Understanding what helium absorption tells us about atmospheric escape from exoplanets

Atmospheric escape is now considered the major contributing factor in shaping the demographic of detected exoplanets. However, inferences about the exoplanet populations strongly depend on the accuracy of the models. Direct observational tests of atmospheric models are still in their infancy. Helium escape from planetary atmospheres has rapidly become the primary observational probe, already observed in $\gtrsim$20 exoplanets. Grounding our understanding in the basic physics of atmospheric escape, we present a new theoretical model to predict the excess absorption from the helium absorption line. We constrain the atmosphere properties, such as mass-loss rates and outflow temperatures, by implementing a Parker wind solution with an energy limited evaporating outflow. Importantly, we self-consistently link the mass-loss rates and outflow temperatures, which are critical to understanding helium absorption as the triplet-level population is typically exponentially sensitive to temperature. Furthermore, helium absorption is typically optically thin and the absorption is dominated far from the planet. Therefore, the absorption depth is not a measure of the size of the helium outflow. Our results indicate that for planets with a detectable signal, typically the helium triplet population in the atmosphere rapidly approaches a statistical equilibrium between populations by recombination and depopulation caused by electron collisions. We suggest that excess helium absorption can be quantified by a scaled equivalent width, which is positively correlated with the mass loss rate. We also show that the helium absorption scales with incident radiation, particularly with the XEUV to FUV flux ratios.