In Jean

1
Hydrodynamic Escape from Planetary Atmospheres

• In Jeans escape, particles at the exobase moving
  in the outward direction with sufficient velocity
  (i.e. high enough kinetic energy) can escape from
  the planettypically the vertical flow from the
  atmosphere is small
• HDE arises when the flow speed becomes large

2

• HDE also differs from gas-kinetic evaporation in
  that in some circumstances a substantial fraction
  of the entire thermospheric energy budget is used
  to power escape of gas from the atmosphere it is
  possible that heavier species can be dragged
  along during HDE
• Under this circumstance, it is expected that
  atmospheric expansion due to HDE will be the
  dominant loss process

3

• HDE is an important process in atmospheric
  evolution of the terrestrial planets and CEGPs
  and can change the composition of planetary
  atmospheres from primordial values irreversibly
• hydrogen escape is of particular importance as it
  affects the oxidation state of the atmosphere and
  because it results in the loss of water vapour

4
For Instance(outstanding problems)

• Did early Venus initially have an ocean? HDE
  modelling using a water-rich atmosphere on Venus
  can help assess this problem (Kasting and
  Pollack, 1983)
• Isotopic ratios (i.e. fractionation D/H, N, and
  noble gases) are very different on terrestrial
  planets even though they are believed to be
  formed from similar material (Hunten et al.,
  1987 Pepin, 1991)

5
and

• Greenhouse warming by methane in the atmosphere
  of the early Earth? CH4 density on early Earth
  dependent on HDE, strongly influencing its
  atmospheric climate and composition, i.e. (Pavlov
  et al., 2000 2001)
• blow-off on HD209458b (Osiris) (Vidal-Madjar et
  al., 2003 2004)

6
HD Escape Equations
7
Some Previous Models

• Watson et al. (1981) shooting method or
  trial-and-error method to solve steady state HDE
  equation for early Earth and Venus
• Set of solutions at the critical point (exobase)
  selected which can match the zero temperature at
  infinity and set temperature at the lower
  boundary.
• Calculated temperature and density at the
  boundary very sensitive to initial settings and I
  couldnt reproduce cases using that method

8

• Kasting and Pollack (1983) numerically solve the
  steady state HDE problem for Venus
• Use an iterative method in which the momentum and
  energy equations are simultaneously solved
• Not able to get an exact soln at the critical
  point obtaining the supersonic solution
• Instead, they obtained subsonic solutions and
  argued that the escape flux can be close to the
  critical escape flux
• Method included infrared cooling by H2O and CO2
  while only EUV absorption considered by Watson

9

• Chassefiere (1996) solves steady state HDE
  problem from lower boundary to exobase level
• Position of exobase level is determined when the
  mean free path becomes greater than the scale
  height
• Outgoing flow at exobase is set to be equivalent
  to a modified Jeans escape (ionization and
  interaction between escaping particles and solar
  wind considered)
• Application to water-rich early Cytherian
  atmosphere

10

• Using the equations 1, 2, and 3 with B.C.s etc,
  the HD equations can be solved using 1st order
  Lax-Friedriechs scheme, Godunov method, or Finite
  Difference scheme since these are linear
  advection equations (hyperbolic)