The size of 3I/ATLAS from non-gravitational acceleration

TL;DR

The paper investigates whether non-gravitational accelerations observed for 3I/ATLAS can constrain the nucleus mass and size by linking NGAs to mass loss via momentum conservation. It adopts a simple outgassing model that relates the total NGA to the mass loss rate through $M |\,\vec{a}_{ng}\,| = \left|\sum \dot{M}_i \vec{v}_i\right| \approx \zeta \dot{M} v_{th}$, with a thermal velocity $v_{th} = 0.8\ \mathrm{km\ s^{-1}} \ (r/1\ \mathrm{au})^{-0.5}$ and an asymmetry factor $\zeta \lesssim 1$ (typically about 0.5). The authors compare NGA-derived mass loss rates against CO$_2$ production measurements from JWST, SPHEREx, ALMA, TRAPPIST-North, and Swift to derive plausible nucleus sizes under different NGA models. They find that, under the time-lag NGA solution of Eubanks et al. 2025, the inferred diameter is between $820\, (\zeta_{0.5}/\rho_{0.5})^{1/3}$ m and $1050\, (\zeta_{0.5}/\rho_{0.5})^{1/3}$ m for $\rho=0.5$ g cm$^{-3}$ and $\zeta=0.5$, consistent with observational upper limits from JWST while the JPL NGA law struggles to fit the same limits. The results depend on $\zeta$, $\rho$, and the assumed time lag $\Delta T$, and the authors emphasize that reliable mass loss rates at other trajectory stages are crucial to reduce systematic uncertainty.

Abstract

The third macroscopic interstellar object detected in the solar system recently passed through perihelion, with the best-fitting models of its trajectory now featuring non-gravitational accelerations. We assess how much mass loss is required to produce plausible non-gravitational acceleration solutions and compare with estimates of the mass loss. We find that they are consistent when the nucleus of 3I/ATLAS is around 1 km in diameter. For a recent solution with a time lag in the acceleration from Eubanks et al, we find diameters between 820 meters and 1050 meters, assuming an outgassing asymmetry factor $ζ=0.5$ and a density of the comet nucleus $ρ=0.5$ g cm$^{-3}$. The limits on the diameter scale as $(ζ/ρ)^{1/3}$. Substantial extrapolation is required in general to compare non-gravitational accelerations to mass loss rates, so reliable estimates of the mass loss rate at other stages of the comet's trajectory will substantially reduce the systematic uncertainty in this estimate.

Figures (1)

• Figure 1: NGAs and their corresponding mass loss rates. Top Non-gravitational acceleration from the JPL Small-Body Database or the final line of Table 1 in eubanks2025. Reported errorbars are shown, and extrapolations into the future or prior to October are shown as dashed lines. Middle NGAs from the top panel are translated into mass loss rates assuming 1 km diameters, with $\zeta=0.5$ and $\rho=0.5\ \mathrm{g}\ \mathrm{cm}^{-3}$. Additionally the JPL Dec 17 solution for other diameters are shown as dotted lines. Data points are from JWST Cordiner2025, SPHEREx lisse2025b, ALMA roth2025, TRAPPIST-North jehin2025, and Swift xing2025. Bottom CO$_2$ production rates measured by JWST are treated as upper and lower limits, and observations where CO$_2$ is inaccessible are shown as lower limits. Given these constraints, the range of $\dot{M}$ and hence diameters for two different reported NGA solutions is shown. The JPL solution is unable to simultaneously fit the upper limit from JWST and the lower limit from TRAPPIST-North.