 Cococubed.com Thermal Escape

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Contact: F.X.Timmes
my one page vitae,
full vitae,
research statement, and
teaching statement.

Given a planet's mass ${\rm M}$, radius ${\rm R}$, and the height of its exosphere ${\rm h}$ at temperature ${\rm T}$, the thermal escape timescale $\tau_{\rm escape}$ for an atom/molecule of mass ${\rm m}$ can be estimated from $${\rm \tau_{escape} = \dfrac{H}{v_{jeans}} } \label{eq1} \tag{1}$$ where the scale height ${\rm H}$ and acceleration due to gravity ${\rm g}$ are $${\rm H =\dfrac{k \ T}{m \ g} } \qquad \qquad {\rm g = \dfrac{G \ M} {(R + h)^2} } \label{eq2} \tag{2}$$ and the Jeans speed ${\rm v_{Jeans}}$ is $${\rm v_{jeans} = v_{{\rm peak}} \dfrac{(1+ \lambda) \ e^{-\lambda}}{\sqrt{4 \pi}} } \ . \label{eq3} \tag{3}$$ The peak speed ${\rm v_{peak}}$, escape speed ${\rm v_{escape}}$, and their ratio $\lambda$ are $${\rm v_{peak} = \sqrt{\dfrac{2 k T}{m}} } \qquad \qquad {\rm v_{escape} = \sqrt {\dfrac{2 G M}{R + h}} } \qquad \qquad {\rm \lambda = \left ( \dfrac{ v_{escape}}{v_{peak}} \right )^2 } \label{eq4} \tag{4}$$
The tool contained in public_jeans_escape.tbz implements these simple analytic formulas along with comparing their results to numerical integrations of the Maxwell-Boltzmann distribution. Here are the speed distributions for hydrogen helium, carbon, nitrogen, and oxygen for Earth's exosphere and their associated thermal escape timescales.

Please cite the relevant references if you publish a piece of work that use these codes, pieces of these codes, or modified versions of them. Offer co-authorship as appropriate.