LIGO Lo(g)Normal MACHO: Primordial Black Holes survive SN lensing constraints

TL;DR

This work re-evaluates constraints on primordial black holes as dark matter using type Ia supernova lensing. By accounting for the degeneracy between the matter density $\Omega_{\rm m}$ and the PBH fraction $\alpha$, incorporating finite supernova sizes, and exploring broad PBH mass spectra (notably lognormal distributions) and potential clustering, the authors show that previous SN-lensing bounds can be significantly weakened. In particular, monochromatic PBH in the few solar-mass range and broad lognormal distributions can still comprise all of the dark matter in the LIGO mass window, with upper bounds on $f_{\rm PBH}$ near or above unity depending on the SN catalog. The results suggest SN lensing remains a promising probe for PBH-DM with upcoming surveys (DES, LSST, Euclid) providing sharper tests.

Abstract

It has been claimed in Ref.[arXiv:1712.02240] that massive primordial black holes (PBH) cannot constitute all of the dark matter (DM), because their gravitational-lensing imprint on the Hubble diagram of type Ia supernovae (SN) would be incompatible with present observations. In this paper, we critically review those constraints and find several caveats on the analysis. First of all, the constraints on the fraction $α$ of PBH in matter seem to be driven by a very restrictive choice of priors on the cosmological parameters. In particular, the degeneracy between $Ω_{\rm M}$ and $α$ is ignored and thus, by fixing $Ω_{\rm M}$, transferred the constraining power of SN magnitudes to $α$. Furthermore, by considering more realistic physical sizes for the type-Ia supernovae, we find an effect on the SN lensing magnification distribution that leads to significantly looser constraints. Moreover, considering a wide mass spectrum of PBH, such as a lognormal distribution, further softens the constraints from SN lensing. Finally, we find that the fraction of PBH that could constitute DM today is bounded by $f_{\rm PBH} < 1.09\ (1.38)$, for JLA (Union 2.1) catalogs, and thus it is perfectly compatible with an all-PBH dark matter scenario in the LIGO band.

Figures (5)

• Figure 1: PDF of the magnification, at $z=1$, for different values of the fraction $\alpha$ of dark matter made of compact objects.
• Figure 2: Top: PDF of the magnitude of lensed SNe at $z=1$, including the intrisinc disperson of luminosities, for different values of the fraction $\alpha$ of compact objects constituting the dark matter. Bottom: same as above but rescaled and shifted so that the maxima coincide.
• Figure 3: Top: The effective PBH fraction as a function of the source redshift for different PBH masses. Bottom: The mass-integrated PBH fraction as a function of the source redshift, for a Lognormal distribution with parameters $\mu=2.5\,M_\odot$ and $\sigma=1.15$, as found in agreement with all present constraints Clesse:2017bsw.
• Figure 4: The JLA and Union 2.1 SN-Ia redshift distributions.
• Figure 5: The constraints on PBH-DM in the range of masses near the LIGO band. We have shown with a dashed line the constraints from EROS because of the assumption of monochromaticity and the absence of clustering, which essentially removes this constraint from the band, see Ref. Garcia-Bellido:2017xvr. The blue contours correspond to the SN lensing constraints for JLA (continuous) and Union 2.1 (dashed) SN catalogs; the green contours arise from Eridanus II dwarf spheroidal Brandt:2016acoGreen:2016xgyLi:2016utv, and the red contours from the disruptiuon of wide binaries in the Milky Way halo MonroyRodriguez:2014ula.