EART160 Planetary Sciences

1. EART160 Planetary Sciences Francis Nimmo

2. 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

3. Talk tomorrow • 4pm in NS101 • Matija Cuk, The lunar cataclysm

4. 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?

5. a Surface Temperature (1) • What determines a planet’s surface temperature? Reflected energy Incident energy Energy re-radiated from warm surface R Sun Absorbed energy warms surface 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, eis emissivity,sis Stefan’s constant (5.67x10-8 Wm-2K-4) • Balancing energy in and energy out gives:

6. Surface Temperature (2) • Solar constantFE=1300 Wm-2 • Earth (Bond) albedo A=0.29, e=0.9 • Equilibrium temperature = 263 K • How reasonable is this value? s is Stefan’s constant 5.67x10-8 in SI units • How to explain the discrepancies? • Has the Sun’s energy stayed constant with time?

7. 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 . . .

8. 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?

9. a Atmospheric Structure (1) • Atmosphere is hydrostatic: • Gas law gives us: • Combining these two (and neglecting latent heat): Here R is the gas constant, m is the mass of one mole, and RT/gmis the scale height of the (isothermal) atmosphere (~10 km) which tells you how rapidly pressure increases with depth • Result is that pressure decreases exponentially as a function of height (if the temperature stays constant)

10. Scale Heights • The scale height tells you how far upwards the atmosphere extends • Scale height H = RT/gm. Does this make physical sense? • Total column mass (per unit area) = r0H=P0/g (where’s this from?) • It turns out that most planets have similar scale heights: * Temperature measured at 1bar pressure

11. a 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 Cp is the specific heat capacity of the gas at constant pressure m is the mass of one mole, r is the density of the gas • Combining these two equations with hydrostatic equilibrium, we get the dry adiabatic lapse rate: • On Earth, the lapse rate is about 10 K/km • What happens if the air is wet?

12. Atmospheric Structure (3) • 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) radiation Temperature (schematic) mesosphere stratosphere tropopause Lapse rate appx. 1.6 K/km – why? clouds troposphere adiabat Measured Martian temperature profiles

13. Giant planet atmospheric structure • Note position and order of cloud decks

14. 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 w decreases (it moves backwards relative to the rotation rate) • Coriolis acceleration = 2 w v sin(q) • How important is the Coriolis effect? Deflection to right in N hemisphere q is latitude is a measure of its importance (Rossby number) e.g. Jupiter v~100 m/s, L~10,000km we get ~30 so important

15. 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 Fast rotator e.g. Jupiter Medium rotator e.g. Earth Ro~0.02 (assumes v=100 m/s) Ro~4 Ro~30

16. 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)

17. 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 w v sinq(Which direction?) • In steady-state these balance, giving: Why? L Does this make sense? L wind • The result is that winds flow along isobars and will form cyclones or anti-cyclones • What are wind speeds on Earth? pressure Coriolis isobars H

18. 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

19. Atmospheric Compositions Isotopes are useful for inferring outgassing and atmos. loss

20. 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: Values are by number of molecules Why is the H/He ratio not constant?

21. 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

22. 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): • 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

23. 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

24. 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/gm 2 w v sin(q)

26. Thermal tides • These are winds which can blow from the hot (sunlit) to the cold (shadowed) side of a planet Solar energy added = t=rotation period, R=planet radius, r=distance (AU) 4pR2CpP/g Atmospheric heat capacity = Where’s this from? Extrasolar planet (“hot Jupiter”) So the temp. change relative to background temperature Small for Venus (0.4%), large for Mars (38%)