  As the only dark matter candidate that does not invoke a new particle that
survives to the present day, primordial black holes (PBHs) have drawn
increasing attention recently. Up to now, various observations have strongly
constrained most of the mass range for PBHs, leaving only small windows where
PBHs could make up a substantial fraction of the dark matter. Here we revisit
the PBH constraints for the asteroid-mass window, i.e., the mass range
$3.5\times 10^{-17}M_\odot < m_{\mathrm{PBH}} < 4\times 10^{-12}M_\odot$. We
revisit 3 categories of constraints. (1) For optical microlensing, we analyze
the finite source size and diffractive effects and discuss the scaling
relations between the event rate, $m_{\mathrm{PBH}}$ and the event duration. We
argue that it will be difficult to push the existing optical microlensing
constraints to much lower m$_{\mathrm{PBH}}$. (2) For dynamical capture of PBHs
in stars, we derive a general result on the capture rate based on phase space
arguments. We argue that survival of stars does not constrain PBHs, but that
disruption of stars by captured PBHs should occur and that the asteroid-mass
PBH hypothesis could be constrained if we can work out the observational
signature of this process. (3) For destruction of white dwarfs by PBHs that
pass through the white dwarf without getting gravitationally captured, but
which produce a shock that ignites carbon fusion, we perform a 1+1D
hydrodynamic simulation to explore the post-shock temperature and relevant
timescales, and again we find this constraint to be ineffective. In summary, we
find that the asteroid-mass window remains open for PBHs to account for all the
dark matter.
