The abundance of primordial black holes from the global 21cm signal and extragalactic gamma-ray background

Primordial black holes (PBHs) formed in the early Universe can accret dark matter particles due to gravity and form ultracompact minihalos (UCMHs). The theoretical researches and simulations have shown that the density profile of dark matter in UCMHs is in the form of $\rho (r) \sim r^{-2.25}$. Compared with the popular dark matter halo model, e.g. NFW model, dark matter annihilation rate is larger in UCMHs. Considering dark matter annihilation, there is a maximum core density $\rho_{\rm max}$ in UCMHs which has been treated independent on redshift. While in this work, we point out that $\rho_{\rm max}$ depends on redshift and dark matter annihilation rate in UCMHs also changes with time. We re-investigate the $\gamma$-ray flux from UCMHs due to dark matter annihilation and focus on their contributions to the extragalactic gamma-ray background (EGB). Utilizing the EGB data of Fermi, the constraints on the abundance of PBHs are derived, $\Omega_{\rm PBH,EGB} \lesssim 2\times 10^{-8}$. Motivated by the recent observations of global 21cm signals by the EDGES experiment, we investigate the influences of dark matter annihilation in UCMHs on global 21cm signals and derive the constraints on the abundance of PBHs, $\Omega_{\rm PBH,21cm} \lesssim 2\times 10^{-10}$. The derived constraints are valid for mass range of $10^{-6} M_{\odot} \lesssim M_{\rm PBH} \lesssim 10^{3} M_{\odot}$.