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. Surface Temperature (1) What determines a planet’s surface temperature? Incident energy Reflected energy Energy re-radiated from warm surface Absorbed energy warms surface Sun Balancing energy in and energy out gives:  R A is albedo, F E is solar flux at Earth’s surface, r E is distance of Earth to Sun, r is distance of planet to Sun,  is emissivity,  is Stefan’s constant (5.67x10 -8 Wm -2 K -4 )

6. Surface Temperature (2) Solar constant F E =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? BodyMercuryVenusEarthMars A0.120.750.290.16 T eq 446238263216 Actual T100-725733288222  is Stefan’s constant 5.67x10 -8 in SI units

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, CO 2 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 CO 2...

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. Atmospheric Structure (1) Atmosphere is hydrostatic: Gas law gives us: Combining these two (and neglecting latent heat): Here R is the gas constant,  is the mass of one mole, and RT/g  is 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/g . Does this make physical sense? Total column mass (per unit area) =  0 H=P 0 /g (where’s this from?) It turns out that most planets have similar scale heights: VenusEarthMarsJupiterSaturnUranusNeptune T surf (K) 733288215165*135*76*72* Albedo 0.750.290.160.34 0.290.31 H (km) 168.518 352019 * Temperature measured at 1bar pressure

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

12. Atmospheric Structure (3) Temperature (schematic) tropopause troposphere stratosphere mesosphere radiation adiabat clouds Measured Martian temperature profiles Lapse rate appx. 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)

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  decreases (it moves backwards relative to the rotation rate) Coriolis acceleration = 2  v sin(  ) How important is the Coriolis effect?  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 Deflection to right in N hemisphere

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

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  v sin  (Which direction?) In steady-state these balance, giving: Why? 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 H isobars pressure Coriolis wind

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) – 40 Ar ( 40 K decay product) is a tracer of outgassing

19. Atmospheric Compositions Isotopes are useful for inferring outgassing and atmos. loss EarthVenusMarsTitan Pressure1 bar92 bar0.006 bar 1.5 bar N2N2 77%3.5%2.7%98.4% O2O2 21%--- H2OH2O1%0.01%0.006%- Ar0.93%0.007%1.6%0.004% CO 2 0.035%96%95%~1ppb CH 4 1.7ppm-?1.6% 40 Ar6.6x10 16 kg1.4x10 16 kg4.5x10 14 kg3.5x10 14 kg H/D30006311003600 14 N/ 15 N272273170183

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: SolarJupiterSaturnUranusNeptune H2H2 8486.4978379 He1613.631518 CH 4 0.070.2 23 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 v e = (2 g R) 1/2 (where’s this from?) Mean molecular velocity v m = (2kT/m) 1/2 Boltzmann distribution – negligible numbers of atoms with velocities > 3 x v m Molecular hydrogen, 900 K, 3 x v m = 11.8 km/s Jupiter v e =60 km/s, Earth v e =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 CO 2 -rich, oxygen-free How do we know? CO 2 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 CO 2 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/g  2  v sin(  )

26. 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%) 4  R 2 C p P/g