Atmospheres of the Terrestrial Planets

In this lecture we consider:

• The origin of the atmospheres
• The retention of an atmosphere
• The Equilibrium Temperature, the Surface temperature of a planet, and the Greenhouse Effect
• The Faint Young Sun Paradox
• The Habitable zone concept

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I. ORIGIN OF THE ATMOSPHERES

Immediately after formation, Terrestrial planets essentially had no atmospheres (if they had captured some hydrogen and helium from the Solar Nebula, it was rapidly lost to space). The atmosphere a Terrestrial planet has today was either captured or generated after the planet formed; Terrestrial planets have secondary atmospheres.

There are two suggestions for the secondary atmospheres:

• Outgassing: Because the planets formed from the accretion of solid rock particles, volatile materials were trapped inside of them. Later, when the interiors of the planets heated and melted, the volatiles could start to be released through volcanic eruptions. Current studies of volcanos show that they do release large amounts of water, carbon dioxide, nitrogen, and sulfur dioxide. Can volcanism explain our atmospheres? Consider water. On Earth, we have enough water to cover the planet to a depth of 3.6 kilometers. This is around 1.5x10²¹ kg of water. The current rate of outgassing of water from volcanos is 10¹¹ kg per year.
  At this rate, it would take about 15 billion years to make the oceans via outgassing. If the rate were 3 times higher in the past, then the oceans could be produced in 4.5 billion years (the age of the Earth). Is a tripling of the rate reasonable?

• Capture/Addition: Suppose the atmosphere was added after formation. This could occur either through comets or asteroids.
  • comets are half rock and half ice and so easily carry enough water. However, it seems that they cannot not be the sole source for the water on Earth as the water in comets is different from the water found on Earth (there is more heavy water found in the water of comets than is found in the water of Earth's oceans, although some comets do contain amounts of heavy water consistent with that of the Earth's oceans). Heavy water is a form of water where the hydrogen atoms have been replaced by atoms of the isotope of hydrogen known as deuterium. A hydrogen atom has one proton in its nucleus. A deuterium atom has one proton and one neutron in its nucleus.

  • Asteroids are roughly 20 % water and so are also potential sources for our atmosphere and oceans and they have the right amount of heavy water. They do, however, have other problems. Asteroids predict that we would have 10 times more Xenon in our atmosphere than do we.

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It is not clear which of the above is correct at this time.

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II. ATMOSPHERIC RETENTION

Why does Venus have an atmosphere while Mercury does not?

There are two competing effects which determine whether a planet retains an atmosphere: the strength of the gravitational field at the surface of the planet as measured by the escape speed of the planet. the speed with which the gas particles move around is determined by the temperature and mass of the particles that make up the atmosphere. The temperature is a measure of the average energy of the particles.

There are then two important points:

• the mass of a Terrestrial planet is crucial because the escape velocity depends strongly on its mass (via the gravitational force); the more massive the Terrestrial planet the higher its escape speed

• the distance of a Terrestrial planet from the Sun because the temperature of the gas depends strongly upon how much energy it absorbs from the Sun; the closer to the Sun the hotter a Terrestrial planet's surface is likely to be, but there are tweaks to this idea.

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Both of the above technically favor Venus, but if you take account of the atmosphere it gets a little muddied. However, it turns out that even if you do, it is still true that Venus is able to maintain an atmosphere while Mercury is not.

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III. EQUILIBRIUM SURFACE TEMPERATURES AND THE GREENHOUSE EFFECT

We now define the Equilibrium Temperature, T_e. Assume:

• the planet absorbs heat from the Sun at a certain rate and then re-radiates this energy at precisely the same rate (hence, the use of the word equilibrium).

• the planet radiates like an idealized creature which is defined to be a perfect emitter and perfect absorber of radiation--a blackbody radiator.

For a planet with an atmosphere, not all of the Solar radiation reaches the surface of the planet. Some of the sunlight is reflected by the cloud layer back into space. We measure this effect by defining the Albedo for the planet. The Albedo, A, is the fraction of the solar radiation which is reflected back into space. This means that only a fraction (1-A) of the sunlight reaches the Earth. The average albedo for each planet is 0.76, 0.35, and 0.15 for Venus, Earth, and Mars, respectively.

The T_e calculation below takes account of the effects of the clouds (through inclusion of the Albedo) but it ignores the important effects the atmosphere has on the sunlight as it travels from the clouds to the surface of the planet.

Actual Atmospheric and Equilibrium Temperatures

	Venus	Earth	Mars
Actual Temperature	>850 F	~60 F	-80 F
Equilirium Temperature	-20 F	-4 F	-70 F

For Mars, the equilibrium temperature and actual atmospheric temperature are roughly the same while for Venus and Earth, the temperatures differ significantly in this approximation for T_e. Why? The atmospheres plays crucial roles. Because both Venus and Earth have significant atmospheres and both exhibit the Greenhouse Effect we see the large differences in the temperatures.

The Greenhouse Effect The Greenhouse Effect arises because the atmosphere of the Earth allows the visible light from the Sun to penetrate to the Earth's surface where it is absorbed. The absorbed sunlight heats the surface of the Earth and the Earth re-radiates the absorbed energy back to space. The thing is the surface of the Sun is 10,000 F while the Earth does not get anywhere near as hot, only heating to around - 4 F initially. Consequently, the Earth emits less energetic radiation, infrared radiation, than the visible radiation the Sun produces. The complication is that the Earth's atmosphere allows visible radiation to pass freely to the surface of the Earth but strongly absorbs infrared radiation not allowing it to escape freely. The gases that do this are the Greenhouse gases, carbon dioxide, water vapor, methane. This traps some of the outgoing radiation re-directing it back toward the Earth where it is again absorbed. This effect raises the surface temperature of the Earth eventually causing it to rise to ~60 F.

Both Venus and the Earth show Greenhouse Effects . The Earth, however, has a much milder Greenhouse effect than found on Venus. The mild Greenhouse effect is crucial because it is what makes the Earth habitable.

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IV. FAINT YOUNG SUN PARADOX

There were liquid oceans on the Earth as far back as 3.8 billion years ago based on the ages of sedimentary rocks in Greenland. Let's see if we can understand why. To do so, we ask the question,

Why were there liquid oceans on the Earth 3.8 billion years ago?

and then answer the question to see if we understand why this is so. Let's go.

First, compare our best model for the temperature of the Earth to see if it matches the measured temperature of the Earth (the gray band). Calculate the current temperature of the Earth's atmosphere. Today, our temperature estimate matches the measured temperature of the Earth. The heavy black line falls in the gray band. Models of the Sun tell us that the Sun gets brighter as it ages; 3.8 billion years ago the Sun was ~25 % fainter than it is today. See red curve. This is the problem. Our model estimate for the temperature of the Earth is now in trouble. The estimated Te for 3.8 billion years ago is around 0o F, well below the freezing point of water. See upper black line. In fact, Te only exceeds the freezing point of water around 1.8 billion years ago.

Our conclusion is that the Earth did not have liquid water 3.8 billion years ago, in contradiction of the data. This is the Faint Young Sun paradox.

To resolve the Faint Young Sun paradox requires that one (or more) of our assumptions was wrong. Which assumption was likely wrong?

• The likely culprit is our implicit assumption that the composition of the atmosphere does not change.

• If we relax this assumption, we can resolve the Faint Young Sun paradox.

• If our atmosphere had more Greenhouse gases in the past than it does today, the Greenhouse Effect would be stronger and there could be liquid oceans. Models suggest increases in levels ranging from 10 to 100 times greater than present levels of CO₂ work. Are such increases plausible?

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V. HABITABLE ZONE

NASA habitable zone

The definition of "habitable zone" is the distance from a star at which liquid water could exist on orbiting planets' surface. Habitable zones are also known as Goldilocks' zones, where conditions might be just right -- neither too hot nor too cold -- for life. NASA, Apr 2, 2021

Just googled NASA habitable zone and up popped the above. The definition stated above for the habitable zone relies on several assumptions. The first is that we are going to look for things that are consistent with Life As We Know It (LAWKI) or essentially associating life with liquid water. Note that the above does not take into account all LAWKI, but only certain types (more on this later).

Also, it is a tad tricky because the defintion assumes that it is only the distance from the Sun that determines whether a planet has liquid water on its surface. We know, at a minimum, that we should also include the effects of clouds and properties of the planet's atmosphere. Without atmospheres, no Terrestrial planet in our Solar System would sit in the habitable zone based on the simplest estimates for their equilibrium temperatures (no atmospheres). Also, we know (suspect), that in the first hundreds of millions of years in the lifetimes of Venus, Earth, and Mars that they all supported liquid water and so were in the habitable zone. Today, only Earth has liquid water and so only Earth sits in the habitable zone.

The habitable zone is an useful concept, but it should be kept in mind that it is not an absolute. As stated above, it is more aligned with the way we used to think. Today, we are more open about where to look for extra-Terrestrial and extra-Solar life. The habitable zone is a nice general way to think about where life is likely to be found in planetary systems, but it is best to keep an open mind when moving forward about where extra-Terrestrial life might be found.

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