Inferring the mass and size of 3I/ATLAS from its non-gravitational acceleration

Abstract

Observations of the interstellar object 3I/ATLAS have revealed a strong production of gas and dust near perihelion, together with rapid brightening. The outgassing from the nucleus has led to a detectable non-gravitational acceleration. In this work, we combine models of the mass loss rate of water and carbon dioxide to derive the non-gravitational parameters and estimate the mass and size of 3I/ATLAS. In addition, we take into account a conservative constraint on the nucleus size from the active surface area required for sublimation. If the mass loss is dominated by the sublimation of CO$_2$, then the nucleus radius and mass are $R_{\rm 3I}=0.42\,\rm{km}$ and $M_{\rm 3I}=1.6\times10^{11}\,\rm{kg}$, assuming a density of $\rho=0.5\,\rm{g\,cm}^{-3}$ and an asymmetry factor of $\zeta=0.5$. This estimate is consistent with the lower bound from the active surface and independently supported by the slight preference of the orbital fit for a $a_{\rm ng}(r)\sim 1/r^2$ scaling of the non-gravitational acceleration. Models that cover the range of reported water production near perihelion give $R_{3I}=0.74-1.15\,\rm{km}$ and $M_{\rm 3I}=8.5-32\times10^{11}\,\rm{kg}$ but require a cometary surface that is in tension with the estimate from the rocket effect. Therefore, our results indicate that a large fraction of water sublimation is occurring in the coma and that CO$_2$ dominates sublimation on the surface. The nucleus radius that we obtain is much smaller than a recent photometric estimate of $R_{\rm 3I}\sim 1.3\,\rm{km}$, which could be resolved if CO$_2$ production is larger than observed or if the density of 3I/ATLAS is significantly lower than assumed. An overall lighter nucleus of 3I/ATLAS might be favored based on its recently claimed origin from a metal-poor environment and the corresponding mass budget of interstellar objects.