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Register a new userRapid Merger of Binary Primordial Black Holes: an Implication for GW150914
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We propose a new scenario for the evolution of a binary of primordial black holes (PBHs). We consider a dynamical friction by ambient dark matter, scattering of dark matter particles with a highly eccentric orbit besides the standard two-body relaxation process to refill the loss cone, and interaction between the binary and a circumbinary disk, assuming that PBHs do not constitute the bulk of dark matter. Binary PBHs lose the energy and angular momentum by these processes, which could be sufficiently efficient for a typical configuration. Such a binary coalesces due to the gravitational wave emission in a time scale much shorter than the age of the universe. We estimate the density parameter of the resultant gravitational wave background. Astrophysical implication concerning the formation of intermediate-mass to supermassive black holes is also discussed.
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We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range $10^{-5}text{--}10^{50}$ g. Those smaller than $sim 10^{15}$ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalactic $gamma$-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than $sim 10^{15}$ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the CDM in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations and $mu$-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-$sigma$ peaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the dark matter, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the dark matter, they could play an important cosmological role and provide a unique probe of the early Universe.
We modify the procedure to estimate PBH abundance proposed in arXiv:1805.03946 so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation $triangle zeta$ and use the values of $triangle zeta$ and $triangle triangle zeta $ at each peak to specify the profile of $zeta$ as a function of the radial coordinate while the values of $zeta$ and $triangle zeta$ are used in arXiv:1805.03946. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in arXiv:1805.03946. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the $k$-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the $k$-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.
Evidences for the primordial black holes (PBH) presence in the early Universe renew permanently. New limits on their mass spectrum challenge existing models of PBH formation. One of the known model is based on the closed walls collapse after the inflationary epoch. Its intrinsic feature is multiple production of small mass PBH which might contradict observations in the nearest future. We show that the mechanism of walls collapse can be applied to produce substantially different PBH mass spectra if one takes into account the classical motion of scalar fields together with their quantum fluctuations at the inflationary stage.
We calculate the exact formation probability of primordial black holes generated during the collapse at horizon re-entry of large fluctuations produced during inflation, such as those ascribed to a period of ultra-slow-roll. We show that it interpolates between a Gaussian at small values of the average density contrast and a Cauchy probability distribution at large values. The corresponding abundance of primordial black holes may be larger than the Gaussian one by several orders of magnitude. The mass function is also shifted towards larger masses.
Primordial black holes might comprise a significant fraction of the dark matter in the Universe and be responsible for the gravitational wave signals from black hole mergers observed by the LIGO/Virgo collaboration. The spatial clustering of primordial black holes might affect their merger rates and have a significant impact on the constraints on their masses and abundances. We provide some analytical treatment of the primordial black hole spatial clustering evolution, compare our results with some of the existing N-body numerical simulations and discuss the implications for the black hole merger rates. If primordial black holes contribute to a small fraction of the dark matter, primordial black hole clustering is not relevant. On the other hand, for a large contribution to the dark matter, we argue that the clustering may increase the late time Universe merger rate to a level compatible with the LIGO/Virgo detection rate. As for the early Universe merger rate of black hole binaries formed at primordial epochs, clustering alleviates the LIGO/Virgo constraints, but does not evade them.
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