Hydrodynamic escape

Hydrodynamic escape refers to a thermal atmospheric escape mechanism that can lead to the escape of heavier atoms of a planetary atmosphere through numerous collisions with lighter atoms. Hydrodynamic escape refers to a thermal atmospheric escape mechanism that can lead to the escape of heavier atoms of a planetary atmosphere through numerous collisions with lighter atoms. Hydrodynamic escape occurs if there is a strong thermally driven atmospheric escape of light atoms which, through drag effects (collisions), also drive off heavier atoms. The heaviest species of atom that can be removed in this manner is called the cross-over mass. In order to maintain a significant hydrodynamic escape, a large source of energy at a certain altitude is required. Soft X-ray or extreme ultraviolet radiation, momentum transfer from impacting meteoroids or asteroids, or the heat input from planetary accretion processes may provide the requisite energy for hydrodynamic escape. Estimating the rate of hydrodynamic escape is important in analyzing both the history and current state of a planet's atmosphere. In 1981, Watson et al published calculations that describe energy-limited escape, where all incoming energy is balanced by escape to space. Recent numerical simulations on exoplanets have suggested that this calculation overestimates the hydrodynamic flux by 20 - 100 times. However, as an special case and upper limit approximation on the atmospheric escape, it is worth noting here. Hydrodynamic escape flux ( Φ {displaystyle Phi } , [m − 2 {displaystyle ^{-2}} s − 1 {displaystyle ^{-1}} ]) in an energy-limited escape can calculated, assuming (1) an atmosphere composed of non-viscous, (2) constant molecular weight gas, with (3) isotropic pressure, (4) fixed temperature, (5) perfect XUV absorption, and that (6) pressure decreases to zero as distance from the planet increases. Φ = F X U V R p R X U V 2 G M p {displaystyle Phi ={frac {F_{XUV}R_{p}R_{XUV}^{2}}{GM_{p}}}} where F X U V {displaystyle F_{XUV}} is the photon flux [J m − 2 {displaystyle ^{-2}} s − 1 {displaystyle ^{-1}} ] over the wavelengths of interest, R p {displaystyle R_{p}} is the radius of the planet, G {displaystyle G} is the gravitational constant, M p {displaystyle M_{p}} is the mass of the planet, and R X U V {displaystyle R_{XUV}} is the effective radius where the XUV absorption occurs. Corrections to this model have been proposed over the years to account for the Roche lobe of a planet and efficiency in absorbing photon flux. However, as computational power has improved, increasingly sophisticated models have emerged, incorporating radiative transfer, photochemistry, and hydrodynamics that provide better estimates of hydrodynamic escape. The root mean square thermal velocity ( v t h {displaystyle v_{th}} ) of an atomic species is