 Solution

Four mechanisms are Jeans escape, hydrodynamic escape, Roche-lobe overflow and nonthermal atmospheric escape.

Jeans escape is loss from the high-speed tail of a nearly Maxwell-Boltzmann velocity distribution near the exobase. It is sensitive to the escape parameter ${\lambda }_J=G{M}_p\mu m_H/(k_B{T}_{\mathrm{exo}}{R}_{\mathrm{exo}})$ and favors light species in a hot, weakly bound atmosphere.

Hydrodynamic escape occurs when strong XUV heating drives a bulk outflow, which can entrain heavier species. An illustrative energy-limited scale is $\dot{M}\sim \eta \pi R_p^3{F}_{\mathrm{XUV}}/(G{M}_p{K}_{\mathrm{tide}})$ when the absorption and planet radii are comparable; efficiency, radiative losses and recombination can invalidate that simple limit.

Roche-lobe overflow removes gas through the low effective-potential barrier toward the inner Lagrange point when the extended atmosphere approaches the Roche lobe. Tides can also assist a wind before actual overflow.

Nonthermal atmospheric escape includes ion pickup, sputtering, charge exchange and energetic photochemical products. Stellar-wind interactions and photoionization supply particles with escape energies not represented by the local thermal tail. These mechanisms can act together rather than constituting four mutually exclusive evolutionary states.