Primordial Black Holes as Dark Matter: Converting Constraints from
  Monochromatic to Extended Mass Distributions
  The model in which Primordial Black Holes (PBHs) constitute a non-negligible
fraction of the dark matter has (re)gained popularity after the first
detections of binary black hole mergers. Most of the observational constraints
to date have been derived assuming a single mass for all the PBHs, although
some more recent works tried to generalize constraints to the case of extended
mass functions. Here we derive a general methodology to obtain constraints for
any PBH Extended Mass Distribution (EMD) and any observables in the desired
mass range. Starting from those obtained for a monochromatic distribution, we
convert them into constraints for EMDs by using an equivalent, effective mass
$M_{\rm eq}$ that depends on the specific observable. We highlight how limits
of validity of the PBH modelling affect the EMD parameter space. Finally, we
present converted constraints on the total abundance of PBH from microlensing,
stellar distribution in ultra-faint dwarf galaxies and CMB accretion for
Lognormal and Power Law mass distributions, finding that EMD constraints are
generally stronger than monochromatic ones.
