Microlensing and dynamical constraints on primordial black hole dark matter with an extended mass function

TL;DR

The paper examines whether PBHs with extended mass functions could constitute all dark matter without violating microlensing and dynamical constraints. It recalculates these constraints for DHFs inspired by inflationary PBH formation, rather than delta-function masses, focusing on $1-10^{3}\,M_
$. It finds that microlensing sets a lower bound on the width of the mass distribution while dynamical heating sets an upper bound, and these bounds do not overlap for the considered DHFs. As a result, none of the modeled extended mass functions can satisfy both constraints, highlighting the need for constraint recalculation for any specific DHF.

Abstract

The recent discovery of gravitational waves from mergers of $\sim 10 \, M_{\odot}$ black hole binaries has stimulated interested in Primordial Black Hole dark matter in this mass range. Microlensing and dynamical constraints exclude all of the dark matter being in compact objects with a delta function mass function in the range $10^{-7} \lesssim M/ M_{\odot} \lesssim 10^{5}$. However it has been argued that all of the dark matter could be composed of compact objects in this range with an extended mass function. We explicitly recalculate the microlensing and dynamical constraints for compact objects with an extended mass function which replicates the PBH mass function produced by inflation models. We find that the microlensing and dynamical constraints place conflicting constraints on the width of the mass function, and do not find a mass function which satisfies both constraints.

Figures (4)

• Figure 1: The constraints on the halo fraction, $f$, of MACHOs as a function of mass, $M$, for a delta function mass function. The green solid line is a digitisation of the result from the EROS-2 microlensing survey (bottom panel of Fig. 15 of Ref. Tisserand:2006zx) and the black dotted line is our implementation of their constraint, as described in the text. The published EROS-2 limit stops at $f \sim 0.6$ because they only plot the limit for halo fractions in the range $0<f<0.6$. The short red and long blue dashed lines are from the disruption of the star cluster in Eridanus II and the heating of ultra-faint dwarfs respectively Brandt:2016aco. See the text for details
• Figure 2: The PBH DHF, ${\rm d} f/{\rm d} M$, for the axion-curvaton (red dotted line) and running mass (blue dashed) inflation models from Ref. Carr:2016drx. The black lines are the least squares fit of the functional form Eq. (\ref{['lnmf']}) to these DHFs. In all cases the DHFs integrate to unity (i.e. all of the halo dark matter is in the form of PBHs).
• Figure 3: Constraints on the width, $\sigma$, of the DHF functional form, eq. (\ref{['lnmf']}), as a function of the central mass $M_{\rm c}$. Parameter values in the red hatched area in the bottom left produce $N_{\rm exp} \geq 3$ microlensing events in the EROS-2 survey and are excluded at $95\%$ confidence. The blue hatched area in the top right is excluded by the heating of ultra-faint dwarfs. The constraint from the disruption of the star cluster in Eri II is tighter and excludes a large region of parameter space
• Figure 4: The differential PBH halo fraction, ${\rm d} f/{\rm d} M$, for the axion-curvaton (dotted red line) inflation model from Ref. Carr:2016drx compared with the broadest differential halo fraction, centered at the same mass, which satisfies the ultra-faint dwarf disruption constraint (solid green) and the narrowest differential halo fraction which satisfies the EROS-2 microlensing constraint (dashed black).