Effects of the shape of curvature peaks on the size of primordial black holes

Abstract

We simulate numerically the formation of spherically symmetric primordial black holes (PBHs) seeded by different families of primordial curvature perturbations profiles on a Friedman-Robertson-Walker (FRW) Universe filled by radiation fluid. We have studied the dependency on the curvature profile of the initial mass $M_{\rm BH,i}$ of the PBHs at the time of apparent horizon formation $t_{AH}$, and the final mass $M_{\rm BH,f}$ after the accretion process, using an excision technique, comparing $M_{\rm BH,i}$ to previous analytical estimations obtained using compensated PBHs model approach. The analytical estimations are in agreement with numerical results, except for large values of the initial perturbation amplitude, when the compensated model is less accurate. The masses $M_{\rm BH,f}$ and $M_{\rm BH,i}$ do not depend only on the shape around the compaction function peak, but on the full profile of the initial curvature perturbation. We also estimate the accretion effects, and for those PBHs with masses relevant for the dark matter abundance, with a final mass equal to the horizon crossing mass, we find $M_{\rm BH,f}\approx 3 M_{\rm BH,i} $.