A Near Surface Temperature Model of Arrokoth

A near surface thermal model for Arrokoth is developed based on the recently released $10^5$ facet model of the body. This thermal solution takes into account Arrokoth's surface re-radiation back onto itself. The solution method exploits Arrokoth's periodic orbital character to develop a thermal response using a time-asymptotic solution method, which involves a Fourier transform solution of the heat equation, an approach recently used by others. We display detailed thermal solutions assuming that Arrokoth's near surface material's thermal inertia ${\cal I} = $ 2.5 W/m$^{-2}$K$^{-1}$s$^{1/2}$. We predict that at New Horizons' encounter with Arrokoth its encounter hemisphere surface temperatures were $\sim$ 57-59 K in its polar regions, 30-40 K on its equatorial zones, and 11-13 K for its winter hemisphere. Arrokoth's orbitally averaged temperatures are around 30-35 K in its polar regions, and closer to 40 K near its equatorial zones. Thermal reradiation from the surrounding surface amounts to less than 5\% of the total energy budget, while the total energy ensconced into and exhumed out Arrokoth's interior via thermal conduction over one orbit is about 0.5\% of the total energy budget. As a generalized application of this thermal modeling together with other KBO origins considerations, we favor the interpretation that New Horizons' REX instrument's $29 \pm 5$K brightness temperature measurement is consistent with Arrokoth's near surface material's being made of sub-to-few mm sized tholin-coated amorphous \water ice grains with 1 W/m$^{-2}$K$^{-1}$s$^{1/2}$ $< {\cal I} < $10-20 W/m$^{-2}$K$^{-1}$s$^{1/2}$, and which are characterized by an X-band emissivity in the range 0.9 and 1.