sign in sign up
<<
Home , Atmospheric temperature, Hydrostatic equilibrium, Jeans (Martian crater), Primary atmosphere, Scale height, Secondary atmosphere

Lecture 12-13: Planetary

o Topics to be covered:

o composition.

o Atmospheric .

o Atmospheric . (Voyager II)

o Atmospheric retention.

PY4A03 PY4A03

o A ’s primary atmosphere comes from nebular material in .

o Mainly H, H2 and He.

o Trace elements also present in CO2, CH4, N2, H2O, NH3. o If planet’s not strong enough or surface temperature is too large, these elements escape, leaving planet without an atmosphere. o Solar can also drag material from the atmosphere. o Relevant for without significant magnetospheres (e.g., ). o For the terrestrial planets, most of the H escaped, leaving heavier gases such as argon, neon and ammonia concentrated near the surface.

PY4A03 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 /meteors containing and gas collided with the planets (H2O, CH4, CO2). Mount Etna - March 2005 o Volcanic gasses account for most of 's (credit Reuters/Irish Times) atmosphere. Primitive atmosphere contained H2, H2O, CO and H2S. o Biological activity: photosynthesis converts CO2 to O2.

PY4A03 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 : 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 . o : T increases with altitude due to absorption of UV. Extends to ~50 km (on Earth). No clouds. o : On Earth T quickly decrease with height o : T increases with altitude due to strong UV flux. Includes the 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. 0.12 o A = 0: Total absorption. 0.65 o Rocks are poor reflectors, ice is a moderate 0.52 reflector, snow is a good reflector. 0.3

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 € 4 R2 T 4 π s σ S 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 o Observed are: Earth T = 288 100 slow rotation K and Moon T = 252 K + Neptune Temperature (K) no atmosphere

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 - 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 => 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 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(). % 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/ near-infrared. o Ground absorbs V-NIR, and heats up. o Then re-radiates energy. T ground lower than ’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 //etc impacts.

o Stable planet orbit. Not too eccentric. 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 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, 1/2mv 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 and mH is mass of H- (mH = 1.67 x 10 kg). so, for hydrogen µ = 1, and€ for helium µ = 4 o hence at a given temperature the He 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. Observations show that Jupiter is a H and He gas giant. PY4A03 Atmospheric retention

-1/2 1/2 o As vtherm ~ m and ~T , light gases have higher speeds and hot gases have higher speeds. Oxygen o Gas giants are massive planets with high escape speeds and cold temperatures, so light gases such as H and He retained. Small rocky bodies are closer to Helium the Sun, have higher temperatures and less mass, and so lack H and He - some have no atmosphere. Hydrogen o Even if vtherm < vesc, some particles will escape due to the ‘high-speed’ tail of the Maxwellian distribution. o For a planet to ‘hold’ an atmosphere over the age of the (~4.5 billion years), the escape condition is more like vesc > 10 vtherm o The factor of 10 accounts for the high-velocity tail of the Maxwellian distribution of speeds.

PY4A03 Atmospheric retention

Retention of Atmospheric Gases

100

2GM Jupiter Hydrogen o Escape velocity: vesc = Saturn R Neptune Helium Uranus Earth H O 10 Venus 2 N o Thermal velocity: 3kT 2 vtherm = Mars CO € 2 m Mercury Xe o Consequences: Moon Velocity

Pluto 1 (km/s) o Light €elements escape more easily. o Hot planets “burn off” their atmosphere. Vesta Planets Galilean Pallas Triton and Titan o Small planets cannot hold onto atmosphere. Minor Planets NB: lines show ten times mean molecular speeds 0.1 100 1000 Temperature (K)

PY4A03 Jeans Escape o The velocity of molecules of mass m have a Maxwellian distribution of velocities:

3 / 2 $ m ' 2 f (v) = 4Nπ −1/ 2& ) v 2e−mv / 2kT % 2kT (

where N is number of molecules per unit volume.

€ o In high-velocity tail, there are velocities vesc greater than the gravitational escape velocity. o The Jeans escape flux is then

ΦJ = ¼ Nex

where Nex is the number at the base of the exosphere and is the average velocity of escaping molecules.

PY4A03 Jeans Escape o The probability that a particle has a velocity between v and v + dv is proportional to exp(-mv2)4πv2dv. The average velocity is then

∞ −mv 2 / 2kT 2 ∫ ve 4πv dv ve < v e >= ∞ 2 Eqn. 1 e−mv / 2kT 4πv 2dv ∫0 o Setting λ = mv2/2kT =>v = (2kTλ/m)1/2 and dv = ½ (2kTλ/m)-1/2 2kT / m dλ

∞ −λ € " %1 / 2 ∫ λe dλ o Substituting for v and dv in Eqn. 1, gives 2kT λesc Eqn. 2 < ve >= $ ' ∞ # m & λ1/ 2e−λ dλ ∫0 o The denominator is a standard integral

∞ λ1/ 2e−λ dλ = π1/ 2 /2 ∫0€ o Integrating by parts, the numerator can be written

∞ −λ −λesc € ∫ λe dλ = (1+ λesc )e λesc

PY4A03

€ Jeans Escape

1/ 2 o Eqn. 2 can then be written # 2kT & < v >= 2% ( (1+ λ )e−λesc e $ πm ' esc o The Jean escape flux (in molecules m-2 s-1) can finally be written:

1 Φ = N < v > € J 4 ex e 1 = N v (1+ λ )e−λesc 2 ex 0 esc π 1/2 where v0 = (2kT/m) is the most probable velocity and λesc is the escape parameter, given by

€ GMm /Rex GMm λ = = esc 1/2mv 2 kTR 0 exo 11 -3 o For Hydrogen on Earth: Nex = 10 m and Tex = 900 K and Rex = 6,900 km. Therefore, λesc ~ 7.8 11 2 -1 and ΦJ ~ 4 x 10 molecules m s , which is smaller by a factor of ~4 than observed value. € o See Pages 441-443 of “The physical universe: an introduction to astronomy” by Frank H. Shu on Google Books and Page 127 of “Planetary Sciences” by de Pater and Lissauer.

PY4A03 Escape timescale o The escape timescale can then be estimated by taking the ratio of the density (neHe) to the flux:

λ τ e = v πe /g(1+ λe ) o Small bodies tend not to have atmospheres because€ escape too rapid.

o Most H comes from H2O. This, when H escapes, O left behind => Terrestrial planets become more oxidised with time. o See Fundamentals of Physics and Chemistry of the Atmosphere (Visconti). Page 72-75.

PY4A03 Venus Express

o What is the mechanism and driving force of the super-rotation of the atmosphere? o What are the basic processes in the general circulation of the atmosphere? o What is composition and chemistry of lower atmosphere and clouds? o What is the past and present water balance in the atmosphere? o What is the role of the radiative balance and greenhouse effect? o Arrived at Venus in April 2006. o Is there currently volcanic and/or tectonic activity on the planet

PY4A03