Effective inspiral spin distribution of primordial black hole binaries

We investigate the probability distribution of the effective inspiral spin, the mass ratio, and the chirp mass of primordial black hole (PBH) binaries, incorporating the effect of the critical phenomena of gravitational collapse. As a leading order estimation, each binary is assumed to be formed from two PBHs that are randomly chosen according to the probability distribution of single PBHs. We find that, although the critical phenomena can lead to large spins on the low-mass tail, the effective inspiral spin of the binary is statistically very small, $\sqrt{⟨{\chi }_{\mathrm{e}\mathrm{f}\mathrm{f}}^2⟩}=8.41\times {10}^{-4}$. We also see that there is almost no anti-correlation between the effective inspiral spin and the mass ratio, which can be inferred from observations.