wiki:u/adebrech/Matlab/IonizationFront

Version 1 (modified by adebrech, 7 years ago) ( diff )

Velocity at

If everything up to is ionized, there must be a constant flow of neutrals from the center of the planet to be ionized in equilibrium. With a planet profile as in Tripathi et al, the sound speed at any particular point can be calculated and compared to the required outflow velocity.

Planet profile (scaled by values at planet surface)

Assuming that everything up to the theoretical surface is completely ionized, that there is no recombination, and that the ionization front is infinitesimally thin, we can calculate the velocity at the surface required to completely capture the ionizing flux:

where np is the number density at the planet's surface. For Jphot = 2x1013 photons/cm2/s and np = 8x107 /cm3, the required velocity is

.

We can also assume that everything prior to some radius is ionized, and calculate the proportion of the sound speed at that location required to completely replenish the neutral density (and vice-versa, of course). For example, for simulations as of 9/8/17, the velocity required at the steady-state surface is one-fifth the sound speed at that location.

See attached Mathematica notebook.

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