How open is the asteroid-mass primordial black hole window?
Matthew Gorton, Anne M. Green
Abstract
Primordial black holes (PBHs) can make up all of the dark matter (DM) if their mass, m <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>m</mml:mi> </mml:math> , is in the so-called “asteroid-mass window”, 10^{17} g ≲ m ≲ 10^{22} g <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>17</mml:mn> </mml:msup> <mml:mi>g</mml:mi> <mml:mo>≲</mml:mo> <mml:mi>m</mml:mi> <mml:mo>≲</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>22</mml:mn> </mml:msup> <mml:mi>g</mml:mi> </mml:mrow> </mml:math> . Observational constraints on the abundance of PBHs are usually calculated assuming they all have the same mass, however this is unlikely to be a good approximation. PBHs formed from the collapse of large density perturbations during radiation domination are expected to have an extended mass function (MF), due to the effects of critical collapse. The PBH MF is often assumed to be lognormal, however it has recently been shown that other functions are a better fit to numerically calculated MFs. We recalculate both current and potential future constraints for these improved fitting functions. We find that for current constraints the asteroid-mass window narrows, but remains open (i.e. all of the DM can be in the form of PBHs) unless the PBH MF is wider than expected. Future evaporation and microlensing constraints may together exclude all of the DM being in PBHs, depending on the width of the PBH MF and also the shape of its low and high mass tails.