  Baryonic gas falling onto a primordial black hole (PBH) emits photons via the
free-free process. These photons can contribute the diffuse free-free
background radiation in the frequency range of the cosmic microwave background
radiation (CMB). We show that the intensity of the free-free background
radiation from PBHs depends on the mass and abundance of PBHs. In particular,
considering the growth of a dark matter (DM) halo around a PBH by non-PBH DM
particles strongly enhances the free-free background radiation. Large PBH
fraction increase the signal of the free-free emission. However, large PBH
fraction also can heat the IGM gas and, accordingly, suppresses the accretion
rate. As a result, the free-free emission decreases when the PBH fraction is
larger than 0.1. We find that the free-free emission from PBHs in the CMB and
radio frequency is much lower than the CMB blackbody spectrum and the observed
free-free emission component in the background radiation. Therefore, it is
difficult to obtain the constraint from the free-free emission observation.
However further theoretical understanding and observation on the free-free
emission from cosmological origin is helpful to study the PBH abundance with
the stellar mass.
