EART160 Planetary Sciences

Francis Nimmo

Last Week• Planetary mass and radius give us bulk density• Bulk density depends on both composition and size • Larger planets have greater bulk densities because

materials get denser at high pressures• The increase in density of a material is controlled by

its bulk modulus• Planets start out hot (due to accretion) and cool• Cooling is accomplished (usually) by either

conduction or convection• Vigour of convection is controlled by the Rayleigh

number, and increases as viscosity decreases• Viscosity is temperature-dependent, so planetary

temperatures tend to be self-regulating

Talk tomorrow• 4pm in NS101

• Matija Cuk, The lunar cataclysm

This Week - Atmospheres• What determines the surface temperature of a planet?• What determines the temperature and pressure

structure of planetary atmospheres?• What are the atmospheres made of, and where do

they come from?• What determines the wind strengths?• How do planetary atmospheres evolve?

Surface Temperature (1)

22)1( rr

EinEFRAE 2 44radE R T

4/12

4

)1(

AF

r

rT EE

eq

• What determines a planet’s surface temperature?

Incident energy

Reflectedenergy Energy re-radiated

from warm surface

Absorbed energywarms surface

Sun

• Balancing energy in and energy out gives:

R

A is albedo, FE is solar flux at Earth’s surface, rE is distance of Earth to Sun, r is distance of planet to Sun, is emissivity, is Stefan’s constant (5.67x10-8 Wm-2K-4)

Surface Temperature (2)• Solar constant FE=1300 Wm-2

• Earth (Bond) albedo A=0.29, =0.9• Equilibrium temperature = 263 K• How reasonable is this value?

• How to explain the discrepancies?• Has the Sun’s energy stayed constant with time?

4/12

4

)1(

AF

r

rT EE

eq

Body Mercury Venus Earth Mars

A 0.12 0.75 0.29 0.16

Teq 446 238 263 216

Actual T 100-725 733 288 222

is Stefan’s constant5.67x10-8 in SI units

Greenhouse effect• Atmosphere is more or less transparent to radiation

(photons) depending on wavelength – opacity• Opacity is low at visible wavelengths, high at infra-red

wavelengths due to absorbers like water vapour, CO2

• Incoming light (visible) passes through atmosphere with little absorption

• Outgoing light is infra-red (surface temperature is lower) and is absorbed by atmosphere

• So atmosphere heats up• Venus suffered from a runaway greenhouse effect –

surface temperature got so high that carbonates in the crust dissociated to CO2 . . .

Albedo effects• Fraction of energy reflected (not absorbed) by surface

is given by the albedo A (0<A<1)• Coal dust has a low albedo, ice a high one• The albedo can have an important effect on surface

temperature• E.g. ice caps grow, albedo increases, more heat is

reflected, surface temperature drops, ice caps grow further . . . runaway effect!

• This mechanism is thought to have led to the Proterozoic Snowball Earth

• How did the Snowball disappear?• How did life survive?• How might clouds affect planetary albedo?

Atmospheric Structure (1)• Atmosphere is hydrostatic:• Gas law gives us:

• Combining these two (and neglecting latent heat):

)()( zgzdzdP

RT

gP

dz

dP

Here R is the gas constant, is the mass of one mole, and RT/gis the scale height of the (isothermal) atmosphere (~10 km) which tells you how rapidly pressure increases with depth

RT

P

• Result is that pressure decreases exponentially as a function of height (if the temperature stays constant)

Scale Heights• The scale height tells you how far upwards the

atmosphere extends• Scale height H = RT/g. Does this make physical sense?

• Total column mass (per unit area) = 0H=P0/g (where’s this from?)

• It turns out that most planets have similar scale heights:

Venus Earth Mars Jupiter Saturn Uranus Neptune

Tsurf (K) 733 288 215 165* 135* 76* 72*

Albedo 0.75 0.29 0.16 0.34 0.34 0.29 0.31

H (km) 16 8.5 18 18 35 20 19

* Temperature measured at 1bar pressure

Atmospheric Structure (2)• Of course, temperature actually does vary with height• If a packet of gas rises rapidly (adiabatic), then it will

expand and, as a result, cool• Work done in expanding = work done in cooling

pC dT

pdzdT

C

g

VdP dP

• Combining these two equations with hydrostatic equilibrium, we get the dry adiabatic lapse rate:

Cp is the specific heat capacityof the gas at constant pressure

is the mass of one mole, isthe density of the gas

• On Earth, the lapse rate is about 10 K/km• What happens if the air is wet?

Atmospheric Structure (3)

Temperature (schematic)

tropopause

troposphere

stratosphere

mesosphereradiation

adiabat

clouds

Measured Martian temperature profiles

Lapse rateappx. 1.6 K/km – why?

• Lower atmosphere (opaque) is dominantly heated from below and will be conductive or convective (adiabatic)

• Upper atmosphere intercepts solar radiation and re-radiates it

• There will be a temperature minimum where radiative cooling is most efficient (the tropopause)

Giant planet atmospheric structure

• Note position and order of cloud decks

Atmospheric dynamics• Coriolis effect – objects moving on a

rotating planet get deflected (e.g. cyclones)• Why? Angular momentum – as an object

moves further away from the pole, r increases, so to conserve angular momentum decreases (it moves backwards relative to the rotation rate)

• Coriolis acceleration = 2v sin()• How important is the Coriolis effect?

is latitude

v

L sin2 is a measure of its importance (Rossby number)

e.g. Jupiter v~100 m/s, L~10,000km we get ~30 so important

Deflection to rightin N hemisphere

Hadley Cells• Coriolis effect is complicated by fact that parcels of

atmosphere rise and fall due to buoyancy (equator is hotter than the poles)High altitude winds

Surface winds • The result is that the atmosphere is broken up into several Hadley cells (see diagram)

• How many cells depends on the Rossby number (i.e. rotation rate)

Slow rotator e.g. Venus Medium rotator e.g. Earth Fast rotator e.g. Jupiter

Ro~30Ro~4Ro~0.02(assumes v=100 m/s)

Zonal Winds

• The reason Jupiter, Saturn, Uranus and Neptune have bands is because of rapid rotations (periods ~ 10 hrs)

• The winds in each band can be measured by following individual objects (e.g. clouds)

• Winds alternate between prograde (eastwards) and retrograde (westwards)

Geostrophic balance• In some situations, the only significant forces acting are

due to the Coriolis effect and due to pressure gradients

• The acceleration due to pressure gradients is

• The Coriolis acceleration is 2 v sin(Which direction?)

• In steady-state these balance, giving:

x

P

1

Why?

x

Pv

sin2

1

Does this make sense?

• The result is that winds flow along isobars and will form cyclones or anti-cyclones

• What are wind speeds on Earth?

L L

Hisobars

pressure

Coriolis

wind

Where do planetary atmospheres come from?

• Three primary sources– Primordial (solar nebula)– Outgassing (trapped gases)– Later delivery (mostly comets)

• How can we distinguish these?– Solar nebula composition well known– Noble gases are useful because they don’t react– Isotopic ratios are useful because they may

indicate gas loss or source regions (e.g. D/H)– 40Ar (40K decay product) is a tracer of outgassing

Atmospheric Compositions

Isotopes are useful for inferring outgassing and atmos. loss

Earth Venus Mars TitanPressure 1 bar 92 bar 0.006 bar 1.5 barN2 77% 3.5% 2.7% 98.4%

O2 21% - - -

H2O 1% 0.01% 0.006% -

Ar 0.93% 0.007% 1.6% 0.004%

CO2 0.035% 96% 95% ~1ppb

CH4 1.7ppm - ? 1.6%40Ar 6.6x1016 kg 1.4x1016 kg 4.5x1014 kg 3.5x1014 kg

H/D 3000 63 1100 360014N/15N 272 273 170 183

Not primordial!• Terrestrial planet atmospheres are not primordial

(How do we know?)• Why not?

– Gas loss (due to impacts, rock reactions or Jeans escape)

– Chemical processing (e.g. photolysis, rock reactions)

– Later additions (e.g. comets, asteroids)

• Giant planet atmospheres are close to primordial:

Solar Jupiter Saturn Uranus Neptune

H2 84 86.4 97 83 79

He 16 13.6 3 15 18

CH4 0.07 0.2 0.2 2 3

Valuesare by number of molecules

Why is the H/He ratio not constant?

Atmospheric Loss• Atmospheres can lose atoms from stratosphere,

especially low-mass ones, because they exceed the escape velocity (Jeans escape)

• Escape velocity ve= (2 g R)1/2 (where’s this from?)• Mean molecular velocity vm= (2kT/m)1/2

• Boltzmann distribution – negligible numbers of atoms with velocities > 3 x vm

• Molecular hydrogen, 900 K, 3 x vm= 11.8 km/s• Jupiter ve=60 km/s, Earth ve=11 km/s• H cannot escape gas giants like Jupiter, but is easily

lost from lower-mass bodies like Earth or Mars• A consequence of Jeans escape is isotopic fractionation

– heavier isotopes will be preferentially enriched

Atmospheric Evolution• Earth atmosphere originally CO2-rich, oxygen-free

• How do we know?

• CO2 was progressively transferred into rocks by the Urey reaction (takes place in presence of water):

3 2 3 2MgSiO CO MgCO SiO • Rise of oxygen began ~2 Gyr ago (photosynthesis &

photodissociation)• Venus never underwent similar evolution because no

free water present (greenhouse effect, too hot)

• Venus and Earth have ~ same total CO2 abundance

• Urey reaction may have occurred on Mars (water present early on), but very little carbonate detected

Summary• Surface temperature depends on solar distance,

albedo, atmosphere (greenhouse effect)• Scale height and lapse rate are controlled by bulk

properties of atmosphere (and gravity)• Terrestrial planetary atmospheres are not primordial –

affected by loss and outgassing• Coriolis effect organizes circulation into “cells” and

is responsible for bands seen on giant planets• Isotopic fractionation is a good signal of atmospheric

loss due to Jeans escape• Significant volatile quantities may be present in the

interiors of terrestrial planets

Key Concepts• Albedo and opacity• Greenhouse effect• Snowball Earth• Scale height• Lapse rate• Tropopause• Coriolis effect• Hadley cell• Geostrophic balance• Jeans escape• Urey reaction• Outgassing

H = RT/g

2 v sin()

Thermal tides• These are winds which can blow from the hot (sunlit)

to the cold (shadowed) side of a planet

Extrasolar planet (“hot Jupiter”)

Solar energy added =

Atmospheric heat capacity =Where’s this from?

So the temp. change relative to background temperature

t=rotation period, R=planet radius, r=distance (AU)

Small for Venus (0.4%), large for Mars (38%)

tr

FAR E

22 )1(

4R2CpP/g

trPTC

gFA

T

T

p

E24

)1(