  Understanding atmospheric escape in close-in exoplanets is critical to
interpreting their evolution. We map out the parameter space over which
photoevaporation and core-powered mass loss dominate atmospheric escape.
Generally, the transition between the two regimes is determined by the location
of the Bondi radius (i.e. the sonic point of core-powered outflow) relative to
the penetration depth of XUV photons. Photoevaporation dominates the loss when
the XUV penetration depth lies inside the Bondi radius ($R_{XUV}<R_B$) and
core-powered mass-loss when XUV radiation is absorbed higher up in the flow
($R_B<R_{XUV}$). The transition between the two regimes occurs at a roughly
constant ratio of the planet's radius to its Bondi radius, with the exact value
depending logarithmically on planetary and stellar properties. In general,
core-powered mass-loss dominates for lower-gravity planets with higher
equilibrium temperatures, and photoevaporation dominates for higher-gravity
planets with lower equilibrium temperatures. However, planets can transition
between these two mass-loss regimes during their evolution, and core-powered
mass loss can ``enhance'' photo-evaporation over a significant region of
parameter space. Interestingly, a planet that is ultimately stripped by
core-powered mass-loss has likely only ever experienced core-powered mass-loss.
In contrast a planet that is ultimately stripped by photoevaporation could have
experienced an early phase of core-powered mass-loss. Applying our results to
the observed super-Earth population suggests that it contains significant
fractions of planets where each mechanism controlled the final removal of the
H/He envelope, although photoevaporation appears to be responsible for the
final carving of the exoplanet radius-valley.
