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Chapter 4 : Planetary Atmospheres H. Equilibrium and Scale Height

Chapter 4 : Planetary Atmospheres H. Equilibrium and Scale Height

Chapter 4 : Planetary

Astro 9601

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Planetary Atmospheres: Topics to be covered • and Scale Height (4.1) • In equilibrium, there is a relation between pressure, density and . • Thermal Structure (4.2) Force from gravity: Force from pressure: • Consider a slab with thickness = − • Observations (4.3.3) – All dz and density ρ. FG Mg Fp = (P + dP)dA − (P)dA • This slab exerts a force on the F = −ρ dA dz g = dPdA • Clouds (4.4) – All slab below it due to its mass G and gravity. • Meteorology (4.5) – All • This force, per unit area, is a For equillibrium: pressure. dP = −ρg dz • Atmospheric Escape (4.8) – All • There is a change in pressure dP across the slab due to its mass. = −ρg • Planetary Evolution (4.9) dz

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H. Equilibrium and Scale Height • We can combine the If g and T are approx. expression for hydrostatic constant, the solution to Part I : Scale height, heat sources, equilibrium with the this is an exponential: law to get the density as a − z / H energy transport, and thermal function of height: ρ ∝ e structure Gas law: P=nkTP = nkT kT where n is the number density. H ≈ gm Assume n ~ ρ / m m=mass per molecule Note that T and g are not P(z) ~ ρ(z)kT / m really constant with z, but it’s a useful approx. dP dρ kT = = −gρ Rearranging the equation dz dz m 3 shows that P, ρ and n all have 6 the same height dependence.

1 Scale heights for planetary atmospheres The mass of the is about 1/300th that of The radius of the Earth is about 1/10th that of Jupiter. The ratio of gravitational accelerations is about 1/3.

• Oddly, the scale heights of the atmospheres of terrestrial and giant are similar, and about 10-20 km. • Exceptions are the tenuous atmospheres of , and various moons, which have larger scale heights. 7 10

Vertical structure of Vertical structure ’s atmosphere • Note that the scale height estimate ignored the possibility that the could depend on • In the troposphere the height. temperature decreases • To get a better model of atmospheric structure, with increasing height because of the we must also consider the thermal structure. greenhouse effect. • P=nkT. Even though the atmospheric scale • As the temperature heights of most planets are similar, their decreases in the and so pressures are NOT similar. troposphere, gas can • Chemical processes and phases are dependent condense, forming upon pressure as well as temperature. So clouds. planets have a wide variety of chemical structure and composition. 8 11

Processes affecting the thermal structure of atmospheres • Solar radiation is absorbed at the top of the atmosphere and by certain layers. • Internal heat sources and reradiated energy from sunlight heat the atmosphere from below. • Clouds, dust and photochemical haze change the opacity and thermal structure. • Changes in composition can also change the opacity and thermal structure. – Volcanoes – Chemical interactions between the air and crust Haze/Cloud layer forms at level where sulfuric acid – Biological processes condenses (50 km and up); too hot for most other gases to condense 9 12 Pressure scale-height ~11 km compared to H~6 km on Earth

2 Atmospheres of the Giant Planets

• In the thermosphere, the temperature increases with height as Part II : Observations of more energy from the Planetary Atmospheres and Sun and solar wind is deposited into the Evolution / Thermal Escape atmosphere. • The mesosphere is the intermediate region which in some cases can be considered isothermal.

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Temperature structure in Earth’s atmosphere Earth, Venus, and • Air heated by IR emission+convection near • Earth’s atmosphere is primarily Nitrogen (78% by the surface volume) and Oxygen (21%), but also contains – Temperature drops with CO , H O, and Ar. altitude initially near 2 2 surface • Mars and Venus are dominated by CO2 (98%) • UV absorption by Ozone • Ozone has been identified on both Mars and Earth from 30-50 km strongly heats stratosphere • Spectra from the planets varies with latitude. • Temperature rises again in • All three planets have deep CO2 absorption the Thermosphere due to bands; much of the atmospheric opacity is from lack of collisions/inability to radiate away solar CO2. absorbed energy • On Earth, much of the atmospheric opacity is from

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Earth-Atmosphere System Radiative Balance Note that the solar constant (1370 W m-2) is the value measured directly by satellites hovering over the earth’s noon-side atmosphere. If we distribute Venus’ atmosphere this amount over the entire globe, we yield a global mean incoming solar radiation of about 342 W m-2. • Almost all carbon dioxide • Very uniform surface temperature • Much less water than in Earth’s atmosphere – Water must be removed from Venus somehow – D/H ratio higher than Earth indicating more water in distant past?

• S & SO2 (from volcanic outgassing) combines with small amounts of water to form sulfuric acid clouds at 30 km altitude • Temperature structure determined by radiation from surface and distribution of greenhouse

Source: Kiehl and Trenberth, 1997: Earth’s Annual Global Mean Energy Budget, Bull. Am. Met. Soc. 78, 197-208. 15 gases 18

3 Origin and Evolution of Venus’ Atmosphere • Wet Greenhouse theory: – Early atmosphere much less dense – Venus’ surface supported water/oceans – Heating caused ~50% of water to evaporate until atmosphere reached water saturation – Water still lost at the top of the atmosphere and (ultimately) all oceans evaporate – BUT, key point is oceans exist for ~millions years before totally boiled away

– Lots of the initial CO2 locked into carbonate rocks – Leads to a much less dense early atmosphere No liquid water to remove CO2 which builds up to increase temperature – Hence when 20% level reached at equilibrium with hydrodynamic escape, it is 20% of a much less dense (and via greenhouse effect. Water is able to diffuse upward to great heights hence less massive) atmosphere (no atmospheric cold trap at low altitudes) and there H2O is dissociated – Hence, much more water lost in this theory than in runaway by UV radiation from the sun. Some H molecules are then able to acquire greenhouse approach enough velocity to escape from Venus. 22 19

Water loss at Venus What happened on Mars? • Lack of Oxygen means no Ozone and no “cold” temperature layer to trap water vapour. 1.Weaker gravity • Dissociated H atoms collided with excited ions of H or 2.Low temperature, leading to freezing out excited O and can reach oflf less vol a tile gasses. escape speeds at ~100 km • Current rate of water loss is 3.Incorporation into rocks same as input rate from • No primordial water left as total escape of all remaining water is of order 50 Ma.

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Origin and Evolution of Venus’ Theories for thin Martian Atmosphere Atmosphere • Atmosphere today is secondary and controlled by 1. Loss by large impact early in its history outgassing from • Two main models of atmospheric evolution: 2. Solar wind ion collisions removing • Runaway greenhouse model: atmospheric gases (some dissociation – Thick atmosppypgphere always present; high from da y one prevent liquid water from occurring and thermal escape as well as on – Large “steam” atmosphere denser than today’s would result Venus), particularly water and carbon – Water vapor high in the atmosphere dissociated by solar UV rays and H escapes removing water dioxide – Process should have stopped once water became minor atmospheric constituent (~20% of atmosphere) 3. Failed carbonate cycle locking up most – But no water (<1 %) detected today? of the gases (particularly CO2) as rock deposits with very little CO2 being 21 outgassed due to weak/absent volcanism24

4 Planets and Satellites with Tenuous Atmospheres • All planets and satellites (and dwarf planets) have an atmosphere, but it may be so tenuous it’s difficult to detect. • Bombardment by energetic particles from the solar wind and micro-meteorites kick up atoms and molecules from the surface • Sputtering forms a corona which can sometimes be seen in emission lines • For small bodies, the acceleration from gravity is small and the tenuous atmosphere can have large scale heights.

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Water in Mars’ atmosphere Mercury and the Moon

• Surface morphological evidence for water • Mercury’s atmosphere was first detected from suggests liquid surface water existed in space with Mariner 10’s airglow the past spectrometer.Later on, ground based observations in sodium have also detected it. • Water either lost (via dissociation and • It consists of atomic species Na, K, Mg and O. escape as on Venus) or trapped beneath • The density is a few thousand atoms per cm3. surface as permafrost (ice). • H, He are captured from the solar wind. • Evidence for a warmer, wetter climate for • Apollo spacecraft detected a similar atmosphere short periods (maybe several periods)? on the Moon with mass and UV spectrometers. • The Moon’s atmosphere is denser in the day time. 26 29

Martian average is just below the point where water could exist as a liquid in warmest areas Mercury’s tenuous atmosphere If the atmosphere were to become thick enough for Spectroscopic sufficient greenhouse warming measurements of sodium to facilitate liquid water periodically at the surface, the in Mercury’s atmosphere. CO2 would get removed as High Na abundance is carbonates and tend to draw the atmosphere gradually back red, low abundance blue. down to 6.1 millibars. This The dotted line is the may be the reason for the “seeing disk”: slit particular value of the atmospheric pressure (and measurements have been hence density) on Mars that interpolated to make an we observe today. Thus the “image”. Martian atmosphere may be self-limiting Anne Sprague 30 with respect to water27

5 Enceladus Pluto and Triton •Enceladus is a small moon of • Both extremely cold (40 – 60 K) . Its diameter is • However, surface temperatures are high enough approximately 500 kilometers to partly sublime some ices (N2, CH4 (methane), •This means the amount of CO2) gravity present on the moon is • The amoun t of vapour on th ese obj ec ts can b e not enough to hold an estimated from the equations for vapour pressure atmosphere for very long. equilibrium. •Therefore, a strong source must •N2 is believed to be the dominant molecule in be present on the moon to "feed" Pluto’s atmosphere. Enceladus's atmosphere. • We know Pluto has an atmosphere because of stellar occultations.

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Io Enceladus •Volcanic or gyser eruptions are • Io’s atmosphere is possible source of Saturn's icy E primarily sulfur ring. dioxide; there is SO 2 • Enceladus is the most reflective ice on the surface. objjy,ect in the , • Other gases include reflecting about 90 percent of the SO, Na, K and O. sunlight that hits it.

• Cl is inferred from its •If Enceladus does have ice presence in the volcanoes, the high reflectivity of plasma torus. the moon's surface might result from continuous deposit of icy particles originating from the 32 35 volcanoes.

Europa and other icy satellites Atmospheres of giant planets

• Europa is covered by • Mostly composed of Molecular water ice. hydrogen • Has an oxygen rich • At UV wavelengths, opacity atmosphere. provided by Rayleigh scattering: • Sputtering knocks H2O you can only see the upper apart. Hydrogen is more atmophsere. likely to escape. This • Optical and IR light is reflected leaves oxygen behind. from clouds. • A tenuous oxygen • Opacity at longer wavelengths atmosphere has also provided by molecular hydrogen been detected on excitation and by scattering from . cloud particles. 33 • Ammonia absorbs in the radio. 36

6 Atmospheres of giant planets Saturn, and

• Thermal infrared spectra • Even in Jupiter, the upper reveal presence of H O, CH 2 4 atmosphere contains CO rather (methane), NH (ammonia) 3 than CH . and H S (hydrogen sulphide) 4 2 • Convection causes methane to on Jupiter. rise and be heated, where it is • However, mixing ratios converted to CO. measured by Galileo probe • Convection also accounts for the are difficult to account for and production of clouds at different the abundances are less than heights. As the pressure drops, expected. water clouds, followed by • Noble gasses such as Ar, Kr, ammonia sulfide (NH4SH), Xe are 2.5 times solar! followed by ammonia clouds. 37 40

Atmosphere Evolution: Terrestrial Atmospheres – In the beginning…

• The for every terrestrial world was probably composed mostly of light gases that accreted during initial formation. • These gases are presumed to be similar to the primordial mixture of gases found in the Sun and Jupiter: 94.2% H, 5.7% He and everything else less that 0.1%. • The evidence for this stage is weak and so there are many variations on just what the first “early” atmosphere of the inner planets was like. 41 38

Saturn, Neptune and Uranus • In general none of the terrestrial worlds has any significant amount of primary atmosphere •CH4 and NH3 are detected on today. Saturn, but only CH on 4 • Loss processes (escape of atoms into space), Uranus and Neptune. • Heavy elements in general are removal by collisional bombardment and more abundant on planets replacement by geological outgassing more distant than Jupiter. (l(volcanos )h) have mo difidhdified the or iiliginal, pr imary • There is evidence that the atmosphere. amount of gas incorporated • These processes (which vary in degree and into each planet depends on stages on all three terrestrial planets with the radial distance from the Sun. atmospheres) produce the secondary atmospheres we see today on Venus, the • The balance of CO vs CH4 and N2 vs NH3 depends on Earth and Mars. temperature and pressure. 39 42

7 Biological modification of Inert gases as tracers of early conditions Earth’s atmosphere • Anaerobic life forms (e.g. blue-green algae) • Inert gases such as Ne are not produced by "poisoned" atmosphere over 1.5 Gyr with O2. radioactive decay, and are too heavy to escape • Photosynthesis converted CO2+water to O2 thermally. • Aerobic lifeforms arose which used the O • The amount of Ne probably hasn’ t changed much . 2 • Plants and Algae act as CO2 “scrubbers” and O2 • However, the Ne/H, Ne/O, and Ne/N abundance “producers”. ratios on Earth, Mars and Venus are much smaller • Only biological systems can produce large than Solar abundances. amounts of oxygen in a terrestrial atmosphere. • Either primitive atmospheres were removed, swept • Presence of O2 indicates non-equilibrium away, or primitive atmospheres were initially very processes (life) small. 43 46

Did the Terrestrial Worlds have Oxygen evolution in the atmosphere Primitive Atmospheres at any time?

One line of reasoning: • Neon is heavy and so none can escape from Earth's atmosphere. • It is inert so it does not bond with rocks or have any other way of escaping into the Earth from the atmosphere. • It is not produced via radioactive decay, so whatever neon is presently in our atmosphere is a measure of the upper limit for the total amount of neon left over from a primitive atmosphere (note that some neon could have entered the atmosphere via outgassing over Earth's history). • Given the known ratio of neon to hydrogen and helium and other gases in the sun, we can estimate the total mass of the Earth's primitive atmosphere. The result is that the primitive atmosphere could have been no more than 0.9% of Earth's present day atmosphere. Red Beds • Therefore, the Earth never had a primitive atmosphere of any significance. BUT – what about early heavy bombardment? 44 47 This could easily have totally removed most of the primitive Ne! BIF

Secondary atmospheres Secondary Atmospheres today…

• Volcanoes outgas, particularly in CO2 and H2O. • Over a long period of time, much of our atmosphere Mars is cold, rarified atmosphere could have been made from volcanic outgassing. Venus is hot, dense atmosphere • Venus, Mars and Earth all have evidence for volcanoes. • Iron rusts, removing oxygen. This could have caused a Earth is moderate , with liquid water on surface and Oxygen -rich (!!) hydrogen rich atmosphere in early times. • There is little evidence for an oxygen rich atmosphere for 1/3 of the Earth’s lifetime. • Oxygen is produced by dissociation of water by UV light, and by photosynthesis.

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8 Terrestrial Atmospheres - Water Faint Sun Paradox… • Water is the key to the final outcome of the Possible solution: evolution of the • Ultraviolet radiation from the sun, could combine • On Earth, because of its distance from the sun, with existing methane to form solid liquid water formed at the surface and CO2 hydrocarbons in the upper atmosphere. This in produced by volcanic outgassing was dissolved in turn would shield ammonia ((potherwise broken up the water to form carbonate rock. by the UV) long enough for the ammonia to • This “locked” the CO into rock and controlled the produce a greenhouse warming adequate for 2 liquid water. amount present in the atmosphere limiting its ability to heat (through the Greenhouse effect) the • Organic haze/smog layer like this exists on atmosphere to higher temperatures • OR lots of CO2 early on, but this is not supported by rock evidence which shows an absence of • No such water cycle was present on Mars and siderite (FeCO3) in ancient soil profiles. Venus and they retained their CO2 in the atmosphere 49 52

Carbon Dioxide Cycle and Temperature Oxidizing vs Reducing Atmospheres

• As more CO2 released, temperature increases, which increases evaporation of water

• More rain removes CO2 faster, reducing levels again, dropping temperature etc. • Self-regulating cycle (feedback mechanism) Giant planets Terrestrial planets

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Faint Sun Paradox… Atmospheric Escape The Faint Young Sun Paradox. Solid line is solar • A particle can escape from an atmosphere if luminosity relative to present (S/S0). Ts is Earth’s surface its kinetic energy exceeds the gravitational temperature and Te is binding energy of the planet, and if it moves Earth’s effective radiating on an upw ar d tr aject or y with out int er sectin g temperature. Thick vertical bars are glaciations. another particle. SOURCE: Modified from • The region of escape is called the Kasting and Catling (2003). . • The location and size of the exosphere can • One problem with this view – the early sun was 25-30% fainter be estimated from the mean free path of than today and so liquid water would NOT be present under current atmospheric conditions moelcules. 51 54

9 Maxwellian velocity distribution Thermal Escape function aka Jean’s Escape 1/ 2 3/ 2 ⎛ 2 ⎞ ⎛ m ⎞ 2 • For a gas in thermal equilibrium, the velocity distribution f (v)dv = N⎜ ⎟ ⎜ ⎟ v2e−mv /(2kT )dv of particles of mass m is given by a distribution function: ⎝ π ⎠ ⎝ kT ⎠ • Because of the exponential, most particles have Note: 1/ 2 3/ 2 ⎛ 2 ⎞ ⎛ m ⎞ 2 −mv2 /(2kT ) 3kT f (v)dv = N⎜ ⎟ ⎜ ⎟ v e dv velocities less than most probable velocity v0 v = ⎝ π ⎠ ⎝ kT ⎠ rms m 2kT v0 = −KE / kT m • Note the Maxwellian distribution f (v) ∝ e 2GM • Compare this to the escape velocity: ve ≈ mv 2 GMm r • Condition for escape: = • Similar to a blackbody distribution of photons 2 r

−hν / kT 2 •Defineλescape ≡ (ve / vo ) Bν ∝ e • The rate at which particles escape can be estimated by 55 integrating the high velocity tail of the Maxwellian dist. 58

Maxwellian velocity distribution Thermal escape (continued)

function - continued 1/ 2 3/ 2 ⎛ 2 ⎞ ⎛ m ⎞ 2 −mv2 /(2kT ) • For a gas in thermal equilibrium, the velocity distribution f (v)dv = N⎜ ⎟ ⎜ ⎟ v e dv ⎝ π ⎠ ⎝ kT ⎠ of particles of mass m is given by:

1/ 2 3/ 2 • To estimate an escape rate we consider ⎛ 2 ⎞ ⎛ m ⎞ 2 f (v)dv = N⎜ ⎟ ⎜ ⎟ v2e−mv /(2kT )dv the number of atoms with velocities v > v ⎝ π ⎠ ⎝ kT ⎠ z e • The ir flux is f(v) vz • This comes from: 3/ 2 2 2 2 • The number of atoms which escape per ⎛ m ⎞ −m(vx +vy +vz )/(2kT ) f (v)dvx dvy dvz = N⎜ ⎟ e dvx dvy dvz ⎝ 2πkT ⎠ unit area per unit time: ∞ 2 2 dv dv dv = v dv 3 −mv/(2 kT ) −λescape • Assuming spherical symmetry gives x y z Ndvvee~~z escape∫ z z • Integrating over all angles gives the 4π vescape 2 λescape= mv e /2 kT 56 59

Equipartition

• The Maxwellian distribution has the following properties:

• Different molecules have approximately the same temperature, providing there are lots of collisions. The result is equipartition of energy, where

2 2 m1v1 = m2v2 • Lower mass molecules have higher mean velocities

• Lighter molecules are more likely to escape. 57 60

10 Timescale for reducing the atmosphere via thermal escape −λ The flux of escaping particles is: φ ~ Nv0 (1+ λ)e N is the number density of particles at the exobase (height at which a particle travelling upward is unlikely to hit another particle) Consider the total number of particles in the atmosphere T ~ NAH (A is the area of the planet, H is the scale height). The number of particles lost per second is: dT T ==ϕλA ve(1 + ) −λ dt H 0 So the timescale to reduce the density by 1/e H eλ (assuming λ>1): tescape ~ 61 v0 λ

Additional Processes that affect atmospheric escape

• Non-thermal distributions • Photodissociation and H escape • Interactions with high speed solar wind particles

These additional processes are needed to explain things like how Venus lost its water (if it ever had any).

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