A Dark-Matter Spike at the Galactic Center?

TL;DR

This work investigates whether a dark-matter density spike can form around the Galactic center through adiabatic growth of the central black hole and what dynamical processes might suppress it. Using semi-analytic adiabatic-invariant methods on NFW and Moore halos, it derives the central spike slope and examines instantaneous growth, off-center formation, and baryonic effects. The main finding is that the canonical GS spike (A ≈ 2.25–2.5) requires the bulk of BH growth to occur within the inner ~50 pc and on timescales longer than ~10^7 years, with the central cold phase-space population intact; more realistic scenarios—off-center seeds, rapid growth, or strong baryonic disruption—generally yield much milder spikes or none at all. Consequently, the absence of strong annihilation signals from the Galactic center does not rule out WIMP dark matter, and the results map out the stringent dynamical conditions under which a GC dark-matter spike could exist.

Abstract

The past growth of the central black hole (BH) might have enhanced the density of cold dark matter halo particles at the Galactic center. We compute this effect in realistic growth models of the present (2-3)*10**6 solar mass BH from a low-mass seed BH, with special attention to dynamical modeling in a realistic galaxy environment with merger and orbital decay of a seed BH formed generally outside the exact center of the halo. An intriguing ``very-dense spike'' of dark matter has been claimed in models of Gondolo and Silk with density high enough to contradict with experimental upper bounds of neutralino annihilation radiation. This ``spike'' disappears completely or is greatly weakened when we include important dynamical processes neglected in their idealized/restrictive picture with cold particles surrounding an at-the-center zero-seed adiabaticly-growing BH. For the seed BH to spiral in and settle to the center within a Hubble time by dynamical friction, the seed mass must be at least a significant fraction of the present BH. Any subsequent at-the-center growth of the BH and steepening of the central Keplerian potential well can squeeze the halo density distribution only mildly, whether the squeezing happens adiabatically or instantaneously.

Figures (6)

• Figure 1: Enhancement of an NFW dark-matter-density profile due to the growth of the Galactic black hole at the center of the dark-matter system. The initial profile (dotted curve) is modified into the solid curve if the growth of the black hole is adiabatic, or into the dash-dot curve for a sudden growth. Also shown is the case of adiabatic growth for an initial profile with all particles on circular orbits (dashed curve). $\rho_{\rm{core}}$ is the maximum WIMP density above which WIMPs are depleted by pair annihilations.
• Figure 2: Initial and final orbits for sudden and adiabatic black-hole growth. If the black-hole grows adiabatically, the initial large circular orbit becomes a final circular orbit of much smaller radius. If the black hole appears suddenly, the initial circular orbit becomes an elliptical orbit shown (assuming that the final potential at these radii is dominated by the black hole).
• Figure 3: Predicted time for a seed black hole of mass $M_{\rm BH}^S=10^4 \;{\rm M}_\odot$ and $10^6 \;{\rm M}_\odot$ to spiral in to the Galactic center from a radius $r$ in an initially pure NFW or pure Moore halo profile (no baryons). It takes longer than a Hubble time for a $10^4 \;{\rm M}_\odot$ black hole to spiral from $r \gg 100$ pc, and for a $10^6 \;{\rm M}_\odot$ black hole to spiral from $r \gg 1$ kpc. The spiral-in time is estimated with Chandrasekhar's formula for dynamical friction, depending slightly on the Coulomb factor and the eccentricity of the orbit of the black hole. Note the curves join together after a break at very small radius when the enclosed ambient mass becomes comparable to the mass of the infalling hole. Inside this radius, the hole would fall in quickly on a dynamical time scale, which is independent of $M_{\rm BH}^S$.
• Figure 4: Modification of an NFW dark-matter-density profile due to the off-center formation of a black-hole seed of mass $M_{\rm BH}^S$, its spiral in the center of the dark-matter system and its adiabatic growth to the present-day mass of the black hole at the Galactic center. The cases for a few different values for the black-hole-seed mass are plotted. $\rho_{\rm{core}}$ is the maximum WIMP density above which WIMPs are depleted by pair annihilations.
• Figure 5: The same as in Fig. \ref{['fig:fig2']}, but for a Moore et al. dark-matter-density profile. Also shown is the modification of the profile for sudden growth of the black hole at the center of the dark-matter system (dashed curve).