The Distribution and Annihilation of Dark Matter Around Black Holes

Abstract

We use a Monte Carlo code to calculate the geodesic orbits of test particles around Kerr black holes, generating a distribution function of both bound and unbound populations of dark matter (DM) particles. From this distribution function, we calculate annihilation rates and observable gamma-ray spectra for a few simple DM models. The features of these spectra are sensitive to the black hole spin, observer inclination, and detailed properties of the DM annihilation cross-section and density profile. Confirming earlier analytic work, we find that for rapidly spinning black holes, the collisional Penrose process can reach efficiencies exceeding 600%, leading to a high-energy tail in the annihilation spectrum. The high particle density and large proper volume of the region immediately surrounding the horizon ensures that the observed flux from these extreme events is non-negligible.

The collisional Penrose process

“…All parameters are identical, except the left-hand plot is for two ingoing particles, and the right-hand plot has an outgoing particle (1). with the results found accidentally in [38]. As with the ingoing annihilation, an analytic expression was derived in [37]: η max = (2 + √ 3)(2 + √ 2)/2.…”

“…In panels (b-d) we show the distribution of the individual momentum components, which are decidedly non-thermal and highly anisotropic. Reproduced from [38]. Despite the fact that the spatial density distribution for unbound particles appears quite uniform in θ in Figure 14, we see that the velocity distribution near the black hole is not at all isotropic.…”

“…The main results of this calculation are shown in Figure 14, reproduced from [38]. The contour plots show 2D cuts in the (r, θ) plane of the density distribution for bound and unbound populations, for spin parameters of a * = 0 and a * = 1.…”

“…The spin axis of the black hole is in the +z direction. Reproduced from [38]. While these earlier works were able to explore a much wider range of parameter space for the collision products, they were still generally limited to a relatively small number of specific initial conditions for the reactants.…”

“…Compared to Figure 15, here we actually see a more symmetric, thermal distribution making up a thick torus of stable, roughly circular orbits near the equatorial plane. Reproduced from [38].…”