Download 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.
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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).
Mount Etna - March 2005
o  Volcanic gasses account for most of Earth's
atmosphere. Primitive atmosphere contained H2,
H2O, CO and H2S.
(credit Reuters/Irish Times)
o  Biological activity: photosynthesis converts CO2
to O2.
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Atmospheric pressure
o  Assume hydrostatic equilibrium:
dP
= −ρg
dh
International Civil Aviation Organisation
(ICAO) Standard Atmosphere
o  As ρ = µP/RT and setting H = RT/ µg =>
$ h
'
€ P = P0 exp&− ∫ 1 dh )
% 0 H (
where P0 is pressure at surface and H is scale
height.
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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:
% h1 (
ρ = ρ 0 exp'− ∫ 0 dh *
&
H )
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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.
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Atmospheric equilibrium temperature
o  Solar luminosity is
PS = ASσTS4
= 4 πRS2σTS4
= 3.84 × 10 26 Watts
where RS = 6.955 x 108 m and TS = 5778 K.
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o  At 1AU, the Earth receives FS = 4πRS2σTS4 /4 πd 2
= 1366
Watts m-2 (the “Solar Constant)
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.
Planet
A
Earth
0.37
Moon
0.12
Venus
0.65
Jupiter
0.52
Pluto
0.3
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Atmospheric equilibrium temperature
o  So, a planet of radius RP will absorb:
Pabs = Fsun × πRP2 × (1 − A)
Watts
where A is the planetary albedo which accounts for radiation reflected by clouds,
etc. Therefore
€
Pabs
4 πRs2σTS4
=
× πRP2 × (1 − A)
2
4 πd
Watts Eqn. 1
o  Assuming planet is blackbody will radiate energy back into space at
€
Pemitt = 4 π RP2 εσ TP4
Watts
Eqn. 2
where e is emissivity. Accounts for fact that planets not perfect blackbodies.
o  In equilibrium, Eqn. 1 = 2.
$ RS2 (1 − A) '1/ 4
TP = TS &
)
2
% 4ε d (
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Atmospheric equilibrium temperature
o  Substituting for constants,
1000
1/4
TP = 279d −1/2 (1− A)
A=0
Venus
(runaway "greenhouse effect")
A = 0.9
where d is in AU. For Earth, T = 248 K
and for Moon, T = 269 K
Moon
Earth
Mars
Perfect blackbody
Jupiter
o  Observed temperatures are: Earth T = 288
K and Moon T = 252 K
Saturn
slow rotation
+
no atmosphere
Temperature (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.
Mercury
100
Uranus
Neptune
Pluto
2 1/4
Tplanet = 278 { (1 - A) / ε d(au) }
A = albedo, ε = emissivity = 1
10
0.1
1
10
Distance (AU)
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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
1/4
" (1− A) %
=> TP = 279 $
2 '
2
d
#
&
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).
% RS2 (1 − A)sin(θ ) (1/ 4
TP (θ ) = TS '
*
εd 2
&
)
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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
$ (1 − A) '1/ 4
TP = TG + 278 &
2 )
ε
d
%
(
where TG = 36 K
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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.
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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
low incidence of flares/CMEs.
http://www.cfa.harvard.edu/news/2015-04
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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:
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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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.
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Atmospheric retention
o  Energy of a molecule in atmosphere can be written:
GMm
=0
r
o  A particle will escape from planet if has enough KE. Escape speed v = vesc, needed
to escape from r = R is therefore:
E total = E k + E p = 1/2mv 2 −
€
v esc =
2GM
R
2
o  From kinetic theory, 1/2mv therm = 3/2kT therefore,
€
3kT
v therm =
m
€
o  Lightest particles (H and He) have highest speeds and escape preferentially if T is
large enough for particles
€ to have vtherm > vesc.
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Atmospheric retention
o 
A planet will retain its atmosphere if v therm < v esc
Escape
o 
The escape condition occurs when
Exosphere
€
3kT
2GM
=
m
R
2GMm
=> Tesc =
3kR
o 
Atmosphere
Random collisions
Ground
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
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Atmospheric retention
o  For a given molecule to be retained:
2GM
>
R
3kT
3kTR
=> m >
m
2GM
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.
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Atmospheric retention
o 
o 
As vtherm ~ m-1/2 and ~T1/2, light gases have higher
speeds and hot gases have higher speeds.
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.
Oxygen
Helium
Hydrogen
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Atmospheric retention
Retention of Atmospheric Gases
100
o  Escape velocity:
v esc =
2GM
R
Jupiter
Hydrogen
Neptune
Saturn
Helium
Uranus
Earth
o  Thermal velocity: v
therm =
€
Venus
10
3kT
m
H2O
N2
Mars
Triton
o  Consequences:
CO2
Mercury
Titan
Xe
Moon
Velocity (km/s)
o  Light€elements escape more easily.
o  Hot planets “burn off” their atmosphere.
o  Small planets cannot hold onto atmosphere.
1
Pluto
Ceres
Vesta
Pallas
NB: lines show ten times
mean molecular speeds
Planets
Galilean moons
Triton and Titan
Minor Planets
0.1
100
1000
Temperature (K)
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Jeans Escape
o  The velocity of molecules of mass m have a Maxwellian distribution of velocities:
f (v) = 4Nπ
−1/ 2
$ m ' 3 / 2 2 −mv 2 / 2kT
&
) ve
% 2kT (
where N is number of molecules per unit volume.
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o  In high-velocity tail, there are velocities
greater than the gravitational escape velocity.
vesc
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.
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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
∞
< v e >=
∫
∫
ve −mv
ve
∞
0
e
2
/ 2kT
−mv 2 / 2kT
4 πv 2 dv
2
4 πv dv
Eqn. 1
o  Setting λ = mv2/2kT =>v = (2kTλ/m)1/2 and dv = ½ (2kTλ/m)-1/2 2kT / m dλ
€
1/ 2
o  Substituting for v and dv in Eqn. 1, gives < v >= "$ 2kT %'
e
# m &
∞
∫ λe
∫ λ e
−λ
dλ
λ esc
∞ 1/ 2 − λ
0
Eqn. 2
dλ
o  The denominator is a standard integral
∞ 1/ 2 − λ
∫ €λ
0
e dλ = π 1/ 2 /2
o  Integrating by parts, the numerator can be written
€
∫
∞
λe − λ dλ = (1+ λesc )e − λ esc
λ esc
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Jeans Escape
# 2kT &1/ 2
< v e >= 2%
( (1+ λesc )e − λ esc
$ πm '
o 
Eqn. 2 can then be written
o 
The Jean escape flux (in molecules m-2 s-1) can finally be written:
€
ΦJ =
=
1
N < ve >
4 ex
1
N ex v 0 (1+ λesc )e − λ esc
2 π
where v0 = (2kT/m)1/2 is the most probable velocity and λesc is the escape parameter, given by
€
o 
λesc =
GMm /Rex GMm
=
1/2mv 02
kTRexo
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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Escape timescale
o  The escape timescale can then be estimated by
taking the ratio of the density (neHe) to the
flux:
τ e = v π e λ /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.
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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.
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