Spins of primordial black holes formed with a soft equation of state

Abstract

We investigate the probability distribution of the spins of primordial black holes (PBHs) formed in the universe dominated by a perfect fluid with the linear equation of state $p=w\rho$, where $p$ and $\rho$ are the pressure and energy density of the fluid, respectively. We particularly focus on the parameter region $0<w\le 1/3$ since the larger value of the spin is expected for the softer equation of state than that of the radiation fluid ($w=1/3$). The angular momentum inside the collapsing region is estimated based on the linear perturbation equation at the turn-around time which we define as the time when the linear velocity perturbation in the conformal Newtonian gauge takes the minimum value. The probability distribution is derived based on the peak theory with the Gaussian curvature perturbation. We find that the root mean square of the non-dimensional Kerr parameter $\sqrt{⟨a_{\ast }^2⟩}$ is approximately proportional to $(M/M_H{)}^{-1/3}(6w{)}^{-(1+2w)/(1+3w)}$, where $M$ and $M_H$ are the mass of the PBH and the horizon mass at the horizon entry, respectively. Therefore the typical value of the spin parameter decreases with the value of $w$. We also evaluate the mass and spin distribution $P(a_{\ast },M)$, taking account of the critical phenomena. We find that, while the spin is mostly distributed in the range of $10^{-3.9}\le a_{\ast }\le 10^{-1.8}$ for the radiation-dominated universe, the peak of the spin distribution is shifted to the larger range $10^{-3.0}\le a_{\ast }\le 10^{-0.7}$ for $w=10^{-3}$.

21 pages, 6 figures, references added: version accepted for publication in JCAP

References in corpus (6)

• Simulations of PBH formation at the QCD epoch and comparison with the GWTC-3 catalog
• Primordial black hole formation during the QCD phase transition: threshold, mass distribution and abundance
• Spins of primordial black holes formed in the radiation-dominated phase of the universe: first-order effect
• Toward the primordial black hole formation threshold in a time-dependent equation-of-state background
• Extreme-Value Statistics of the Spin of Primordial Black Holes
• Effective inspiral spin distribution of primordial black hole binaries

Cited by in corpus (2)

• Superradiant Leptogenesis
• Spinning Primordial Black Holes from First Order Phase Transition