Primordial black holes capture by stars and induced collapse to low-mass stellar black holes

Primordial black holes in the asteroid-mass window ($\sim 10^{-16}$ to $10^{-11} \rm M_{\odot}$), which might constitute all the dark matter, can be captured by stars when they traverse them at low enough velocity. After being placed on a bound orbit during star formation, they can repeatedly cross the star if the orbit happens to be highly eccentric, slow down by dynamical friction and end up in the stellar core. The rate of these captures is highest in halos of high dark matter density and low velocity dispersion, when the first stars form at redshift $z \sim 20$. We compute this capture rate for low-metallicity stars of $0.3$ to $1\rm M_{\odot}$, and find that a high fraction of these stars formed in the first dwarf galaxies would capture a primordial black hole, which would then grow by accretion up to a mass that may be close to the total star mass. We show the capture rate of primordial black holes does not depend on their mass over this asteroid-mass window, and should not be much affected by external tidal perturbations. These low-mass stellar black holes could be discovered today in low-metallicity, old binary systems in the Milky Way containing a surviving low-mass main-sequence star or a white dwarf, or via gravitational waves emitted in a merger with another compact object. No mechanisms in standard stellar evolution theory are known to form black holes of less than a Chandrasekhar mass, so detecting a low-mass black hole would fundamentally impact our understanding of stellar evolution, dark matter and the early Universe.