Monday, March 16, 2015

Another Brief Statement of the Obvious

There are four chief obstacles to grasping truth, which hinder every man, however learned, and scarcely allow anyone to win a clear title to knowledge: namely, submission to faulty and unworthy authority, influence of custom, popular prejudice, and concealment of our own ignorance accompanied by ostentatious display of our knowledge.

                        - Roger Bacon (1266)

Wednesday, March 11, 2015

A naive look at comets

Okay, the relentless drip-drip-drip of Marco's comet obsession has finally gotten to me. I said I was going to post something about how you could get a mass distribution in comets that was consistent with the 'brittle crust, gooey low-tensile strength centre' required for the observed morphology of 67P-Churyumov-Gerasimenko.

So here it is.

I’m going to assume we start with a homogeneous mass containing all the things that will be solid grains out at a temperature of very few K and that have been shown to be in comets. So sodium and magnesium silicates, and ammonia, and methanol, and carbon dioxide, and carbon monoxide, and water, and methane – and importantly some higher hydrocarbons, which haven’t showed up in the gas from 67P-Churyumov-Gerasimenko but seem to be attested in other systems. I guess the primordial assumption behind this is that comets formed from the outer edges of the big solar system Ur-cloud, so weren’t subjected to much in the way of fractionation processes beforehand. If this is some terrible error in cometology, please let me know.
We roll all these things into a ball using gravityTM and hurl it towards the sun.
As it gets warmer on the surface stuff that is most volatile, like methane, will sublime first, and leave behind a very fluffy residue of stuff that doesn’t want to sublime as easily.

Some of this fluffy stuff will flake off and float away; probably a lot; but it will also invariably compact as bits flake off and lodge with other bits, and at temperatures where higher organics are not volatile but the small molar mass stuff is, these latter will end up concentrated on the surface where they can soak up all those lovely cosmic rays and start forming larger crosslinked molecules by radical-radical recombination.
Okay, if the mass of the comet  is small this evaporation process will just continue until you are left with a relatively dense mass of non-volatiles. But if the mass is bigger, this surface layer – which is gradually getting more compact and more enriched in high molar mass organics as we approach the sun – will start acting as a barrier to the progress of gas molecules from the warming interior.
And eventually, I can imagine this means there won’t be vacuum at the interior surfaces where sublimation is occurring, but appreciable pressure. There seem to be abundant studies in the literature for gas building up in comets.

Now, once the pressure and temperature increase above the triple point of any of the constituents of the comet interior, there will be the possibility for liquid to exist there.
I’ve plotted the triple points of some constituents of comets below.

(Note, if you are unfamiliar with triple points, that these are the bottom points of triangular areas where the liquid state can exist. The exact phase diagrams of things are much more difficult to find than the triple points and may not have been mapped out in detail for all of these.)
The species that are going to be liquid at relatively low temperatures and pressures are relatively minor constituents of comets, of the order of a few percent in total (probably), so we won’t get a gooey liquid core, but a ‘moist’ core with liquid on the surfaces of solid grains, like a fairly dry soil. This will happen at temperatures and pressures far below what we would need to liquefy water, and these liquids will persist in the core as more volatile components turn into gas and bubble out, while the shape of the comet is maintained by the outer layer of non-volatiles gummed together by organic polymer.

Now, when the comet flies out into the cold again, the interior part of this liquid core is likely to freeze before it evaporates, leaving the core of the comet no longer a loose aggregation of stuff, but particles of relatively non-volatile components sintered together with a layer of frozen hydrocarbons. This will still have a low tensile strength, but I would think this sintering would significantly improve its compressive strength. And the different levels of degassing possible from a fairly rigid external shell would fit the great variability in comet densities observed.  There may also be interesting fractionation of one component freezing before another, depending on how good the outer layer is at retarding heat and mass transfer from the interior. How hot can it get inside? How high can the pressure get? I guess I should look up people's best guesses for those questions. I can imagine the shell getting stronger and stronger on repeated passes of the sun if it doesn't break, sustaining higher pressures inside, and eventually allowing the same sintered morphology to be reproduced with water ice holding inorganic particles together.

So, in summary, comets should end up kind of like MaltesersTM.