Formation and Evolution of Primordial Black Hole Binaries in the Early Universe. (arXiv:1812.01930v1 [astro-ph.CO])

Formation and Evolution of Primordial Black Hole Binaries in the Early Universe. (arXiv:1812.01930v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Raidal_M/0/1/0/all/0/1">Martti Raidal</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Spethmann_C/0/1/0/all/0/1">Christian Spethmann</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Vaskonen_V/0/1/0/all/0/1">Ville Vaskonen</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Veermae_H/0/1/0/all/0/1">Hardi Veerm&#xe4;e</a>

The abundance of primordial black holes (PBHs) in the mass range $0.1 – 10^3
M_odot$ can potentially be tested by gravitational wave observations due to
the large merger rate of PBH binaries formed in the early universe. To put the
estimates of the latter on a firmer footing, we first derive analytical PBH
merger rate for the general mass function considering only initial
configurations that give a conservative result. We then study the formation and
evolution of PBH binaries before recombination by performing N-body
simulations. We find that the analytical merger rate estimate based on the
tidally perturbed 2-body problem fails when PBHs comprise all dark matter, as
most initial binaries are disrupted by the surrounding PBHs. This is due to the
formation of compact N-body systems at matter-radiation equality. However, if
PBHs make up a small fraction of the dark matter, $f_{rm PBH} lesssim 10%$,
these estimates become more reliable. In that case, the merger rate observed by
LIGO imposes the strongest constraint on the PBH abundance in the mass range $2
– 160 M_odot$. Finally, we argue that, even if most initial PBH binaries are
perturbed, the present BH-BH merger rate of binaries formed in the early
universe is larger than $mathcal{O}(10),{rm Gpc}^{-3} {rm yr}^{-1}, f_{rm
PBH}^3$.

The abundance of primordial black holes (PBHs) in the mass range $0.1 – 10^3
M_odot$ can potentially be tested by gravitational wave observations due to
the large merger rate of PBH binaries formed in the early universe. To put the
estimates of the latter on a firmer footing, we first derive analytical PBH
merger rate for the general mass function considering only initial
configurations that give a conservative result. We then study the formation and
evolution of PBH binaries before recombination by performing N-body
simulations. We find that the analytical merger rate estimate based on the
tidally perturbed 2-body problem fails when PBHs comprise all dark matter, as
most initial binaries are disrupted by the surrounding PBHs. This is due to the
formation of compact N-body systems at matter-radiation equality. However, if
PBHs make up a small fraction of the dark matter, $f_{rm PBH} lesssim 10%$,
these estimates become more reliable. In that case, the merger rate observed by
LIGO imposes the strongest constraint on the PBH abundance in the mass range $2
– 160 M_odot$. Finally, we argue that, even if most initial PBH binaries are
perturbed, the present BH-BH merger rate of binaries formed in the early
universe is larger than $mathcal{O}(10),{rm Gpc}^{-3} {rm yr}^{-1}, f_{rm
PBH}^3$.

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