Notes from today's meeting with Jim Kasting

Background

  • Habitable zone limited near by by runaway greenhouse at 1 AU and limited far away by the Maximum CO2-H2O greenhouse effect at 1.8 AU
  • With H2 green house gas you can extend out to 10 AU (3 M_earth with 40 bars of H2 atm)
  • Homopause (turbopause) at 100 km - where turbulent mixing ceases and atmosphere is not well mixed. Transport of hydrogen governed by molecular diffusion
  • Exopause at 500 km - where gas becomes collisionless and fast moving hydrogen particles can escape. Velocity distribution no longer Boltzmann. Rate governed by Jeans evaporation rate.
  • On Earth, exopause is fairly warm - and Jeans evaporation is quick - so H2 loss rate controlled by diffusion through the Homopause
  • On early Mars, the exopause is colder and therefore Jeans evaporation is slower and might have been responsible for regulating H2 loss. Going from 1D to 2D reduced jeans evaporation rate by ~4 which could increase the steady state H2 concentration to the 20% needed to create enough of a green house effect to place early Mars in the habitable zone - and explain the fluvial features on Mars.

Goal

Calculate an upper limit on the escape rate from the Exopause and show that it is lower than the diffusion limit and hopefully consistent with the 20% concentration necessary to explain the fluvial features on Mars

Complexities of the physical model

  • Geometry - Obliquity, magnetic fields,
  • Multi-species
  • Chemistry
  • diffusion
  • non-Lte
  • heating and cooling
  • multi-line
  • collisionless - moment equations from the boltzmann equation

Possible simulations

  • 1D - 2 fluid with most of the physics (apply an approximation to model the moments of the velocity distribution where it becomes collisionless) to demonstrate the h2 loss rate < diffusion limit
    • Evenly spaced in log altitude (not radius)?
    • 3 points per pressure scale height
    • multi-fluid?
    • diffusion
    • line transfer - would need multi-bin line transfer
    • cooling
    • equation of state
  • Redo Stone and Proga in 3D and measure the Jeans evaporation rate.
    • MHD
    • rotation

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