Effects of the surrounding primordial black holes on the merger rate of primordial black hole binaries

We develop an analytic formalism for computing the merger rate of primordial black hole binaries with a general mass function by taking into account the torques by the surrounding primordial black holes and linear density perturbations. We find that α = − ( m i + m j ) 2 ∂ 2 ln R ( m i , m j ) / ∂ m i ∂ m j = 36 / 37 is independent of the mass function. Moreover, the ratio of the merger rate density of primordial black hole binaries by taking into account the torques by the surrounding primordial black holes to the nearest primordial black hole is independent of the masses of binaries.