Conservative limits on primordial black holes from the LIGO-Virgo-KAGRA observations

Abstract

Primordial black holes (PBH) 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. Our derived limits on the mass fraction of dark matter composed of PBHs is 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 5-80 $M_{\odot}$. Our work provide some of the most competitive limits in the mass range of 5-50 $M_{\odot}$. [abridged]

Figures (10)

• Figure 1: The total merger rate of PBH binaries at $z = 0$, due to t body captures and binary-single interactions and unperturbed binaries as a function of $m_{\textrm{PBH}}$. The blue solid line gives the rate for a monochromatic distribution. The red dashed line gives instead the rate for a log-normal mass distribution with $\mu \equiv \textrm{ln}(m_{c}) =\textrm{ln}(m_{\textrm{PBH}})$ and $\sigma = 0.6$. In all cases we assumed $f_{\textrm{PBH\, binaries}}=0.5$
• Figure 2: Normalized $m_{1}$-histogram (top) and $q$-histogram (bottom) of the simulated (in blue) and detected by LVK (in gray) black hole binaries with a SNR> 8. The simulated binaries are a combination of a dominant PL population (in brown) and a population of PBH binaries (in green). See text for further details.
• Figure 3: Our results on $f_{\textrm{PBH}}$ as a function PBH mass, assuming $f_{\mathrm{PBH \, binaries}}$=0.5. Dots are for a monochromatic distribution, while "x" symbols for a log-normal distribution where $m_{\textrm{PBH}} = m_{c} = e^{\mu}$ of Eq. (\ref{['eq:MassPDF_lognormal']}). Blue symbols represent best fit values for $f_{\textrm{PBH}}$, i.e. there is statistical preference for a PBH contribution to the LVK observations. Red symbols are for the $95\%$ upper limits on $f_{\textrm{PBH}}$. We also provide for comparison upper limits from other probes on PBHs. See text for more details.
• Figure 4: We present here the $\chi^2$ fit for different choices of $f_{\textrm{PBH}}$ at different masses for the monochromatic (top plot) and the log-normal (bottom plot) PBH distribution. The color gradient indicates the difference between the $\chi^2$ values using a power-law + PBH component and the best fit $\chi^2$ value of the power-law component only. The black dashed, dotted-dashed and dotted lines give the region of parameter space that is within $95\%$, $99.5\%$ and $99.87\%$ upper limits respectively. See text for further details.
• Figure 5: Top panel: for the monochromatic PBH mass-distribution, we show how the $95\%$ upper bound on $f_{\textrm{PBH}}$ changes with $m_{\textrm{PBH}}$. We evaluate these limits by fixing $f_{\rm{PBH \, binaries}}$ to $(0.1, 0.3, 0.7, 1)$. Bottom panel: the $95\%$ upper limits on $f_{\rm{PBH \, binaries}}$ as a function of $m_{\textrm{PBH}}$, fixing for each line $f_{\textrm{PBH}}$ to $(0.02,0.04 , 0.06,0.1)$.