CERN Accelerating science

Lower bound on the suppression factor of the merger rate of initial binaries as a function of PBH abundance shown at different redshifts. It is estimated as the fraction of PBHs that reside in (sub)haloes that are gravitationally stable until the given redshift.

The blue lines show the lower bound on the merger rate of perturbed binaries today and the green ones the merger rate of unperturbed initial binaries today for $m=20M_\odot$. The upper bound for the blue region corresponds to $\gamma=1$ and the lower to $\gamma=2$. In the upper panel $f_{\rm PBH}=1$ and in the lower panel $\alpha=1$. The gray band depicts the merger rate indicated by LIGO/Virgo observations. The green solid line and the green dashed line show the merger rate of unperturbed binaries~\eqref{eq:R_unperturbed} with and without the suppression factor~\eqref{eq:pnp}, respectively.

The blue lines show the lower bound on the merger rate of perturbed binaries today and the green ones the merger rate of unperturbed initial binaries today for $m=20M_\odot$. The upper bound for the blue region corresponds to $\gamma=1$ and the lower to $\gamma=2$. In the upper panel $f_{\rm PBH}=1$ and in the lower panel $\alpha=1$. The gray band depicts the merger rate indicated by LIGO/Virgo observations. The green solid line and the green dashed line show the merger rate of unperturbed binaries~\eqref{eq:R_unperturbed} with and without the suppression factor~\eqref{eq:pnp}, respectively.

Constraints on the PBH abundance for monochromatic mass functions: The red solid line shows the $2\sigma$ constraint from the observed merger rate and the purple solid line the constraint from the nonobservation of the stochastic GW background. The red and purple dashed lines give projections of the final LIGO/Virgo design sensitivity. The gray dot-dashed line shows the $N<3$ O2 constraint if the disruption of binaries, by both mechanisms (1) and (2), is neglected. The black dashed contours depict the likelihood fit for a log-normal PBH mass function with width $\sigma = 0.4$ on the observed rate and masses.