Cosmic microwave background limits on accreting primordial black holes

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 the angular temperature and 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 ≳1 0² M_⊙ as the dominant component of dark matter.