lecture 12-13: planetary atmospheres - trinity college, · pdf filelecture 12-13: planetary...

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Lecture 12-13: Planetary atmospheres

o  Topics to be covered:

o  Atmosphere composition.

o  Atmospheric pressure.

o  Atmospheric temperature.

o  Atmospheric retention.

Neptune (Voyager II)

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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.

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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).

o  Volcanic gasses account for most of Earth's atmosphere. Primitive atmosphere contained H2, H2O, CO and H2S.

o  Biological activity: photosynthesis converts CO2 to O2.

Mount Etna - March 2005 (credit Reuters/Irish Times)

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Atmospheric pressure

o  Assume hydrostatic equilibrium:

o  As ρ = µP/RT and setting H = RT/ µg =>

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.

o  Can also write:

€

dPdh

= −ρg

€

P = P0 exp −1Hdh

0

h∫

$

% &

'

( )

€

ρ = ρ0 exp −1Hdh

0

h∫

%

& '

(

) *

International Civil Aviation Organisation (ICAO) Standard Atmosphere

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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.

Atmospheric equilibrium temperature

o  Solar luminosity is

where RS = 6.955 x 108 m and TS = 5778 K. o  At 1AU, the Earth receives

where d = 1.49598 x 1011 m = 1 AU. o  But, fraction (A) of power reflected – called albedo.

o  A = 1: Total reflection. o  A = 0: Total absorption.

o  Rocks are poor reflectors, ice is a moderate reflector, snow is a good reflector.

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€

PS = ASσTS4

= 4πRS2σTS

4

= 3.84 ×1026 Watts

€

FS = 4πRS2σTS

4 /4πd2

=1366 Watts m-2 (the “Solar Constant)

Planet A Earth 0.37

Moon 0.12

Venus 0.65

Jupiter 0.52

Pluto 0.3

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o  So, a planet of radius RP will absorb:

where A is the planetary albedo which accounts for radiation reflected by clouds, etc. Therefore

o  Assuming planet is blackbody will radiate energy back into space at

Watts Eqn. 2

where e is emissivity. Accounts for fact that planets not perfect blackbodies.

o  In equilibrium, Eqn. 1 = 2.

€

Pabs = Fsun × πRP2 × (1− A)

€

TP = TSRS2(1− A)4ε d2

$

% &

'

( )

1/ 4

Watts Eqn. 1

Pemitt = 4 π RP2 εσ TP

4 €

Pabs =4πRs

2σTS4

4πd2× πRP

2 × (1− A)

Watts

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o  Substituting for constants,

where d is in AU. For Earth, T = 248 K and for Moon, T = 269 K

o  Observed temperatures are: Earth T = 288 K and Moon T = 252 K

o  Earth is not a perfect blackbody: o  Some solar heat is conducted into

surface rock and oceans - this is a form of ‘stored’ heat energy

o  Earth has atmosphere which acts like thermal blanket, ‘trapping’ infrared radiation.

TP = 279d−1/2 1− A( )1/4

Distance (AU)0.1 1 10

Temperature (K

)

10

100

1000

A = 0

Mercury

Venus

Moon

EarthMars

Jupiter

Saturn

UranusNeptune

Pluto

Tplanet = 278 { (1 - A) / ε d(au)2 }1/4

slow rotation +

no atmosphere

(runaway "greenhouse effect")

Perfect blackbody

A = 0.9

A = albedo, ε = emissivity = 1

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Temperature for tidally locked planet

o  For tidally locked planet, same face always facing star => surface area re-radiating will be much reduced.

Pemitt = 2 π R2 εσ TP4

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).

=> TP = 279(1− A)2d 2

"

#$

%

&'

1/4

€

TP (θ) = TSRS2(1− A)sin(θ)

εd2%

& '

(

) *

1/ 4

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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.

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Greenhouse effect

o  Can model using

where TG = 36 K €

TP = TG + 278 (1− A)ε d2

$

% &

'

( )

1/ 4

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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.

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.

o  Stability of host star’s luminosity and low incidence of flares/CMEs.

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Kepler Transiting Planets in the Habitable Zone (Torres et al., ApJ, 2015). http://www.cfa.harvard.edu/news/2015-04


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: o  Using TP = 279 d-1/2 (1 - A)1/4

=> d = TP2 / 2792 (1 – A)1/2

o  Assuming life can exist at 0 ± 50 C => CHZ = 0.68 – 1.44 AU.

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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.

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Atmospheric retention

o  Energy of a molecule in atmosphere can be written:

o  A particle will escape from planet if has enough KE. Escape speed v = vesc, needed to escape from r = R is therefore:

o  From kinetic theory, therefore,

o  Lightest particles (H and He) have highest speeds and escape preferentially if T is large enough for particles to have vtherm > vesc.

€

Etotal = Ek + Ep =1/2mv 2 − GMmr

= 0

€

vesc =2GMR

€

vtherm =3kTm€

1/2mvtherm2 = 3/2kT

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o  A planet will retain its atmosphere if

o  The escape condition occurs when

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

€

vtherm < vesc

€

3kTm

=2GMR

=> Tesc =2GMm3kR

Random collisions

Ground

Atmosphere

Exosphere Escape

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o  For a given molecule to be retained:

o  Definition: m = µ mH o  where m is molecular weight and mH is mass of H-atom (mH = 1.67 x 10-27 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 o  Tatm = 288 K and vesc = 11.2 km s-1 o  Hence, escape for all molecules with µ ≤ 4 o  So, don’t expect to find much H or He.

o  For Jupiter o  Tatm = 134 K and vesc = 59.5 km s-1 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.

€

2GMR

>3kTm

=> m >3kTR2GM

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Oxygen

Helium

Hydrogen

o  As vtherm ~ m-1/2 and ~T1/2, light gases have higher speeds and hot gases have higher speeds.

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 the Sun, have higher temperatures and less mass, and so lack H and He - some have no atmosphere.

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 Solar System (~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.

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€

vesc =2GMR

€

vtherm =3kTm

Retention of Atmospheric Gases

Temperature (K)

100 1000

Velocity (km

/s)

0.1

1

10

100

PlanetsGalilean moonsTriton and TitanMinor PlanetsNB: lines show ten times

mean molecular speeds

Jupiter

Saturn

Uranus

Neptune

Mercury

Moon

Venus

Earth

Mars

Pluto

Triton

Ceres

Titan

Vesta

Pallas

Hydrogen

Helium

H2O

N2

CO2

Xe


o  Escape velocity:

o  Thermal velocity:

o  Consequences:

o  Light elements escape more easily. o  Hot planets “burn off” their atmosphere. o  Small planets cannot hold onto atmosphere.

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Jeans Escape

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

where N is number of molecules per unit volume.

o  In high-velocity tail, there are velocities greater than the gravitational escape velocity.

o  The Jeans escape flux is then ΦJ = ¼ Nex <ve> where Nex is the number density at the base of the exosphere and <ve> is the average velocity of escaping molecules.

vesc €

f (v) = 4Nπ−1/ 2 m2kT$

% &

'

( ) 3 / 2

v 2e−mv2 / 2kT

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

Eqn. 1

o  Setting λ = mv2/2kT =>v = (2kTλ/m)1/2 and dv = ½ (2kTλ/m)-1/2 2kT / m dλ

o  Substituting for v and dv in Eqn. 1, gives Eqn. 2 o  The denominator is a standard integral

o  Integrating by parts, the numerator can be written

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€

< ve >=ve−mv

2 / 2kT 4πv 2dvve

∞

∫e−mv

2 / 2kT 4πv 2dv0

∞

∫

€

< ve >=2kTm

"

# $

%

& ' 1/ 2 λe−λdλ

λesc

∞

∫λ1/ 2e−λdλ

0

∞

∫

€

λ1/ 2e−λdλ0

∞

∫ = π1/ 2 /2

€

λe−λdλλesc

∞

∫ = (1+ λesc )e−λesc

Jeans Escape

o  Eqn. 2 can then be written

o  The Jean escape flux (in molecules m-2 s-1) can finally be written:

where v0 = (2kT/m)1/2 is the most probable velocity and λesc is the escape parameter, given by

o  For Hydrogen on Earth: Nex = 1011 m-3 and Tex = 900 K and Rex = 6,900 km. Therefore, λesc ~ 7.8

and ΦJ ~ 4 x 1011 molecules m2 s-1, 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.

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€

< ve >= 2 2kTπm

#

$ %

&

' ( 1/ 2

(1+ λesc )e−λesc

€

λesc =GMm /Rex

1/2mv02 =

GMmkTRexo

€

ΦJ =14Nex < ve >

=12 π

Nexv0(1+ λesc )e−λesc

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Escape timescale

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

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.

€

τ e = v πeλ /g(1+ λe )

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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  Is there currently volcanic and/or tectonic activity on the planet

o  Arrived at Venus in April 2006.

lecture 12-13: planetary atmospheres - trinity college, · pdf filelecture 12-13: planetary...

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