Energy Transport II photo: Francisco Negroni

Convection operates in planetary atmospheres (near surfaces), liquid and molten environments occurs when the temp decreases with height so rapidly that pressure equilibrium not reached … rising blobs of gas/liquid continue to rise if adiabatic lapse rate (dT/dz) followed, then no convection (10 K/km in Earth atm) if superadiabatic conditions, convection occurs (temp gradient steeper than adiabatic) derivation of adiabatic lapse rate begins with assumption of hydrostatic equilibrium, the condition when pressure and gravity forces are balanced: dP/dz = – g(z) ρ(z) variables can be swapped if the equation of state (relates pressure, temp, and density in any material) follows the ideal gas law: P = ρ R T / μ assume first law of thermodynamics (energy conserved) and that no heat is exchanged with surroundings (i.e. the air blob moves adiabatically) dT/dz = – g(z) / c P where c p is the specific heat capacity (erg g -1 K -1 ) at constant pressure

Radiation heat transport by radiation in atmospheres where optical depth not large or small typically upper troposphere and stratosphere (where we fly) PHOTONS interact with ATOMS and MOLECULES observe interaction using spectroscopy

Atomic and Molecular Spectra H2HH2H

Radiation B ν blackbody radiation I ν specific intensity (blackbody is one example) J ν mean intensity (integral of I ν over solid angle / solid angle) Einstein A coeff: probability/time emission occursA ul Einstein B coeff: probability/time event occursB lu J ν (normal absorption) B ul J ν (stimulated emission) Classic Case: “When in thermodynamic equilibrium…” the following are true 1. isotropic blackbody radiation fieldI ν = J ν = B ν 2. absorption rates = emission ratesN l B lu J ν = N u A ul + N u B ul J ν 3. temperature of gas determines number density of atoms in given energy stateN i ~ e – E i /kT

Radiative Transfer I What does “radiative transfer” actually mean?  used when the primary way that energy is transported is via photons!  so, the pressure-temperature profile is determined by the following radiative transfer equation, where dI ν is the change in intensity inside a gas cloud: dI ν / dτ ν = – I ν + S ν where I ν is the incident intensity to the gas parcel, and S ν is the source function (effectively, these are absorption and emission factors) τ is the optical depth, given by τ ν = ∫ α(z) ρ(z) dz in which α(z) is the extinction (absorption + scattering) and ρ(z) is the density Integrating the first equation (assuming S ν does not vary with τ) yields I ν (τ ν ) = S ν + e -τ ν ( I ν,o – S ν )

Radiative Transfer II I ν (τ ν ) = S ν + e -τ ν ( I ν,o – S ν ) Real world considerations…what intensity, I ν, do you see? If τ ν >> 1, then the second term goes away and I ν = S ν so, the emission you receive is determined entirely by the source function, or by the ratio of the emission/absorption in the thick atmosphere If τ ν << 1, then e -τ ν ~ 1, the source function becomes irrelevant, and I ν = I ν,o so, the incident radiation completely defines the radiation you measure from a very thin atmosphere If τ ν ~ 1, then the source function of the atmosphere and the incident intensity battle it out to see which has the most effect on what you see If the gas is non-emitting, S ν = 0 and any incident radiation is attenuated by the optical depth in a (nearly) directly observable way If the gas is in LTE, the source function is a blackbody function, S ν = B ν

What’s it all good for? conduction measurements probe surfaces to various depths in radio for temp variations …what’s it made of? convection measurements atmospheric structure and temperature variations …where are the molecules? photochemical rates of reaction at various levels …where is the chemistry? radiation measurements colors are seen at various wavelengths … what’s in the atmosphere/on surface? temperature profiles with height … where is it raining, and what is it? if T eff ≠ T equil then you know something is fishy…

Planets at Radio Wavelengths JupiterVenus Mercury MarsMoonSaturn

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Reading in Planetary Sciences for Thursday, February 16 Chapter 4

Reality Check Greenhouse effect…does it make sense? Assuming an atmosphere that is in radiative equilibrium and LTE (g = ground) T g 4 = T eff 4 ( τ g ) Implies that Venus has optical depth to ground= 119 Earth has optical depth to ground= 0.6 Mars has optical depth to ground= 0.2

Solar System Explorers Quiz What is the distance from the Sun to the Earth, in kilometers? 1.5 X 10 8 km 2. What is the (annual) parallax of an Oort Cloud member at 0.2 parsecs? 5 arcseconds 3. If the Earth orbited a binary M dwarf system (two Suns with 0.25 M o each) at 1 AU, what would our orbital period be? 1.4 years 4. If Enceladus’ tiger stripes have a temperature of 180 K, at what wavelength do they emit the most photons? 16 microns 5. What is the resolution of a 1m telescope at 0.5 microns? arcseconds

Solar System Explorers Quiz What is the (annual) parallax of an Oort Cloud member at 0.1 parsecs? 10 arcseconds 2. If the Earth orbited a binary M1.0V dwarf system (two Suns with 0.5 M o each) at 4 AU, what would our orbital period be? 8 years 3. If Enceladus’ tiger stripes have a temperature of 180 K, at what wavelength do they emit the most photons? 16 microns 4. List two factors that determine the equilibrium temperature of a planet. solar flux, distance from Sun, orbital eccentricity planet albedo, emissivity, obliquity, rotation rate 5. In hydrostatic equilibrium in a planetary atmosphere, what two forces are balanced? gravity and pressure