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) 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 )

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 A T eq Actual T  is Stefan’s constant 5.67x10 -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, 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...

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) 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) 

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=P 0 /(  0 g) (where’s this from?) It turns out that most planets have similar scale heights: VenusEarthMarsJupiterSaturnUranusNeptune T surf (K) *135*76*72* Albedo H (km) * 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  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 m is the mass,  is the 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? mC p dT VdP= (m/  )dP

Atmospheric Structure (3) adiabat 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) Chemistry can affect temperature structure. Uppermost atmospheric layer: the thermosphere – temperature increases due to short wavelength solar radiation – little total energy though Chemistry affects temperature Stable 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 = 2  v sin(  ) How important is the Coriolis effect?  is latitude, v particle velocity,  planet rotational elocity 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 right in 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~30 Ro~4 Ro~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: 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? High Low isobars 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) – 40 Ar ( 40 K decay product) is a tracer of outgassing

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 %96%95%~1ppb CH 4 1.7ppm-?1.6% 40 Ar6.6x10 16 kg1.4x10 16 kg4.5x10 14 kg3.5x10 14 kg H/D N/ 15 N

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 H2H He CH Values are 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 v e = (2 g R) 1/2 (where’s this from?) Mean molecular velocity v m = (2kT/m) 1/2 (equipartition) Boltzmann distribution – small numbers of atoms with velocities > 3 x v m

Atmospheric Loss Atmospheres can lose atoms from thermosphere, 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 (equipartition) Boltzmann distribution – small 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, 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, 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 CO 2 -rich, oxygen-free. Nitrogen was released by volcanism, and primordial H 2 was lost by escape. 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) 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 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%) 4  R 2 C p P/g