The Maximal-Density Mass Function for Primordial Black Hole Dark Matter

Abstract

The advent of gravitational wave astronomy has rekindled interest in primordial black holes (PBH) as a dark matter candidate. As there are many different observational probes of the PBH density across different masses, constraints on PBH models are dependent on the functional form of the PBH mass function. This complicates general statements about the mass functions allowed by current data, and, in particular, about the maximum total density of PBH. Numerical studies suggest that some forms of extended mass functions face tighter constraints than monochromatic mass functions, but they do not preclude the existence of a functional form for which constraints are relaxed. We use analytical arguments to show that the mass function which maximizes the fraction of the matter density in PBH subject to all constraints is a finite linear combination of monochromatic mass functions. We explicitly compute the maximum fraction of dark matter in PBH for different combinations of current constraints, allowing for total freedom of the mass function. Our framework elucidates the dependence of the maximum PBH density on the form of observational constraints, and we discuss the implications of current and future constraints for the viability of the PBH dark matter paradigm.

19 pages, 3 figures. Matched published version

References in corpus (4)

• GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence
• Primordial Black Holes as Dark Matter
• Limits on the Macho Content of the Galactic Halo from the EROS-2 Survey of the Magellanic Clouds
• Cosmic microwave background limits on accreting primordial black holes

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