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Super-Earths and sub-Neptunes are commonly thought to have accretedhydrogen/helium envelopes, consisting of a few to ten percent of their totalmass, from the primordial gas disk. Subsequently, hydrodynamic escape driven bycore-powered mass-loss and/or photo-evaporation likely stripped much of theseprimordial envelopes from the lower-mass and closer-in planets to form thesuper-Earth population. In this work we show that after undergoing core-poweredmass-loss, some super-Earths can retain small residual H/He envelopes. Thisretention is possible because, for significantly depleted atmospheres, thedensity at the radiative-convective boundary drops sufficiently such that thhecooling time-scale becomes less than the mass-loss time-scale. The residualenvelope is therefore able to contract, terminating further mass loss. Usinganalytic calculations and numerical simulations, we show that the mass ofprimordial H/He envelope retained as a fraction of the planet's total mass,$f_{ret}$, increases with increasing planet mass, $M_{c}$, and decreases withincreasing equilibrium temperature, $T_{eq}$, scaling as $f_{ret} \proptoM_{c}^{3/2} T_{eq}^{-1/2} \exp{[M_{c}^{3/4} T_{eq}^{-1}]}$. $f_{ret}$ variesfrom $< 10^{-8}$ to about $10^{-3}$ for typical super-Earth parameters. Tofirst order, the exact amount of left-over H/He depends on the initial envelopemass, the planet mass, its equilibrium temperature, and the envelope's opacity.These residual hydrogen envelopes reduce the atmosphere's mean molecular weightcompared to a purely secondary atmosphere, a signature observable by currentand future facilities. These remnant atmospheres may, however, in many cases bevulnerable to long-term erosion by photo-evaporation. Any residual hydrogenenvelope likely plays an important role in the long-term physical evolution ofsuper-Earths, including their geology and geochemistry.

To cool is to keep: Residual H/He atmospheres of super-Earths and sub-Neptunes