Probing Primordial Black Hole Dark Matter with Gravitational Waves

Primordial black holes (PBHs) have long been suggested as a candidate for making up some or all of the dark matter in the Universe. Most of the theoretically possible mass range for PBH dark matter has been ruled out with various null observations of expected signatures of their interaction with standard astrophysical objects. However, current constraints are significantly less robust in the $20M_{\odot }\lesssim M_{\mathrm{PBH}}\lesssim 100M_{\odot }$ mass window, which has received much attention recently, following the detection of merging black holes with estimated masses of $\sim 30M_{\odot }$ by LIGO and the suggestion that these could be black holes formed in the early Universe. We consider the potential of advanced LIGO (aLIGO) operating at design sensitivity to probe this mass range by looking for peaks in the mass spectrum of detected events. To quantify the background, which is due to black holes that are formed from dying stars, we model the shape of the stellar-black-hole mass function and calibrate its amplitude to match the $O1$ results. Adopting very conservative assumptions about the PBH and stellar-black-hole merger rates, we show that $\sim 5\mathrm{yr}$ of aLIGO data can be used to detect a contribution of $>20M_{\odot }$ PBHs to dark matter down to $f_{\mathrm{PBH}}<0.5$ at $>99.9\%$ confidence level. Combined with other probes that already suggest tension with $f_{\mathrm{PBH}}=1$, the obtainable independent limits from aLIGO will thus enable a firm test of the scenario that PBHs make up all of dark matter.

Figure 1

Hunting for dark matter: The left panel is the popular illustration of the different search methods for dark matter particles. One avenue is direct detection, whereby dark matter particles are targeted by looking for their effect on standard model particles (e.g., recoil on heavy nuclei in underground experiments). The second is known as indirect detection, where the goal is to observe the products of dark matter self-interaction (e.g., gamma rays produced from annihilating WIMPs [18]). Analogously, we group all the methods focusing on the effect of PBHs on standard astrophysical objects as “direct” detection (including probes such as microlensing [19, 20, 21], cosmic microwave background (CMB) anisotropies [22, 23, 24], dynamical heating of ultrafaint dwarf galaxies [25, 26], number counts of compact x-ray objects [27], etc., and in the future, strong lensing of fast radio bursts [28] and pulsar timing [29]). “Indirect” detection of PBH dark matter involves looking for gravitational waves emitted when a PBH pair is “annihilated” by merging into a larger BH [30].

Figure 2

Constraints on the fraction of dark matter in primordial black holes, as a function of their mass. It is conventional to assume a delta-function PBH mass function when calculating constraints such as these. In practice, however, the measurement error will widen the observed distribution, so we model the PBH mass function as a Gaussian with a 5% width. The dashed lines correspond to $3\sigma$ limits (i.e., requiring that the fraction of DM in PBHs is low enough such that the number of PBHs does not exceed the Poisson noise of the stellar mergers by more than a factor of 3), and the solid lines are more stringent $5\sigma$ limits. Constraints based on the 1D mass distribution are shown in red, those using the 2D distribution (which are tighter as the noise per bin is smaller) in blue. For $30M_{\odot }$, we get $f_{\mathrm{PBH}}\lesssim 50\%$ at $5\sigma$ ($3\sigma$) in the 2D (1D) case. The bands above the solid lines extend up to a factor 400% (200%) uncertainty in the background (signal) amplitude.