Constraints on primordial black holes as dark matter candidates from star formation

By considering adiabatic contraction of the dark matter (DM) during star formation, we estimate the amount of DM trapped in stars at their birth. If the DM consists partly of primordial black holes (PBHs), they will be trapped together with the rest of the DM and will be finally inherited by a star compact remnant --- a white dwarf (WD) or a neutron star (NS), which they will destroy in a short time. Observations of WDs and NSs thus impose constraints on the abundance of PBH. We show that the best constraints come from WDs and NSs in globular clusters which exclude the DM consisting entirely of PBH in the mass range $10^{16}{\rm g} - 3\times 10^{22}{\rm g}$, with the strongest constraint on the fraction $\Omega_{\rm PBH} /\Omega_{\rm DM}\lesssim 10^{-2}$ being in the range of PBH masses $10^{17}{\rm g} - 10^{18}$ g.