How could Mars' atmosphere be shed by solar winds, when Venus has a thick atmosphere despite no magnetic field?

Question

Our current understanding of how Mars lost its atmosphere is because it lost it magnetic field, due to a barrage of reasons, such as core cooling due to low volume and cooling off quickly. This resulted in solar winds stripping away its atmosphere, turning it into a near-vacuum.

However, Venus is nearly 2x closer to the Sun, than Mars, and thus should have shed out its atmosphere really quickly, as it too has no magnetosphere. Yet Venus is the exact opposite of Mars. It is extremely hot, and its atmosphere is so dense that it can crush humans like a paper-cup.

How could Mars have lost its atmosphere due to solar winds, when Venus didn't?

Answer 1

I am not certain that the main cause of Mars losing most of its atmosphere was the solar winds.

Long before the solar wind was discovered scientists calculated other factors which affect how long a planet can retain its atmosphere. They included the velocity of the air particles in the exosphere, the upper atmosphere of the planet, and the escape velocity of the planet - not, repeat not, its surface gravity. The velocity of the air particles in the exosphere depends on their temperature, which is often very different from the temperature of the atmosphere at the surface.

Stephen H. Dole, in Habitable Planets for Man, 1964, pages 33 to 39 discusses the capture and retention of atmosphere. He gives a simple formula on pages 34 and 35 to calculate approximately how long a planet can retain a gas in its atmosphere before it escapes into space.

And Dole uses that formula to calculate how fast a world loses gas enough to bring the total amount down to 1/e, or 0.368, of the original amount of that gas, based on the ratio of the escape velocity of that world divided by the root-mean-square velocity of the gas in the exosphere.

Table 5 on page 35 shows that if the ratio is one or two the amount of gas will fall to 0.368 of the original amount instantly, while if the ratio is 5 it will take about 100 million years for the amount to fall to 0.368 of the original amount, and if the ratio is 6 it will take about infinite time for the amount of the gas to fall to 0.368 of the original time.

Thus changing the ratio by a relatively small factor will change the time for the amount of a gas to fall to 0.368 of the original amount from zero to infinity. Other factors like the solar wind or a giant impact can speed up the atmospheric loss, but nothing can make it slower. Though it is possible that when the loss of a gas is slow, new amounts of that gas can be produced by various methods as fast or faster than it is lost.

On page 54 Dole says the temperature in Earth's exosphere varies from 1000 degrees K to 2000 K. Dole says that if -repeat if- a planet could have Earth like surface temperatures (about 288 degrees K) while having a maximum exosphere temperature of only 1000 K, it would need an escape velocity of about 6.25 kilometers per second to retain atomic oxygen long enough to be habitable.

Dole describes 6.25 kilometers per second as 5 × 1.25, so the root-mean-square velocity of atomic oxygen at 1000 K should be 1.25 kilometers per second, and a world with an escape velocity of 6.25 kilometers per second could retain 0.368 of an original amount of atomic oxygen for about 100 million years. And thus a world with an escape velocity of 7.50 kilometers per second take an infinite time for for atomic oxygen to fall to 0.368 of the original amount.

Earth has an escape velocity of 11.186 kilometers per second, which is 1.49 times 7.50 kilometers per second, the escape velocity necessary to retain 0.368 of atomic oxygen forever at 1000 degrees K. Since the exosphere temperatures of Earth get up to 2000K, the root-mean-square velocity of atomic oxygen the exosphere is faster than 1.25 kilometers per second, and the ability of Earth to retain atomic oxygen is somewhat less than it would if the maximum exosphere temperature was only 1000 K.

Venus has a surface gravity of 8.87 meters per second per second, 0.904 that of Earth, and an escape velocity of 10.36 kilometers per second, 0.92615 that of Earth. The escape velocity is a higher fraction of Earth's than the surface gravity is.

So if atomic oxygen in the exosphere of Venus had a temperature of only 1000K, and thus a root-mean-square velocity of 1.25 kilometers per second, the escape velocity of Venus would be 1.3813 times as much as necessary for it to take an infinite time for the amount of atomic oxygen to be reduced to 0.368 of the original amount. Of course the exosphere temperatures of Earth get as high as 2000K and the temperatures in the exosphere of Venus might be hotter than 2000K, so Venus probably loses atomic oxygen by escape into space faster than Earth does.

Mars has a surface gravity of 3.72076 meters per second per second, 0.3794 that of Earth, and an escape velocity of 5.027 kilometers per second, 0.4494 that of Earth. And note that the escape velocity of Mars is also higher relative to that of Earth than the surface gravity is.

If atomic oxygen in the exosphere of Mars has a temperature of 1000 K and thus a root-mean-square velocity of 1.25 kilometers per second, the ratio of the escape velocity, 5.027 kilometers per second, divided by the root-mean-square velocity of 1.25 kilometers per second, would be only 4.0216.

According to table 5 on page 35, a ratio of 4.0 would mean that the amount of a gas would wall to only 0.368 in a few thousand years. Suppose that a ratio of 4.0216 would cause a drop to 0.368 of the original amount of a gas to take as long as 100,000 years, which seems too long a time, but I will use it. In that case Mars would retain 0.1354 of the original amount in 200,000 years, 0.498 of the original amount in 300,000 years, 0.183 of the original amount in 400,000 years, 0.0067477 of the original amount after 500,000 years and so on.

Mars wold retain 0.0000455 of the original amount after 1,000,000 years, 0.000000002 of the original amount after 2,000,000 years, and so on. Thus Mars would have to have to produce or acquire atomic oxygen rather rapidly to replace it as fast as it loses it, and clearly doesn't replace atomic oxygen as fast as it loses it.

Oxygen is usually in molecular form, O₂, which as a molecular weight of 32, twice that of atomic oxygen, 16. Atomic oxygen is usually the the result of ultraviolet light breaking up molecules of O₂, or water, H₂O, nitric oxide, NO, Carbon dioxide, CO₂, etc. Most of the compounds likely to be found in planetary atmospheres contain oxygen and either solids or gases as light or lighter than oxygen. So the ultraviolet light breaks up molecules in the Martian atmosphere into atoms which are either solid or escape rapidly into space.

So it is my opinion that that Venus and Earth have escape velocities enabling them to lose gases by escape into space very, very slowly. Mars has an escape velocity low enough that it loses gases into space much faster than they can be replaced, which is also hurried by the solar wind. Earth and Venus mostly lose gases by the solar wind and other processes which are much slower than gravitation escape in my opinion.

And here is a link to a Wikipedia article discussing various processes of atmospheric loss.

https://en.wikipedia.org/wiki/Atmospheric_escape

Answer 2

One of the main loss mechanisms of atmospheres escape is thermal escape (Jeans escape) into space. The average thermal velocity at a given temperature $T$ for a molecule of mass $m$ is $$ v_{th} = \sqrt{\frac{k_b T}{m}}$$. However this is only the mean, and the velocity is really a Maxwellian velocity distribution, so that there are always some molecules of a velocity greater than the escape velocity $v_e$ at distance $r$ from the body $$v_e = \sqrt{\frac{2GM}{r}}$$

A magnetic field helps indeed though to to limit the non-thermal escape so that the main atmospheric loss mechanism on Venus is indeed due to charge exchange and photochemical reactions with the solar wind - despite its higher thermal temperature. Yet the induced ionospheric currents indeed limit this solar wind pickup considerably, and limit it especially dominantly hydrogen while the atmosphere of Venus consists of $CO_2$ and sulphuric acid.

However Mars is so small that the thermal escape velocity is lower AND it does not have any significant magnetic field anymore so that both loss mechanisms are higher - and its atmosphere likely was given the planetary size less massive to begin with.