Primordial black holes (PBHs) may constitute a considerable fraction of dark matter. In this work we use the recent observations by the LIGO-Virgo-KAGRA (LVK) collaborations to set direct limits on stellar-mass range PBHs. We evaluate the merger rates of PBH binaries by accounting for the binaries formed by two-body captures inside dark matter halos and by studying the evolution of PBH binaries inside such halos through binary-single interactions. Those type of interactions contribute to what is a minimum of PBH merger rates at low redshifts detectable by LVK. Thus, they allow us to derive what is the most conservative upper limits on the presence of merging PBH binaries in the gravitational-wave observations. We study both the case where PBHs have a monochromatic mass distribution and the case where that distribution is described by a log-normal function. To derive limits on PBHs, we simulate binaries with masses following the relevant mass distributions and merger rates as a function of redshift, up to $z\sim 0.8$, relevant for the current LVK observations. In those simulations we also take into account that the LVK observatories measure the detected black hole binaries’ masses with a finite resolution. In comparing to the LVK observations, we combine the simulated PBH binaries with the binaries following a power-law mass- and redshift distribution. The latter binaries dominate the observed population of LVK detections. Our derived limits on the mass fraction of dark matter composed of PBHs are in the range of ${10}^{-4}$ to $2\times {10}^{-2}$, depending on the exact assumptions relating to the PBH binaries properties. For reasonable assumptions on those PBH binaries’ properties before their evolution inside dark matter halos, we get that fraction to be in the range of ${10}^{-3}-{10}^{-2}$, for PBH masses of $5-80M_{\odot }$. Our work provides some of the most competitive limits in the mass range of $5-50M_{\odot }$.

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• Dark matter
• Gravitational waves