The clustering of massive Primordial Black Holes as Dark Matter: measuring their mass distribution with Advanced LIGO

Abstract

The recent detection by Advanced LIGO of gravitational waves (GW) from the merging of a binary black hole system sets new limits on the merging rates of massive primordial black holes (PBH) that could be a significant fraction or even the totality of the dark matter in the Universe. aLIGO opens the way to the determination of the distribution and clustering of such massive PBH. If PBH clusters have a similar density to the one observed in ultra-faint dwarf galaxies, we find merging rates comparable to aLIGO expectations. Massive PBH dark matter predicts the existence of thousands of those dwarf galaxies where star formation is unlikely because of gas accretion onto PBH, which would possibly provide a solution to the missing satellite and too-big-to-fail problems. Finally, we study the possibility of using aLIGO and future GW antennas to measure the abundance and mass distribution of PBH in the range [5 - 200] Msun to 10\% accuracy.

Figures (4)

• Figure 1: PBH capture rate (solid lines) and direct merging rate (dashed lines) in the Milky-Way, for a massive PBH-DM model uniformly distributed with an Einasto profile, within the Milky-Way halo, and for several values of the PBH mass.
• Figure 2: The gravitational slingshot effect converts a small peculiar velocity $\vec{v}_1$ of a star of mass $~m~$ into a larger than escape velocity $\vec{v}_2$, thanks to the exchange of energy and momentum with the more massive PBH of mass $M$.
• Figure 3: Cosmological merging rate as a function of the width $\sigma_{\mathrm{\rm PBH}}$ of the PBH density spectrum, for different values of the central mass of the distribution $\mu_{\mathrm{\rm PBH}} = 10 /30 / 60 M_\odot$ (respectively dotted, solid and dashed lines), and of the local density contrast $\delta_{\mathrm{\rm PBH}}^{\mathrm{loc.}} = 10^7 / 10^8 /10^9 /10^{10}$ (respectively blue, red, green and brown lines). The colored band corresponds to the bounds inferred by aLIGO. PBH with broader density spectra or higher masses require less intense clustering but can lead to merging rates within these bounds.
• Figure 4: Cosmological merging rates of BHs with masses $m_{\mathrm A}$ and $m_{\mathrm B}$, the color scale representing $\log (\tau~\mathrm{yr}~\mathrm{Gpc}^3 )$. The PBH density follows a lognormal distribution in logarithmic mass scale, of central value $\mu_{\mathrm{\rm PBH}}$ and width $\sigma_{\mathrm{\rm PBH}}$. The panels are for $\mu_{\mathrm{\rm PBH}} = 30 M_\odot$ and $\sigma_{\mathrm{\rm PBH}} = 0.1$ (1st panel), $\sigma_{\mathrm{\rm PBH}} = 0.3$ (2nd), and $\mu_{\mathrm{\rm PBH}} = 300 M_\odot$ with $\sigma_{\mathrm{\rm PBH}} = 0.7$ (3rd) The corresponding local density contrast and total merging rate of BHs with masses $m_{\mathrm{\rm PBH}} \gtrsim 5 M_\odot$ is indicated above each panel. Those total rates lie all within the bounds inferred by aLIGO, but with different distributions in the $(m_A, m_B)$ plane, which is potentially detectable and makes possible to reconstruct the PBH density spectrum.