The Maximum Mass-Loss Efficiency for a Photoionization-Driven Isothermal Parker Wind

Observations of present-day mass-loss rates for close-in transiting exoplanets provide a crucial check on models of planetary evolution. One common approach is to model the planetary absorption signal during the transit in lines like He I 10830 with an isothermal Parker wind, but this leads to a degeneracy between the assumed outflow temperature $T_0$ and the mass-loss rate $\dot{M}$ that can span orders of magnitude in $\dot{M}$. In this study, we re-examine the isothermal Parker wind model using an energy-limited framework. We show that in cases where photoionization is the only heat source, there is a physical upper limit to the efficiency parameter $\varepsilon$ corresponding to the maximal amount of heating. This allows us to rule out a subset of winds with high temperatures and large mass-loss rates as they do not generate enough heat to remain self-consistent. To demonstrate the utility of this framework, we consider spectrally unresolved metastable helium observations of HAT-P-11b, WASP-69b, and HAT-P-18b. For the former two planets, we find that only relatively weak ($\dot{M}\lesssim 10^{11.5}$ g s$^{-1}$) outflows can match the metastable helium observations while remaining energetically self-consistent, while for HAT-P-18b all of the Parker wind models matching the helium data are self-consistent. Our results are in good agreement with more detailed self-consistent simulations and constraints from high-resolution transit spectra.