Why does Titan have an atmosphere given its relatively small mass (comparable to our moon)? Why is it not lost to space or is Titan's atmosphere constantly being replenished?
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1$\begingroup$ en.wikipedia.org/wiki/Atmospheric_escape may help; graphs indicate a combination of decreased temperature and increased escape velocity $\endgroup$– CoderTaoCommented Jul 5, 2017 at 21:37
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$\begingroup$ physics.stackexchange.com/questions/31909/… $\endgroup$– leftaroundaboutCommented Jul 5, 2017 at 22:16
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3 Answers
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The mass of Titan is 1,345 · 1023 kg, but the mass of the Moon is 7,349 · 1022 kg. The gravity at the surface is 1,35 m/s² for Titan and 1,62 m/s² for the the Moon.
But the surface temperatures are very different, 94 K for Titan but the mean surface temperature of the Moon is 218 K and the peak about 300 K.
Due to the high surface temperature of the Moon, a small part (due to the Bolzman distribution) of the gas atoms have a velocity bigger than the escape velocity of the Moon. Over millions of years, this small part is enough to let escape most of the gas.
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2$\begingroup$ lower solar flux may also be a factor. $\endgroup$– HobbesCommented Jul 5, 2017 at 10:41
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11$\begingroup$ Titan has more mass but less surface gravity? Is it substantially less dense? $\endgroup$– jkavalikCommented Jul 5, 2017 at 10:43
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4$\begingroup$ IIRC there's either a high order polynomial or exponential factor of temperature in the loss rate equations; so being 2-3x colder is a really huge advantage not just marginal tinkering around the edges. $\endgroup$ Commented Jul 5, 2017 at 20:30
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2$\begingroup$ @Ben Crowell Thanks for writing about the Boltzmann distribution. But if there is a lot of time like millions of years, the very thin tail of the Boltzmann distribution would be enough for most of O2 molecules to finally leave the Moon. $\endgroup$– UweCommented Jul 5, 2017 at 22:23
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The primary factor is the lower temperature of Titan that results in the highest speed of the gas molecules in Titan's atmosphere being less than the escape velocity. Hypothetically, the incoming solar wind bombardment also increases the kinetic energy of the gas molecules over the escape velocity so that over time an atmosphere not protected by a magnetic field would lose its atmosphere due to the solar wind.
The flux of the solar wind decreases as the square of the distance from the sun. Being that its host planet, Saturn, is 10 Astronomical Units from the sun. It is 9 times farther from the sun than our moon. So the solar wind flux reaching Titan is 9 squared or 81 times weaker than at our moon. Since, unlike our moon, Titan has a significant magnetic field, plus it spends 95% of its orbit within Saturn's very strong magnetic field, the little solar wind that does get in the vicinity of Titan is totally deflected or weakened by these magnetic fields.
In fact, one can assume that the plasma particles of the solar wind would be so deflected and weakened that their average speed would be much less than Titan's escape velocity by the time they penetrate Titan's atmosphere at its poles, thus the solar wind actually is increasing Titan's atmosphere rather than blow it away as what happened to our moon.
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1$\begingroup$ I think you mean that 10 AU is ten times the distance and therefore the flux is 1/(10^2) or 1%. $\endgroup$ Commented Jul 6, 2017 at 3:45
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$\begingroup$ @Nathan Tuggy 1AU would be used up by the distance from Sun to our moon. Therefore Titan would be 9AU further away from that point. $\endgroup$ Commented Jul 6, 2017 at 3:53
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4$\begingroup$ 10 AU is 10 times as far away as 1 AU. That's all there is to it. $\endgroup$ Commented Jul 6, 2017 at 3:54
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Titan also has more of the right stuff to work with, in order to make an atmosphere. Remember our own, massive (by comparison) Earth did not come with an atmosphere; it outgassed as it cooled. Our Moon, if formed by a collision, had its volatile matter escape between the time of the collision and its re-formation into a massive body, whereas Titan retained more volatile matter.
Titan may also be compared with Neptune's large moon Triton and with the dwarf planet Pluto. The latter have plenty of good stuff on the surface but not enough volatility to match Titan because they are too cold.
answered Feb 10, 2019 at 9:55
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1$\begingroup$ +1 as this is the only answer touching on the important topic of outgassing history. There are other bodies of equal mass and similar density in the solar system, which don't possess and atmosphere. It is much more important to understand that, than to look at the $v_{\rm thermal}/v_{\rm escape}$-parameter, which really doesn't explain nonexistence of atmospheres. $\endgroup$ Commented Feb 10, 2019 at 14:17