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Lecture 12-13: Planetary Atmospheres

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Lecture 12-13: Planetary Atmospheres Lecture 12-13: Planetary atmospheres o Topics to be covered: o Atmosphere composition. o Atmospheric pressure. o Atmospheric temperature. Neptune (Voyager II) o Atmospheric retention. PY4A03 PY4A03 Primary atmosphere o A planet’s primary atmosphere comes from nebular material in accretion disk. o Mainly H, H2 and He. o Trace elements also present in CO2, CH4, N2, H2O, NH3. o If planet’s gravity not strong enough or surface temperature is too large, these elements escape, leaving planet without an atmosphere. o Solar wind can also drag material from the atmosphere. o Relevant for planets without significant magnetospheres (e.g., Mars). o For the terrestrial planets, most of the H escaped, leaving heavier gases such as argon, neon and ammonia concentrated near the surface. PY4A03 Secondary atmosphere o Rocks and planetesimals which combined to form each planet had trapped gasses. o During formation, gases released from interior. o Differentiation caused them to rise to the outer surface of the planet. o Released via volcanism. o Comets/meteors containing water and gas collided with the planets (H2O, CH4, CO2). Mount Etna - March 2005 o Volcanic gasses account for most of Earth's (credit Reuters/Irish Times) atmosphere. Primitive atmosphere contained H2, H2O, CO and H2S. o Biological activity: photosynthesis converts CO2 to O2. PY4A03 Atmospheric pressure o Assume hydrostatic equilibrium: International Civil Aviation Organisation dP = −ρg (ICAO) Standard Atmosphere dh o As ρ = µP/RT and setting H = RT/ µg => $ h 1 ' € P = P exp& − dh) 0 % ∫0 H ( where P0 is pressure at surface and H is scale height. € o For Earth, H ~ 8 km o Scale height implies planets with low gravity or high temperature will have extended atmosphere. % h 1 ( o Can also write: ρ = ρ exp' − dh* 0 & ∫0 H ) PY4A03 € Atmospheric temperature o Atmosphere not isothermal. Structured as function of height. o Troposphere: Lowest region in atmosphere. On Earth, goes from ground to ~17 km. Weather and clouds form from trace elements of condensable gases. Temperature generally decreases with altitude. o Stratosphere: T increases with altitude due to absorption of UV. Extends to ~50 km (on Earth). No clouds. o Mesosphere: On Earth T quickly decrease with height o Thermosphere: T increases with altitude due to strong UV flux. Includes the exosphere and part of the ionosphere. On Earth, T~1000K at 500 km. PY4A03 Atmospheric equilibrium temperature o Solar luminosity is 4 PS = ASσTS 2 4 = 4πRSσTS = 3.84 ×1026 Watts 8 where RS = 6.955 x 10 m and TS = 5778 K. € o At 1AU, the Earth receives F = 4πR2σT 4 /4πd 2 S S S =1366 Watts m-2 (the “Solar Constant) where d = 1.49598 x 1011 m = 1 AU. Planet A o But, fraction (A) of€ power reflected – called albedo. Earth 0.37 o A = 1: Total reflection. Moon 0.12 o A = 0: Total absorption. Venus 0.65 o Rocks are poor reflectors, ice is a moderate Jupiter 0.52 Pluto 0.3 reflector, snow is a good reflector. PY4A03 Atmospheric equilibrium temperature o So, a planet of radius RP will absorb: 2 Watts Pabs = Fsun × πRP × (1− A) where A is the planetary albedo which accounts for radiation reflected by clouds, etc. Therefore € 2 4 4πRs σTS 2 Pabs = 2 × πRP × (1− A) Watts Eqn. 1 4πd o Assuming planet is blackbody will radiate energy back into space at € 2 4 Pemitt = 4 π RP εσ T P Watts Eqn. 2 where e is emissivity. Accounts for fact that planets not perfect blackbodies. $ 2 '1 / 4 o In equilibrium, Eqn. 1 = 2. RS (1− A) TP = TS& 2 ) % 4ε d ( PY4A03 € Atmospheric equilibrium temperature o Substituting for constants, 1000 −1/2 1/4 A = 0 Venus TP = 279d (1− A) (runaway "greenhouse effect") A = 0.9 Moon where d is in AU. For Earth, T = 248 K Earth Mars and for Moon, T = 269 K Perfect blackbody Jupiter Mercury o Observed temperatures are: Earth T = 288 100 Saturn slow rotation K and Moon T = 252 K + Neptune Temperature (K) no atmosphere Uranus Pluto o Earth is not a perfect blackbody: 2 1/4 o Some solar heat is conducted into Tplanet = 278 { (1 - A) / ε d(au) } surface rock and oceans - this is a A = albedo, ε = emissivity = 1 form of ‘stored’ heat energy 10 0.1 1 10 o Earth has atmosphere which acts like Distance (AU) thermal blanket, ‘trapping’ infrared radiation. PY4A03 Temperature for tidally locked planet o For tidally locked planet, same face always facing star => surface area re-radiating will be much reduced. 2 4 Pemitt = 2 π R εσ TP 1/4 "(1− A) % => TP = 279$ 2 ' # 2d & o For Earth, gives a “hot” side to the planet, with an average temperature of >330 K. o The “cold” side of a tidally locked planet would have extremely low temperatures. Strong winds would act to redistribute heat between hemispheres. o There would also be a latitudinal variation of heating. The incident radiation power on a unit area of the planet varies as sin(latitude). % 2 (1 / 4 RS (1− A)sin(θ) TP (θ) = TS ' * & εd 2 ) PY4A03 € Greenhouse effect o When sunlight reaches Earth, much passes to surface, because atmosphere is transparent to visible/very near-infrared. o Ground absorbs V-NIR, and heats up. o Then re-radiates energy. T ground lower than Sun’s surface, so radiation emitted at longer wavelengths (Wien’s Law) in the mid-IR (MIR). o Atmosphere was transparent to V-NIR light, is opaque to the MIR. On Earth, H2O and CO2 absorb strongly in MIR. o Energy trapped near surface. Eventually equilibrium is achieved, but at a higher T. PY4A03 Greenhouse effect o Can model using 1/ 4 $ (1− A) ' TP = TG + 278& 2 ) % ε d ( where TG = 36 K € PY4A03 Runaway Greenhouse effect o Greenhouse effect is much more prominent on Venus. o Venus has thick atmosphere of 96% CO2, 3.5% N2 and 0.5% other gases. o Venus originally cooler and had greater abundance of water several billion years ago. Also, most of its carbon dioxide was locked up in the rocks. o Because Venus was closer to Sun than Earth, water never liquified and remained in the atmosphere to start the greenhouse heating. As Venus heated up, CO2 in the rocks was “baked out”. Increase of atmospheric CO2 enhanced greenhouse heating and baked more carbon dioxide => runaway feedback loop. PY4A03 Continuously Habitable Zone (CHZ) o Defined as range of distances from host star where liquid water maintained. o Need: o Liquid water sustained over billions of years. o Low occurrence of comet/asteroid/etc impacts. o Stable planet orbit. Not too eccentric. Kepler Transiting Planets in the Habitable Zone (Torres et al., ApJ, 2015). o Stability of host star’s luminosity and http://www.cfa.harvard.edu/news/2015-04 low incidence of flares/CMEs. PY4A03 Continuously Habitable Zone (CHZ) o Empirical: o Earth (1.0 AU) is in habitable zone. o Mars (1.5AU): Water is frozen in soil, thin atmosphere. o Venus (0.72AU): Runaway green house effect, most CO2 is in the atmosphere. o So CHZ is between 0.72 and 1.5 AU. o Theoretical: -1/2 1/4 o Using TP = 279 d (1 - A) 2 2 1/2 => d = TP / 279 (1 – A) o Assuming life can exist at 0 ± 50 C => CHZ = 0.68 – 1.44 AU. PY4A03 Continuously Habitable Zone (CHZ) o Most Kepler exoplanets that are Earth-sized and smaller are in orbits too close to host star to allow liquid water on surfaces. o Kepler-186f (1.11 REarth) planet is in the stellar habitable zone,. o If has Earth-like atmosphere, then some water likely to liquid. o See Quintan et al., Science, 2014. PY4A03 Atmospheric retention o Energy of a molecule in atmosphere can be written: GMm E = E + E =1/2mv 2 − = 0 total k p r o A particle will escape from planet if has enough KE. Escape speed v = vesc, needed to escape from r = R is therefore: 2GM € vesc = R 2 o From kinetic theory, 1/2 mv therm = 3 / 2 kT therefore, € 3kT vtherm = € m o Lightest particles (H and He) have highest speeds and escape preferentially if T is large enough for particles€ to have vtherm > vesc. PY4A03 Atmospheric retention o A planet will retain its atmosphere if vtherm < vesc Escape o The escape condition occurs when Exosphere € 3kT 2GM = Atmosphere m R Random collisions 2GMm => T = esc 3kR Ground o The region where this condition is met is called the exosphere. € o If surface temperature is large, planet will loose atmosphere. Also, small planets find it difficult to hold onto atmospheres. o For a given planet or satellite of mass M and radius R the atmospheric retention condition is Tatm < Tesc PY4A03 Atmospheric retention 2GM 3kT 3kTR o For a given molecule to be retained: > => m > R m 2GM o Definition: m = µ mH -27 o where m is molecular weight and mH is mass of H-atom (mH = 1.67 x 10 kg). so, for hydrogen µ = 1, and€ for helium µ = 4 o hence at a given temperature the He atoms will be moving slower than H atoms o For Earth -1 o Tatm = 288 K and vesc = 11.2 km s o Hence, escape for all molecules with µ ≤ 4 o So, don’t expect to find much H or He. o For Jupiter -1 o Tatm = 134 K and vesc = 59.5 km s o Hence, escape for all molecules with µ < 0.06 o So, nothing escapes, since hydrogen with µ = 1 is the ‘lightest’ gas element.
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