Dark matter annihilation at the galactic center

TL;DR

This work analyzes how a central black hole can induce a steep dark matter density spike at the Galactic Center through adiabatic growth, potentially enhancing annihilation signals. It derives the spike by conserving adiabatic invariants of the phase-space distribution, relating the final density $\rho'(r)$ to the initial $f(E,L)$ via $f'(E',L')=f(E,L)$ and the actions, yielding a spike profile in $r \lesssim R_M$. For halos with finite cores the spike slope is $\gamma_{\mathrm{sp}}=3/2$, while cusped inner halos produce $\gamma_{\mathrm{sp}}>3/2$, with a concrete relation for a power-law density $\rho(r) \propto r^{-\gamma}$ giving $\gamma_{\mathrm{sp}}=(9-2\gamma)/(4-\gamma)$ and $\rho'(r)=\rho_R\, g_{\gamma}(r)\,(R_{\rm sp}/r)^{\gamma_{\mathrm{sp}}}$ and $R_{\rm sp}=\alpha_{\gamma} r_0 (M/(\rho_0 r_0^3))^{1/(3-\gamma)}$. For $0\le \gamma \le 2$, $\gamma_{\mathrm{sp}}$ lies between $2.25$ and $2.5$, and annihilation products include neutrinos that escape and can be used to constrain the inner halo slope; current limits already provide such constraints, with future neutrino telescopes offering improved tests.

Abstract

If cold dark matter is present at the galactic center, as in current models of the dark halo, it is accreted by the central black hole into a dense spike. Particle dark matter then annihilates strongly inside the spike, making it a compact source of photons, electrons, positrons, protons, antiprotons, and neutrinos. The spike luminosity depends on the density profile of the inner halo: halos with finite cores have unnoticeable spikes, while halos with inner cusps may have spikes so bright that the absence of a detected neutrino signal from the galactic center already places interesting upper limits on the density slope of the inner halo. Future neutrino telescopes observing the galactic center could probe the inner structure of the dark halo, or indirectly find the nature of dark matter.