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INTRODUCTION TO PLANETARY ATMOSPHERES

Modified from the paper by Kurt Retherford

The Solar System is a diverse and wonderful place that is ripe for exploration and scientific study. The science currently being done with the planets often provides us with a new and exciting understanding of our own planet and the environment we live in. Planetary science increases our knowledge of how we came into existence. This, along with the potential of finding evidence for life in other parts of the solar system and universe, tends to stagger one's imagination and changes how we view our lives. Anyone who breaths can appreciate the study of planetary atmospheres. The planets, and several satellites, or moons, of these planets have atmospheres. Some are sizeable, others are harder to detect. Each is unique, but they all follow the laws of nature. For planetary scientists, it is useful to look at their similarities and differences in the context of the basic physical properties that are involved.

Let's suppose we discovered some new planet around some distant star. To make a first order approximation as to whether life as we know it could exist there, we assume that liquid water must be present. For this the temperature needs to be somewhere between the freezing and boiling points for water. To make this first order approximation we use a simple thermal model. This involves equating the power of the light from the nearby star that intersects the planet to the power of the heat that the planet absorbs and reradiates over it's surface. For a state of equillibrium we must equate the radiation input and output as follows. Radiation input equals {pR2 f(1-A)} and radiation output equals {4 p R2 S T4} to give us {T =[f(1-A)/4 S]1/4}. Here, f is the solar irradiation which equals 1.35 x 106 ergs cm2 sec-1 at 1 AU which is the the distance of the Earth from the sun. The value of f dereases with increasing distance from the sun since the light per area gets spread out among larger and larger spheres. The albedo A is the average amount of light reflected from the surface of the planet so 1-A is the amount it ends up absorbing. The radius of the planet is given by R in this equation and the amount of radiation input is proportional to the circular area the planet intersects, while the amount of radiation output is proportional to the surface area of the planet. The rotation of most planets is faster than the time needed to radiate the input area so we use the whole surface area of the planet instead of just that of the hemisphere exposed to the sun.

As we can see this model does a reasonably good job for a first approximation. On inspection the simple thermal model's prediction for the average surface temperature of the Earth is right around the freezing point of water. Well we know this is not the case. There is an important effect that additionally heats the atmosphere called the green house effect. The green house effect arises from the fact that the light coming fom the sun is mainly in the visible region of the spectrum, but the light emitted from the surface of the earth is in the infrared. While the atmosphere allows most of the visible light to pass right through, we can see the sun just fine, the infrared light is well absorbed by the atmosphere. This infrared radiation is then emmitted in all directions, about half of which is back towards the Earth, and reheats the Earth's surface (see Figure 1). While carbon dioxide is a stronger absorber in the infrared, water vapor is the primary green house gas on the earth since there is so much more of it. In astronomical terms we say the atmosphere is optically thin in the visible range but optically thick in the infrared. Although the green house effect increases the surface temperature of the Earth along with the temperature of the lower atmosphere, the temperature of the atmosphere tends to change as a function of height for several other reasons as well.

Figure 1 The Greenhouse Effect

Planetary Scientists are interested in determining how the atmospheric temperature, pressure and density changes as a function of height. This knowledge provides a foundation for understanding other points of interest such as the dynamics of the atmosphere, the chemistry occuring in the atmosphere, and the atmosphere's interaction with it's surrounding environment. This environment includes the solar wind, magnetic fields, geological features, and a variety of other phenomena. Several simple approximations can be made to describe the temperature and pressure as a function of height. The idea of hydrostatic equilibrium can be used to come up with what's called the barometric law. Hydrostatic equilibrium is simply when a parcel of air is at a high enough pressure to support the weight of air above it. Let's call the weight of the parcel g dm = g p dV = g p dz dA where p is the density dm/dV which also equals m n. The force per area, the pressure, need to hold up this parcel of air is just dP = -g p dz. Assuming that the atmosphere is an ideal gas we can use the law P = n k T = p k T/m. Substituting p from the ideal gas law into the hydrostatic equation we get dP/P = - (g m/k T) dz. Integrating this we get the barometric law p=p(0) Exp[-(m g/k T)(z-z(0))]. For conveinience sake we refer to the quantity H = (k T/m g) as the scale height. This is just the value where p=p(0)/e, the "e-folding distance". The value of m in the scale height and preceeding equations is the mean mass of the molecules in the atmosphere. Alternately, we can refer to the scale height of a particular molecule by using it's mean molecular mass. The value of k is just boltzman's constant, k=1.38x1023 J/K.

The previous barometric result has assumed that the temperature and density are constants. We might also want to determine how the density and temperature are changing as well. We can do this by differntiating the ideal gas law P=n k T as such dP/P = dn/n +dT/T. Remembering dP/P = -dz/H we can equate to get dn/n = -(1/T (dT/dz) + 1/H) dz integrating to get n=n(0) Exp[-z-z(0))/H* where the scale height H* is now defined as H*=[1/T(dT/dz) + 1/H)]-1. Notice the dT/dz term. This is called the adiabatic lapse rate which applies only when there is heat transfer by convection, like we have in the troposphere.

The adiabatic lapse rate can be calculated using the first law of thermodynamics. Adiabatic expansion is when a parcel of air changes it's volume with changes in temperature and pressure without using any external heat. The troposphere is defined as the part of the atmosphere that transfers heat by this convective motion. The troposphere is the lowest part of our atmosphere and it is responsible for most of our weather. So using the first law of thermodynamics we have dE+dW=dQ=0. Writing in terms of specific heat at constant volume c(v), pressure and temperature we have c(v) dT + P dV=0. Writing the ideal gas law as V=RT/P and differentiating we get dV=R(dT/P - (T/P^2)dP). Substituting this back into the first law equation gives c(v)dT=-PR(dT/P - (T/P^2)dP). Further, (c(v)+R)dT=RTdP/P=-g(z)dz. Using c(P)=(c(V)+R) we get c(p)dT=-g(z)dz and dT/dz=-g(z)/c(p) remembering that the gravitational acceleration constant is only constant for a specific height. On Earth this formula would give -9.8 degrees Kelvin/km but this neglects one additional thing. With air that is saturated with water we must include the latent heat of vaporization in our equation. This gives dT/dz=-g(z)/c(p)/[1+(L/c(p))(dw/dT)] where w is the mass of saturated water per mass of air and L is the latent heat of vaporization. Using this revised formula we get -6.5 degrees Kelvin/km which we can see is approximately the slope of the line through the troposphere in Figure 2.

Figure 2 Earth's atmospheric thermal structure

Figure 2 shows the thermal structure of Earth's atmosphere. The different levels of the atmosphere are characterized by certain revealing aspects. As we've discussed, the defining aspect of the troposphere is it's convective heat transfer. Above the Earth's tropopause, the boundary between the troposphere and the adjoining stratosphere, heat is transfered radiatively and conductively. Different molecular species tend to be the dominating radiative influences depending on their various concentrations as a function of their altitude. As we've said the troposphere is affected by infrared heating from the ground and adiabatic cooling. The stratosphere takes an upturn in temperature from the heating resulting from the strong absorption of ultraviolet light by the ozone that's found here. Next, we find the stratopause, which delineates the stratosphere from the mesosphere. In the mesosphere carbon dioxide tends to cool the atmosphere by radiating the energy faster that it and the diminishing ozone concentrations can absorb it. The mesopause, defined as the place of temperature upturn between the meosphere and thermosphere, shows a slope dT/dz=0 in Figure 1. The temperature rises again here in the thermosphere due to the heat from the dissociation of molecular oxygen by ultraviolet light and photoionization by x-rays. Since the slope dT/dz becomes positive, convection can't occur. Also since the abundant molecules in the atmosphere here are diatomic oxygen and nitrogen, radiation is an ineffective form of heat transfer. Oxygen and nitrogen are forbidden to radiate in the infra-red through electric-dipole radiation because of their symmetry. This leaves us with conduction as the main form of heat transfer in the thermosphere. Together, these heat transfer processes throughout the atmosphere allow the overall thermal equilibrium of the planet. The other planetary atmosphere's have a thermal structure that resembles the Earth's with a variety of interesting exceptions and differences.

Before we begin to compare the planets, it will be useful to discuss atmospheric escape, the escape of the lightest molecules in an atmosphere. The exosphere is defined as the region beyond which a particle is not likely to encounter another in a collision. Now, if a particle at the base of the exosphere, aptly named the exobase, should have a velocity that allows it to escape Earth's gravity, it will leave the atmosphere. This velocity is determined by equating the gravitational potential energy to the kinetic energy of the particle as such: GMm/r=(1/2)(mv^2) giving v(escape)= Squareroot(2GM/r). Now once the particle is in the exosphere it isn't necessarily gone for good, it's orbit could bring it back to the Earth, or if it's a charged particle, it's likely to be caught up by the Earth's magnetic field lines and brought back to Earth in the form of an aurora at one of the Earth's magnetic poles. But on average this is how the lightest elements tend to escape to space, depleating the atmosphere over a given amount of time of this molecule. On Earth, Venus, and Mars, there is very little molecular hydrogen. While on Jupiter,Saturn, Uranus, and Neptune there is mostly hydrogen.
 

Comparative Planetology

Comparative planetology is the name given to an approach to studying the planets. This approach is based on the idea that the individual planets can be better understood by comparing the physical processes of all the planets. These comparisons yield important information and useful insights. There are, for example, many similarities between the terrestrial planets, Mercury, Venus, Earth, and Mars, and likewise many similarities among the Jovian planets Jupiter, Saturn, Uranus, and Neptune. The basic physical ideas in our physical models for one planet must hold true in general for the other planets. This second part of the paper will discuss several interesting aspects of the various planetary atmospheres in the context of the similarities amongst them. The thermal structure of an atmosphere is often the most useful tool for discussing the physical properties of an atmosphere and so several thermal structure figures are included in the following discussion. Along with the nine planets, the satellites that have a mentionable atmosphere are Io, Titan, and Triton, and to a lesser extent, the Moon, Europa and Ganymede. The thermal structure of the various planetary atmospheres are basically very similar but the exceptions and differences are particularly noteworthy and quite interesting.

Mercury and the Moon

The planet Mercury and the Moon are actually very similar objects. With very faint and tenuous atmospheres their inactive surfaces are therefore both heavily cratered, giving them a similar appearence as well. The outgassing of the elements in their crusts provide the gases for their atmospheres. Emission from sodium atoms has been detected around the Moon and Mercury. It is a good tracer for this process as it is more easily observed than other potential elements. A large part of Mercury's atmosphere also comes from the capture of the solar wind from the sun. While these gases, mostly hydrogen and helium, escape readily from Mercury due to it's low gravity and high temperature at it's surface, the high rate of capture of these particles allows for an atmosphere.

Venus

Images of Venus taken with HST reveal sulfuric acid clouds in Venus' troposphere. Venus' troposphere, as the thermal structure reveals, is super heated by a large greenhouse effect that creates an average surface temperature of about 750 degrees Kelvin.

Venus


Venus' atmosphere is made up mostly of carbon dioxide (97%) with the rest mostly nitrogen (3%). It is believed that at one time water existed on Venus' surface. The process in which the water was destroyed is called the run away greenhouse effect. The greenhouse effect heats the atmosphere, evaporating the water which gets photodissociated. After breaking up, the hydrogen rises to the top of the atmosphere and escapes. At the same time there is extra heating from a positive feedback loop due to the release of carbon dioxide that would otherwise be condensed in the liquid water. This loop continued until radiative equilibrium was reached and the current state with a carbon dioxide rich atmosphere was reached. While plants and bacteria would find the richness of carbon dioxide on Venus to their liking, there is very little of the essential water. There is slightly more water vapor above the troposphere where the temperature is cooler. Current research leads us to think that if there could be life on Venus it would exist amongst the clouds, feeding on the sulfur found there.

Earth
As we discussed above, the Earth's atmosphere is made of nitrogen (80%) and oxygen (20%) with trace amounts of other gases. These other gases, mainly water vapor, carbon dioxide, and ozone play a large role in obtaining radiative equilibrium at different levels. The differing concentrations of these gases along with their radiative properties allow them to dictate the thermal structure of the atmosphere.

Earth


While the Earth has about the same amount of carbon dioxide as Venus, it's ocean along with a somewhat lower effective surface temperature due to it's further distance to the sun, prevent a run away green house effect like that found on Venus. It is however, concievable that the actions of mankind could artificially release enough of the carbon dioxide that has been trapped in the Earth to allow the atmosphere to run away. As we know, green house warming is currently a hotly pursued line of scientiic research and political debate, as it should be.

Mars

 

Mars's atmosphere, like Venus, is made mostly of carbon dioxide (95%) and nitrogen (3%) with 2% argon and other trace gases. The above image shows Mars as seen from the Hubble Space Telescope at one of the view times when Mars is as close as it gets to the Earth. More importantly Mars was at a time of northern winter which is on average cooler than the southern winter due to Mars' distance to the sun. This allows for viewing the surface of Mars better because the violent dust storms that are otherwise found subside. Instead we clearly see the surface of Mars with it's two sizable polar caps made of water ice and carbon dioxide ice (dry ice). Also seen in the Hubble image are wisps of ice clouds in Mars' atmosphere. The vertical structure diagram below describes where these dust and ice clouds are found in Mars's atmosphere.

Mars


Jupiter


Moving on to the Jovian planets, Jupiter is made mostly of hydrogen (%90%) and helium (10%). Jupiter is incredibly large and has a strong magnetic field. This magnetic field, like the Earth's gives rise to interesting aurora (pictured aove) and other electromagnetic phenomenon in the Jovian system (we call Jupiter, it's satellites and general environment the Jovian system). The visible features on Jupiter's surface are due to cloouds of the trace amounts of ammonia and methane as diagramed below. Recent galileo spaceprobe results have revealed much less water and lightning than thought at the time this drawing was made.

Jupiter


Io

Jupiter's moon Io has an interesting and volatile atmosphere. As seen in the above image, Io is highly volcanic. This volcanic plume, Loki, ejects sulfur and sulfur compounds like sulfur dioxide. It is this sulfur dioxide and sulfur monoxide that make up Io's atmosphere. The gases arise from either these plumes or sputtering from sulfur frost on the surface. Along with solar heating and heating from the Io plasma torus smashing into Io, the main source of atmospheric heating is from Joule heating of Io's Ionosphere. Jupiter's corotating magnetic field sweeps across Io's ionosphere, rapidly vibrating the molecules. Io's atmosphere is not uniform. The atmosphere is found to be thicker above the volcanic plumes than average. The following temperature profiles (Strobel 1995) depict the different structure we can expect above these plumes. In fact we can expect a troposphere above these turbulent plumes complete with a mesopause. This doesn't describe the rest of Io's atmosphere which is all thermosphere.

Io


Saturn

On Saturn we find many similarities to Jupiter with 94% hydrogen and 6% helium. It's large percentage of hydrogen makes the average density of saturn less than that of water.

Saturn



Titan

While this image of Titan portrays it as rather benign, it is actually a very interesting and active environment. Being made up of mostly nitrogen (80%) and hydrocarbons such as methane (20%), Titan offers a unique environment that may possibly be suitable for some form of life. The large amount of methane in the atmosphere combined with our knowledge that methane is photodissociated at the top of Titan's atmosphere by ultraviolet light tells us that something is replenishing this large amount of methane. The current models and information suggest that vast seas of methane are found on Titan's surface. Titan is very chemically active with the hydrocarbons methane and ethane reacting with ammonia and other nitriles. The orange appearence of Titan is due to this methane and diagramed in the followin image. The Cassini-Huygens mission to Saturn will send the Huygens probe into Titan's atmosphere and could possibly provide the much desired solid evidence for liquid water on it's surface.

Titan

 

Uranus and Neptune

Uranus and Neptune are both very far from the sun and their atmospheric heating is almost totally internal. They are similar in composition with 89% hydrogen and 11% helium. Neptune, however, is very dynamically active, while Uranus is not. Neptune, in fact, has a great dark spot, much like Jupiter's Great Red spot (Saturn also has been found to have large cyclonic storms). This dark spot was just south of it's equator at the time of the voyager flyby but recent observations with the Hubble Space Telescope have found this storm near Neptune's North pole.

Triton
 

Triton's mysterious surface pictured above is characterized by a mixture of nitrogen and methane ice, it's major atmospheric components. At the bottom of this image are found black features that have been interpreted to be geysers from which some of the atmosphere's gases originate, the other gases coming from sputtering from the surface frosts. Looking at the temperature profile of Triton, we see Triton actually has no stratosphere, which we defined as a region where radiative heat transfer dominates. Instead we find a region of convection and latent heat close to it's surface running right into thermal conduction transfer at the kink in the temperature profile shown below (Strobel).

Triton


Pluto

Pluto is actually very similar to Triton but since pluto is closer to the sun than Neptune and Triton, pluto is warmer. Current thinking describes the collapse of Pluto's atmosphere once it's highly elliptical orbit takes it out to around the distance of Triton. The gases will condense and form a frost on Pluto's surface.