available nucleus surface area, which means that large parts of this area is ice-free and inactive. The inactive areas, that dominates the surface of comets, could perhaps consist of grains similar to type A or D, that lack ice.

Therefore it is interesting to compare our theoretical calculations to the actual observations. As it turns out, a porous medium consisting of 0.1 micrometer type A grains with 70% porosity, will reflect 9% of the sunlight if they are not forming clusters. This is a bit too much, but we also found that the reflectivity is strongly dependent on the size of the grains – if the grain size is cut in half, the reflectivity drops to 2%. This is very close to the reflectance of real comets. However, there is a problem – our modeled medium is strongly blue – it reflects the short-wavelength light more effectively than the long-wavelength light, which is not the case for real comets.

If the grains are allowed to form small clusters (like in panel D), something interesting happens – the reflected radiation becomes very red, and is similar to that of real comets. A medium consisting of small clusters of type D do reflect a bit too much radiation, about 13%. However, this is possibly due to the porosity of the medium. We had assumed a very high porosity in our calculations, about 76%, but laboratory experiments show that this type of media may be even more porous, reaching values in excess of 90%. Such a high porosity makes it even easier for radiation to enter, and if a reflection takes place, the radiation most likely does not manage to exit, but illuminates some other part of the medium, where it may get absorbed. Therefore, if the porosity is increased further, the reflectivity could be substantially lowered.

It is therefore possible that the inactive parts of cometary surfaces are dominated by extremely small grains of rock and organics, that often form little clusters, and that this medium is extremely porous. In fact, such a medium would be as dark and as red as real comet nuclei.

How would a spot of dirty ice look like? According to our calculations, a porous medium consisting of type E clusters would not look much different than a porous medium of ice-free clusters. It is still very red, but reflects a bit more – about 20% of the sunlight if the ice is clean, but only 13% if the ice is dirty. These clusters contain three times as much ice as rock. An icy spot therefore does not necessarily look white and shiny like newly fallen snow, but can be very dark. The reflectivity depends on the way ice, organics and rocks are mixed with each other, and the size of pieces of “pure” rock and organics compared with the wavelength of the light that illuminates them.

If the grains look like those in panel F, the calculations show that the material may become very dark – it only reflects 3% of the light and the color is fairly neutral. There is not a big difference in reflectivity at long and short wavelengths.

How deep does the radiation penetrate?

The single most important property of the medium that decides where and how sunlight is absorbed is the size of the cavities between the grains. If a medium consists of 0.1-1 micrometer grains or clusters that are homogeneously distributed, the cavities will also have sizes of a few micrometers. On its way through the medium, the radiation is “forced” to pass through grains, where it rapidly becomes absorbed.

If the grains look like those in panel B, about 90% of the radiation will be absorbed at a depth of 10 micrometers, while 99% of the radiation is absorbed in the upper 45 micrometers. This is very deep in a relative sense – the grains are assumed to have a radius of merely 0.16 micrometers – but is very short in an absolute sense. For such a medium, an assumption of immediate absorption at the surface is probably accurate.

If the grains look like those in panel F, and if they have a size of 100 micrometers (i.e., a tenth of a millimeter) due to repeated cycles of sublimation and condensation, about 1% of the sunlight is still present at a depth of two millimeters. If the grains instead have a size of a centimeter, there may be unabsorbed sunlight even at a depth of 20 centimeters. This is because the cavities have sizes of 0.01-1 centimeters in these media, which allows radiation to reach rather large depths.

It is therefore clear that the properties of the surface material – not only its composition and porosity, but also its purely geometrical arrangement – has a potentially important effect on the absorption of sunlight, and hence the heating and outgassing of comets. Many other factors play a role as well – but that is for another post!

Literature

Brown, R. H., Matson, D. L. (1987). Thermal effects of insolation propagation into the regoliths of airless bodies. Icarus 72, 84-94.

Davidsson, B. J. R., Skorov, Y. V. (2002). On the light-absorbing surface layer of cometary nuclei. I. Radiative transfer. Icarus 156, 223-248.

Urquhart, M. L., and Jakosky, B. M. (1996). Constraints on the solid-state greenhouse effect on the icy Galilean satellites. Journal of Geophysical Research 101, 21,169-21,176.

Mysteries of the asteroid belt

Most of the asteroids in the Solar System are located between 2.1 and 3.3 AU from the Sun and constitute a population called the main belt (1 AU = one astronomical unit, corresponding to the mean distance between Earth and the Sun, or roughly 150 million kilometers). The main belt is outside Mars that is located at 1.5 AU, and interior to Jupiter that is 5.2 AU from the Sun. This post is about two of the largest mysteries of the main belt – why does it contain such a small mass and why are the orbits of asteroids around the Sun so extreme?

Lutetia_at_Closest_approach

The Asteroid (21) Lutetia with a diameter of about 100 kilometers, imaged with the camera OSIRIS onboard the European spacecraft Rosetta.
Copyright ESA 2010 MPS for OSIRIS Team MPS/UPD/LAM/IAA/RSSD/INTA
/UPM/DASP/IDA
Original image: http://www.esa.int/spaceinimages/Images/2010/07
/Lutetia_at_closest_approach

The total mass of main belt asteroids is only about 0.0005 Earth masses, which means that one would need about 2000 asteroid belts to build a planet of Earth’s size. If we also consider that Mars only has 0.1 Earth masses, it means that the region between about 1.3-5.0 AU from the Sun only contains roughly a tenth of an Earth mass, although there should have been several Earth masses there. Where has all of this mass gone? Furthermore, the orbits of main belt asteroids are characterized by rather high eccentricities (their orbits are clearly elliptic) and inclinations (they often tilt significantly with respect to Earth’s orbital plane). We say that the population is dynamically hot, which is different from the large bodies in the region – Venus, Earth, Mars and Jupiter – that all have more or less circular orbits in almost the same plane, which makes them dynamically cold. How have the asteroids obtained these strange orbits?

There are currently two different scenarios that seek to explain both why the area between Earth and Jupiter is almost empty, and why most bodies there are dynamically hot. Both scenarios are very dramatic. If we could decide which of them that is correct, an important but yet unwritten part of the history of our Solar System could be clarified. By describing these scenarios in detail we also touch upon some other important questions – how is natural science conducted, what does it take to prove a scientific theory, and what is the difference between unfounded opinions and scientific hypotheses? However, before addressing these questions it is necessary to describe how the asteroids formed, and how the asteroid belt looks like today.

Planetesimals in the Solar Nebula

About 4.57 billion years ago, something happened that frequently takes place in our galaxy, the Milky Way – a part of a molecular cloud (see an earlier post about the interstellar medium) contracted due to its self-gravity and formed a starless core – a cold lump of gas and dust that measured 10,000 AU across. It may have maintained an equilibrium configuration for a long time, up to one million years, before it collapsed further and formed the protosun – a structure from which the Sun formed – and the Solar Nebula, a flat and warm cloud of gas and dust that revolved around the protosun. This final collapse could have happened spontaneously, but it is more likely that it was initiated by the explosion of a nearby type II supernova – such supernovae produce a cocktail of short-lived radioactive isotopes such as aluminum-26, iron-60, chlorine-36, manganese-53, and calcium-41, whose decay products are found in the meteorites that impact Earth.

We can see such young, newly collapsed systems around us and they are called class 0 or I protostars, depending on how far they have come in their evolution. These phases last a couple of hundred thousand years in total. The hot environment in the Solar Nebula close to the protosun was suitable for creating a kind of grain cluster called calcium-aluminum-rich inclusions or CAI. They consist of different minerals like melilite (a mix of åkermanite and gehlenite) and fassaite that are rich in calcium and aluminum. These can be found in meteorites and can be dated through radiometric methods – it is the age of these grains of 4.57 billion years that we define as the age of the Solar System. The measurement of time in the Solar System use CAI as a reference – a given moment in time is clocked as a certain numbers of years “after CAI”.

Also other types of particles formed at lower temperature, that were rich in oxygen, silicon, magnesium, iron, and sulphur, such as amoeboid olivine aggregates (AOA) and agglomeratic olivines (AO). All these particles have typical sizes of 0.01-1 centimeters, are often very porous, and there are reasons to believe that the vast majority of grains stopped growing at this size due to a phenomenon called the bouncing barrier – if two particles of these kinds collide with each other, the probability that they will stick to each other and build something bigger, is very low.

A fraction of these CAI, AOA and AO managed, in spite of the difficulties, to merge early on into boulders measuring decimeters or meters across. These could, in turn, merge to form even larger bodies – planetesimals – with sizes measuring hundreds of kilometers. The planetesimals that formed to within one million years after CAI contained sufficient amounts of radioactive aluminum-26 to get heated to the point that they melted. Thereby the grains were destroyed, and the minerals broken down into their atomic constituents. The gravity of the planetesimal forced heavy elements like iron, nickel and sulphur to sink towards the center of the body, where they formed a nucleus rich in metal and sulfides. On top a mantle formed that contained lighter elements – mostly oxygen, silicon, and magnesium – recombining to form minerals like olivine and pyroxene. Possibly, an outer crust formed that consisted of the lightest minerals, like pyroxene and feldspar – the latter rich in the aluminum and calcium that originally had been located in the CAI. Such a layered planetesimal is said to be differentiated.

However, we have reason to believe that the vast majority of the CAI, AOA and AO did not participate in this process. They continued to orbit the protosun, along with the differentiated planetesimals. The heat generated within such small particles due to the decay of the short-lived radioactive substances could easily escape to space, and the particles remained rather cold. After 2-3 million years, the gas began to leave the inner parts of the Solar System, and the disk around the protosun became much dustier. This appear to have given rise to some form of electromagnetic phenomenon – perhaps current sheets or electric discharges – capable of flash-melting large amounts of CAI, AOA and AO, which transformed the porous clusters of dust to small, hard, compact balls of rock. These new types of particles are known as Type C CAI and chondrules, respectively. Large amounts of chondrules have been found in meteorites, and radiometric dating shows that the majority have been formed 2-4 million years after CAI. The process also seem to have given rise to a fine-grained mixture of grains consisting of olivine, pyroxene, sulfide, metal, and organic substances called matrix material. Although chondrules and matrix material individually have a chemical composition that differs from that of the Sun in terms of elements heavier than hydrogen and helium, the sum of chondrules and matrix material is very solar-like.

The chondrule formation appears to have given rise to a second, and perhaps dominating, wave of planetesimal formation. It seems like the bouncing barrier suddenly could be crossed as soon as the porous collections of grains (AOA and AO) were transformed to smaller compact spheres of rock (chondrules). The large bodies that formed at this stage did not contain very high abundances of aluminum-26 since most of the substance already had decayed. Therefore, these relatively late planetesimals were never molten, and they did not differentiate. Their interiors still contain surviving and largely unmodified grains – calcium-aluminum-rich inclusions (CAI), amoeboid olivine aggregates (AOA), agglomeratic olivines (AO) and matrix material.

Asteroids and meteorites

The asteroids we see today are a few surviving examples of these different types of planetesimals – the rest have been used to build the planets in the Solar System. Some of these asteroids are very old, and constitute the oldest differentiated type. For example, Asteroid (4) Vesta is a body that is known to contain a core of iron, nickel and sulphur, a mantle of olivine and pyroxene, and a basaltic crust – volcanic rock rich in olivine, pyroxene, silica and feldspar. We also know that many of these extremely old differentiated asteroids have been smashed to pieces in violent collisions. Such pieces of differentiated asteroids often impact Earth as meteorites – iron meteorites from the metallic core of the parent body, stony irons from the transition region between the core and mantle, and achondritic meteorites from their crusts. Vesta itself is the parent body of a large group of achondritic stony meteorites called howardites, eucrites, and diogenites, or HED with a common name. A few asteroids, apart from Vesta, also seem old enough to have differentiated. For example, so called M-asteroids may be parts of the iron core of larger smashed-up planetesimals, while A-asteroids possibly are parts of the mantle from such bodies.

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The Asteroid (4) Vesta photographed by the NASA spacecraft Dawn.
Image credit: NASA/JPL-Caltech/UCAL/MPS/DLR/IDA

However, the majority of main belt asteroids seem to belong to the younger undifferentiated variant of planetesimals, and their collision fragments. Pieces from these undifferentiated bodies also frequently impact Earth, and are called chondritic meteorites, since they are so rich in chondrules. The innermost parts of the main belt is rich in E-asteroids, that are believed to be related to a certain type of stony meteorite called enstatite chondrites. Besides that, the inner half of the main belt is dominated by S-asteroids, that are known to be related to another type of stony meteorite called ordinary chondrites. We know this since the Japanese spacecraft Hayabusa went to an S-type asteroid named Itokawa, and brought back small parts of its surface material to Earth. When investigated in the laboratory they turned out to be identical to ordinary chondrite meteorites. The Chelyabinsk meteorite that I have written about previously, was also an ordinary chondrite. Finally, the outer parts of the main belt is dominated by C-asteroids, that are believed to be related to yet another type of meteorite – the carbonaceous chondrites. All chondrites have one thing in common – they contain a mixture of chondrules and matrix material, in different proportions. The differences between enstatite chondrites, ordinary chondrites and carbonaceous chondrites include; the mixing ratio of chondrules and matrix material; whether iron is located in separate metallic grains (is reduced) or finely distributed within the minerals (is oxidized); whether olivine is present among the dominating pyroxene; the abundances of rare oxygen isotopes compared with the most common form, oxygen-16. These differences reflect systematic changes in temperature and pressure within the Solar Nebula, as function of time and distance from the protosun.

The asteroid belt today

There are in total 220 asteroids in the main belt with diameters D of 100 kilometers or larger. The four largest ones are called (1) Ceres (D=930 km), (2) Pallas (D=580 km), (4) Vesta (D=525 km) and (10) Hygiea (D=410 km). There are in total 680 asteroids with diameters of 50 kilometers or more, and the number of asteroids with diameters in the 10-50 kilometer interval is about 7,000. The known population is considered complete down to sizes of 10-15 kilometers, which means that we know all individual objects that are at least that big. The number of asteroids larger than a kilometer is estimated to be 1.3-1.4 million. Currently, we know about 630,000 asteroids, which means that about half of all asteroids larger than a kilometer already have been discovered.

The largest asteroids – the 220 objects larger than 100 kilometers – are most likely surviving planetesimals, i.e., they formed 4.57 billion years ago in their current form. Almost all other asteroids are considered collision fragments, i.e., they are pieces of even larger objects that have been broken up in collisions. Therefore, they have not had their current appearance since Solar System childhood, but have formed throughout the long history of the Solar System during violent collisions. There are three properties of asteroids that change systematically around a size of 100 kilometers. First, there is a clear change in the size distribution of asteroids, i.e., a list of the number of asteroids having a given size. If one consider the total number of asteroids larger than a certain size (the cumulative size distribution), it increases fast when D is reduced from 930 kilometers to 120 kilometers. But if D is reduced further, the cumulative size distribution does not change very fast at all, until a size of about 30 kilometers is reached, at which the increase is fast anew. Second, asteroids larger than 100 kilometers are almost spherical, while smaller asteroids systematically become more irregular the smaller they are. Third, there are systematic changes in the rotational periods of asteroids – in the D=100-930 kilometer interval the rotational period increases with decreasing size, which means that the smaller asteroids tend to rotate slower than the larger ones. But around D=100 kilometers this trend is reversed, so that even smaller asteroids tend to have shorter rotational periods – small asteroids spin faster the smaller they are. These three properties show that we are dealing with a population of objects with diameters larger than 100 kilometers that are primordial surviving planetesimals – their sizes, shapes and spin properties are consequences of the process or processes that formed planetesimals early in Solar System history. Instead, objects with diameters smaller than 100 kilometers are collision fragments – their sizes, shapes and spin properties are consequences of what happens when to large asteroids collide with each other at a high velocity.

Most of the mass in the main asteroid belt is locked up in the largest objects. The fact is that it is sufficient that 10-20 asteroids with sizes in the range 100-1000 kilometers collide, to explain the number of all asteroids that are smaller than this. Since we know all asteroids larger than 10-15 kilometers, and have a fairly good idea of how the size distribution looks like at even smaller sizes, we can say with certainty that the total mass in the main belt is not higher than about 0.0005 Earth masses.

However, the original amount of mass (in the form of rock, metal, sulfides and organic substances) in the 1-4 AU region must have been significantly higher, and may have been 5-8 Earth masses. This estimate is based on our observations of circumstellar disks around foreign protostars in the Milky Way, that currently are in the same stage of evolution as our Solar System was 4.57 billion years ago. In such disks, the amount of mass in the disk changes in a characteristic way with increasing distance to the parent star. If this is compared to the amount of matter that has been locked up by the planets in our own Solar System internal and external to the 1-4 AU region, we can conclude that the primordial asteroid belt must have been several thousand times more massive than today. A very dramatic event, or chain of events, must have led to this drastic mass loss in the asteroid belt.

We also know that the main belt asteroids originally must have moved on almost circular orbits, that all were located more or less in the same plane. The consequence of having such orbits is that the objects meet at low velocity when they collide – perhaps a few tens of meters per second. Such gentle collisions are needed to allow gravity to keep colliding bodies together, so that a larger body can form as a result of the collision. In order to build bodies with sizes measuring several hundreds of kilometers, it is necessary that even smaller bodies collide with each other at very low speed.

However, today the asteroid orbits have high eccentricities and inclinations. The orbits are no longer circular but are shaped as ellipses. The ellipse has a center, but the Sun is not located there but in a focus point that is displaced towards the point in the orbit where the asteroids is as closest to the Sun as possible, called the perihelion. The eccentricity is defined as the distance between the center and the focus point, divided by the distance between the center and the perihelion. The average value for the eccentricity of asteroids is 0.15, which means that the displacement of the Sun from the center of the ellipse is 15% of the distance between the center and perihelion. The average value of the orbital inclinations is 8 degrees, which is the average tilt of the asteroid orbital planes compared to the orbital plane of Earth. These high eccentricities and inclinations mean that asteroids have very high velocities when they collide – the average velocity is 5 kilometers per second. It is not possible to build anything during such powerful crashes – all collisions become destructive and only makes the population slowly grind itself to dust. Something must have happened in the asteroid belt that changed growth in dynamical cold to grinding in dynamical heat.

The first scenario – embryos in the asteroid belt

According to the first scenario the main belt originally was a few thousand times more massive than today, and all bodies moved more or less on circular orbits in a common plane. For this reason, small planetesimals could merge into larger planetesimals rather fast. Computer simulations show that it takes about one million years to form bodies as large as the Moon. The Moon has a diameter of D=3470 kilometers and a mass of about 0.01 Earth masses. It is even possible that bodies formed with masses around 0.1 Earth masses, that would be as large as the planet Mars. Bodies with masses of 0.01 Earth masses or larger are normally not referred to as planetesimals, but are called embryos.

The presence of embryos in the main belt had a large effect on the orbits of smaller planetesimals. They could no longer maintain their circular orbits in a common plane, but gradually obtained ever higher eccentricities and inclinations due to gravitational perturbations. Paradoxically, the formation of embryos – a consequence of efficient growth due to low collision velocities – therefore leads to the end of growth, and increasingly efficient fragmentation since the collision velocities are too high.

However, we know that Jupiter formed around the same time – the gas giants must have formed at most five million years after CAI since observations of gas disks around foreign protostars show that they do not live longer than that. Jupiter and Saturn must have had time to grow by consumption of such gas while it was still available. Uranus and Neptune, that mostly consist of ice, only managed to bind smaller amounts of gas since they formed at a stage when the gas disk already was dispersing. The formation of Jupiter had an extremely important effect on the asteroid belt – mean motion resonances were formed.

mainbelt_ai

The asteroid mean distance to the Sun measured in Astronomical Units (AE in the figure) on the horizontal axis, and the orbit inclination on the vertical axis. Every dot in the diagram corresponds to a known asteroid. The vertical lines show the location of strong mean motion resonances. The name of the resonance as well as its distance to the Sun is marked at the top of the figure. Note that several resonances virtually lack objects (so-called Kirkwood gaps). The 3:2-resonance contains a population of objects called Hilda asteroids.

The orbital periods of the asteroids increase systematically with increasing distance to the Sun. At certain specific distances from the Sun, the orbital period will constitute a small-integer fraction of Jupiter’s orbital period. For example, in the inner parts of the asteroid belt we find the 3:1 resonance at 2.50 AU – here the asteroids revolve exactly three times around the Sun in the same time as Jupiter performs one revolution. Further out, at 2.82 AU we find the 5:2 resonance, where the asteroids complete exactly five orbits around the Sun in the same time as Jupiter makes two revolutions. There are several such resonances and they all have one thing in common – objects that end up in these resonances are subjected to very strong gravitational perturbations by Jupiter. The most common effect is a strong increase of the orbital eccentricity, which means that the perihelion point is moved closer to the Sun. It is exactly this mechanism that creates Near Earth Asteroids. The asteroid is normally destroyed by colliding with the Sun, or more rarely, by colliding with one of the terrestrial planets.

Embryos and mean motion resonances is a deadly combination for asteroids – it took about one million years for the embryos to shuffle about 99% of the asteroids into the resonances, so that these objects left the main belt. The embryos also perturbed each others orbits, and disappeared one by one via the resonances. When the last embryo disappeared from the main belt, only traces remained of the once so massive population, and the remaining objects had received a high degree of dynamical heating – a memory of the ravaging of the embryos. If this scenario is correct, the current asteroid belt is therefore the remains of a region where the planet formation process had time to progress rather far, before Jupiter cleaned away all large bodies and only left a few smaller asteroids behind. The E-, S- and C-asteroids, the parent bodies of enstatite meteorites, ordinary chondrites and carbonaceous chondrites, thus formed very close to each other which means that the physical and chemical properties of the Solar Nebula changed very fast with distance to the protosun. The embryos that redecorated the main belt did not manage to fully erase this strong chemical gradient within the asteroid belt.

The second scenario – Jupiter visits the asteroid belt personally

However, it is possible that the clean-up and dynamical heating of the asteroid belt happened in a completely different manner. In another scenario, the entire 0.5-2.0 AU region initially consists of E-asteroids while the 2.0-5.0 AU region is completely dominated by S-asteroids. The C-asteroids are formed among and beyond the giant planets, which are jostled in a region around 5-15 AU from the Sun. If this is correct, the difference between the various chondritic meteorites is caused by a change in the chemical and physical properties of the Solar Nebula that happened very gradually across a region that covered a vast range of distances from the Sun.

In this scenario Jupiter is formed somewhere beyond 5 AU, but does not stay there since it starts to drift towards the protosun. This is called migration. As is evident from my previous post about the Kepler exoplanets, such migration is rather common for gas giants around other stars in the Milky Way. It has been investigated what would happen if Jupiter was allowed to drift all the way to 1.5 AU – were we find the planet Mars today – before Saturn catches up with Jupiter, and both gas giants drift back outwards in formation. As it turns out, a smaller external gas giant can reverse the migration of an internal larger gas giant.

If Jupiter plowes through the main belt twice – once on its way in and a second time on its way out – the asteroid belt will be heavily depleted, and subjected to dynamical heating. On the way in, Jupiter will force many S-asteroids to relocate to larger distances where they mix with C-asteroids. When Jupiter travels back, such S- and C-asteroids are replanted into the asteroid belt, which could explain why we observe such a variety of bodies within a fairly narrow region from the Sun. This scenario is called The Grand Tack.

The difference between scientific hypotheses and unfounded opinions

The two scenarios above have one thing in common – they are both solutions to the so-called N-body problem. This problem can be formulated in the following way: if there are N bodies with known masses, that are located in specific positions and are having specific velocities at a given moment, where will the bodies be at a later moment of time, and what will the velocities be, if every body feels the gravitational pull of all the other bodies? In brief, the N-body problem is about tracking the motion of a swarm of bodies as function of time, where the movements of any given body is the result of the gravitational pull from the other bodies in the swarm.

This problem was formulated very early, e.g. by Robert Hooke in 1674 and by Isaac Newton in 1687. The latter found an analytical solution to the problem for N=2, which is called the two-body problem. It is this solution that states that a single planet that orbits a star will move in an elliptic, parabolic or hyperbolic orbit, depending on its distance to the star and its velocity at the beginning of the calculation. The equation that describes how the acceleration of the body depends on the forces that acts on it – the so-called equation of motion – can be formulated rather easily when N bodies are involved. However, it is not easy to solve the equation, which means that one get access to the positions and velocities of the bodies at a given moment of time. Massive efforts were made in the 19th century to find such solutions, but it was only possible to find exact analytical solutions for N=3 under very special conditions – this is the so-called restricted three-body problem. However, methods were developed that yielded approximate solutions, that turned out to be extremely useful.

For example, it was possible to show that Uranus did not move as expected, when taking into account the gravitational force from the Sun, Jupiter and Saturn (a four-body problem). Independently of each other, the Englishman John Couch Adams and the Frenchman Urbain Jean Joseph LeVerrier used these discrepancies between the theoretical and observed orbit of Uranus to calculate the position of an hitherto unknown planet, assumed to be responsible for these discrepancies. By observing the sky in the vicinity of the calculated position of the unknown planet, the German astronomer Johann Gottfried Galle could located the object in 1846 – the planet that is now known as Neptune. While Uranus was found by accident in 1781, Neptune was found since the mid-19th century scientists had perfected the art of measuring and calculating the positions of planets in the sky to a level where they almost had complete control over the mechanical properties of the Solar System.

In a similar manner, LeVerrier could later show that the innermost planet, Mercury, did not move exactly as is was supposed to, even if the gravity of the other planets were taken into consideration. This discrepancy was later to become one of the most important proofs that the general theory of relativity by Albert Einstein was correct, since it led to an adjustment of Newtonian mechanics that exactly matched the “error” in Mercury’s movements.

Astronomers and physicists have therefore studied the problem of calculating the motion of a body affected by the gravitational forces from several other moving bodes for a long time, and fantastic progress in this field was made already 150 years ago. Nowadays, when we have access to computers with enormous capacity, it is no longer a problem to solve the N-body problem with extreme accuracy, even when N is a rather large number. For example, a spacecraft that travels through interplanetary space will be subjected to significant gravitational forces from the Sun and all planets. Yet there are no problems for ESA, NASA or any other organization to navigate in space – this sort of calculations is routine.

It is the same type of calculations that are made in order to understand how the asteroids in the main belt will react when they are exposed to the gravitational force from embryos and Jupiter. De scenarios described above are therefore based on very accurate and detailed calculations, and are extremely realistic. The starting point is some basic assumption (i.e., whether Jupiter is migrating or not), and then well-known physics and established methods are used to calculate the consequences of this assumption. Details on how these calculations are made, and the results of the calculations, are published in scientific journals, that only can be read by experts since they are filled with mathematics, physics and technical terminology. Such documentation describes a scientific hypothesis. It is a hypothesis in the sense of being a proposal, but this proposal is scientific since it is substantiated and supported by arguments and calculations that are based on centuries of research, and methods that have a demonstrated correctness.

Popularization of science aims at describing the essence of a scientific hypothesis, using few and simple words, which e.g. is made in this blog. This is an important task, because it allows large numbers of people to take part of scientific discoveries, which enriches the mind of every human, increases his or her understanding of the world and the capability to interpret what happens around us. However, it is impossible for a popularized text to give justice to the richness, complexity and depth of the investigations on which the hypothesis is based – if one wishes to understand the hypothesis at depth one must consult the original texts. The simplicity and brevity that characterizes a popularization of science can therefore be treacherous – it is difficult or impossible to imagine the complexity of the underlying machinery. It is easy to get the impression that a hypothesis is nothing but an opinion – that some scientist “believes something”. It is easy to confuse this with opinions and beliefs that are not based on any form of deeper knowledge, or investigation of the actual properties of Nature. This is what we may called unfounded opinions. In an increasingly media-based world, where the internet and social media have given people the possibility to express their opinions at an unprecedented extent, and were the flow of information is accelerating, it can be difficult to tell the difference between scientific hypotheses and unfounded opinions – at a first glance they may look similar. This becomes even clearer when unfounded opinions are presented by using a language and a “technical terminology” that gives the impression of being scientific – that is to say, pseudo science.

To claim that the Earth is a few thousand years old is an unfounded opinion, and if one tries to sell this opinion by using various technical arguments it is pseudo science. When a scientist claims that Earth was formed about 50-150 million years after CAI, that are 4.57 billion years old themselves, it is not an opinion. It is not even a scientific hypothesis, since this specific example is not a proposal – it is a fact.

Astronomers and physicists therefore do not sit and do “philosophy” in some general manner. The idea that embryos or a migrating Jupiter are responsible for the current properties of the asteroid belt are not just fantasy or speculation, it is not a matter of opinion or believing – they are scientific hypotheses since they have been formulated by using scientific methods. But if so, how come there can be two or more hypotheses claiming to explain the same thing – is not natural science about “knowing” and telling right from wrong? Why do we speak of facts and “to know” when the age of Earth is concerned, while the properties of the asteroid belt is the subject of hypotheses? The answer to that question gives further insight into the workings of the scientific process.

When a scientific hypothesis becomes fact

A scientific hypothesis is built on a number of basic circumstances, established and well-known physics, and mathematical calculations performed with the goal to explore the consequences of the basic circumstances. In order for a hypothesis to dominate over other hypotheses, and finally be referred to as a fact, comprehensive comparisons with Nature itself are needed. Such empirical data must lend support to the basic circumstances, as well as to the consequences of the hypothesis. If measurements or observations of Nature do not agree with the hypothesis, the hypothesis must be rejected or reformulated so that it no longer contradicts reality. The problem is that such empirical data often are not known, why two or more hypotheses may co-exist for a long time, until observations, measurements or laboratory experiments can shed light over the unknown circumstances needed to prove one hypothesis, and disprove all others.

Scientists are working hard to figure out how grains, not larger than a thousandth of a millimeter, merge to build boulders that are a few decimeters or meters across. There are several hypotheses on how such boulders grow to planetesimals with sizes in the 100-1000 kilometer range. The following process – the formation of embryos – is better known. In spite of this, it is difficult to know exactly how long it took for embryos to form, what size distribution planetesimals and embryos had at that time, and exactly how large the eccentricities and inclinations had grown. Another source of uncertainty is exactly when Jupiter had grown big enough that its mean motion resonances in the main belt were strong enough to effect the evolution there – did this happen only once the embryos had existed for a few hundred thousand years, or were they present even before the embryos formed? Yet another source of uncertainty is whether Jupiter migrated substantially or not. Scientists send spacecraft to asteroids and comets, make advanced computer calculations, perform experiments in laboratories and measure the properties of meteorites to answer such questions as far as possible, or at least limit the range of possible answers.

In such an uncertain situation, there is room to formulate various realistic but hypothetic basic assumption. For example, one can assume that embryos have formed, that these and planetesimals have a certain size distribution, that they have dynamically cold orbits, that Jupiter forms at a time when embryos already exist, and that Jupiter does not move substantially – one then ask, what happens then? The answer can be found in the detailed computer calculations that tracks the motion of thousands of planetesimals and embryos. Once the calculations are finished, one can explore what has happened – how many asteroids are left, what distances to the Sun do they have, what are their eccentricities and inclinations? If E-, S-, and C-asteroids initially are placed within well-defined regions at different distances from the Sun, to what extent have these populations mixed due to the ravaging of the embryos? It is exactly this type of detailed information from the computer models that are compared with observations of the Solar System today – accounting, as far as possible, for processes that may have changed various properties during the long history of the Solar System.

nssdc_nea_19970627

The Asteroid (253) Mathilde photographed by the NASA spacecraft NEAR. Mathilde is a C-asteroid, that are parent bodies of the meteorites called carbonaceous chondrites.
Image Credit: NASA
Credit: NSSDC Photo Gallery
Original image: http://solarsystem.jpl.nasa.gov/multimedia/gallery
/nssdc_nea_19970627.jpg

As it turns out, the eccentricities and inclinations of the surviving asteroids in computer models that include embryos are very similar to those seen in Nature, which is encouraging. However, there are some difficulties – the innermost parts of the main belt become too sparsely populated, since embryos in those regions turn out to have a long lifetime before they are removed, and in the meantime they manage to clear the region completely. Furthermore, the region around the orbit of Mars is not cleared enough – models of this kind lead to a mass of Mars that is many times larger than that of the real planet.

The Grand Tack scenario seems to solve these problems. If Jupiter is given the opportunity to drift into the asteroid belt, and then head back out again, the amount of matter around 1.5 AU from the Sun is reduced to a level that explains why Mars only carries a tenth of an Earth mass. The distribution of matter within the modeled asteroid belt corresponds fairly well to the observed one. The computer model makes a very good reproduction of the distribution of S- and C-asteroids at different distances from the Sun, if they originally formed within, and far outside, today’s main belt, respectively. The asteroids in the computer model have inclinations very similar to those in the asteroid belt today. But also this hypothesis has problems – the eccentricities of the modeled asteroids do not resemble the ones found in the main belt today. This may be explained by the Late Heavy Bombardment, a powerful disturbance to the main belt caused by the giant planets, that is believed to have happened when the Solar System reached an age of about 700-800 million years.

Both these scientific hypotheses constitute advanced working models, that will co-exist until the amount of data gathered about the Solar System becomes large enough to prove one of the hypotheses and disregard the other – unless it turns out that a hybrid of the hypotheses is more suitable, or a third yet unexplored scenario turns out to be the right one.

This shows that Solar System science is alive and is constantly evolving. It shows that the asteroid belt contains traces of large-scale dramatic events that took place early in the history of the Solar System. The exploration of the main belt is therefore extremely important, since it helps us to understand what happened near the region where our own planet formed. Assume, for example, that Jupiter actually penetrated deep into the inner parts of the Solar System. An interesting consequence of the Grand Tack scenario is that the inner Solar System receives large amounts of mass from farther regions. If this was the case, could it be that our planet would not have formed, or that it would have looked very different, had Jupiter stayed away? Does our planet, and thereby humanity itself, exist as a result of Jupiter’s migration? It is questions like this that starts to erase the difference between Solar System history and human history – we cannot understand our own past without describing that of the Solar System.

Literature

Petit, J.-M., Morbidelli, A., Chambers, J. (2001). The primordial excitation and clearing of the asteroid belt. Icarus 153, 338-347.

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., Mandell, A. M. (2011). A low mass for Mars from Jupiter’s early gas-driven migration. Nature 475, 206-209.

Walsh, K. J., Morbidelli, A., Raymond, S. N., O’Brien, D. P., Mandell, A. M. (2012). Populating the asteroid belt from two parent source regions due to the migration of giant planets – ”The Grand Tack”. Meteoritics & Planetary Science 47(12), 1941-1947.

What is a comet?

Now and then, a bright comet appears in the sky. It develops a fuzzy head and a long tail while it slowly drifts through the constellations. Such a sight has always fascinated humanity and given rise to stories, myths and superstition. It has also inspired scientists to investigate the nature of comets, and it turns out that they are not only beautiful to watch, but they can also reveal important secrets about the early history of the Solar System.

Comets are among the oldest and least altered bodies that revolve around the Sun, and therefore they constitute a unique source of knowledge about the origin of the Solar System and its early evolution. They constitute left-overs of the material that built the giant planets and their satellites. If one seeks to understand the earliest phase of the planet formation process, and the chemical and physical properties of the environment in which the giant planets formed, one must study comets. We also know that comets bombarded the young Earth and that a substantial fraction of the water we drink every day once were part of comet nuclei that circled the Sun outside the orbit of Neptune. We know that comets are rich in organic species, and that these may have been necessary for the emergence of life on Earth. We also know that comets impact Earth on rare occasions, which has led to local or global changes to the environment during shorter or longer periods, which has forced the ecosystems to adapt. These impacts are therefore parts of our own evolutional-biological history.

Below I will describe the physical and chemical properties of the comet nucleus, the characteristics of the orbits of visible comets and how comets are transported from such relatively nearby orbits from more distant parts of the Solar System. Then I will describe the components of the active comet, i.e., the properties of the coma and the tail. Finally, I will describe the reasons why comets are important from a scientific point of view.

The comet nucleus

The impressive head and tail of a comet originates from a small solid body called the nucleus. A typical comet nucleus is less than 10 kilometers in diameter and is darker than charcoal, since the nucleus only reflects 2-4% of the incoming sunlight. The comet nucleus has a very irregular shape and displays a variety of detail on its surface – highly irregular terrain mixed with smooth surface, valleys, mountains, ridges, hills and craters. The comet nucleus is extremely porous and a large fraction of its volume (60% or more) is just empty space. This makes comets very fragile, and dozens of comets have been seen to split or pulverize. The high porosity and the low strength is due to the fact that the nucleus is made up of weakly bound grains, that typically are a micrometer across (i.e., one part of a thousand of a millimeter).

Halley

The nucleus of Comet 1P/Halley photographed by the European Space Agency (ESA) spacecraft Giotto in 1986.
Copyright: ESA/MPAE, 1986, 1996
Original image: http://www.esa.int/spaceinimages/Images/2002/01
/A_composite_image_of_the_nucleus_of_comet_P_Halley

The grains are primarily consisting of four different types of material. About a third of the mass is silicates and sulfides, another third is organic species, while the rest are volatile species. I will now describe these in some detail.


Silicates constitute a large family of minerals that are rich in silicon, oxygen and various metals, and is the stuff that rock primarily is made of. About half of the comet silicates is olivine, which consists of two metal atoms, one silicon atom and four oxygen atoms. If the two metal atoms are magnesium, we have an olivine called forsterite. If the two metal atoms instead are iron, we have another olivine called fayalite. Comets seem to be rich in forsterite and contain less fayalite. The Earth mantle is made of different types of rocks that are very rich in olivine.
The other half of the comet silicates is pyroxene, that consists of a metal atom, a silicon atom and three oxygen atoms. If the metal atom is magnesium, we have a pyroxene called enstatite, but if the metal is in the form of iron we have ferrosilite. Comets seem to be richer in enstatite than ferrosilite, so on average the comet silicates are magnesium-rich. Pyroxene is an important component in the basalt that makes up most of Earth’s ocean floors.

Sulfides are chemical species consisting of sulfur mixed with iron and nickel. Troilite is the most simple member among the sulfides. It consists of an iron atom and a sulfur atom and is very common in comets. The most complex sulfide found so far in comet material is pentlandite that contains eight sulfur atoms and a total of nine metal atoms that are a mixture of iron and nickel. On Earth, large amounts of sulfur and iron are found in molten form in the outer core.

We now consider the organic species, that all have one thing in common – they contain carbon. Carbon is the most important element in the periodic table since it readily binds to other atoms, which means that carbon can form an extreme variety of molecules. It is this diversity that makes organic molecules suitable as building-blocks of life. The living organism needs a large “tool box” of molecules to solve all sorts of tasks, and only the family of organic species is large enough to provide a sufficiently rich variety.

An example of organic species found in comets are polycyclic aromatic hydrocarbons or PAHs. The most simple PAH, benzene, has six carbon atoms that form a ring, to which six hydrogen atoms are connected. By joining such rings, other PAHs can be formed, such as naphthalene (two rings), phenanthrene (three rings) and pyrene (four rings). All these PAHs have been found in comet material. On Earth, PAHs form during incomplete combustion of carbon-rich material, e.g., when wood is burning. The fact is that naphthalene is extracted from charcoal (this molecule happens to be the active substance in mothballs). Other environments where PAHs are formed are burning cigarettes, car exhaust fumes, and in the frying pan. Comets also contain other forms of organic species, e.g. glycine, the most simple amino acid. Living organisms use amino acids to manufacture proteins, i.e., macro-molecules that perform all sorts of tasks in the cell. To find such pre-biotic molecules in interplanetary space is extremely fascinating.

However, it is the large amount of volatile species that make comets special. Volatile species are basically substances that are liquid or gaseous at room temperature, but that turn solid at the low temperatures found in interplanetary space, i.e., they have turned into ice. Water is the most common volatile in a comet, while carbon monoxide and carbon dioxide come in second and third. Methanol, hydrogen sulfide, formic acid, methane, ammonia and hydrogen cyanide have concentrations of about a percent each relative to water. Methanol is the most simple alcohol, while it is hydrogen sulfide that give rotten eggs their unpleasant smell. Formic acid is used as a disinfectant and during industrial production of plastic, while methane (on Earth) is formed during putrefaction, i.e., when bacteria decompose organic material. Ammonia gives window polish its strong and irritating smell, while hydrogen cyanide is a deadly poison. This rich chemistry has formed in the Solar Nebula, the cloud of gas and dust that surrounded the young Sun, from which the planets formed.

The comet orbits

Objects that are gravitationally bound to the Sun move along trajectories shaped as ellipses. The degree of flattening of the ellipse, or the eccentricity, is very small for the planets (their orbits are almost circular), but is generally large for the comets. The Sun is not located at the center of the ellipse, but in one of the two focal points of the ellipse. These are located on either side of the center, on the the largest of the diameters of the ellipse (the major axis), at distances from the center that are determined by the eccentricity. For this reason, the distance between the Sun and a comet may vary significantly during a revolution, which is not the case for the planets. The point in the orbit where the comet is closest to the Sun is called the perihelion, while the most distant point is called the aphelion. The orbital planes of the planets more or less coincide with a plane called the ecliptic. However, comet orbits can tilt significantly with respect to the ecliptic – they are said to have high inclination.

ellipse

Comets move along elliptical paths around the Sun. The ellipse has two focus points, f1 and f2. The shape of the ellipse is determined by the fact that the distance l1 from the focus f1 to the ellipse, plus the distance l2 from the focus f2 to the ellipse, remains constant for all points on the ellipse. The Sun is here located in f1, while the comet is located at the point P. The smallest distance between the comet and the Sun (q) is called the perihelion, while the longest distance (Q) is called the aphelion.

Visible comets are comets that have orbits that bring the sufficiently close to the Sun and the Earth for us to be able to see them. Visible comets are grouped into a number of families based on the properties of their orbits. Jupiter-family comets have orbital periods shorter than 20 years and move in orbits around the Sun that are near the ecliptic plane. They regularly pass in the vicinity of Jupiter’s orbit. When passing close to Jupiter, they may be subjected to strong gravitational perturbations that may change the perihelion distance, the eccentricity and the inclination. It is these perturbations from Jupiter that have given the group its name.


We also have Halley-type comets that differ from the Jupiter-family comets by having longer orbital periods (up to 200 years), and often significantly higher inclinations. Comet 1P/Halley itself has such a high inclination that the orbit has “flipped over” so that the comet moves clockwise around the Sun (as seen from a point high above Earth’s north pole), while all planets, asteroids and most comets move counter-clockwise.

New comets are barely gravitationally bound to the Sun, and approach the Sun from large distances along an orbit shaped as a parabola. If the comet manages to cross the inner Solar System without suffering a perturbation of a planet, it will continue to move along its parabolic orbit and leaves the Solar System for good, never to return. However, it is not unusual that smaller perturbations take place that transforms the orbit into an extremely eccentric ellipse. This is a long period comet, with an orbital period that could be thousands of years.

How come there are so many different types of comet orbits? Why do some comets belong to the Jupiter family while others are Halley-type comets or new comets? These populations arise for two reasons – there are different reservoirs of comets at very large distance from the Sun, and there are different mechanisms that transport comets from these distant reservoirs to orbits close enough to Earth so that we can see them. There are several large reservoirs of comets that constantly feed objects into the inner part of the Solar System – the Edgeworth-Kuiper belt, the scattered disk, and the Oort cloud.


Distant reservoirs

The Edgeworth-Kuiper belt is a population of icy bodies located beyond the orbit of Neptune. The largest known member is called Eris. The second largest, and the first to be discovered, is Pluto. Both Eris and Pluto are dwarf planets, a category that was introduced in 2006 to distinguish between the largest of the Solar System bodies (the planets), the smallest bodies (asteroids, comets and meteoroids), and intermediate-sized bodies (dwarf planets).

Currently, about 1,200 objects in the Edgeworth-Kuiper belt are known, that all have been discovered after 1992, except Pluto that was found already in 1930. The Edgeworth-Kuiper belt has an inner edge that coincides with the 3:2 mean motion resonance with Neptune, which means that these objects move twice around the Sun in the same time as Neptune completes three revolutions. This corresponds to a distance of 39 AU (one AU, or Astronomical Unit, is the average distance between Sun and Earth, or roughly 150 million kilometers). This can be compared to the outermost planet Neptune, located 30 AU from the Sun. The outer edge is located at the 2:1 mean motion resonance with Neptune, which means that objects near this edge orbit the Sun once during the time it takes Neptune to complete two revolutions. This corresponds to a distance of roughly 48 AU.

Beyond the Edgeworth-Kuiper belt we find the scattered disk. It consists of objects that have had their originally circular orbits strongly perturbed by Neptune. They are characterized by large eccentricities and often have substantial inclinations. The perihelion distances typically fall between 30-40 AU, i.e., between the orbit of Neptune and the inner edge of the Edgeworth-Kuiper belt. The aphelion distances can be larger than 80 AU from the Sun.

However, these distances are very modest compared to that of the largest reservoir of comets in the Solar System – the Oort cloud. The comets in the Oort cloud have more or less circular orbits located 10,000-50,000 AU from the Sun. At such distances the gravitational attraction of the Sun is rather weak, and galactic tides start to become comparable to the pull of the Sun. The galactic tide is essentially the combined gravitational force of the stars and molecular clouds scattered throughout the disk of our galaxy, the Milky Way. The gravitational attraction from individual stars that temporarily come close to the Sun may also become comparable to that of the Sun. Due to such perturbations, the orbital planes of the comets have obtained random tilts, so that a given comet may have any possible inclination. Therefore, the comets in the Oort cloud are spread within a more or less spherical envelope at very large distances from the Sun.

Transport routes

The comets in the Jupiter family, and most Halley-type comets, are believed to originate from the scattered disk or the outer parts of the Edgeworth-Kuiper belt, but they have taken very different routs to reach their current orbits.

Computer simulations of the dynamics of comets show that comets in the Jupiter family slowly are dragged into the inner parts of the Solar System from the scattered disk or the outer parts of the Edgeworth-Kuiper belt, due to the influence of the gas giants. This process normally starts when Neptune changes the orbit of a distant object in such a way that it starts to feel the gravitational force of Uranus at the inner parts of its orbit. Thereafter, Uranus is modifying the orbit further, and is passing on the object towards Saturn. Finally, Saturn directs the object towards Jupiter, which subsequently creates the typical orbit of a Jupiter family comet. This is a very slow process that may take hundreds of thousand or millions of years to complete. The fact is that we can observe objects that are in the midst of this transport route. They are called Centaurs and orbit the Sun at distances that typically fall between the orbits of Saturn and Neptune. Some Centaurs even display comet activity in spite of their large distance to the Sun, like the comets 95P/Chiron and 29P/Schwassmann-Wachmann 1. Both objects are unusually large for being comets (Chiron has a diameter of about 200 kilometers), which is why we can see them over such large distances. This means that the inner Solar System has been visited by extremely large and bright comets during its long history.

Halley-type comets follow a completely different orbital evolution. Typically, Neptune starts to change the orbit of an object in the scattered disk or the Edgeworth-Kuiper belt in such a way that the aphelion distance increases dramatically, while the perihelion distance remains at about 30-40 AU from the Sun. Eventually, such objects can be 10,000 AU from the Sun at aphelion, where they are exposed to the galactic tide and the gravitational force of nearby stars. These forces may change the inclination of the orbit, but may also decrease the perihelion distance. This means that the comet periodically approaches much closer to the Sun than previously, and it may cross the orbits of Jupiter or Saturn. If this happens, these gas giants may change the orbit further by bringing the aphelion point back to the planetary region, while the perihelion distance remains roughly the same. In such a way, another Halley-type comet has been created.

However, it is not only the scattered disk and the Edgeworth-Kuiper belt that provides comets to the inner Solar System. Galactic tides and the gravity of nearby stars can perturb the orbits of comets in the Oort cloud, so that they start to fall towards the inner parts of the Solar System on parabolic orbits. Eventually, when they reach our part of space, we see them as new comets. If a new comet is unaffected by the planets it will simply return to interstellar space, and it is very likely that it never will come back again. However, a small disturbance from Jupiter may slow the comet down a bit, which forces it to return repeatedly although one need to wait for hundreds or thousands of years between each return – the comet has become long-periodic. Some long period comets can be transformed to Halley-type comets over time, which means that some of these object originally may have come from the Oort cloud.

The active comet

When a comet nucleus is far from the Sun (about three times as distant from the Sun as Earth), the temperature is too low for the frozen volatiles to sublimate at a high rate. The comet nucleus is then said to be inactive, and it can only be seen with the largest telescope if visible at all. If the comet instead approaches sufficiently close to the Sun it starts to heat up and the frozen species are vaporized – we say that the comet has become active. Solid grains of silicates, sulfides and organic species are liberated from the surrounding ice and are dragged along with the outwelling gas that rushes out into space. A dusty gas cloud is formed around the comet nucleus which is called a coma. A coma can have a diameter of 100,000 kilometers, which is ten times larger than Earth. The coma contains large-scale structures like jets since the nucleus outgassing is not evenly distributed across the surface of the nucleus. The coma is sufficiently thick to hide the nucleus from view. If we also remember that the inactive nucleus is distant and faint, it means that comet nuclei rarely can be observed at all, except from flyby spacecraft.

The solid grains soon lose contact with the gas, and their future orbits in space are only determined by two factors – the solar gravity and the solar radiation pressure. If solar gravity alone would influence the grains, they would follow trajectories around the Sun that resemble the orbit of the nucleus itself. However, when the radiation pressure is added, it means that the grains are pushed further away from the Sun compared to the nucleus, which means that they are smeared into a curved structure called the dust tail. This tail can be seen from the Earth due to the sunlight reflected by the grains. Color photographs shows that the dust tail has a yellow or white color, i.e., the same color as the Sun.

Hale_Bopp

Comet C/1995 O1 (Hale-Bopp). The yellow-white comet dust tail consists of small dust grains that reflect the solar light. The blue plasma tail consists partially of ionized carbon monoxide that absorbs and re-emit the blue light of the Sun.
Copyright: E. Kolmhofer, H. Raab; Johannes-Kepler-Observatory, Linz, Austria
Original image: http://en.wikipedia.org/wiki/File:Comet_Hale-Bopp_1995O1.jpg


The gas molecules in the coma have arrived to a very hostile environment. No longer protected in the nucleus interior, they are exposed to hard ultraviolet radiation from the Sun that literally smash them to pieces. Molecules and their fragments (radicals and atoms) are also ionized by the solar light, which means that they loose one or several electrons. This process make them electrically charged, which means that they start to interact with the solar wind. The solar wind consists of fast electrically charged particles that emanates from the Sun and drags along the solar magnetic field. The ions from the comet are picked up by this outwelling magnetic field, are swept backwards and therefore forms a structure known as the plasma tail. The plasma tails of comets have a clearly blue color in photographs. The blue color originates from singly ionized carbon monoxide, that only absorbs and re-emits the blue light of the Sun. However, the most common gaseous species in the coma in terms of number is atomic hydrogen and hydroxyle (a radical consisting of a hydrogen atom and an oxygen atom). These are the photodissociation products of the water molecule, and form when water is smashed to pieces by the ultraviolet radiation. The solar radiation that is absorbed and re-emitted by these species cannot be seen by the human eye, but can be detected with ultraviolet detectors on spacecraft.

Comet tails can become huge. In some cases, they stretch over distances larger than that between the Sun and Earth, i.e., more than 150 million kilometers. When a bright comet with such tails passes Earth, it gives rise to a spectacular show. Historical sources speak of comets that were bright enough to be seen in full daylight, and comets have been seen with tails so long that they stretched across the sky, from one horizon to the opposite one.

Why are comets important from a scientific point of view?

One of the most fascinating problems of astrophysics is to understand our Solar System. When did it form, and how did it look like when it was very young? How did it evolve and why does it look the way it does today? What events led to the formation of an environment that was suitable for the emergence of life (i.e., our planet)? Will Earth remain to be an environment suitable for life, or are there processes in the Solar System that threaten our survival?

Some more specific questions we would like to answer are the following. What was the chemical composition of the Solar Nebula, i.e., the could of gas and dust from which the Solar System formed? How did dust grains form out of the cooling hot gas? How did the properties of the Solar Nebula change with distance from the Sun, and to what degree did material from different parts of the Solar Nebula mix? Why and when did planetesimals start to form, that later grew to embryos and eventually to planets? What was the internal structure and physical properties of these planetesimals?

To answer this type of questions today, 4.6 billion years after the Solar System formed, is not easy. The Solar System has changed beyond recognition during its lifetime and there are not many things from its earliest history left to study. Among all the bodies in the Solar System, comets appear to be the ones that have changed the least. Comets look more or less the same as when they formed 4.6 billion years ago, which makes them unique. If we want to learn about the earliest epochs of the Solar System, the study of comets is extremely important.

What makes us think that comets are primordial and rather unaltered bodies? Firstly, due to their sizes. Comets are too small to have experienced a high level of geologic activity. Basically, their content of radioactive material has been too small to generate the heat that is necessary to drive such activity. Secondly, due to their low heat conductivity. For active comets, the solar heat is strong enough to erode the very surface by sublimation. However, the high porosity of comets means that they conduct heat very poorly, which means that the solar heat does not penetrate very far. Ice at rather shallow depths are therefore probably completely pristine. Thirdly, it is not likely that comets have experienced substantial alterations due to collisions. The reason is that the number of objects in the scattered disk is rather low, which means that they collide rarely with each other.

The best evidence that comets have not experienced substantial heating or other forms of alteration, and therefore contain more or less unchanged Solar Nebula material, is that they still are so rich in highly volatile species like carbon monoxide. Therefore we can learn about the chemical and physical properties of the Solar Nebula by studying comets from ground or by the aid of spacecraft. By studying the cometary grains and the internal structure of nuclei, we learn about the earliest stages of planetary formation. By studying comets up close, we can therefore learn about the very earliest stages in the history of our own planet.

Another fascinating thing about comets is their high content of organic materials and water. Without organics and water on the young Earth, life would never have formed. The question is to what extent carbon and water in the biosphere was a natural component of the material from which the Earth formed, and how much that was brought here subsequently. For example, we know that Earth formed through the mergers of planetesimals and embryos during a period of time that lasted for 50-150 million years, starting 4.6 billion years ago. But we do not know how much water that could be found at the surface of Earth at that time, or what types of organic species that were available.

Subsequently, about 0.6 billion years after the formation of Earth, the number of large impacts increased dramatically during an epoch known as the Late Heavy Bombardment (LHB). The LHB was most likely caused by a fundamental change of the giant planet orbits, from an original rather compact configuration close to the Sun, to the distant and well-separated orbits we see today. During this process, thousands of asteroids and comets were sent towards the inner parts of the Solar System, where they collided with Earth and the other terrestrial planets. The large impact structures seen on the Moon today were formed during the LHB. It is reasonable that a large amount of organic substances and water was brought to Earth during this event. We also know that the first evidence of life on Earth comes from the time right after the LHB. The question is therefore – how important was the water and organic compounds that comets brought to Earth during the LHB for the emergence of life that followed? Would life have emerged also without these cometary impacts, or did they bring vital components not present previously?

The fact is that large objects still impact on Earth now and then (typically a few hundred of thousands years pass between large impacts). Along with super volcanos, such impacts are the most violent natural disasters we have on Earth. The effects on Earth’s climate will be global if the impacting object is about a kilometer in diameter or larger.

If the object impact takes place on land, enormous amounts of dust is launched into the atmosphere, furthermore, wildfires are ignited that may spread over entire continents. What follows is a so called atomic winter, when the dust and ash in the atmosphere prevents the sunlight from reaching the surface of Earth. Our planet then becomes very cold, plants can no longer survive, which also causes a massive extinction of animal life. If the impact occurs at sea, there is in addition a huge tsunami with waves reaching tens or hundreds of meters that can flood vast areas. It is believed that the cause of the extinction of the dinosaurs 65 million years ago was a large impact at the Yucatan peninsula in Mexico.

The risk of impacts is yet another reason for studying comets. How many comets are there, what orbits do they have, and do any of them threaten Earth? How large are the comets, what masses do they have, and what would happen if they entered Earths atmosphere? How does the effects of an impact depend on the physical properties of the nucleus?

Comet research is a rather young science. Normally we consider 1950 as the year when the modern comet astronomy was born. This is the year when Fred Whipple for the first time made an accurate description of the properties of comet nuclei, and when Jan Oort discovered the distant reservoir of comets that bears his name. Another important era began in 1986 with the first spacecraft to visit Comet 1P/Halley, e.g., Giotto. These were followed by other spacecraft in 2001 (Deep Space 1 to Comet 19P/Borrelly), in 2004 (Stardust to Comet 81P/Wild 2), in 2005 (Deep Impact to Comet 9P/Tempel 1), and in 2010 (EPOXI to Comet 103P/Hartley 2). Every new spacecraft to a comet has made fascinating discoveries. A new era in the exploration of comets starts in 2014 when the European Space Agency (ESA) spacecraft Rosetta arrives at Comet 67P/Churyumov-Gerasimenko. Rosetta will not only fly past the comet, as has been the case with previous spacecraft, it will go into orbit around the nucleus, and even send a lander to the nucleus surface. Rosetta will undoubtedly revolutionize our understanding of the oldest members of the Solar System – the mysterious comets.

Looking back at 2013. Part IV – The Chelyabinsk meteorite

The American news channel CNN have selected what they consider to be the ten most important news about natural science and space in 2013. Gladly, planetary systems research top the list, with four different news. Other news concern fundamental physics (two), paleoanthropology and biology (two), cosmology (one) and climate (one). The four planetary news are about a fresh water lake on Mars, the spacecraft Voyager 1 that is leaving the Solar System, the space telescope Kepler looking for exoplanets, and the spectacular meteorite impact in Chelyabinsk, Russia. In four posts I will comment on each of these four top news of 2013.

On February 15, 2013, Earth collided with a small asteroid. It gave rise to an extremely bright light that lit up the sky over the Russian city Chelyabinsk – a superbolide that shone up to 30 times brighter than the Sun. While breaking in the atmosphere an energy was released that corresponded to the detonation of an atomic bomb 25 times more powerful than the one dropped on Nagasaki. The energy was transferred to the air and caused a shockwave called an airburst. The shockwave knocked people off their feet, crushed windows on more than 3,600 buildings in Chelyabinsk alone, blew in doors, and made house walls crack. 1,500 people had to seek medical care, primarily to treat cuts from flying glass. A large number of fragments of the rock fell around the city and are collectively referred to as the Chelyabinsk meteorite. Here, I will describe the fall itself and discuss how common this type of events are.

Some terminology

During a clear night it is not unusual to see one or several “shooting stars”. Such a light phenomenon, called a meteor by experts, happens when a small rock from space collides with Earth and burn in its atmosphere. These rocks are often not bigger than a tenth of a millimeter. Before atmospheric entry they are referred to as meteoroids. These meteoroids orbit the Sun, just like the planets, and collide with Earth since their orbits cross our own, if both bodies happen to be at the same place at the same time.

A really large meteoroid, measuring millimeters or even centimeters across, gives rise to a very bright light when entering the atmosphere. Such an unusually bright meteor is often called a bolide. If a part of the rock survives the passage through the atmosphere and falls to the ground, it is called a meteorite.

There is no official definition of how large a meteoroid can be – but in reality one ceases to talk about meteoroids when the rock in question is about ten meters across. Larger objects are called asteroids. When a small asteroid travels through Earth’s atmosphere, an extremely bright light appear, that sometimes is called a superbolide.

Below I will write about objects with sizes in the range 2-50 meters – for simplicity I call them all (small) asteroids, and if they enter the atmosphere I call the light a meteor.

The size of the asteroid

Since the fall at Chelyabinsk took place in a densely populated area, the meteorite was very well documented, thanks to surveillance cameras mounted on buildings and in cars. Several of the movies can be seen here. However, there were also other types of instruments that registered the meteorite. The most important of these were US military satellites, that accurately measured the brightness and velocity of the meteor. The measurements made public show that the kinetic energy just prior to entry corresponded to the energy liberated when 450-640 kilotons of TNT explode (the Nagasaki atomic bomb explosion released an energy corresponding to about 20-22 kiloton of TNT). The velocity at entry was 19.16 kilometers per second – it is this huge velocity that is responsible for the enormous energy carried by the asteroid. By using a rather simple mathematical relation, the kinetic energy and the velocity can be used to calculate the asteroid mass, which measured 10-15 thousand tons, which corresponds to a boulder with a diameter of 18-20 meters.

When the airburst hit ground, shockwaves formed that were registered by about seventy seismic stations located up to 4,000 kilometers away. Analysis of such seismic data shows that an energy corresponding to 220-630 kilotons of TNT was released. But there is also data from twelve different infrasound stations, facilities that listen for sound with such a low frequency that it cannot be heard by humans. They are part of the International Monitoring System (IMS), whose construction began in 1996, and that will control that the Comprehensive Nuclear Test-Ban Treaty (CTBT) is respected (a ban against nuclear test explosions put in place by the UN general assembly in 1996). These stations can not only hear distant nuclear blasts, but also registered the meteor at Chelyabinsk. These measurements shows that the released energy corresponds to the explosion o f 350-990 kilotons of TNT. A reconstruction of how the meteor brightness varied during the fall, based on films taken from ground, shows that the liberated energy was corresponding to at least 470 kilotons of TNT. Taken together, these measurements give a fairly coherent picture of the fall – it corresponded to about 500 kilotons of TNT and was due to the impact of an asteroid with a size just under 20 meters.

The meteor

Movies from 15 cameras on the ground around Chelyabinsk have been used to reconstruct the behavior of the meteor. According to this reconstruction, the meteor traveled at an angle of only 18 degrees with respect to Earth’s surface. When it first became visible, it was at a height of 97 kilometers and traveled at a speed of 19.16 kilometers per second. At a height of 45 kilometers an extreme erosion started, a process called ablation that leads to heavy mass loss through evaporation. The rock also started to fragment, and when it passed a height of 29 kilometers, it had broken up into about twenty pieces, each weighing about 10 tons. A larger fragment, weighing 20 tones moved a bit ahead of the rest of the swarm. This is when the meteor was brightest. The smaller pieces started to fragment in turn at a height of 25 kilometers. At that point, about 13 seconds had passed since the beginning of the fall, and the velocity was still very high, about 18 kilometers per second.

However, the air density increases steeply close to ground, and the forces acting on the fragments became extreme. During just two seconds the fragments decelerated strongly, and passed the height of 17 kilometers at a velocity of just 6 kilometers per second. As a comparison, passenger jets normally fly at an altitude of 10 kilometers. At this point, the leading fragment had been reduced to a small rock of only 15 kilograms. The meteor left behind a trail of fine rocky dust in the form of a cylindric cloud with a thickness of a couple of kilometers and a length of about 50 kilometers.

One of the pieces that broke off one of the slower fragments at a height of 25 kilometers is called F1 and has an estimated mass of 400-500 kilograms. F1 survived all the way down to the ground, and calculations show that it landed in Lake Chebarkul, located 70 kilometers west of Chelyabinsk. About 300 meters from the calculated impact site is the actual crater – a seven meter large hole in the 70 centimeter thick ice. On October 16, a team of divers recovered a 570 kilogram rock on this site – if this boulder actually is a part of the Chelyabinsk meteorite remains to be seen.

In addition to this large fragment, thousands of smaller ones have been found with a confirmed extra-terrestrial origin, having a total mass in excess of 100 kilograms. The largest fragment found so far has a mass of 3.4 kilograms.

The impact frequency of small asteroids

An asteroid with a two meter diameter releases and energy corresponding to one kiloton of TNT when it enters Earth’s atmosphere. If the diameter increases to five-six meters, about 20 kilotons of TNT is released – as much as the Nagasaki atomic bomb. If the diameter is increased to 50 meters, and energy of 10 megaton TNT, or 500 Nagasaki-bombs. The question is – how common is it that small asteroids with diameters in the 2-50 meter range impact on Earth?

There are several ways of closing in on this issue. The first is to consider the near-Earth asteroids we actually know and calculate theoretically how frequently they should impact Earth. It is necessary to compensate for the fact that we often do not know all near-Earth asteroids of a certain size – but it is often possible to estimate how many that have been missed. Such estimates relies on statistics of how often and for how long asteroid surveys have been active, compared to the number of actual discoveries. For example, we believe that about 90% of all near-Earth asteroids with a size of a kilometer or more have been discovered. For such objects it is relatively easy to calculate impact frequencies. When it comes to asteroids in the size range 10-20 meters, we know of 500 such objects. However, this is nothing compared to the 20 million asteroids of this size we think is lurking around Earth’s orbit. In such cases the compensation is uncertain, the the calculated impact frequency is unreliable.

However, there is another way of investigating the existence of small near-Earth asteroids – by counting the number of small craters on the Moon. Asteroids with sizes of a few tens of meters will cause craters with a size of a few hundred meters on the Moon – these are easily counted thanks to the large number of spacecraft that has mapped the lunar surface. As it turns out, these two methods yield very consistent estimates of the impact frequency.

According to these calculations, there should be about four impacts every year, by asteroids being at least two meters in diameter. Asteroids that are five meters or larger should impact every second year. Asteroids that are ten meters or larger should impact every thirty years. Asteroids as large as the one that fell in Chelyabinsk should impact every 150 years. Asteroids that have diameters of 25 and 50 meters, respectively, who delivers an energy corresponding to 1 to 10 megatons of TNT, should impact on 300 and 3000 year intervals, respectively.

These somewhat uncertain estimates can be compared to actual observations of large impacts made by satellites and infrasound stations. Such facilities have virtually global coverage and detects impact both over land and sea, regardless if the area is populated or not. They have no difficulties in detecting impact by asteroids with sizes as small as a couple of meters. The problem is that these observations only have been running during a fairly short period of time – from 1994 to present, and at a small scale, between 1960-1974. The results may therefore not be entirely reliable, since the statistics is based on a fairly small number of objects. It is still interesting to compare the impact frequency we expect, based on observations of asteroids and lunar craters, with the actual number of impacts, as observed by satellites and infrasound facilities.

Data from satellites and infrasound stations turn out to agree very well with estimates based on lunar craters and asteroid observations, concerning the smallest objects. But the larger the objects become, the larger the difference between estimates and observations seems to be. The actual number of impactors being five meters or larger, is double compared with expectations. Objects that are ten meters or larger impacted every fifth year, which is about six times more frequently than expected.

We may now as if the Chelyabinsk meteor was an unusual event or not. The answer depends on how the comparison is made. We have had an essentially global surveillance of Earth’s “airspace” during the last twenty years. Based on the expected impact frequency, an event like that in Chelyabinsk only has a 13% probability of happening during such a short time span. If this is correct, the meteor over Chelyabinsk could be classified as a rather rare event. In almost nine cases out of ten should a twenty year long hunt for impacts of this magnitude come up with nothing – yet we hit the jackpot at the first attempt. This could simply be due to luck – or that the impact frequency actually is higher than previously assumed. However, if one uses the higher impact frequency obtained by extrapolation from the actual impacts of smaller objects, it is no longer surprising that the Chelyabinsk event took place – such impacts should happen every twenty years.

If Chelyabinsk had been an isolated case, it had been easier just to blame chance. But there are another two events that also seem out of place. During the period 1960-1974, infrasound surveillance of nuclear tests took place. On August 3, 1963, a large impact was registered that passed rather unnoticed since it happened over the ocean, outside South Africa. During this event, the energy equivalent of at least a megaton of TNT was released, which is twice as much as in Chelyabinsk. The probability that such an impact shall take place during such a fourteen period is just 3% – according to expectations.

To this list one can add the large impact at Tunguska in 1908, which is the largest we know of in historical times. During this event, up to 15 megatons of TNT could have been released, which is 30 times more than at Chelyabinsk. This impact was registered both by seismographs and meteorological stations around the globe. If we assume that we have had the possibility to detect such events during the last 150 years, when we have had seismographs, there is only a 5% probability that such an impact will take place during such a time period, according to expectations.

One may therefore ask if our expectations simply are wrong. Is it possible that impacts by 2-50 meter bodies in fact happens ten times more often, than we would expect from studying lunar craters and asteroids. If this is the case – what does it mean, and why is this kind of questions important?

Consequences

The craters on the Moon constitute an archive that shows how the population of near-Earth asteroids has looked like throughout lunar history. Studies of the Moon shows that this population has looked pretty much the same during the last three billion years. Throughout all of this time, the number of asteroids has been fairly constant and the size distribution, i.e., the number of objects within any given size interval, has been more or less the same. This tells us that the population is a system in equilibrium. The number of near-Earth asteroids surely decreases steadily through collisions with the Sun and the planets, but since a re-population takes place due at the same rate, through transfer from the main asteroid belt located between Mars and Jupiter, the number of near-Earth asteroids at any given moment remains fairly constant. Asteroids of a certain size may disappear when they collide and smash each other to pieces, but they get replaced when even larger asteroids break up. During such a collisional equilibrium, a particular type of size distribution is formed. For example, for every asteroid with a 100 meter diameter, there should be about 150 asteroids with 10 meter diameter. Such a collisional equilibrium is clearly maintained in the main asteroid belt.

However, this kind of balance is never exact – there are natural fluctuations over time. For example, a collision between two main belt asteroids may cause a temporary increase in the number of smaller fragments, and it takes a while before they grind each other down and the balance is regained. It means that the influx of small asteroids to our region of space may increase temporarily as well. If the suspected elevation of the impact frequency is real, it is possible that we now experience such a temporary deviation from equilibrium.

Final words

Natural science aims at developing an understanding of the world around us and to describe it in detail. It is a matter of finding out how things really work and function, so that one do not have to guess or rely on unfounded assumptions. This urge to acquire knowledge is as old as humanity itself – the better we know our surroundings and environment, the easier it is for us to adapt, and the higher are our chance of survival. The more we know about actual conditions in nature, the better decisions we can make – decisions that affects our future life. Our thirst for knowledge is hardwired into our genes and is a prerequisite for our existence.

The efforts to characterize the properties of near-Earth asteroids aim at understanding the processes that are responsible for these properties. We want to know what happens when asteroids collide with each other, and we want to know how these fragments leave the main asteroid belt and find their ways onto Earth-crossing orbits. We want to know how often asteroids of different size collide with Earth, and we want to know what happens during such a collision. The meteor over Chelyabinsk is important in this context since it fills out gaps in our knowledge, it gives us opportunity to test models and theories, and it reminds us that we do not live in isolation on our planet – we are parts of an interplanetary environment that affects us, and we must get to know it.

Literature

Borovicka, J., Spurny, P., Brown, P., Wiegert, P., Kalenda, P., Clark, D., Shrbeny, L. (2013). The trajectory, structure and origin of the Chelyabinsk asteroidal impactor. Nature 503, 235-237.

Brown, P. G., Assink, J. D., Astiz, L., Blaauw, R., Boslough, M. B., Borovicka, J., Brachet, N., Brown, D., Campbell-Brown, M., Ceranna, L., Cooke, W., de Groot-Hedlin, C., Drob, D. P., Edwards, W., Evers, L. G., Garces, M., Gill, J., Hedlin, M., Kingery, A., Laske, G., Le Pichon, A., Mialle, P., Moser, D. E., Saffer, A., Silber, E., Smets, P., Spalding, R. E., Spurny, P., Tagliaferri, E., Uren, D., Weryk, R. J., Whitaker, R., Krzeminski, Z. (2013). A 500-kiloton airbust over Chelyabinsk and an enhanced hazard from small impactors. Nature 503, 238-241.

Popova, O. P, and 59 colleagues (2013). Chelyabinsk airburst, damage assessment, meteorite recovery, and characterization. Science 342, 1069-1073.

Looking back at 2013. Part III – The exoplanets of Kepler

The American news channel CNN have selected what they consider to be the ten most important news about natural science and space in 2013. Gladly, planetary systems research top the list, with four different news. Other news concern fundamental physics (two), paleoanthropology and biology (two), cosmology (one) and climate (one). The four planetary news are about a fresh water lake on Mars, the spacecraft Voyager 1 that is leaving the Solar System, the space telescope Kepler looking for exoplanets, and the spectacular meteorite impact in Chelyabinsk, Russia. In four posts I will comment on each of these four top news of 2013.

The idea of planets orbiting other stars is as old as the realization that Earth and the other planets in the Solar System revolve around the Sun. Already Isaac Newton mentions the possibility that other stars are surrounded by planets in his Principia from 1687, and he was not the first to express such ideas. For the generation that grew up with science fiction and imaginative films about events taking place in galaxies far away a long time ago, the thought of other planets than our own is natural. Therefore it is valuable to remember that no known examples of such extrasolar planets (usually called exoplanets) existed twenty years ago – the technology that made it possible to detect them was not developed until the early 1990s.

The first definitive detection of a planet around an ordinary so-called main sequence star was announced in November 1995, when the Swiss astronomers Michel Mayor and Didier Quelos showed that the star 51 Pegasi surrounded itself with a planet that was between half and twice as massive as Jupiter, located only 0.05 AU from the star (one astronomical unit, AU, is the average distance between the Sun and Earth, corresponding to nearly 150 million kilometers). In the following years many discoveries were made, and in early 2009 no less than 334 exoplanets were known, orbiting around 285 different stars. In March that year, NASA launched the Kepler space telescope in orbit around the Sun, whose sole task was to discover new exoplanets. When the telescope became unfit for such observations in May 2013, it had accumulated a database of almost 3800 planet candidates – the Kepler team is currently busy with the time-consuming task of verifying the authenticity of these exoplanets, and at the time of writing (late January 2014) they have confirmed that 242 of the Kepler planets are genuine. Along with all other discoveries, there is now a total of 1070 known and verified exoplanets that orbit 810 different stars, of which 177 stars are home to more than one exoplanet.

I will first describe how Kepler finds planet candidates, how their authenticity is verified, and why Kepler is able to find an extremely interesting type of object that is difficult or impossible to detect with other methods – extrasolar planets that are as small as Earth, and are located far enough from its star not to be scorching hot. I will then use examples of extrasolar planets detected by Kepler to illustrate how different these systems can be compared to our own. Finally, I will write about the reasons why these findings are important and what they can tell us about the process that gives rise to planets.

The Kepler space telescope

Kepler utilizes an idea that is very simple, and that humanity has observed in the form of solar eclipses throughout our existence – if an object gets between us and a distant star, the stellar light fades temporarily. When the Moon gets between us and the Sun, there is a total solar eclipse that will remove all the Sun’s light because the Moon happens to have the same apparent size in the sky as the Sun. When an exoplanet moves between its parent star and Kepler, it will obscure a small fraction of the stellar disk. Kepler can not see the planet or discern the stellar surface, but it can detect a sudden reduction of the stellar brightness, that remains at a lower level until the planet leaves the line of sight and the star returns to its previous brightness. This is called the transit method.

This may sound easy, but there are two substantial technical complications. First, the decrease in brightness of the star due to the planet’s passage is extremely small – one must therefore be able to determine the brightness with extremely high accuracy, so that the slight decrease in signal strength does not drown in various random variations caused by the surroundings or the telescope and the instrument itself. The problem is not the telescope mirror size or the sensitivity of the detector – nowadays, these can fairly easily be manufactured with the required level of performance.The reason that these observations cannot be made from ground is not about the technology itself, but the disturbances caused by Earth’s atmosphere. When light from a star passes through the atmosphere on its way toward a telescope, it will be diffracted in pockets of air having different temperatures and densities, causing the light beam to partially divert from its original path. A telescope on Earth will then measure fairly strong and random changes of the stellar brightness, caused by the atmosphere, which makes it impossible to reach the precision required to detect an eclipse taking place hundreds of light years away. So, the telescope must be sent into space.

The second difficulty has to do with the probability that a randomly selected star would have a planet with such an orbit that it happens to pass right through our line of sight. A planet revolves around a star in a fixed plane, and for us to be able to see an eclipse, we must also be located almost exactly in the same plane. Since this is the case only for a small fraction of the stars, Kepler must observe a huge number of stars to catch the few who actually have planets and are causing eclipses that we can see. Kepler does this by observing about 156,000 different stars. Because it is impossible to tell when an eclipse will take place, Kepler must stare continuously at these stars. This requires Kepler to have a large field of view – it covers a square with a side of 10 degrees, which is 20 times longer than the apparent diameter of the Moon in the sky. It has been staring at the exact same area, located between the constellations Cygnus and Lyra, ever since the first observations began in April 2009 until the telescope lost its full attitude control in May 2013. By then the space telescope had observed for four years – six months more than originally anticipated. The original goal was that Kepler would operate for three and a half years, for two reasons. Firstly, one needs to see the same planet perform at least three or four eclipses in order to be sure that it indeed is a periodic phenomenon. Secondly, the orbital period increases the farther the planet is from its star, and in order to discover planets similar to Earth, whose orbital period is one year, one must observe for at least 3-4 years.

Kepler_FOV_hiRes-br

The picture shows an area in the sky between the constellations Cygnus and Lyra
that Kepler has been observing for four years. The boxes shows the areas that the
CCD cameras can survey simultaneously. The original picture can be found at
http://kepler.nasa.gov/multimedia/photos/?ImageID=12
Image credit: Software Bisque

Transit observations provide two different types of information. The duration of the eclipse shows how fast the planet crosses the stellar disk, providing the orbital period of the planet. Since there is a mathematical relationship between the orbital period, the mass of the star, and the distance between the star and planet, called Kepler’s third law, knowledge about the first two parameters can be used to calculate the average distance between the planet and the star. This relationship was described in 1619 by the German astronomer Johannes Kepler (1571-1630), after whom the space telescope is named.

One can also use the degree of attenuation of the stellar brightness to calculate the diameter of the planet. The larger the planet, the stronger the decrease of the brightness, since a larger fraction of the stellar surface is blocked during eclipse.

Additional observations from Earth

Before one can be sure that a candidate indeed is a planet, other possibilities must be ruled out. For example, it is very common that stars are not alone, but that two revolve around each other at close range. About two-thirds of the stars we see in the sky are in fact such double stars. If we happen to find ourselves being close to the plane in which the two stars move, they will alternately obscure each other as seen from Earth. If one star is slightly fainter than the other, their combined brightness thus undergoes a periodic weakening – they form a so-called eclipsing binary. If such an eclipsing binary happens to be located near the line of sight between Kepler and a bright star that is observed, the fluctuations of the eclipsing binary may be misinterpreted as a planet around the bright star. In order to eliminate the risk of misunderstandings, all candidates – the 3800 objects – must be observed from ground with large telescopes that have much better magnification than Kepler. Thereby, it is possible to see if something undesirable is located very close to the star in question. At the moment, 242 candidates have passed this needle’s eye and are considered real planetary systems. During the process, dozens of candidates turned out to be nothing but eclipsing binaries, showing the necessity of this procedure.

If possible, observers on ground also try to prove the existence of Kepler’s exoplanets in an entirely different way, using the radial velocity method. The method exploits the fact that the star itself will move, if it surrounds itself with planets. Two bodies whose movements are controlled by the gravitational force acting between them, will move around a point in space called the center of mass, which is located somewhere on the line between the bodies. If the bodies have the same mass, as is the case for some double stars, the center of mass is placed midways between them. In such cases, it is possible that the stars both move along the same circle, centered on the center of mass, in each moment being placed on opposite sides of this center. If the mass of one of the bodies is greater than the other, the center of mass will be located closer to the heavier body. The heavier body then moves in a small circle around the center of mass, while the lighter body travels in a wider circle around the center of mass. If the mass difference between the bodies is very large – as is the case for a star and a planet – the center of mass may lie near the surface of the star, or even inside it. In the Solar System, the center of mass, called the barycenter, is located up to a solar diameter outside the center of the Sun. All the planets revolve around this point, but so does the Sun – it therefore follows a path whose size is about as big as the Sun itself. Since all stars that are surrounded by planets wobbles in the same way, the existence of planets is revealed by such movements.

The movement of the star about the center of mass is far too small for us to see – no telescope has such high magnification. What we can observe is instead the stellar radial velocity, i.e., the speed by which the star alternately approaches us and recedes from us. This is done by observing the stellar spectrum. The star emits light at a variety of wavelengths – the shorter the wavelength of a specific beam of light, the more energy the beam carries. When this beam hits a human eye, the energy is used in order to generate a weak electric signal that is transmitted through the optic nerve to the brain. When the brain registers such an electrical signal, we “see” light. The brain does not only tell us that we see light, it also gives us a rough indication of the wavelength of the light. We experience the relatively long wavelength of energy-poor light as red. The relatively short wavelength of high-energy light is perceive as blue. In a similar way, we can build instruments that have the ability to measure exactly how much light there is at different wavelengths. This is called a spectrometer. When a stellar spectrum is observed – i.e., a list of how much light there is at a large number of specific wavelengths – one can see that the intensity of light is severely weakened at certain wavelengths. This is called a spectral line, and it appears since there is a chemical element in the outer parts of the stellar atmosphere that absorbs this type of light and prevents it from leaving the star. The spectral lines of a stellar spectrum therefore tell us what chemical elements are being present. However, they also tell us something more. From laboratory studies, we know that a light source at rest will have its spectral lines at specific wavelengths. But if the light source is set in motion, the spectral lines corresponding to a particular chemical element will shift slightly, by an amount that tells us exactly how fast the light source moves. This is known as Doppler shift. If the light source moves away from us, the spectral lines show up at slightly longer wavelengths compared to rest, and we say that the light is redshifted. If the light source moves toward us, the spectral lines show up at slightly shorter wavelengths than at rest, and we say that the light is blueshifted. Stars that alternately exhibit red- and blueshifted light are therefore performing some sort of wobbling motion, caused by the presence of invisible planets. By measuring the magnitude of these shifts, and the rate by which they increase and decrease, one can calculate both the distance between the star and the planet, and the planetary mass.

The radial velocity method has traditionally been the most important way of detecting exoplanets. For example, the first exoplanet around the star 51 Pegasi was discovered with this method, and by early 2009, 75% of all exoplanets had been discovered in this way. The transit method had been used in only 16% of the cases. The problem with the radial velocity method is that the planet must have a very high mass, and it must be located very close to the parent star, otherwise the Doppler shift will not be large enough to be measurable. Finding a planet similar to Earth – having a relatively small mass and a quite large distance to the star – is extremely difficult with the radial velocity method.

This is exactly what makes Kepler so unique and important. It makes it possible to search for a large number of exoplanets by using the transit method. With the transit method, it is possible to find smaller planets that are farther from their parent star than with the radial velocity method. Kepler was designed with the explicit goal of being able to find planets similar to Earth, both in terms of size and distance to the star.

Kepler has found a large number of planets that are described in terms of their diameters and orbital periods. In order for this information to make sense, it must be compared to something more familiar. Therefore, before examining some of Kepler’s findings, we should first remember how our own planetary system looks like. This is also necessary in order to understand the terminology that has emerged around exoplanets.

The Solar System

The Solar System has eight planets, which are divided into three different groups based on size and composition – the terrestrial planets, the gas giants, and the ice giants. The terrestrial planets have relatively small masses, are quite close to the Sun, and are mainly composed of rock and metal. The terrestrial planets are Mercury, Venus, Earth and Mars. Measured in terms of Earth masses, with the symbol M, we have 0.055M for Mercury, 0.815Mfor Venus, 1M for Earth (by definition), and 0.107M for Mars. Mercury and Mars are thus very small, with masses amounting to only 5% and 11% of Earth’s mass. This can be compared to the mass of the Moon, which is only one percent of Earth’s mass. Venus is almost as massive as Earth. Comparing the planetary masses with each other is far more interesting than looking at their sizes – the mass is a direct measure of the amount of material consumed to form the planet. It is also the mass that determines the strength of the planetary gravitational force, thus how strongly the planet affects the motion of nearby bodies.

For a majority of the exoplanets detected by Kepler we do not know their masses, but only their sizes. If we, in a similar way, measure the sizes of the terrestrial planets, using the Earth radius R as a yardstick, Mercury’s size is 0.38R, Venus’ size is 0.95R, Mars’ size is 0.53R, and the size of the Moon is 0.27R♁. These numbers do not differ much from each other – for example, it is not obvious at first glance that the Moon, which is about one third the size of Earth, actually only has a mass that is 1.2% of that of Earth. The reason is that the body volume, and therefore the mass, increases very fast when the radius is increasing. When doubling the radius, the volume increases a factor eight. When tripling the radius, the volume increases 64 times. The Earth has a volume that is about 50 times that of the Moon. However, the difference in mass between the Earth and the Moon is not a factor of 50, but a factor of 80. The reason is that there is yet another property to consider – the density of the celestial body, i.e., how many kilograms of mass that each cubic meter of the planetary material contains. Earth has an average density of 5500 kilograms per cubic meter, which is almost 65% larger than the lunar density – partly because our planet is much richer in iron than the Moon, partly because the enormous gravitational force of Earth is capable of compressing its material to a higher degree than the Moon, which increases the average density. This must be remembered when comparing planets sizes – volume changes strongly with radius, and the density can differ significantly between different types of planets, which can lead to very large differences in mass.

The distances of the terrestrial planets from the Sun are 0.39 AU for Mercury, 0.72 AU for Venus, 1 AU for the Earth by definition, and 1.52 AU for Mars. It would have been easier to compare these distances directly with those between the exoplanets and their parent stars. The problem is that the parameter that we actually measure is the orbital period. The period can be converted to distance by using Kepler’s third law, but only if knowing the stellar mass. These masses are indeed known, but not with very high accuracy. An approximate distance expressed in AU, may gradually have to be adjusted, as the stellar mass becomes more precisely known. It is therefore more convenient to compare the orbital periods, although these numbers may be slightly more difficult to assimilate intuitively. I will therefore refer to planetary orbital periods rather than distances, which are 88 days for Mercury, 225 days for Venus, 365 days for Earth, and 687 days for Mars.

The gas giants consist of Jupiter and Saturn. Their masses amount to 318M and 95M, respectively, while the radii amount to 11.21R and 9.45M♁. These numbers are huge compared to the terrestrial planets, and it is difficult to tell from the radii that Jupiter actually is three times as massive as Saturn. Besides size, the compositions of terrestrial planets and gas giants differ markedly – the former are mostly made up of rock and iron, while 70%-95% of the gas giants is hydrogen and helium. While the density of the Earth is 5500 kilograms per cubic meter, the corresponding values for Jupiter and Saturn are only 1300 and 690. Jupiter is 5.20 AU from the Sun while Saturn has an average distance that is almost twice as high, 9.54 AU. In terms of orbital periods, this corresponds to 11.86 years (4332 days) and 29.46 years (10,760 days).

Finally, we have the ice giants Uranus and Neptune. These planets differ dramatically from the gas giants. Firstly, only 5-15% of their masses are hydrogen and helium, whereas the majority (60-70%) is ice, and the remainder is made up of rock and metal. Secondly, their masses are very modest compared to those of the gas giants – only 14.5M for Uranus and 17.1M for Neptune. Their sizes equal 4.01R and 3.88R, respectively. It may seem paradoxical that the heavier Neptune is actually slightly smaller than the lighter Uranus. This is because the mean density of Neptune is higher due to a somewhat larger fraction of ice and rock. The orbital periods of the ice giants are very long, 84 years for Uranus and 165 years for Neptune.

Some terminology

The planets discovered by Kepler are divided into a number of categories based on size. A planet with radius between 0.8-1.25R is simply called an earth. With such a definition Venus and Earth would qualify as “earths” while Mars, Mercury and the Moon would be too small. The next category is called super-Earths, having radii in the range 1.25-2R. In our Solar System, there are no examples of such celestial bodies. If a “super-Earth” consists of rock and metal, and if it has the same density as Earth, it will have a mass of 2-8M. If it instead is made of ice, the mass can be considerably smaller. The transit method can only be used to show that a “super-Earth” exists – the radial velocity method is needed to determine if a “super-Earth” is indeed a large ball of rock and metal, or if it primarily consists of ice and thus looks like a small Uranus.

If the planet has a radius of 2-4R it is called a small Neptune. For example, both Uranus and Neptune would be typical examples of a “small Neptune”. If the radius is between 4-6R it is called a large Neptune. As was the case with “super-Earths”, this type of planet is missing in our own Solar System. If the radius is between 6-22R it is called a giant planet.

A similar unofficial terminology is used for extrasolar planets detected by the radial velocity method, but is based on the planetary mass. Early on, only objects as large as Jupiter or larger were discovered, and they were located extremely close to their parent stars, often within 0.05 AU where the orbital period is only four days or less (compared to Mercury’s heliocentric distance of 0.39 AU and the orbital period of 88 days). Such objects were therefore called hot Jupiters. Giant planets located slightly farther away from the parent star are sometimes called warm Jupiters. With time, discoveries included objects with smaller mass, and if smaller than a tenth of a Jupiter mass, i.e., less than 30M, they are called exo-Neptunes. Since these often are found close to the star as well, they are often referred to as hot or warm Neptunes. If the mass is less than 10M the planet is called a super-Earth.

By using the radial velocity method, mostly large planets located close to their parent stars are discovered. However, thanks to Kepler and the transit method, it has now become possible to detect smaller exoplanets, located farther away from their parent stars. A region known as the habitable zone is particularly interesting. It is a fairly narrow strip where the stellar light is strong enough to melt the ice on an Earth-like planet, but not so strong that the water evaporates. It is an area where liquid water can exist for a long time, which probably is a prerequisite for life to arise and thrive. There are various estimates on the location of the habitable zone boundaries. In a recent investigation, the inner edge was placed at 0.77 AU, just outside the orbit of Venus. The same study showed that the outer edge may lie at 1.18 AU, about midways between Earth and Mars. This corresponds to an orbital period of approximately 250 to 470 days. Stars that are smaller than the Sun radiate less heat and light – in such cases the habitable zone is closer to the star, where the orbital periods are shorter. Stars that are bigger than the Sun radiate more heat and light – in such cases the habitable zone is farther away from the star, where the orbital periods are longer.

One of Kepler’s primary goals is to find an “earth” with radius of 0.8-1.25R and a period of about 250-470 days, orbiting a solar type star – it would be the Earth’s twin, and a place where there possibly is life. We shall now take a closer look at Kepler’s actual discoveries – first some examples of individual systems, then some statistical properties telling us how common the various planetary types are.

Kepler’s discoveries – individual systems

Kepler has discovered various types of planetary systems – some have been seen before, while other types are completely new. Here we shall focus on some examples of planets in the habitable zone, but also “earths” and even smaller planets closer to the star. Furthermore, we look at systems where many planets coexist, but also so-called resonant planets, and double stars that have planets.

Planets in the habitable zone

The search for a planet in the habitable zone around a solar-type star bore fruit in December 2011, when it was announced that Kepler had found a “small Neptune” with a radius of 2.4R called Kepler-22b, which completes one orbit around its parent star, Kepler-22, in 289 days. If this beast has a composition similar to the Earth, its mass is at least 14M – it is then as massive as Uranus. It cannot be ruled out that the planet is dominated by water, which would make it much lighter – in any case, this planet is very different from our own.

An even more interesting finding was published in April 2013. The smallest known planet in the habitable zone of a solar-type star so far had been found – the “super-Earth” Kepler-69c with radius 1.7R and an orbital period of 242 days. Although this corresponds to the orbit of Venus, the planet is still in the habitable zone as the star emits 20% less light and heat than the Sun. The star in question, Kepler-69, also has yet another planet in its possession. This is a “hot small Neptune” called Kepler-69b with radius 2.2R, having a period of only 13 days. This planet is thus at a distance much shorter than the heliocentric distance of Mercury, whose orbital period is as long as 88 days.

The smallest extrasolar planet ever found within the habitable zone, however, is Kepler-62f, a “super-Earth” with a radius of only 1.4R and a period of 267 days. Its parent star, Kepler-62, is not at all similar to the Sun, but is much smaller, cooler, and fainter. Its mass is only 70% of that of the Sun, and it emits only one fifth as much radiation as the Sun. Interestingly, it has yet another “super-Earth” within the habitable zone – Kepler-62e with a radius of 1.6R and a period of 267 days. Hence, this is a system where there are two planets that potentially could be suitable for life. If these two planets would have the same average density as the Earth, their masses would be 2.7M and 4.1M, respectively. If that was not enough, there are also three other planets – the “hot super-Earths” Kepler-62b (1.3R) and Kepler-62d (1.9R), and the planet Kepler-62c (0.54R) which is as small as Mars. The orbital periods of these planets are just 5-18 days, which means they are located extremely close to the star.

Kepler has not yet found an “earth” within the habitable zone of a solar-type star. It remains to see what is hiding among the yet unconfirmed planet candidates.

HZplanetLineup1

These drawings show the possible appearances of four of Kepler’s planets that all are located in the habitable zone (plus an image of Earth to the far right). From left; a “small Neptune” named Kepler-22b; the “super-Earth” Kepler-69c; the “super-Earth” Kepler-62e; the “super-Earth” Kepler-62f. The original picture is found at
http://kepler.nasa.gov/news/nasakeplernews/index.cfm?FuseAction=ShowNews&NewsID=243
Image credit: NASA/Ames/JPL-Caltech

“Earths” and even smaller planets

At the time of writing, four of Kepler’s planets have also been detected by the radial velocity method and shown to have masses similar to that of Earth or smaller. The most Earth-like of these, Kepler-42d, has the mass 0.95M and radius 0.57R and is very close to its star – the orbital period amounts to only 1.9 days. The planet has almost the same mass as Earth, but is not much larger than Mars – a sign that it consists of a large iron core covered by a very thin mantle of rock. Another two planets circle the same star. These have much larger masses than Earth, but are noticeably smaller, which also indicates a higher abundance of iron than for Earth – Kepler-42c (1.9M and 0.73R) has the period 11 hours, and Kepler-42b (2.9M and 0.78R) has the period 1.2 days.

The other three low-mass planets are also extremely close to their parent stars – KOI-1843b (0.32M and 0.52R) with period 4.2 hours, Kepler-70c (0.67M and 0.87R) with period 8.2 hours, and KOI-2700b (0.86M and 1.06R) with period 22 hours.

In addition to the six planets with smaller radii than Earth already mentioned, we know of seven others smaller than our planet. The smallest of these is called Kepler-37b and has a radius of only 0.32R, making it almost as small as the Moon. Around the same star revolves another small planet, Kepler-37c, whose radius of 0.75R places it between Mars and Venus in terms of size. There is also Kepler-37d, a “super-Earth” with a radius of 1.94R. These three planets have orbital periods of 13, 21, and 40 days.

Multiple systems

As we have seen, there are several stars that surround themselves with more than one planet – these are called multiple systems. So far, Kepler has discovered no less than twelve systems containing four planets or more, which doubles the known number of planet-rich systems. The Kepler star with the largest number of known planets is called Kepler-90 and is home to no less than seven planets. Three of these have periods shorter than Mercury (7-60 days) and consist of an “earth” and two “super-Earths”. At distances corresponding to the region between Mercury and Venus (92-211 day period) are three more planets – two “small Neptunes” and a giant planet with radius 8.1R, which means it is not quite as large as Saturn. Farthest away, with a period of 332 days, which would have placed it just inside Earth in our own solar system, is a giant planet with a radius of 11.3R, meaning it is slightly larger than Jupiter.

Resonant planets

Some of the multiple systems Kepler discovered have very strange properties. They have an outer planet that happens to have an orbital period that is exactly twice as long as the period of an inner planet. This is called a 1:2 resonance. At least five stars have planets with such properties – Kepler-25, -27, -30, -31 and -32. Moreover, there are examples of 2:3 resonances, which means that an outer planet performs three revolutions around the star, while an inner planet makes two revolutions in exactly the same time. The stars Kepler-23, -24, -28 and -32 have planets with such properties.

Planets around binary stars

Kepler has also discovered a class of systems that previously were completely unknown – planets on wide orbits around two stars that are very close together. The first of these, Kepler-16b, was announced in September 2011. The two stars have masses of 69% and 20% of the solar mass, and orbit each other with a period of 41 days. If they were placed in our Solar System, they would both fit inside Mercury’s orbit. The planet has a mass of 106M, which is slightly more than that of Saturn, and a radius of 8.4R, which is less than for the same planet. The planet’s orbital period is 229 days, which roughly corresponds to the orbit of Venus in our own system.

In January 2012, there were two new cases. At a distance of 4900 light years in the constellation of the Swan is Kepler-34, which consists of two solar-type stars that orbit each other with a period of 28 days – around them, the giant planet Kepler-34b (70M) that orbits with a period of 289 days. At a distance of 5400 light years in the same constellation is also Kepler-35 consisting of two stars which are slightly smaller than the Sun. The orbit each other every 21 days. In orbit around the two stars we find the giant planet Kepler-35b (40M) with an orbital period of 131 days.

In August 2012 a system of two stars was revealed to have two planets in orbit around them – a “small Neptune” named Kepler-47b which has period of 50 days, as well as a “large Neptune” named Kepler-47c, with a 303 day period which places it in the habitable zone.

In October 2012, a system of two stars was described, having 1.5 and 0.41 solar masses, circling each other with a period of 20 days. At a greater distance is a giant planet, PHI-Kepler-64b (168M) which has a period of 139 days. Far beyond are two other stars that orbit the first two at a distance of nearly 1000 AU.

Kepler’s discoveries – statistical properties

Kepler’s observations of a large number of stars, combined with the number of actual planet discoveries, makes it possible to calculate the probability that a particular star will have a planet of a given type. One then takes into account that Kepler missed a large number of planets, simply because they do not move in the plane close to our line of sight. The goal is to say what percentage of all stars in the Milky Way that have planets of certain types. We limit ourselves to stars with roughly 0.6-1.5 solar masses – so-called FGK stars. It is only possible to make firm statements about the planets with short orbital periods. The reason is that Kepler only observed for four years, which limits the selection to planets with periods of less than about 400 days, because it is necessary to see at least three consecutive eclipses. To detect planets like Jupiter, whose orbital period is around 11 years, a telescope like Kepler would have to observe for at least thirty years. Even with such limitations, important results have been found.

For example, about half of all FGK-stars should have a planet with a period less than 85 days, thus having the same distance as Mercury or being even closer to the star. This means that the Milky Way is teeming with planets – every second star has one. Among these planets, the “earths”, “super-Earths” and “small Neptunes” are equally common. Together, they account for over 90% of the cases, whereas every tenth planet is either a “large Neptune” or a “giant planet”. We do not yet know the statistics for smaller planets at slightly greater distance from the star. But we do know that about 8% of all FGK stars have a “large Neptune” or a “giant planet” at a distance similar to Earth’s or smaller.

A special study focused exclusively on small, cool, and faint so-called M-stars, whose surface temperature is between 3030°C-3720°C. They have masses of approximately 0.4-0.6 solar masses, and their emitted light and warmth is only 2%-11% of the solar radiation. The benefit of considering these stars is that the habitable zone is located fairly close to the star, in the region where the orbital periods are less than one year. Thus, the habitable zone coincides with the area where it currently is technically possible to detect many planets, if they exist. About 90% of the M-stars turn out to have an “earth”, “super-Earth” or “small Neptune” with an orbital period of 50 days or less. Almost half of these are “earths”. Therefore it is almost twice as likely to find planets close to the cool M-stars compared to the warmer FGK-stars. The smaller and colder the star, the more difficult it is to find a “super-Earth” or “small Neptune”. The presence of “earths” does not follow such a trend – they are equally common in all M-stars. About 15% of the M-stars have an “earth” which is located in the habitable zone.

Another important discovery has to do with the chemical composition of the host star. In a previous post about the interstellar medium, I have described its typical chemical composition, which is also inherited by the stars formed therefrom. About 99% of the mass is hydrogen and helium, while all the other heavier elements make up about 1%. But there are significant differences between the stars, as some very old stars were formed at a time when there was even less heavier elements than today. Such stars are called metal-poor. Previous studies have shown a clear trend regarding the likelihood of finding a giant planet around a normal FGK-star. The metal poorer the star is, the smaller the chance that there will be a giant planet in orbit around it. Now it is possible to extend this type of study to stars hosting smaller planets. The chemical composition of 152 stars having 226 planets within a distance of at most 0.5 AU have been investigated. It turns out that the chance of finding an “earth”, a “super-Earth” or a “small Neptune” does not depend particularly strongly on the chemical composition of the star – small planets are abundant even around relatively metal-poor stars. Some stars in the study have four times less heavy elements than the Sun, and still have managed to form planets. While stars with slightly higher metal content than the Sun statistically has 2.7 planets with radius less than 4R for every giant planet, this number has risen to 5.9 for the metal-poor stars. This is because the giant planets are becoming increasingly rare as the star’s metal content decreases.

In another study the properties of planetary systems having large planets at very short distances from the star were explored – how does this affect the existence of other planets at similar distances? This study examined three different groups. The first group, including 63 system, consisted of planets with radii 0.6-2.5 times that of Jupiter, with orbital periods of 1-5 days, i.e., “hot Jupiters.” All attempts to find another planet near the star of these systems failed – a hot Jupiter reigns alone in this inner region.

The second group also had very short orbital periods, only 0.8-6.3 days, but consisted of planets with radii of 1.4-6.7R, roughly equivalent to a “small” or “large Neptune ” – and a very hot one. The study included 222 such systems. When looking for additional planets on somewhat smaller or larger distances from the star in these systems, the outcome is extremely different from the first group. In the second group there are 73 cases of smaller planets with orbits close to the large one, i.e., every third system. The probability of finding two planets close to each other near the star increases dramatically when the larger of the planets is not extremely large.

The third group consists of planets similar to those in the first, i.e. planets about the size of Jupiter, except that they are slightly farther from the host star and thus have slightly longer orbital periods, 6.3-15.8 days. This is what is called a “warm Jupiter.” Here it is also rare with other planets in the vicinity, but three systems where found including a second planet, near the 1:2 resonance. Although the statistics are uncertain because these are so few planetary systems, these results suggest that about 10% of the “warm Jupiters” are not alone.

The significance of Kepler’s results

Kepler’s observations have resulted in the discovery of a series of very remarkable planetary system, which differ significantly from our own Solar System. We are fascinated and amazed by these odd and alien worlds. The press releases by the scientists are spread further by newspapers and TV channels, along with imaginative drawings by artists of how these planets might look like, to a curious and interested public. The discoveries increase people’s knowledge about their environment and lead to conversation, debate, and speculation. They become a part of popular culture and sooner or later become parts of science fiction books or movies. They inspire many young people to study natural science in schools and universities, some of them becoming scientists that will uncover new knowledge about Nature. This situation is not unlike the collection of strange herbs, plants, and animals from all parts of the world, made by European explorers in the 17th and 18th centuries, that were exhibited in museums, botanical gardens, zoological parks or shown in various collections of curiosities, to the amusement of the general public.

All this is fine, but says rather little about how scientists actually use this new knowledge. It says little about the purpose of building a space telescope like Kepler. To understand the real purpose we can return to the botanical and zoological collections – their real significance was to offer such a high degree of information about Nature, and so many concrete examples of its diversity, that it was possible to begin to see patterns, identify connection and strengthen hypotheses, which eventually made it possible to understand how the species have emerged and evolved on Earth. It was this huge amount of concrete information, that made it possible for Charles Darwin and others to begin to understand the processes by which species evolve and the mechanisms that control the evolution. Similarly, Kepler’s observations are not exclusively about revealing one planetary system that is more spectacular than the other, and the final goal is not only to gather facts about these systems that can be stacked in well-ordered tables. Instead, Kepler is there to provide information that helps us understand how planetary systems are formed and how they evolve over time. We want to understand the underlying processes and mechanisms, and this requires detailed information of how the world actually looks like. That is where Kepler comes in, and this is the light in which we have to see its discoveries.

The physical processes and mechanisms responsible for planet formation are described in mathematical terms, but these equations must be solved in some way. Previously, we were forced to solve these equations by hand, which severely limited the complexity of the equations one could study. Today, the equations are solved numerically with the aid of powerful computers, which means that more realistic processes and mechanisms can be studied.

Computer models of planet formation

From observations of very young stars around us, which currently are in the same stage of development as the Solar System was when it formed 4.6 billion years ago, we know that these young stars are surrounded by vast but thin disks. This disk material has the same composition as the interstellar medium, which means that about 99% of the mass consists of hydrogen and helium, while 1% of the mass is dust grains.

There is currently a large number of computer models developed by researchers to describe what happens when these dust grains gradually merge to form larger bodies. There are models that follow the entire chain from grain to planet, but it is more common to study selected sub-problems and specific aspects of the process. Some models focus on the very first period, when small grains build bodies that are at most a few hundred kilometers in size – so-called planetesimals. These models keep track of a large number of positions, velocities and masses of individual particles, follow their motions over time, as the particles feel the gravitational force of the star and are slowed down or dragged along by the gas in the disk, which often is allowed to have turbulent properties. During collisions between grains, decisions are made regarding the outcome – do particles merge into larger units, do they fragment into a variety of smaller particles, or just bounce against each other? These decisions often rely heavily on laboratory experiments, that studies what actually happens when two grains or clusters of grains with specific masses collide with each other at specific speeds. As the model marches forward in time, one can track how particles grow and determine how long it takes to reach a certain particle size.

Other models describe how these planetesimals merge to form embryos – bodies that are as large as the Moon, Mercury and Mars. Yet other models study how embryos are merged in gigantic collisions to form planets like Venus or Earth. Some models focus on the interactions between the planets and the surrounding gas – when will the planet’s gravitational pull become strong enough to absorb large amounts of gas and grow into a gas giant? How does the gas disk properties change by the presence of a gas giant, and how does this in turn modify the ability of the gas giant to grow further? It was models like these, in the mid 1980s, that showed that a gas giant would not remain at its birthplace, but start drifting towards the star, a phenomenon known as migration. It is this type of modeling that is the basis for most of the ideas, thoughts, claims and knowledge regarding planet formation today – the models are invaluable tools for building our understanding of the world.

The purpose of the models is to show exactly what type of planetesimals, embryos and planets that form at different distances from the star, and how long it takes. They also show how the end results are altered when the basic conditions of the simulations are changed – such as the stellar mass, gas disc mass, or the amount of dust present in the disc. This is not casual work – computer models of this type is often the result of lifelong work that takes decades to develop, refine, and perfect. Despite all efforts, it is inevitable that such models are based on a wide range of assumptions and simplifications, that are necessary for practical reasons. The difficult question is always – exactly how correct, realistic and relevant are these models? We know that the predictions differ among models – sometimes in a fundamental way. In order to know which models are more accurate than others, and for improving these models further, it is necessary to compare the model predictions with reality.

Our Solar System is of course extremely important in this context. It is the only planetary system we can study up close. Here we can use radiometric dating of meteorites and material from Earth, the Moon and Mars to verify the timescales of formation suggested by the models. It is possible to investigate asteroids and comets – surviving planetesimals – in situ, to see what internal structure they have and compare it to the predictions of the models. At the same time, the Solar System is only one system out of many, and in order to claim with certainty that we understand how our own Solar System formed, it is necessary to explain how other planetary systems form as well. Here, Kepler’s observations constitute an invaluable source of information – the models must conform with this reality.

In order to sketch how Kepler’s observations may improve our understanding of planet formation, it is first necessary to summarize some aspects that are of great importance in planet formation.

The early stages of Solar System evolution

In our own Solar System there are fundamental differences between terrestrial planets, gas giants and ice giants. We have also seen that exoplanet systems have a similar mix of very small planets and extremely large planets. There are essentially two factors that cause these differences – the existence of a snowline and the fact that the gas disc has a limited lifespan.

The snowline exists because the temperature in the disk falls steadily with distance from the heat and warmth of the central star. Within the snowline, located around 4 AU from the star, it is so hot that the abundant water cannot freeze – the water vapor mixes with the other gases of the disk, and the grains consist exclusively of rock, metal and sulfides. Outside the snowline, it is cold enough for the vapor to freeze – outside 4 AU the grains of rock, metal and sulfide are covered with thick layers of ice.

Observations of young stars show that the gas in the disks only survives for about 3-5 million years. The gas simply evaporate, due to the heating from the star at the center of the disk. If gas giants are to form in the disk, they need to develop before the gas takes off. It is a race against time, which does not always lead to victory. We shall now see how these two factors have shaped our own Solar System.

Models of planetesimal growth within the snowline shows that it may have been very slow. Grains of rock, metal and sulfides have difficulties to stick to each other, preventing rapid growth. Radiometric dating of meteorites seem to confirm that planetesimal formation was a sporadic process that took place repeatedly throughout the first 4-5 million years. Once formed, they merged into embryos rather quickly. However, being scattered at large distances from each other, it took a long time, tens of millions of years, for the embryos to unite in collisions. The Earth was not fully formed until 50-150 million years had passed, when the Moon formed in the last giant collision with an embryo that our planet experienced. These time scales are supported by both simulations and radiometric dating. The terrestrial planets therefore grew long after the gas had disappeared. Mercury and Mars can probably be considered surviving embryos that escaped from being devoured by Venus or Earth.

Outside the snowline, in the outer part of the Solar System, the development was completely different. Here the grains were significantly larger, since they largely consisted of ice, in addition to the rock, metal and sulfides. This ice is very sticky, making it easy for the grains to attach to each other. Models show that it is possible to build very large planets of rock, metal, sulfides and ice in just a couple of million years. The models also show that it is extremely difficult for the planet to soak up any gas, unless it is heavier than ten Earth masses. But when the planet reaches a mass of 10M the gravitational force becomes strong enough to absorb cold gas directly from the disk and quickly grow into a gas giant. It is critically important that the growth to 10M has time to occur before the gas disappears 3-5 million years into Solar System history. The ice giants Uranus and Neptune are probably examples of planets not formed fast enough to consume large quantities of gas, unlike the gas giants Saturn and Jupiter. The gas and ice giants were therefore in place long before Venus and Earth had time to form in the inner Solar System.

Kepler helps to answer important questions

Models show that it is not possible to form a gas giant extremely close to a star. There is usually not enough material to reach 10M, the time it takes to build a large body is too long compared to the gas disk lifetime, and even in the unlikely event that a sufficiently massive planet forms before the gas disappears, this gas is so hot and is moving so fast that it cannot easily be collected by the planet. In our Solar System there are no gas giants close to the Sun. But according to Kepler, a tenth of the stars with masses close to the Sun, have a “large Neptune” or a “giant planet”, within a few tenths of an AU from the star.

Such giant planets must have formed outside the snowline, and have moved closer to the star at a later stage. Computer simulations of interaction between a gas giant and the disk, show that migration can be a very common phenomenon – the gas giant gradually drifts towards the star, and may not stop until it reaches the inner edge of the disc, located only a few hundredths of an AU from the stellar surface. But the move may also have happened in an entirely different way. If two or more gas giants formed close to each other outside the snowline, the gravitational perturbations may have been strong enough to give one of the planets a very elliptical orbit, that occasionally brought it very close to its star. During these close encounters with the star it may happen, according to other models, that the star is forcing the planetary orbit to become more circular, so that it eventually is given a permanent residence in the immediate vicinity of the star.

So here we have two interesting questions. Which of the two possible mechanisms – migration or gravitational perturbations followed by circularization of the orbit – is actually responsible for moving the planet? What is it that makes some planetary systems experience extensive movements of their giant planets while others, like our own, did not experience such a strong redecoration? Kepler’s observations are indispensable by addressing this kind of issues.

Kepler observations show that migration undoubtedly has taken place. The primary proof of that is that resonant systems have been detected. When the migration moves the planet slowly inwards, the resonances of the planet will also drift inwards. The resonances are located at the distances from the star where the gas and dust has an orbital period that is a small integer fraction of the planet’s orbital period. When the planet migrates, its orbital period keeps changing, why the resonances slowly move as well. If such a resonance accidentally passes the orbit of a smaller planet, the planet gets stuck in the resonance. Then the planets move towards the star in formation, while being constantly locked in the resonance. When the gas finally disappears and the migration ceases, the planets remain locked in their common resonances. So far, Kepler has discovered nine resonant systems. Kepler-90 could also be the result of migration – perhaps the six planets located within the 332 day orbit of the giant planet were pushed there by the drifting giant planet? It is possible that planets eventually will detach from the resonances, for example by gravitational perturbations. If so, the absence of resonant planets today, cannot be used to claim that migration has not occurred. It is therefore possible that the “hot Jupiters” that have smaller planets in their vicinity (about 10%), and the “hot Neptunes” that have small neighbors (about 30%), have picked these planets up during their migration.

But if migration is the only mechanism responsible for large-scale relocation of gas giants, how come that the most extreme planets – the “hot Jupiters” – all are alone near their stars? Why have they not also pushed planets in front of them or dragged them along behind? Could it be that they have arrived in a very different way – for example by strong gravitational perturbations followed by circularization?

A second problem concerns the location of the “earths”. About half of the stars with masses similar to the Sun (FGK-stars) have planets within a few tenths of an AU from the star, of which 30% are “earths”. Among the small M-stars 90% have a planet within a few tenths of an AU from the star, half of which are “earths”. Thus it seems to be very common to find Earth-sized planets, at distances no greater than that between the Sun and Mercury. Does that mean that they formed there? Or do they necessarily form at slightly greater distances, where Venus and Earth are located in our own system, and then migrate inwards? If so, why did not Venus and Earth migrate? No matter which model is used to simulate the formation and migration of Earth-like planets emergence, it must result in a statistical distribution of planets with distance from the star that is consistent with observations, for stars with different mass. If we can produce models that closely reproduces reality, we can be fairly sure that they give us a true picture of how our own planet has formed.

A third problem concerns the very earliest stage – the formation of planetesimals. Today this is an intensive field of research, with a number of competing theories, which paint quite different pictures of planetesimal growth. According to the hierarchical agglomeration scenario bodies are built gradually, as small planetesimals merge into larger ones. Here, objects of all sizes, from a few centimeters to hundreds of kilometers are represented, at least at some stage during the simulations. But there are also alternative scenarios, such as streaming instabilities, where the gas is able to sweep up decimeter-sized boulders into huge swarms which later collapse gravitationally and directly form planetesimals that are hundreds of kilometers in diameter, without the formation of objects with intermediate sizes. Hierarchical agglomeration will proceed no matter how little dust there is in a gas disk – but the smaller the amount the dust, the longer it takes to build planetesimals. Streaming instabilities are extremely sensitive to the amount of dust compared to the amount of gas. If planetesimals are to form very early through streaming instabilities, the gas cannot be metal poor – it should be as rich in heavy elements as the Sun, and preferably twice as rich in metals.

It is therefore interesting that stars whose metal content is only a quarter of the solar metallicity, still have been able to form “earths” and “super-Earths” with the same efficiency as the metal-rich stars. It either means that hierarchical agglomeration dominates, or planetesimals begin to form only once the gas is partially dispersed after 3-5 million years. Kepler observations of the presence of planets around stars of different metallicity thus provide important information that helps us understand the mechanisms that are responsible for the formation of planetesimals, and when these mechanisms are active.

Afterword

The exploration of our planetary system aims at building an image of the world based on natural science, and to be able to describe in detail how the Earth and the other planets formed. This reconstruction of our own history and our attempts to understand the environment in which we live, is a deeply humanistic quest. It is based in the uniquely human urge to understand ourselves, our environment and our origin. Today we have reached a point where only advanced technology can bring us further – space telescopes like Kepler, or the powerful computers used for model calculations are necessary tools for us to change and improve our image of the world. It may not be obvious at first glance, but the truth is that this technology – despite its industrial appearance and mathematical inaccessibility – is actually part of a humanistic cultural project.

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NASA’s website about Kepler: http://kepler.nasa.gov/

The Extrasolar Planet Encyclopaedia : http://exoplanet.eu/catalog/