The impact of stripped cores on the frequency of Earth-size planets in the habitable zone

The frequency of Earth-size planets in the habitable zone of Sun-like stars, hereafter $\eta_\oplus$, is a key parameter to evaluate the yield of nearby Earth analogues that can be detected and characterized by future missions. Yet, this value is poorly constrained as there are no reliable exoplanet candidates in the habitable zone of Sun-like stars in the Kepler field. Here, we show that extrapolations relying on the population of small ($< 1.8\,R_\oplus$) short-period ($< 25\,$days) planets bias $\eta_\oplus$ to large values. As the radius distribution at short orbital periods is strongly affected by atmospheric loss, we re-evaluate $\eta_\oplus$ using exoplanets at larger separations. We find that $\eta_\oplus$ drops considerably, to values of only $\sim 5-10$%. Observations of young ($< 100$ Myr) clusters can probe short-period sub-Neptunes that still retain most of their envelope mass. As such, they can be used to quantify the contamination of sub-Neptunes to the population of Kepler short-period small planets and aid in more reliable estimates of $\eta_\oplus$.