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.