The sub-Neptune desert and its dependence on stellar type: Controlled by lifetime X-ray irradiation

Short-period sub-Neptunes with substantial volatile envelopes are among the most common type of known exoplanets. However, recent studies of the Kepler population have suggested a dearth of sub-Neptunes on highly irradiated orbits, where they are vulnerable to atmospheric photoevaporation. Physically, we expect this "photoevaporation desert" to depend on the total lifetime X-ray and extreme ultraviolet flux, the main drivers of atmospheric escape. In this work, we study the demographics of sub-Neptunes as a function of lifetime exposure to high energy radiation and host star mass. We find that for a given present day insolation, planets orbiting a 0.3 $M_{sun}$ star experience $\sim$100 $\times$ more X-ray flux over their lifetimes versus a 1.2 $M_{sun}$ star. Defining the photoevaporation desert as a region consistent with zero occurrence at 2 $\sigma$, the onset of the desert happens for integrated X-ray fluxes greater than 1.43 $\times 10^{22}$ erg/cm$^2$ to 8.23 $\times 10^{20}$ erg/cm$^2$ as a function of planetary radii for 1.8 -- 4 $R_{\oplus}$. We also compare the location of the photoevaporation desert for different stellar types. We find much greater variability in the desert onset in bolometric flux space compared to integrated X-ray flux space, suggestive of photoevaporation driven by steady state stellar X-ray emissions as the dominant control on desert location. Finally, we report tentative evidence for the sub-Neptune valley, first seen around Sun-like stars, for M & K dwarfs. The discovery of additional planets around low-mass stars from surveys such as the TESS mission will enable detailed exploration of these trends.