Blackbody Radiation from Isolated Neptunes

TL;DR

This paper models the blackbody radiation of isolated Neptune-like planets to use their thermal emission as a means of detection and to constrain the properties of hypothesized distant planets like Planet Nine.

Contribution

It introduces an analytical model linking blackbody temperature and atmospheric mass of isolated Neptunes, aiding in their detection and characterization.

Findings

Blackbody temperature relates weakly to atmospheric mass as T_eff ∝ M_atm^{1/12}.

Flux measurements at the Wien tail can constrain atmospheric mass within a factor of a few.

Null survey results set limits on the size and composition of distant Neptune-like planets.

Abstract

Recent analyses of the orbits of some Kuiper Belt objects hypothesize the presence of an undiscovered Neptune-size planet at a very large separation from the Sun. The energy budget of Neptunes on such distant orbits is dominated by the internal heat released by their cooling rather than solar irradiation (making them effectively "isolated"). The blackbody radiation that these planets emit as they cool may provide the means for their detection. Here we use an analytical toy model to study the cooling and radiation of isolated Neptunes. This model can translate a detection (or a null detection) to a constraint on the size and composition of the hypothesized "Planet Nine". Specifically, the thick gas atmosphere of Neptune-like planets serves as an insulating blanket which slows down their cooling. Therefore, a measurement of the blackbody temperature, $T_{\rm eff}\sim 50\textrm{K}$, at which a Neptune emits can be used to estimate the mass of its atmosphere, $M_{\rm atm}$. Explicitly, we find the relation $T_{\rm eff}\propto M_{\rm atm}^{1/12}$. Despite this weak relation, a measurement of the flux at the Wien tail can constrain the atmospheric mass, at least to within a factor of a few, and provide useful limits to possible formation scenarios of these planets. Finally, we constrain the size and composition of Planet Nine by combining our model with the null results of recent all-sky surveys.