Rosetta’s comet in 3D!

The colorful image of Comet 67P/Churyumov-Gerasimenko is an anaglyph – by looking at it through glasses with a red and a green filter, a three-dimensional image is seen. This is a good way to get a feel for how irregular the terrain actually is.


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The two images used to create this anaglyph were taken by our camera OSIRIS on ESA’s spacecraft Rosetta on August 7, 2014. The images were taken 17 minutes apart to change the viewing geometry, through Rosetta’s motion and the nucleus rotation, which is necessary to create the 3D sensation. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


For those who do not have such glasses – enjoy one of the original images below.


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An original image from OSIRIS used to create the anaglyph above. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


The scientific imaging system OSIRIS was built by a consortium led by the Max Planck Institute for Solar System Research (Germany) in collaboration with CISAS, University of Padova (Italy), the Laboratoire d’Astrophysique de Marseille (France), the Instituto de Astrofísica de Andalucia, CSIC (Spain), the Scientific Support Office of the European Space Agency (The Netherlands), the Instituto Nacional de Técnica Aeroespacial (Spain), the Universidad Politéchnica de Madrid (Spain), the Department of Physics and Astronomy of Uppsala University (Sweden), and the Institute of Computer and Network Engineering of the TU Braunschweig (Germany). OSIRIS was financially supported by the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), and Sweden (SNSB) and the ESA Technical Directorate.

 

Meet the heart of Comet 67P/Churyumov-Gerasimenko!

Our new images from the camera system OSIRIS on ESA’s spacecraft Rosetta shows that Comet 67P/Churyumov-Gerasimenko has a spectacularly shaped nucleus! The nucleus consists of two large pieces with different shape, connected at a small contact surface.


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A sequence of 36 processed images of Comet 67P/Churyumov-Gerasimenko taken 20 minutes apart on July 14, 2014, from a distance of about 12,000 kilometers. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


 

One should not look too closely for details in a movie like this. The reasons is clear once we look at one of the original images below. The camera has a limited resolution and the original image consists of a number of squares, or “pixels”, that each have recorded a certain light intensity. We do not know how the nucleus looks like within each pixel – but we can guess!


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An original picture from OSIRIS before image processing. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


 

During so-called image processing, mathematical algorithms are used in an attempt to re-create how an object really looks like, before it got smeared out by the pixels. Such algorithms are good at re-creating lost information, but they are not perfect. Real surface structures may have been lost completely, while false features that do not exist in reality may have been added.


Abbildung 1 b

A processed image from OSIRIS. Credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


 

The only way to find out how the comet surface really looks like is to get closer – and in a short while Rosetta will be much closer to the comet!


The scientific imaging system OSIRIS was built by a consortium led by the Max Planck Institute for Solar System Research (Germany) in collaboration with CISAS, University of Padova (Italy), the Laboratoire d’Astrophysique de Marseille (France), the Instituto de Astrofísica de Andalucia, CSIC (Spain), the Scientific Support Office of the European Space Agency (The Netherlands), the Instituto Nacional de Técnica Aeroespacial (Spain), the Universidad Politéchnica de Madrid (Spain), the Department of Physics and Astronomy of Uppsala University (Sweden), and the Institute of Computer and Network Engineering of the TU Braunschweig (Germany). OSIRIS was financially supported by the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), and Sweden (SNSB) and the ESA Technical Directorate.

OSIRIS: First glimpse of the comet nucleus!

Up to just a few days ago, the target of ESA’s Rosetta mission, Comet 67P/Churyumov-Gerasimenko, was just a dot in the sky, barely distinguishing itself from the stars by displaying a small temporary dust coma. But now Rosetta is getting so close to the comet, 40 000 kilometers – about a tenth of the distance between Earth and the Moon – that the OSIRIS camera starts to resolve the nucleus. The comet nucleus is still just a couple of camera pixels across, but as seen in the movie below, there is a hint of nucleus irregularity. The nucleus size and shape changes slightly, while it is rotating with its 12.4 hour period. From now on, the comet nucleus will just grow in size until it fills the entire field of view of the Narrow Angle Camera (NAC) in mid August. Stay tuned for more cool pictures from OSIRIS!


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First resolved images of comet 67P/Churyumov-Gerasimenko show the nucleus rotating with a rotation period of 12.4 hours. This set of 36 images was obtained by OSIRIS’ narrow angle camera (NAC) on June 27th and June 28th and covers one such period. © ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA


The scientific imaging system OSIRIS was built by a consortium led by the Max Planck Institute for Solar System Research (Germany) in collaboration with CISAS, University of Padova (Italy), the Laboratoire d’Astrophysique de Marseille (France), the Instituto de Astrofísica de Andalucia, CSIC (Spain), the Scientific Support Office of the European Space Agency (The Netherlands), the Instituto Nacional de Técnica Aeroespacial (Spain), the Universidad Politéchnica de Madrid (Spain), the Department of Physics and Astronomy of Uppsala University (Sweden), and the Institute of Computer and Network Engineering of the TU Braunschweig (Germany). OSIRIS was financially supported by the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), and Sweden (SNSB) and the ESA Technical Directorate.

 

Organics in space

This article was originally posted on the blog Dinner Table Science were I was guest blogging – please visit and follow Rachel’s blog, it is great!


Life, as we know it, would not have been possible without the carbon atom. The scientific discipline dealing with all the molecular relationships that the carbon atom is getting itself into – organic chemistry – is essential for understanding how living organisms function and evolve. We take it for granted that organic chemistry is flourishing on Earth, because it is teeming of life, but only in the last few decades have we come to realize that such processes also are common far beyond our own planet – in the depths of space. No form of extraterrestrial life has been discovered so far, but a surprisingly rich variety of organic compounds has been found within the Solar System, as well as in the interstellar medium. None of these organic molecules have a biological origin but some may, or may not, have been prebiotic, i.e., involved in the processes that eventually led to the emergence of life on our planet.


Organic molecules are found in many different Solar System objects or space environments, but here we will focus on two of them – a type of meteorite called a carbonaceous chondrite, and the interstellar medium. After reviewing what we know about these organic substances, we will also discuss the processes believed to have created them.

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The Murchison meteorite is a carbonaceous chondrite. It is one of our most important sources of information on organics from space due to its large mass (more than 100 kg) and the fact that it was recovered right after it fell, and has suffered a minimum of terrestrial contamination. This picture shows a piece of Murchison at the The National Museum of Natural History (Washington). Original image: http://en.wikipedia.org/wiki/File:Murchison_crop.jpg

 


Carbonaceous chondrites

Most of the meteorites that impact Earth, almost 90%, are so-called chondrites. They got their name because they are rich in chondrules, a type of millimeter-sized grain formed in huge numbers 4.57 billion years ago during the earliest phase of Solar System history. They still contain these ancient particles because the chondritic meteorite parent bodies never melted (these 10-100 km parent bodies later broke up in devastating collisions, and the chondritic meteorites are tiny fragments from such collisions). This distinguishes the chondritic meteorites from achondritic meteorites (8% of the falls) and iron meteorites (2% of the falls) that both originate from parent bodies that once were heated by radioactive decay to the point that they actually melted and differentiated, e.g. separated into a rocky mantle and a metallic core. Such melting erased all memory of previous history, and that is why chondritic meteorites are so valuable – they can tell us about the time before the formation of the parent bodies (most of which eventually were merging to form the planets).


Most chondritic meteorites are so-called ordinary chondrites that are related to the rocky S-type asteroids in the inner main asteroid belt. This region was generally too warm to allow molecular compounds with a low boiling point to condense into solids. However, some of the meteorites are carbonaceous chondrites, believed to be related to the more distant C-type asteroids from the outer main asteroid belt. They formed in conditions sufficiently cold to allow condensation of very volatile species – they are therefore rich in water (up to 20% by mass) and they also contain organic molecules that are rare or absent in the inner Solar System.


The carbonaceous chondrites got their name because they are unusually dark – they look like charcoal. The name is actually misleading, because the dark color is not due to carbon, but due to iron, an atom that is very efficient in absorbing light. In ordinary chondrites, the iron is gathered into small metallic particles mixed with the chondrules (we say that the iron is reduced), leaving the rocky material virtually iron-free and thus fairly bright in color. In carbonaceous chondrites, the iron is finely distributed throughout the rocky material on an atomic level (we say that the iron is oxidized), which makes the entire rock an efficient light absorber, thus being dark.


The typical carbonaceous chondrite contains only about 2-5% carbon by mass. However, this organic material is amazing, particularly the 25% that is referred to as “extractable organic matter” that is either liquid or solid at room temperature. In decreasing order of abundance the extractable organic matter consists of the following cocktail, of which a selection is described below – carboxylic acids, sulfonic acids, amino acids, sugars, urea, aliphatic and aromatic hydrocarbons, ketones, ammonia, alcohols, purines and pyrimidines. The remaining 75% is called “macromolecular material” and is a solid substance with an extremely complex composition. In some cases, the organics in meteorites is partially terrestrial contaminations. However, the risk of contamination is low if meteorites are recovered directly after a fall, and in most cases the meteoritic organics have such unusual concentrations of the isotopes carbon-13, nitrogen-15 and hydrogen-2 (deuterium), that a terrestrial origin can be excluded. Thus, the compounds discussed below are definitively from space.


In order to understand how the macromolecular material looks like, we need to know how carbon atoms interact with their own kind and with other atoms. A carbon atom can bind itself to up to four other atoms simultaneously. Often, carbon atoms form linear chains of various length. A given carbon atom within the chain then connects with two of its carbon neighbors, meaning that it can afford to connect also with two other atoms, typically hydrogen (but sometimes oxygen, nitrogen or other atoms). The carbon atom sitting at the end of a chain only connects with one other carbon, allowing it to attach three hydrogen atoms to it. These chain-like structures are called aliphatic hydrocarbons. However, it is also common that six (and sometimes five) carbon atoms form a ring. Here, a given carbon atom uses two of its connections to bind to the first of its carbon neighbors, and one for the second, leaving space for a single foreign atom (often hydrogen) to attach itself externally to the ring. Such ring-like structures are called aromatic hydrocarbons. Rings can also attach to each other, so that two carbon atoms simultaneously are members of two rings. Molecules that contain several such rings are called polycyclic aromatic hydrocarbons (or PAHs).


The macromolecular material in carbonaceous chondrites has proven to be a gigantic web, where aromatic rings use aliphatic chains to connect to each other. Often there are single rings that have replaced one or several of their external hydrogen atoms with an aliphatic chain – typically with 2-4 carbon atom links – in order to connect to another aromatic ring located farther away. However, it is not unusual that two, three or four rings form a little aromatic island, that connects itself to other islands through the aliphatic bridges. The fraction of macromolecular carbon that is aromatic is about 60-70% for Murchison, about 70-80% for Orgueil and almost 100% for Tagish Lake (these are three different carbonaceous meteorites). A typical elemental composition of the macromolecular material is about 70 hydrogen atoms (H), 12 oxygen atoms (O), three nitrogen atoms (N) and two sulphur atoms (S), for every 100 carbon atoms (C).


The extractable organic matter is dominated by carboxylic acids – these are basically aliphatic chains where one carbon atom at the end of the chain has replaced two of its hydrogen atoms with a single oxygen atom, and replaced the last hydrogen atom with a hydroxyle group consisting of an oxygen atom with a hydrogen attached to it (thus there is a COOH group). If both ends of the chain has COOH groups, the molecule is called a dicarboxylic acid. Examples include formic acid (HCOOH) used by ants as a venom, acetic acid (CH3COOH) used in cooking in diluted from under the name vinegar, butyric acid (C3H7COOH) that gives rancid butter its unpleasant smell, and valeric acid (C4H9COOH) that is named after the valerian herb (Valeriana officinalis) that produces this molecule. They are all found in carbonaceous meteorites, that often contain carboxylic acids with up to ten carbon atoms.


If a carboxylic acid has one of its hydrogen atoms in the aliphatic chain replaced by the amino group NH2, it is called an amino acid. Amino acids are fundamental to life, because they are the building blocks of proteins. Humans and other animals need to eat proteins, and the body break them down into their amino acid constituents, that are then used by cells to build other proteins (a process called translation) that we need to function. To find amino acids in meteorites is extremely fascinating, just because they play such a central role in the chemistry of living organisms.


More than 70 different amino acids have been identified in carbonaceous meteorites. Some of these meteorites, like Murchison, Orgueil and Ivuna are rather rich in amino acids. Others, like Tagish Lake, have extremely low abundances of amino acids. Murchison contains eight of the protein amino acids, eleven that are biologically common, and several others that are not used by terrestrial organisms. The five most common, in decreasing order of abundance, is glycine (NH2[CH2]COOH), alpha-aminoisobutyric acid (NH2[C3H6]COOH), D-alanine and beta-alanine (NH2[C2H4]COOH), and isovaline (NH2[C4H8]COOH), where the chemical formulae have been written to highlight the amino and carboxyl groups. Here, the prefixes “alpha” and “beta” is a way to tell which carbon atom the amino group is attached to.


Most amino acids have so-called chirality, which means that there are two variants of each molecule (called enantiomers), that have the same chemical composition but geometrically are mirror images of each other. They are distinguished through the prefixes L and D such as in L-alanine and D-alanine. All proteins built by translation contain L enantiomers. In carbonaceous chondrites both enantiomers appear to be equally common, although some controversial studies show that there may be a slight L-excess for certain amino acids like alanine, proline and leucine.


Aromatic hydrocarbons are not only found in the macromolecular material, but also in the extractable organic material. The most common compounds are the PAHs fluoranthene and pyrene. They both have the formula C16H10 but are structurally different – flouranthene consists of three standard rings with six carbon atoms, joined by a ring containing just five carbon atoms, while pyrene is made of four standard rings.

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The structural formula of pyrimidine, showing how carbon (C) and nitrogen (N) atoms form a ring, to which a number of hydrogen (H) atoms are attached. Original image: http://en.wikipedia.org/wiki/File:Pyrimidine_2D_aromatic_full.svg

 

The really interesting thing starts when the carbon atoms in aromatic rings are replaced by nitrogen. If the starting point is a single six-atom ring (called benzene if all atoms are carbon), and two specific carbon atoms are exchanged with nitrogen, a substance called pyrimidine (C4H4N2) is formed. By replacing hydrogen atoms by amino groups or oxygen atoms, a variety of molecules can be formed, including the nucleobases cytosine (C), thymine (T) and uracil (U), that are basic building blocks in DNA and RNA. The pyrimidine uracil has been found in carbonaceous chondrites.

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The structural formula of uracil. The aromatic ring is here somewhat abstract since corners are meant to indicate the location of a carbon atom (sometimes with a hydrogen atom attached to it), while only nitrogen and oxygen atoms, with associated hydrogen atoms, are shown explicitly. Original image: http://en.wikipedia.org/wiki/File:Uracil.svg

 

If the starting point is a six-atom ring joined to a five-atom ring, and two specific carbon atoms in each ring are replaced with nitrogen, a compound called purine (C5H4N4) is obtained. As before, the replacement of hydrogen atoms with amino groups and oxygen atoms gives rise to a variety of molecules, including two other nucleobases that are found in DNA – adenine (A) and guanine (G). Both adenine and guanine has been found in carbonaceous chondrites, along with other purines, such as xanthine and hypoxanthine.

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The structural formula of various kinds of purines. Adenine, guanine, hypoxanthine and xanthine have been found in carbonaceous chondrites. Original image: http://en.wikipedia.org/wiki/File:Purines.svg

 

It is therefore clear that carbonaceous chondrites contain a variety of fairly complex organic molecules. Comet nuclei are likely to be as rich or even richer in such compounds, although we know much less about comets than meteorites since actual samples of comet material is restricted to very small amounts, collected by the Stardust spacecraft in the coma of Comet 81P/Wild 2 and brought back to Earth. Both carbonaceous chondrites and comets bombarded the young Earth, thereby bringing organic substances to the inner region of the Solar System, where such compounds initially may have been rare. The possibility that these organics were involved in the formation of life on Earth is a fascinating thought. But what is the origin of these compounds – where did they form and how? To answer that question, we must leave the Solar System and head out into interstellar space.


The interstellar medium

The space between the stars in our galaxy, the Milky Way, is not empty – about 90% of the galactic mass is bound in stars, while the rest forms an extremely thin mixture of gas and solid dust particles that fill the space between the stars – the interstellar medium. About 98-99% of the mass is hydrogen and helium, while the remaining fraction is shared between all heavier elements. Among these, oxygen is the most common element by number, followed by carbon, neon, and nitrogen. These elements mainly exist as unbound atoms in the gas phase, while the solid grains primarily consist of silicates and sulfides rich in oxygen, magnesium, silicon, iron and sulphur (these are the ten most common chemical elements in the universe, by number).


In places where the interstellar medium is particularly dense – the molecular clouds – atoms in the gas phase form small molecules, primarily molecular hydrogen (H2), carbon monoxide (CO), and molecular nitrogen (N2), but also water (H2O), carbon dioxide (CO2), ammonia (NH3), methane (CH4), and methanol (CH3OH). Over time, some of these gases will condense on top of the grains, thus forming mantles of ice that surround the rocky cores.


When such ice is exposed to ultraviolet radiation from nearby stars, it gets damaged. Molecules are cut into small pieces called radicals. These are extremely reactive, but due to the extreme cold (typically 10K or -260C) the radicals have little mobility and do not manage to get in physical contact with each other. Over time, large deposits of radicals are built up within the ice. Only a small amount of heating, perhaps due to rare collisions between icy grains, is sufficient to trigger an explosive chain reaction, were radicals unite to form a variety of complex organic molecules. Many of these leave the grain surfaces and can be observed as free molecules in the interstellar gas, while others remain on the grain surfaces.


This process is at least partially responsible for the rich variety of organic molecules that has been observed in interstellar space. Observations are made with radio telescopes, that pick up the long-wavelength radiation that the molecules emit when they change their rotation or vibration rates. More than 150 molecular compounds have been identified in the interstellar medium, of which a third contain six atoms or more. Some large molecules that have been identified include propylene (CH3CHCH2), methyltriacetylene (CH3C6H), vinyl alcohol (C2H3OH), acetic acid (CH3COOH), ethylene glycol (HOCH2CH2OH), cyanopentaacetylene (HC11N), and acetamide (CH3CONH2).


The processes taking place in the interstellar medium can be reproduced in laboratories. A mixture of ice (for example, water, carbon monoxide, carbon dioxide, ammonia, and methanol in proportions expected in interstellar ice) is deposited on a 10K substrate, and the mixture is irradiated by ultraviolet radiation and then slowly heated to trigger the chain reaction. An organic residue is thus formed, sometimes called “yellow stuff”. The material is particularly rich in carboxylic acids and hexamethylenetetramine (C6H12N4). In one particular experiment, no less than 16 amino acids where identified in this yellow stuff. These included glycine, alanine, sarcosine, valine and serine. In these samples both enantiomers of each amino acid were equally common, to within measurement uncertainties.


Stellar and planetary systems form when interstellar gas and dust collapse due to its self-gravity, in regions where the interstellar medium has become exceptionally dense. According to the “interstellar parent-body hypothesis” the organic compounds seen in carbonaceous chondrites are interstellar organics that survived the turmoil of Solar System formation. That is to say, these substances did not primarily form here, and at least a fraction of the material must have avoided heating to the point where they would have disintegrated into their atomic constituents. The material may have been processed or altered in various ways, but the key idea is that the carbonaceous chondrite parent bodies contained complex organics already when they formed. The very unusual isotopic composition that characterize these organics are often interpreted as evidence of an interstellar origin.


Although the carbonaceous chondrite parent bodies formed sufficiently late not to melt (perhaps 1-2 million years after differentiated bodies, at a time when the short-lived radioactive heat source aluminum-26 almost had vanished), they still experienced mild warming. The temperature was sufficiently high to melt ice within the parent body, and allowing liquid water to percolate through the granular interior. This has led to various levels of so-called aqueous alteration – characteristic changes of the mineralogical composition of the meteorite caused by liquid water. The presence of liquid water has also modified the composition of the organics. It appears increasingly unlikely that the organics we see today in carbonaceous chondrites were formed from scratch during aqueous alteration – they must have had a long and complex previous evolutionary history that started in interstellar space.


The exploration of organics in space has merely begun. The presence of complex organic molecules in distant asteroids and comet nuclei are strong reasons for performing sample return missions to such bodies. The answers to some of our most profound questions about our existence may lay buried within these ancient survivors of planetary formation – how did the Solar System form, what kind of material rained down on the young Earth, and is it possible that life got a jump start thanks to organics from space?

We just have to go and have a look.


Literature

Gilmour, I. (2003). Structural and isotopic analysis of organic matter in carbonaceous chondrites. Treatise on Geochemistry, 1, 269-290.

Herbst, E., van Dishoeck, E. F. (2009). Complex organic interstellar molecules. Annual Review of Astronomy and Astrophysics, 47, 427-480.

Muñoz Caro, G. M., Meierhenrich, U. J., Schutte, W. A., Barbier, B., Arcones Segovia, A., Rosenbauer, H., Thiemann, W. H.-P., Brack, A., Greenberg, J. M. (2002). Amino acids from ultraviolet irradiation of interstellar ice analogues. Nature 416, 403-406.

Comet 67P/Churyumov-Gerasimenko wakes up as ESA’s Rosetta spacecraft approaches!

I was at the OSIRIS Full Team meeting held at the Max Planck Institut für Sonnensystemforschung in Göttingen, Germany, last week. We had a great meeting, and the good news are piling up – the spacecraft Rosetta performs well, our imaging camera system OSIRIS is fully operational (as are all the other instruments), orbit manoeuvres are successfully executed to enable Rosetta to rendezvous with the comet in early August, and we have already started to do science.

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Between March 24th and May 4th, Rosetta approached comet 67P/Churyumov-Gerasimenko from a distance of around 5 million to 2 million kilometers. This sequence of images shows the comet’s movement against the background star field during this time. Rosetta (and the comet) are between 640 and 610 million km from the Sun. The comet is seen to develop a dust coma as the sequence progresses, with clear activity already visible in late-April. Exposure times are 720s for each image, taken with the OSIRIS/NAC through the Orange filter. credits: ESA/Rosetta/MPS for OSIRIS Team MPS/UPD/LAM/IAA/SSO/INTA/UPM/DASP/IDA

 

First of all, we have detected the nucleus of Comet 67P/Churyumov-Gerasimenko and are tracking its motion. Secondly, the lightcurve is being monitored regularly, which has allowed us to measure a 12.4 hour rotation period of the nucleus. The lightcurve is a periodic variation in the observed brightness of the nucleus. The variations arise since the nucleus is not spherical but irregular, so that the amount of solar light that is reflected by the nucleus towards the spacecraft is changing with time as the nucleus rotates. The third discovery is that the comet nucleus – which was dormant and quiet at our first observations in late March – now has become active.

Comet activity means that the ice in the nucleus surface layers has become heated sufficiently by sunlight to sublimate, i.e., turn directly to vapor without first becoming liquid. At these distances, at the time of writing 4.03 AU from the Sun, the temperature is too low to allow water ice to sublimate. Instead, more volatile substances like carbon monoxide and carbon dioxide are responsible for the activity. OSIRIS do not see these gases directly. However, the sublimation also liberates a large amount of micrometer-sized dust grains that are entrained in the gas as it rushed into space. OSIRIS detects the solar light that is reflected by this dusty coma, that currently measures about 2600 kilometers across.

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The OSIRIS Team. Yours truly is marked with the arrow. Credits: MPS

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!

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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.