Merger rate of primordial black-hole binaries

Abstract

Primordial black holes (PBHs) have long been a candidate for the elusive dark matter (DM), and remain poorly constrained in the ∼ 20 − 100 M mass range. PBH binaries were recently suggested as the possible source of LIGO's first detections. In this paper, we thoroughly revisit existing estimates of the merger rate of PBH binaries. We compute the probability distribution of orbital parameters for PBH binaries formed in the early Universe, accounting for tidal torquing by all other PBHs, as well as standard large-scale adiabatic perturbations. We then check whether the orbital parameters of PBH binaries formed in the early Universe can be significantly affected between formation and merger. Our analytic estimates indicate that the tidal field of halos and interactions with other PBHs, as well as dynamical friction by unbound standard DM particles, do not do significant work on nor torque PBH binaries. We estimate the torque due to baryon accretion to be much weaker than previous calculations, albeit possibly large enough to significantly affect the eccentricity of typical PBH binaries. We also revisit the PBH-binary merger rate resulting from gravitational capture in present-day halos, accounting for Poisson fluctuations. If binaries formed in the early Universe survive to the present time, as suggested by our analytic estimates, they dominate the total PBH merger rate. Moreover, this merger rate would be orders of magnitude larger than LIGO's current upper limits if PBHs make a significant fraction of the dark matter. As a consequence, LIGO would constrain ∼ 10 − 300 M PBHs to constitute no more than ∼ 1% of the dark matter. To make this conclusion fully robust, though, numerical study of several complex astrophysical processes -such as the formation of the first PBH halos and how they may affect PBH binaries, as well as the accretion of gas onto an extremely eccentric binary -is needed.

Primordial black hole merger rates: distributions for multiple LIGO observables

“…For z, the narrower mass distribution leads to an enhancement across the whole range because, for a given total mass, equal mass mergers are easier to detect. 2D perturbations σ eq = 0.005 in [26] and [28]. However, this value is found by extrapolating the power spectrum amplitude and spectral index measured from the CMB.…”

Merger history of primordial black-hole binaries

“…Because the standard priors on masses for each event in LIGO/Virgo analysis are taken to be uniform [3,7], the likelihood of an individual event p(d i |λ) is proportional to the posterior of that event p(λ|d i ). The total likelihood for an inhomogeneous Poisson process can be evaluated as [63][64][65][66] (15) where β(θ) is defined as…”

“…The progenitors of these BBHs are still unknown and under intensively investigation (see e.g. [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]). These LIGO/Virgo BBHs present a much heavier mass distribution (in particular the sourceframe primary mass of GW170729 event can be as heavy as 50.2 +16.2 −10.2 M [7]) than that inferred from X-ray observations [28][29][30][31], which would challenge the formation and evolution mechanisms of astrophysical black holes.…”

Primordial black holes survive SN lensing constraints

“…Furthermore, other surveys of M31 stars and distant quasars found numerous microlensing events [19,20], which seems to contradict the EROS results. On the other hand, more detailed computations of the impact of early matter accretion on the CMB shows that Planck limits on PBH abundances are very sensitive to the PBH velocity with respect to baryons, whereas there is no relevant constraint from CMB spectral distortions [21,22]. At the same time, new constraints have been established in this range [10 − 100]M , especially from the dynamical heating of faint dwarf galaxies and their star clusters [23][24][25].…”