Deuterium Escape on Photoevaporating Sub-Neptunes

We investigate the evolution of the deuterium-to-hydrogen (D/H) mass ratio driven by EUV photoevaporation of hydrogen-rich atmospheres of close-in sub-Neptunes around solar-type stars. For the first time, the diffusion-limited approach in conjunction with energy-limited photoevaporation is considered in evaluating deuterium escape from evolving exoplanet H/He envelopes. We find that the planets with smaller initial gas envelopes and thus smaller sizes can lead to weaker atmospheric escape, which facilitates hydrogen-deuterium fractionation. Specifically, in our grid of simulations with a low envelope mass fraction less than 0.005, a low-mass sub-Neptune (4-$5M_\oplus$) at about 0.25-0.4 au or a high-mass sub-Neptune (10-$15M_\oplus$) at about 0.1-0.25 au can increase the D/H values by greater than 20% over 7.5 Gyr. Akin to the helium-enhanced envelopes of sub-Neptunes due to photoevaporating escape, the planets along the upper boundary of the radius valley are the best targets to detect high D/H ratios. The ratio can rise by a factor of $\lesssim$ 1.65 within 7.5 Gyrs in our grid of evolutionary calculations. The D/H ratio is expected to be higher in thinner envelopes as long as the planets do not become bare rocky cores.