Gravitational wave background from mergers of large primordial black holes

Abstract

The Peters formula, which tells how the coalescence time of a binarysystem emitting gravitational radiation is determined by the initial sizeand shape of the elliptic orbit, is often usedin estimating the merger rate of primordial black holes and the gravitational wave background from the mergers. Valid as it is in some interestingscenarios, such as the analysis of the LIGO-Virgo events,the Peters formula fails to describe the coalescence time if the orbital period of the binary exceedsthe value given by the formula. This could underestimate the event rateof mergers that occur before the cosmic time t ∼ 1013 s.As a result, the energy density spectrum of the gravitational wave background could develop a peak, which is from mergers occurring at either t ∼ 1013 s (for black holes with mass M ≳ 108 M ⊙) or t ∼ 1026(M/M ⊙)-5/3 s (for 105 M ⊙ ≲ M ≲ 108 M ⊙). Thiscan be used to constrain the fraction of dark matter inprimordial black holes (denoted by f) if potential probes(such as SKA and U-DECIGO) do not discover such a background,with the result f ≲ 10-6–10-4 for the mass range 10– 109 M ⊙. We then consider the effect of mass accretion onto primordial black holes at redshift z ∼ 10, and find that the merger rate could drop significantly at low redshifts. The spectrum of the gravitational wave background thus gets suppressed at the high-frequency end. This feature might be captured by future detectors such as ET and CE for initial mass M = \U0001d4aa(10–100) M ⊙ with f ≳ 10-4.