Abstract
Recent observations and analysis of low mass (<10 M (⊕) ), exoplanets have found that rocky planets only have radii up to 1.5-2 R (⊕) . Two general hypotheses exist for the cause of the dichotomy between rocky and gas-enveloped planets (or possible water worlds): either low mass planets do not necessarily form thick atmospheres of a few wt. %, or the thick atmospheres on these planets easily escape driven by x-ray and extreme ultraviolet (XUV) emissions from young parent stars. Here we show that a cutoff between rocky and gas-enveloped planets due to hydrodynamic escape is most likely to occur at a mean radius of 1.76±0.38 (2σ) R (⊕) around Sun-like stars. We examine the limit in rocky planet radii predicted by hydrodynamic escape across a wide range of possible model inputs using 10,000 parameter combinations drawn randomly from plausible parameter ranges. We find a cutoff between rocky and gas-enveloped planets that agrees with the observed cutoff. The large cross-section available for XUV absorption in the extremely distended primitive atmospheres of low mass planets results in complete loss of atmospheres during the ~100 Myr phase of stellar XUV saturation. In contrast, more massive planets have less distended atmospheres and less escape, and so retain thick atmospheres through XUV saturation and then indefinitely as the XUV and escape fluxes drop over time. The agreement between our model and exoplanet data leads us to conclude that hydrodynamic escape plausibly explains the observed upper limit on rocky planet size and few planets (a "valley") in the 1.5-2 R (⊕) range.