Undergrad Comet Sublimation: Why Does Halley's Comet Still Exist?

[hexanol]

TL;DR

a question regarding sublimation of comets

Having watched a dropped cube of ice sublime to nothing at the bottom of the freezer of my refrigerator in my kitchen over the course of a week, I would like to know why comets don't do this. Presumably the tail is the product of sublimation, but how long can that go on? How can Halley's Comet even still exist? Seems like the vacuum of space would make up for for the reduced temperature that might reduce sublimation. Help me finally get some sleep. What's the story?

 

[Baluncore]

A significant tail is formed from volatile components only when the comet is close to the Sun.
https://en.wikipedia.org/wiki/Halley's_Comet#Structure_and_composition

 

[TeethWhitener]

TL;DR Summary: a question regarding sublimation of comets

Having watched a dropped cube of ice sublime to nothing at the bottom of the freezer of my refrigerator in my kitchen over the course of a week, I would like to know why comets don't do this. Presumably the tail is the product of sublimation, but how long can that go on? How can Halley's Comet even still exist? Seems like the vacuum of space would make up for for the reduced temperature that might reduce sublimation. Help me finally get some sleep. What's the story?

The dependence of vapor pressure on temperature is exponential. Your freezer is probably somewhere around -10 to -20 degrees C (250K) whereas space is much much colder. Take a look at this chart of the vapor pressure of ice and compare -20 to the lowest temperature they list (-82C, or 191K), and note that the difference in vapor pressure is almost 4 orders of magnitude.
https://www.lyotechnology.com/vapor-pressure-of-ice.cfm
And this is only at roughly dry ice temperatures. Once you get out to Pluto, the temperature is roughly 40K, and for long period comets it’s even colder. Here’s a paper with ice vapor pressure extrapolations down to colder temperatures of astrophysical and atmospheric relevance:
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2002GL016183
Note that at 165K, you’re down to a vapor pressure of about $10^{-4}$ Pa, or a billionth of an atmosphere, and this is still a much higher temperature than comets encounter for the vast majority of their orbits.

 

[hexanol]

Thank-you!

 

[russ_watters]

The vapor pressure issue is true, but in my opinion a bit of a tail wagging the dog way of looking at the issue. Sublimation carries away energy, so it can't happen without a continuous heat source, otherwise the comet cools down to absolute zero. Obviously that heat source is the sun. The sublimation rate is exactly determined by the heat transfer from the sun minus heat radiated into space, times the energy lost to sublimation per unit mass. It's probably a straightforward exercise to lcalculate the lifespan of a comet in a simple example. Back of envelope (someone please check me):

At Earth's distance, solar irradiance is 1,000 w/sq m, which will sublimate about 8,000 kg/yr from a square meter surface. At Pluto's distance it is 1/1000th that, and for a comet hanging out in the Oort cloud at 10,000AU, 1/100,000,000th.

Assuming a spherical cow cylindrical comet of 1,000 sq m cross section, 10 trillion kg, pointed at the sun and at Earth's distance, it would last a million years. In the Oort cloud, much longer than the universe has been around.

We can refine that...

 

[snorkack]

The vapor pressure issue is true, but in my opinion a bit of a tail wagging the dog way of looking at the issue. Sublimation carries away energy, so it can't happen without a continuous heat source, otherwise the comet cools down to absolute zero. Obviously that heat source is the sun. The sublimation rate is exactly determined by the heat transfer from the sun minus heat radiated into space, times the energy lost to sublimation per unit mass. It's probably a straightforward exercise to lcalculate the lifespan of a comet in a simple example. Back of envelope (someone please check me):

We can refine that...

I think that the insolation is the dominating factor at high temperatures and vapour pressure at low temperatures.
Note that the heat radiated into space is proportional to 4th power of temperature. Which means that compared to ice at 273 K, the thermal radiation of ice is halved at around 230 K - which is -43 C. The table gives vapour pressure around 9 Pa, which means about 70 times less than at 0 C. And the thermal radiation is halved again at 193 K - -80 C, which gives 0,05 Pa. Which is 180 times less. This kind of exponential decrease of vapour pressure, and therefore the rate of evaporation and latent heat expenditure, far faster than radiation that only falls off with fourth power of temperature, means that at a sufficiently low incident light, most of it will be radiated and the evaporation falls exponentially.
For a derivation in the example of mercury, see:
https://www.physicsforums.com/threads/what-would-happen-to-a-blob-of-mercury-in-space.949070/

 

[hexanol]

Thanks everyone for a great discussion of this.