Primordial Black Holes as Dark Matter

TL;DR

This work evaluates primordial black holes as dark matter candidates, emphasizing three broad mass windows and Planck-mass relics. It develops a novel, model-independent framework to test extended PBH mass spectra against a comprehensive set of observational constraints, incorporating key formation physics such as critical collapse, non-sphericity, and non-Gaussianity. By applying this framework to two inflationary models (running-mass and axion-like curvaton), the paper shows that PBHs could still account for all dark matter in some windows but that realistic extended spectra and astrophysical uncertainties complicate the picture. The findings highlight the necessity of treating extended mass functions carefully when deriving inflationary constraints from PBH observations and point to ongoing opportunities and challenges for future gravitational-wave and astrophysical data.

Abstract

The possibility that the dark matter comprises primordial black holes (PBHs) is considered, with particular emphasis on the currently allowed mass windows at $10^{16}$ - $10^{17}\,$g, $10^{20}$ - $10^{24}\,$g and $1$ - $10^{3}\,M_{\odot}$. The Planck mass relics of smaller evaporating PBHs are also considered. All relevant constraints (lensing, dynamical, large-scale structure and accretion) are reviewed and various effects necessary for a precise calculation of the PBH abundance (non-Gaussianity, non-sphericity, critical collapse and merging) are accounted for. It is difficult to put all the dark matter in PBHs if their mass function is monochromatic but this is still possible if the mass function is extended, as expected in many scenarios. A novel procedure for confronting observational constraints with an extended PBH mass spectrum is therefore introduced. This applies for arbitrary constraints and a wide range of PBH formation models, and allows us to identify which model-independent conclusions can be drawn from constraints over all mass ranges. We focus particularly on PBHs generated by inflation, pointing out which effects in the formation process influence the mapping from the inflationary power spectrum to the PBH mass function. We then apply our scheme to two specific inflationary models in which PBHs provide the dark matter. The possibility that the dark matter is in intermediate-mass PBHs of $1$ - $10^{3}\,M_{\odot}$ is of special interest in view of the recent detection of black-hole mergers by LIGO. The possibility of Planck relics is also intriguing but virtually untestable.

Figures (6)

• Figure 1: Effect of critical collapse on the fraction $f$ as a function of black-hole mass in units of solar mass for a nearly monochromatic mass function ( left panel), and for axion-like curvaton (red) as well as running-mass inflation (blue) ( right panel). The latter models are specified in Sec. \ref{['sec:SpecificModelsInRelevantRanges']}. Solid lines show the PBH abundances for the horizon-mass collapse estimate, dashed lines show the same models with critical collapse included.
• Figure 2: Fraction $f$ as a function of black-hole mass in units of solar mass for axion-like curvaton (red) as well as running-mass inflation (blue); the models are specified in Sec. \ref{['sec:ExtendedPBH']}. Left panel: Effect of non-sphericity (dotted lines), with parameters $\kappa = 9 / \sqrt{10\space\pi\,}$ and $\gamma = 1 / 2$ (see Eq. \ref{['eq:Sheth-Mo-Tormen']}). Right panel: Effect of non-Gaussianity (dot-dashed curves), where we chose $f_{\rm NL} = +\,0.005$ (lower curve) and $f_{\rm NL} = -\,0.005$ (upper curve). In both cases the parameter choices are made for illustrative purpose (see main text for details). Critical collapse is assumed throughout the plots.
• Figure 3: Constraints on $f( M )$ for a variety of evaporation (magenta), dynamical (red), lensing (cyan), large-scale structure (green) and accretion (orange) effects associated with PBHs. The effects are extragalactic $\gamma$-rays from evaporation (EG) Carr:2009jm, femtolensing of $\gamma$-ray bursts (F) Barnacka:2012bm, white-dwarf explosions (WD) 2015PhRvD..92f3007G, neutron-star capture (NS) Capela:2013yf, Kepler microlensing of stars (K) Griest:2013aaa, MACHO/EROS/OGLE microlensing of stars (ML) Tisserand:2006zxNovati:2013fxa and quasar microlensing (broken line) (ML) 2009ApJ...706.1451M, survival of a star cluster in Eridanus II (E) Brandt:2016aco, wide-binary disruption (WB) Quinn:2009zg, dynamical friction on halo objects (DF) Carr:1997cn, millilensing of quasars (mLQ) Wilkinson:2001vv, generation of large-scale structure through Poisson fluctuations (LSS) Afshordi:2003zb, and accretion effects (WMAP, FIRAS) Ricotti:2007au. Only the strongest constraint is usually included in each mass range, but the accretion limits are shown with broken lines since they are are highly model-dependent. Where a constraint depends on some extra parameter which is not well-known, we use a typical value. Most constraints cut off at high $M$ due to the incredulity limit. See the original references for more accurate forms of these constraints.
• Figure 4: Four windows in which PBHs could conceivably provide the dark-matter density. Upper left panel$\mspace{1.5mu}$: (A) Intermediate-mass black holes. The constraints in this mass range are EROS and MACHO microlensing bounds Tisserand:2006zx (in blue), dynamical constraints (in red) from the life-time of the central star cluster in the Eridanus II dwarf galaxy Brandt:2016aco, as well as dynamical constraints (in green) from the existence of wide-binary star systems Quinn:2009zg. Upper right panel$\mspace{1.5mu}$: (B) Sublunar black holes; In this case the constraints (in blue) are again the femtolensing of GRBs from Barnacka:2012bm, while the limits from neutron-star capture (in green) are taken from Capela:2013yf. The red-shaded region to the right-hand side of the plot denotes microlensing constraints from the Kepler survey Griest:2013aaa, , while the red-shaded region to the plot's left-hand side shows constraints from white-dwarf explosions 2015PhRvD..92f3007G. Lower left panel$\mspace{1.5mu}$: (C) Subatomic black holes. The constraints here (red-shaded region) stem from non-detections of extragalactic $\gamma$-rays that would be observable from the evaporation of PBHs of these masses Carr:2009jmCarr:2016hva, and (in blue) femtolensing of $\gamma$-ray bursts (GRBs) taken from Fermi data Barnacka:2012bm. Lower right panel$\mspace{1.5mu}$: (D) Planck-mass relics from PBH evaporations. This shows the mass range of the initial PBHs if they derive from inflation Carr:1994ar but there are no observational constraints on such relics. Details on all these regimes and the meaning of the constraints can be found in the subsections on the respective scenarios.
• Figure 5: Constraints on the dark-matter fraction of primordial black holes in the intermediate-mass range $M_{\odot} < M < 10^{3}\,M_{\odot}$. Excluded regions are shaded. EROS constraints are taken from Ref. Tisserand:2006zx and are depicted in blue. Wide-binary (WB) constraints Chaname:2003fnYoo:2003fr correspond to the green region in the plot. The latest constraints from the survival of the star cluster near the core of Eridanus II Brandt:2016aco are shown in the red-shaded areas. For all red curves we assume a cluster age of $3\,{\rm Gyr}$. The various constraints are due to different choices of values for the velocity dispersion $\sigma$ and $\rho$, the dark-matter density in the center of the galaxy. Specifically, we chose $( \sigma, \rho ) = ( 5\,{\rm km}\space{\rm s}^{-1}, 0.1\,M_{\odot}\space{\rm pc}^{-3} )$ (red solid), $( \sigma, \rho ) = ( 10\,{\rm km}\space{\rm s}^{-1}, 0.1\,M_{\odot}\space{\rm pc}^{-3} )$ (red dashed), $( \sigma, \rho ) = ( 5\,{\rm km}\space{\rm s}^{-1}, 0.01\,M_{\odot}\space{\rm pc}^{-3} )$ (red dot-dashed), and $( \sigma, \rho ) = ( 10\,{\rm km}\space{\rm s}^{-1}, 0.01\,M_{\odot}\space{\rm pc}^{-3} )$ (red dotted).