Cosmic microwave background limits on accreting primordial black holes

TL;DR

This study develops a conservative, semi-analytic model of accreting PBHs in the early Universe, incorporating Bondi-like spherical accretion with Compton drag/cooling, local feedback limits, and energy deposition into the plasma to predict CMB signatures. By coupling this to energy deposition calculations and modifying recombination histories, the authors compare against Planck CMB anisotropies and FIRAS spectral data. They find that Planck data constrain PBHs with masses above roughly 10^2 solar masses from being the dominant dark matter component under their most conservative assumptions, while spectral distortions from PBHs remain undetectable with current and near-future experiments. The results differ from earlier ROM limits primarily due to a more physically grounded, lower radiative efficiency and a reduced accretion rate, plus a careful treatment of PBH–baryon velocities, yet substantial uncertainties remain in disk formation, clustering, and ionization feedback that warrant further study.

Abstract

Interest in the idea that primordial black holes (PBHs) might comprise some or all of the dark matter has recently been rekindled following LIGO's first direct detection of a binary-black-hole merger. Here we revisit the effect of accreting PBHs on the cosmic microwave background (CMB) frequency spectrum and angular temperature/polarization power spectra. We compute the accretion rate and luminosity of PBHs, accounting for their suppression by Compton drag and Compton cooling by CMB photons. We estimate the gas temperature near the Schwarzschild radius, and hence the free-free luminosity, accounting for the cooling resulting from collisional ionization when the background gas is mostly neutral. We account approximately for the velocities of PBHs with respect to the background gas. We provide a simple analytic estimate of the efficiency of energy deposition in the plasma. We find that the spectral distortions generated by accreting PBHs are too small to be detected by FIRAS, as well as by future experiments now being considered. We analyze Planck CMB temperature and polarization data and find, under our most conservative hypotheses, and at the order-of-magnitude level, that they rule out PBHs with masses >~ 10^2 M_sun as the dominant component of dark matter.

Figures (14)

• Figure 1: Schematic temperature profile for the gas accreting onto a BH. If Compton cooling is efficient ($\gamma \gg 1$), the gas temperature remains close to the CMB temperature down to $r \sim \gamma^{-2/3} r_{\rm B}$, where $r_{\rm B}$ is the Bondi radius. The temperature then increases adiabatically as $T \propto \rho^{2/3} \propto 1/r$. If photoionizations can be neglected, and if the background gas is partially neutral, the gas gets collisionally ionized at nearly constant temperature once it reaches $T_{\rm ion} \approx 1.5 \times 10^4$ K. Once the gas is fully ionized, the temperature resumes increasing adiabatically as $T \propto 1/r$ until electrons become relativistic, at which point the change in the adiabatic index implies $T \propto \rho^{4/9} \propto r^{-2/3}$. If the luminosity of the accreting PBH is large enough, the gas is photoionized instead of collisionally ionized. In that case the gas temperature reaches larger values near the black hole horizon.
• Figure 2: Characteristic dimensionless Compton drag rate $\beta$ [Eq. \ref{['eq:beta-def']}, upper panel] and Compton cooling rate $\gamma$ [Eq. \ref{['eq:gamma-def']}, lower panel], as a function of redshift, and for PBH masses $M = 1, 10^2$ and $10^4\, M_{\odot}$, from bottom to top. Both are evaluated for a standard recombination and thermal history, with the substitution $v_{\rm B} \rightarrow v_{\rm eff}$ as described in Section \ref{['sec:velocities']}.
• Figure 3: Dimensionless accretion rate $\lambda$ as a function of the dimensionless Compton cooling rate $\gamma$. Black circles are our numerical results and the purple line is our analytic fit, Eq. \ref{['eq:lambda_fit']}.
• Figure 4: Characteristic dimensionless accretion rate $\lambda$ (upper panel) and accretion rate normalized to the Eddington value $\dot{m} \equiv \dot{M} c^2/L_{\rm Edd}$ (lower panel) as a function of redshift, for PBH masses $1, 10^2$ and $10^4\, M_{\odot}$. These quantities are evaluated with substitution $v_{\rm B} \rightarrow v_{\rm eff}$ as described in Section \ref{['sec:velocities']}.
• Figure 5: Characteristic temperature of the accreting gas near the Schwarzschild radius, evaluated with the substitution $v_{\rm B} \rightarrow v_{\rm eff}$ as described in Section \ref{['sec:velocities']}.