Implications of evaporative cooling by H${}_2$ for 1I/`Oumuamua

The first interstellar object observed in our solar system, 1I/Oumuamua, exhibited several peculiar properties, including extreme elongation and non-gravitational acceleration. Bergner and Seligman (hereafter BS23) proposed that evaporation of trapped H$_2$ created by cosmic rays (CRs) can explain the non-gravitational acceleration. However, their modeling of the thermal structure of 1I/Oumuamua ignored the crucial cooling effect of evaporating H${}_2$. By taking into account the cooling by H${}_2$ evaporation, we show that the surface temperature of H${}_2$-water ice is a factor of 9 lower than the case without evaporative cooling. As a result, the thermal speed of outgassing H${}_2$ is decreased by a factor of 3. Our one-dimensional thermal modeling that takes into account evaporative cooling for two chosen values of thermal conductivity of $\kappa =0.01$ and $0.1$ WK${}^{-1}$m${}^{-1}$ shows that the water ice volume available for H${}_2$ sublimation at $T>30$ K would be reduced by a factor of 9 and 5 compared to the results of BS23, not enabling enough hydrogen to propel 1I/`Oumuamua.