Dark matter heating of Planet 9, and its observational implications

Abstract

The observed unusual behaviors of the orbits of Trans-Neptunian objects as well as the gravitational anomalies detected by the Optical Gravitational Lensing Experiment can be explained by assuming the existence of a ninth planet in the Solar System, having a mass of the order of $5-10M_{\oplus }$, and located at the distance of 300-1000 AU from the Sun. Since no optical counterpart of Planet 9 was observed, it is reasonable to assume that it has a very low luminosity. Various proposals on the nature of Planet 9 have been advanced, including the possibility that it is a black hole, an axion or a dark matter star. We propose that dark matter heating of Planet 9 could generate a thermal radio flux that could allow its observational detection, even if Planet 9 is a very dark object. We estimate the dark matter impact parameter, the mass and the kinetic energy deposition rates, as well as the surface temperature of Planet 9. By adopting a specific model for the time evolution of the planet, and assuming a long time capture of dark matter, the surface temperature of Planet 9, and the spectral features of the emitted radiation are obtained. Our results indicate that dark matter capture may provide an efficient mechanism for the heating of Planet 9, and also provide a specific observational signature of the planet. The numerical evaluations depend on the unknown value of the dark matter-ordinary matter interaction cross-section, with the estimates obtained as a function of its ratio and the saturation cross section for dark matter to deposit its entire energy. For a value of this ratio of $10^{-10}$, and for a dark matter density of the order of $1.32\times 10^{-17}$ g/cm${}^3$, in a few Gyrs the surface temperature of Planet 9 can reach values of the order of 200 K, or even higher, with a maximum wavelength of around ${\lambda }_{max}=1.44\times 10^{-3}$ cm, situated in the infrared domain.

22 pages, 3 figures

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