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 $ρ=0.5\,\rm{g\,cm}^{-3}$ and an asymmetry factor of $ζ=0.5$. 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.

Figures (3)

• Figure 1: Compilation of observational data on the mass loss rates $\dot{M}$ of H$_2$O (blue), OH (orange) and CO$_2$ (green) for 3I/ATLAS. Individual references are given in the text. The colored dashed lines show empirical models for the mass loss rate, defined in Equations \ref{['eq:co2_model']}, \ref{['eq:Mdot_H2O_low']}, and \ref{['eq:h2o_model']}. The solid pink and red curves display two models used in this work to describe the combined total emission rate from water and carbon dioxide, given by Equations \ref{['eq:mdotA']} and \ref{['eq:mdotB']}. The gray dotted line illustrates the model implicitly assumed in the determination of the rocket effect by Hui.
• Figure 2: Residuals in RA and DEC between the data from the MPC and the orbital solution JPL #54. The orange points indicate high-fidelity observations from large telescopes (specified in Section \ref{['sec:sensitivity']}), including the reported residuals. Green color indicates measurements from interplanetary spacecraft (Trace Gas orbiter, Lucy spacecraft, Psyche spacecraft) that are valuable in constraining the orbit due to the triangulation.
• Figure 3: Minimum radius of 3I/ATLAS required to sustain the observed production rate with the entire surface being active. The solid lines correspond to the models described in Section \ref{['sec:production']} and the dotted lines are the corresponding estimates of the radius of 3I/ATLAS from the non-gravitational effect.