Gravitational Waves from Primordial Black Hole Mergers

TL;DR

The paper investigates whether LIGO-detected black hole mergers could originate from primordial black holes by modeling PBH binary formation in the early Universe and via GW emission in the late Universe, including an extended lognormal mass function and possible clustering. It derives merger-rate predictions, computes the resulting stochastic gravitational-wave background, and compares these with LIGO observations and cosmological constraints, finding that PBHs can explain the events only for modest PBH fractions (percent level) and broad mass spectra. A lognormal mass function with best-fit parameters around m_c ≈ 33 M⊙ and σ ≈ 0.8 can match the LIGO data, but the non-detection of the GW background would challenge a PBH origin; conversely, the predicted background could be detectable by upcoming LIGO runs and by LISA. The cosmological impact of PBH mergers after recombination is negligible (F ≲ 1%), implying PBH mergers do not resolve the Hubble tension.

Abstract

We study the production of primordial black hole (PBH) binaries and the resulting merger rate, accounting for an extended PBH mass function and the possibility of a clustered spatial distribution. Under the hypothesis that the gravitational wave events observed by LIGO were caused by PBH mergers, we show that it is possible to satisfy all present constraints on the PBH abundance, and find the viable parameter range for the lognormal PBH mass function. The non-observation of gravitational wave background allows us to derive constraints on the fraction of dark matter in PBHs, which are stronger than any other current constraint in the PBH mass range $0.5-30M_\odot$. We show that the predicted gravitational wave background can be observed by the coming runs of LIGO, and non-observation would indicate that the observed events are not of primordial origin. As the PBH mergers convert matter into radiation, they may have interesting cosmological implications, for example, in the context of relieving the tension between the high and low redshift measurements of the Hubble constant. However, we find that these effects are negligible as, after recombination, no more that $1\%$ of DM can be converted into gravitational waves.

Figures (4)

• Figure 1: Left panel: The results of maximum likelihood fit to the LIGO GW events for the lognormal mass function parameters $m_c$ and $\sigma$. The dot depicts the best fit value and the green, light green and yellow contours show, respectively, the relative likelihoods $\ell-\ell_{\rm max} = -1/2, -4/2, -9/2$. The contours of maximum allowed fraction of DM in PBHs in the LIGO sensitivity range $f_{\rm max}(m_{\rm min}<m<m_{\rm max})=10^{-2},10^{-3},10^{-4}$ are shown by the black solid, dashed and dotted lines, respectively. Right panel: The probability density function of the symmetric mass ratio of the binary for lognormal PBH mass function. The solid lines correspond to the binaries merging today, and the dashed lines to all binaries formed. The numbers denote the fraction of binaries with $\eta>0.2$ for the solid lines.
• Figure 2: The predicted stochastic GW background from the PBH mergers for the monochromatic (blue) and lognormal (red) mass functions. The fraction of DM in PBHs is chosen such that the merger rate in the LIGO sensitivity range today is $12\, {\rm Gpc}^{-3} {\rm yr}^{-1}$ for the lower lines and $213\, {\rm Gpc}^{-3} {\rm yr}^{-1}$ for the upper lines, corresponding to $f_{\rm PBH}\sim0.001-0.01$. For the solid lines $m_c=30M_\odot$, and for the dashed and dot-dashed lines $m_c=10,100M_\odot$, respectively. The black solid line shows the sensitivity of the first LIGO observing run (O1), and the gray dashed lines (O2, O5) below it show the expected sensitivities of the next observing runs TheLIGOScientific:2016wyq. The dashed grey lines on the left (C1-C4) show the sensitivities of different configurations of LISA Caprini:2015zlo.
• Figure 3: The constraints on the fraction of DM in PBHs, $f_{\rm PBH}$, from non-observation of the stochastic GW background for the monochromatic (left panel) and lognormal (right panel) PBH mass functions. The black solid line (O1) shows the constraint from the first LIGO observing run and the grey dashed lines (O2, O5) present the projected sensitivities of next phases of LIGO. The yellow and purple regions are excluded by the microlensing results from EROS Tisserand:2006zx and MACHO (M) Allsman:2000kg, respectively. The dark blue, orange, red and green regions on the right are excluded by Planck data Ali-Haimoud:2016mbv, survival of stars in Segue I (Seg I) Koushiappas:2017chw and Eridanus II (Eri II) Brandt:2016aco, and the distribution of wide binaries (WB) Monroy-Rodriguez:2014ula, respectively. On the right panel the thin dotted lines show, for comparison, the constraints calculated for the lognormal mass function from the ones in the monochromatic case by the method of Ref. Carr:2017jsz which has been used for all other constraints. The red lines show the values of $f_{\rm PBH}$ for which the merger rate in the LIGO sensitivity range today is $12\, {\rm Gpc}^{-3} {\rm yr}^{-1}$ (lower) and $213\, {\rm Gpc}^{-3} {\rm yr}^{-1}$ (upper).
• Figure 4: The red and blue lines show the fraction $F$ of DM converted into GWs as a function of the early density contrast, $\delta_{\rm dc}$, for $m_c=30M_\odot$ and $f_{\rm PBH}=1$. The dashed line shows the approximation \ref{['zetaapprox']}, and the grey horizontal line corresponds to the upper bound $F<4\%$.