  Recent observations and analysis of low mass (<10$M_{\oplus}$), exoplanets
have found that rocky planets only have radii up to 1.5-2$R_{\oplus}$. 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$\pm$0.38 (2$\sigma$) $R_{\oplus}$ 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" or "radius gap") in the
1.5-2$R_{\oplus}$ range.
