Binary Black Holes population synthesis based on the current LVK observations

Abstract

The ongoing observations from ground based gravitational-wave observatories have led to the detection of more than a hundred merger events between black holes. We use the LIGO-Virgo-KAGRA (LVK) observations from 2015 to early 2024, to test the population synthesis of these merging binaries; which will allow us to probe the formation mechanisms and environments of these black holes. We test if the current sample of binary black holes can be explained only by the merger of black holes coming from the collapse of the cores of massive stars, i.e. as just first generation black holes merging with each other. Those black holes' masses will roughly follow a power-law distribution. We also test if in addition to the merger between first generation black holes, there is evidence for a second population of black hole binaries in which at least one the binaries' members is the product of an earlier merger between black holes. These binaries are typically referred to as signals of hierarchical mergers. Such a population can possibly explain the observation of very massive black hole binaries by the LVK collaboration. We find that the LVK observations give a statistical preference in log-likelihood of up to $- 2 Δln\mathcal{L} = -150$ or in log-Bayes factor of up to $ln\textrm{BF} = 71$, for the full sample of black hole binaries originating from a combination of black holes following a power-law distribution and black holes from hierarchical mergers. The ratio of black holes following a power-law mass-distribution to a mass-distribution expected from hierarchical mergers is found to be as high as one-to-one. We also consider that some of the LVK black hole merging binaries are the result of primordial black holes (PBHs), merging inside dark matter halos and in the intergalactic medium. Adding a third population is preferred. [abridged]

Figures (14)

• Figure 1: Histogram of primary mass (top), redshift (middle), and secondary mass (bottom) distribution for BBHs, with Poisson error bars from the GWTC4 events.
• Figure 2: The primary mass of events from the O1 to O4a LVK runs, as a function of redshift with their $90\%$ credible interval ranges.
• Figure 3: PDF of primary mass of BHs that are at least second generation BHs. The top histogram is for $\lambda=0.5$, the middle one for $\lambda=1$ i.e the PDF obtained from Ye:2025ano, and the bottom histogram is for $\lambda=1.5$.
• Figure 4: The comoving merger rate of PBHs binaries as a function of redshift $z$ for monochromatic and for lognormal mass distributions described by Eq.\ref{['eq:MassPDF_lognormal']} with $\sigma=0.6$. The rate is calculated as the sum of three merger channels: unperturbed binaries, binary-single interactions within halos, and two body captures using Eq.\ref{['Rtotal']}. In all cases, we assume $f_{\rm PBH}=3\times 10^{-3}$ and a binary fraction of $f_{\rm PBH\,binaries}=0.5$.
• Figure 5: Corner plot representing the fit parameter values for a simple power-law model (blue lines and contours) and the fit parameter values for a power-law with an exponential cutoff (red lines and contours). The contour lines represent the $34\%$, $68\%$, $85\%$ and $95\%$ credible intervals. We also show in the dashed lines the 90$\%$ credible interval ranges for each of the parameters values are given in Table \ref{['table:posteriors_neg_beta']}. We universally use the symbol $R_{\textrm{PL}}$ to describe the comoving merger rate parameter in $\textrm{Gpc}^{-3}\,\textrm{yr}^{-1}$ at $z=0$ (see text for more details).