  Making use of the publicly available 1D photoionization hydrodynamics code
ATES we set out to investigate the combined effects of planetary gravitational
potential energy ($\phi_p\equiv GM_p/R_p$) and stellar X-ray and Extreme
Ultraviolet (XUV) irradiation ($F_{\rm XUV}$) on the evaporation efficiency
($\eta$) of moderately-to-highly irradiated gaseous planets, from sub-Neptunes
through hot Jupiters. We show that the (known) existence of a threshold
potential above which energy-limited escape (i.e., $\eta\simeq 1$) is
unattainable can be inferred analytically. For $\log \phi_p\gtrsim \log
\phi_p^{\rm thr}\approx [12.9-13.2]$ (in cgs units), most of the energy
absorption occurs where the average kinetic energy acquired by the ions through
photo-electron collisions is insufficient for escape. This causes the
evaporation efficiency to plummet with increasing $\phi_p$,. Whether or not
planets with $\phi_p\lesssim \phi_p^{\rm thr}$ exhibit energy-limited outflows
is regulated primarily by the stellar irradiation level. Specifically, for
low-gravity planets, above $F_{\rm XUV}\simeq 10^{4-5}$ erg cm$^{-2}$s$^{-1}$
Ly$\alpha$ losses overtake adiabatic and advective cooling and the evaporation
efficiency of low-gravity planets drops below the energy-limited approximation,
albeit remaining largely independent of $\phi_p$Further, we show that whereas
$\eta$ increases as $F_{\rm XUV}$ increases for planets above $\phi^{\rm
thr}_p$, the opposite is true for low-gravity planets. This behavior can be
understood by examining the relative fractional contributions of advective and
radiative losses as a function of atmospheric temperature. This novel framework
enables a reliable, physically motivated prediction of the expected evaporation
efficiency for a given planetary system; an analytical approximation of the
best-fitting $\eta$ is given in the appendix.
