EART160 Planetary Sciences

Logistics• HW 4 due Today • Mid-term on Tuesday

– Mix of qualitative and quantitative problems– Equation “cheat sheet” will be given to you– Covers material on HWs 1-4, and up to slide 7 of

Atmospheres lecture.– Study advice: review all lecture slides, HWs, and major

in-class derivations.

• First draft of paper: Now due Tues. Nov. 7 by 5 pm.

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

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

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r

rT EE

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• 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

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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

Lunar subsurface temperatures

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 (assuming isothermal structure)

)()( zgzdzdP

RT

gzP

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?

• Also, H=P0/(0g) (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• Why does the atmosphere get heated?

– Near-surface

– High atmosphere heating due to ozone - stratosphere

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

expand and, as a result, cool, and fall again (stable).– If a tiny amount of energy is input initially, it can keep rising.

• Work done in expanding = energy lost to cooling

pdzdT

C

g

• 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

m is the mass, isthe density of the gas

• Earth’s lapse rate? What is the temp out side an airplane?• What happens if the air is wet? What about latent heat?

mCpdTVdP= (m/)dP

Atmospheric Structure (3)

adiabat

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)

• Chemistry can affect temperature structure.

• Uppermost atmospheric layer: the thermosphere – temperature increases due to short wavelength solar radiation – little total energy though

Chemistry affects temperatureStable against convection

Giant planet atmospheric structure

• Note position and order of cloud decks

Venus

Does the Moon have an atmosphere?

Ballistic Regime: Exospheres

What causes sodium to be released from the surface?

Atmosphere Color

• Why is the sky blue?

Atmosphere Color• Why is the sky blue?

• Rayleigh scattering by particles smaller than the wavelength of the incoming light.

Atmosphere Color

• What color do we predict for Mars?

Atmosphere Color

One of the first photos from Viking 1,1976.

• What color do we predict for Mars?

• Predict dark blue due to effect of some scattering + blackness of space

• In reality, dust dominates. The Viking photo was overcorrected, the

above photo was taken by the rover Spirit.

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 particle velocity, planet rotational elocity

v

L sin2 is a measure of its importance, L is the length scale of interest (inverse 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 and the 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)

First look at side view

On Earth

Surface flows converge.

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?

High High

Lowisobars

pressure

wind Coriolis

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

Atmospheric Loss• Atmospheres can lose atoms from thermosphere,

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 (equipartition)

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

Atmospheric Loss• Atmospheres can lose atoms from thermosphere,

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 (equipartition)

• Boltzmann distribution – small 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, Moon = 2.4 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

Isotopic fractionation. Comet contribution to Earth’s atmosphere/water?

Some water?

High rel. H

Jupiter H/D ratio

• Jupiter H/D ratio measured by the Galileo probe: 40,000 +/- 10,000.

• Earth: 3600

• Venus: 63

Galileo probe, 1995.47 km/s entry speed.230 g’s.Parachute deployed, 58 min of data.

Magnetic fields• The solar wind is a plamsa flowing from

the sun.– Can help strip away a mid-size planet’s

atmosphere. (Venus?)

• Global magnetic field offers some protection.

• Did Mars lose its atmosphere when it lost its dynamo, and thereby its surface water?

• MAVEN mission and the history of water on Mars.

MAVEN carries ion detectors and a UV

spectrometer to measure the atmospheric properties of Mars and its interaction

with the sun and solar wind.

Launch: Nov. 2013

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

• Nitrogen was released by volcanism, and primordial H2 was lost by escape.

• 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)

• Venus never underwent similar evolution because no free water present (greenhouse effect, too hot)

• Venus and Earth have ~ same total CO2 abundance

• Urey reaction probably occurred on Mars (water present early on), small carbonate deposits detected

Mars Carbonates• Why so hard to find?

– Small outcrops?– Dust contamination?

Spirit rover image. Comanche contains carbonate.

Mars reconnaissance orbiter images of Nili Fossae.

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%)

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