Solving puzzles of GW150914 by primordial black holes

TL;DR

This paper proposes that GW150914’s heavy, low-spin black holes can be explained by primordial black holes produced via a slightly modified Affleck-Dine baryogenesis mechanism, which yields a log-normal PBH mass distribution and predominantly negligible spins. The model links PBHs to dark matter and to seeds of early supermassive black holes, and it argues that a portion of PBHs can form binaries early enough to account for LIGO observations without violating existing constraints. It derives an inflationary-time–dependent upper mass limit for PBHs, discusses cosmological growth scenarios, and shows that PBHs with masses around 10^4–10^5 solar masses could plausibly seed galaxy formation. The authors fit their distribution parameters to observed SMBH demographics and LIGO event rates, producing testable predictions for PBH mass and spin distributions in future observations.

Abstract

The black hole binary properties inferred from the LIGO gravitational wave signal GW150914 posed several serious problems. The high masses and low effective spin of black hole binary can be explained if they are primordial (PBH) rather than the products of the stellar binary evolution. Such PBH properties are postulated ad hoc but not derived from fundamental theory. We show that the necessary features of PBHs naturally follow from the slightly modified Affleck-Dine (AD) mechanism of baryogenesis. The log-normal distribution of PBHs, predicted within the AD paradigm, is adjusted to provide an abundant population of low-spin stellar mass black holes. The same distribution gives a sufficient number of quickly growing seeds of supermassive black holes observed at high redshifts and may comprise an appreciable fraction of Dark Matter which does not contradict any existing observational limits. Testable predictions of this scenario are discussed.

Figures (5)

• Figure 1: Left: behavior of the effective potential of $\chi$ for different values of the inflaton field $\Phi$. The upper blue curve corresponds to $\Phi \gg \Phi_1$ which gradually decreases to $\Phi = \Phi_1$, the red curve. Then the potential returns back to an almost initial shape, as $\Phi\to 0$. The evolution of $\chi$ in such a potential is similar to the motion of a point-like particle (shown as the colored ball) in Newtonian mechanics. First, due to quantum initial fluctuations, $\chi$ left the unstable extremum of the potential at $\chi = 0$ and "tried" to keep pace with the moving potential minimum and later starts oscillating around it with decreasing amplitude. The decrease of the oscillation amplitude is due to the cosmological expansion. In mechanical analogy, the effect of the expansion is equivalent to the liquid friction term, $3H \dot \chi$. When $\Phi<\Phi_1$, the potential recovers its original form with the minimum at $\chi = 0$, and $\chi$ ultimately returns to zero, but before that it could give rise to a large baryon asymmetry ad-mk-nk. Right: The evolution of $\chi$ in the complex $[ {\rm Re} \chi, {\rm Im} \chi ]$-plane ad-mk-nk. One can see that $\chi$ "rotates" in this plane with a large angular momentum, which exactly corresponds to the baryonic number density of $\chi$. Later $\chi$ decays into quarks and other particles creating a large cosmological baryon asymmetry.
• Figure 2: Fraction of PBH density ${\rho(0.1-1)/\rho_{DM}}$ in the mass range $0.1 - 1 M_\odot$ as a function of parameter ${\gamma}$. See Eq. (\ref{['dn-dM']}).
• Figure 3: Space density of PBH (per Mpc${^{-3}}$ per ${d\log M)}$, to be compared to those derived from observations of SMBH in large galaxies (purple rectangle).
• Figure 4: Constraints on PBH fraction in DM, $f=\rho_{\rm PBH}/\rho_{\rm DM}$, where the PBH mass distribution is taken as $\rho_{\rm PBH}(M)=M^2dN/dM$ (see 2016arXiv160706077C). The existing constraints (extragalactic $\gamma$-rays from evaporation (HR), femtolensing of $\gamma$-ray bursts (F), neutron-star capture constraints (NS-C), MACHO, EROS, OGLE microlensing (MACHO, EROS) survival of star cluster in Eridanus II (E), dynamical friction on halo objects (DF), and accretion effects (WMAP, FIRAS)) are taken from 2016arXiv160706077C and reference therein. The PBH distribution is shown for ADBD parameters $\mu=10^{-43}$ Mpc$^{-1}$, $M_0=\gamma+0.1\times\gamma^2-0.2\times\gamma^3$ with $\gamma=0.75-1.1$ (red solid lines), and $\gamma=0.6-0.9$ (blue solid lines).
• Figure 5: Merging rate of binary BH $R$ (1/Gpc${^{3}}$/yr) per logarithmic mass interval over the universe age. The observed LIGO event rate is shown by the purple rectangle 2016arXiv160203842T.