Pulsar timing can constrain primordial black holes in the LIGO mass window

The recent discovery of gravitational waves from merging black holes has generated interest in primordial black holes as a possible component of dark matter. In this paper, we show that pulsar timing may soon have sufficient data to constrain $1–1000M_{\odot }$ primordial black holes (PBHs) via the nondetection of a third-order Shapiro time delay as the black holes move around the Galactic halo. We present the results of a Monte Carlo simulation which suggests that future data from known pulsars may be capable of constraining the PBH density more stringently than other existing methods in the mass range $\sim 1–30M_{\odot }$. We find that timing new pulsars discovered using the proposed Square Kilometre Array may constrain primordial black holes in this mass range to comprise less than $\sim 1\%–10\%$ of the dark matter.

Figure 1

Schematic observational setup for a single pulsar. The top diagram shows the geometry from a side view, while the bottom shows a cross section from the point of view of the observer.

Figure 2

Projected constraints from searching for individual motions of PBHs near the 143 distinct LOSs of stable MSPs in the ATNF catalogue (known pulsars) as well as for 2000 MSPs that can be detected and monitored using the SKA [53]. Also shown are the most stringent observational constraints from microlensing [16], constraints from ultrafaint dwarf galaxies and Eridanus II assuming conservative dynamical parameters [22], conservative projected constraints from lensing of $10^4$ fast radio bursts [25], and existing constraints from the nondisruption of wide stellar binaries [19]. For emphasis, dashed lines denote projected constraints.