In atmospheric science, hydrodynamic escape is a thermal atmospheric escape mechanism that can lead to the escape of heavier atoms of a planetary atmosphere through numerous collisions with lighter atoms, typically hydrogen. This mechanism may explain why some planetary atmospheres are depleted in oxygen, nitrogen, and heavier noble gases, such as xenon.This process can be thought of like planetary winds where solar radiation heats up the upper atmosphere a lot, eventually leading to lighter atoms escaping and creating a flow that helps drag the heavier ones along.
Description Particles in the atmosphere need to achieve sufficiently high velocity (higher than the escape velocity) to escape from the planetary gravity field. There are different ways to achieve this velocity. Those processes in which the high velocity is related to the temperature are called thermal escape. The root mean square thermal velocity (vth) of an atomic species is v t h = 3 k T m {\displaystyle v_{\mathrm {th} }={\sqrt {\frac {3kT}{m}}}}
where k is the Boltzmann constant, T is the temperature, and m is the mass of the species. Lighter molecules or atoms will therefore be moving faster than heavier molecules or atoms at the same temperature. Thus they are easier to escape from planetary gravity field. This is why atomic hydrogen escapes preferentially from an atmosphere. If there is a strong thermally driven atmospheric escape of light atoms, heavier atoms can achieve the escape velocity through viscous drag by those escaping lighter atoms. This is another way of thermal escape, called hydrodynamic escape. 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 (solar EUV heating), momentum transfer from impacting meteoroids or asteroids, or the heat input from planetary accretion processes may provide the requisite energy for hydrodynamic escape. Such conditions may have been reached in H- or He-rich thermospheres heated by the strong extreme ultraviolet radiation flux of the young Sun. Thus hydrodynamic escape is more likely to occur in the early atmosphere of planets.
Hydrodynamic escape flux 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.[30] However, as a special case and upper limit approximation on the atmospheric escape, it is worth noting here. Hydrodynamic escape flux (Φ, [m-2s-1]) in an energy-limited escape can be calculated, assuming (1) an atmosphere composed of non-viscous, (2) constant-molecular-weight gas, with (3) isotropic pressure, (4) fixed temperature, (5) perfect extreme ultraviolet (XUV) absorption, and that (6) pressure decreases to zero as distance from the planet increases. Hydrodynamic escape flux of hydrogen Φ H {\displaystyle \Phi _{H}} can be expressed as:
Φ H = F X U V R p R X U V 2 G M p {\displaystyle \Phi _{H}={\frac {F_{\mathrm {XUV} }R_{p}R_{\mathrm {XUV} }^{2}}{GM_{p}}}}
where (in SI units):
FXUV is the photon flux [J m-2s-1] over the wavelengths of interest, Rp is the radius of the planet [m], G is the gravitational constant [ms-2], Mp is the mass of the planet [kg], RXUV is the effective radius where the XUV absorption occurs [m]. 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. On the other hand, the hydrodynamic escape flux of heavier species Φ i {\displaystyle \Phi _{i}} can be expressed as:
Φ i = ( Φ H − ( m i − m H ) g b ( i , H ) k T ) f i {\displaystyle \Phi _{i}=(\Phi _{H}-{\frac {(m_{i}-m_{H})gb(i,H)}{kT}})f_{i}}
where
… excerpt ends here. Continue reading the full article.
