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

The recent discovery of gravitational waves from mergers of $\sim 10M_{\odot }$ black hole binaries has stimulated interested in primordial black hole (PBH) dark matter in this mass range. Microlensing and dynamical constraints exclude all of the dark matter 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.

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 digitization of the result from the EROS-2 microlensing survey (bottom panel of Fig. 15 of Ref. [15]) 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 ultrafaint dwarfs respectively [16]. See the text for details.

Figure 2

The PBH DHF, $\mathrm{d}f/\mathrm{d}M$, for the axion-curvaton (AC) (red dotted line) and running-mass (RM) (blue dashed) inflation models from Ref. [5]. The black lines are the least squares fit of the functional form Eq. (10) 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. (10), as a function of the central mass $M_{\mathrm{c}}$. Parameter values in the red hatched area in the bottom left produce $N_{\exp }\ge 3$ 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 ultrafaint 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, $\mathrm{d}f/\mathrm{d}M$, for the axion-curvaton (dotted red line) inflation model from Ref. [5] compared with the broadest differential halo fraction, centered at the same mass, which satisfies the ultrafaint dwarf disruption constraint (solid green) and the narrowest differential halo fraction which satisfies the EROS-2 microlensing constraint (dashed black).