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 ${10}^{16}-3\times {10}^{22}\mathrm{g}$, with the strongest constraint on the fraction ${\Omega }_{\mathrm{PBH}}/{\Omega }_{\mathrm{DM}}\lesssim {10}^{-2}$ being in the range of PBH masses ${10}^{17}–{10}^{18}\mathrm{g}$.

Figure 1

DM density profile obtained from the simulation after the adiabatic formation of a star. The inner part of the profile has the slope close to $-3/2$, as expected from Liouville’s theorem for the uniform initial velocity distribution.

Figure 2

The dependence of the size $r_c$ of the collection region (the region from which the PBHs captured by the star at its formation have enough time to sink to within the radius of the future compact remnant, WD or NS) on the PBH mass, corresponding to the case of WD for $M_{*}=M_{\odot }$.

Figure 3

Constraints on the fraction ${\Omega }_{\mathrm{PBH}}/{\Omega }_{\mathrm{DM}}$. Purple shaded region is excluded by observations of WDs and NSs in the centers of globular clusters. Thin curves show the exclusions from different star masses.