Limits on stellar-mass compact objects as dark matter from gravitational lensing of type Ia supernovae

TL;DR

The paper tests whether stellar-mass compact objects, especially primordial black holes, can make up the dark matter by analyzing gravitational lensing signatures in Type Ia supernovae. It builds a lensing framework combining PBH-induced magnification PDFs with large-scale structure and finite-source effects, and applies a Bayesian hierarchical approach to SN data from JLA and Union 2.1. The study derives tight 95% confidence upper limits on PBH abundance for M_PBH ≳ 0.01 M_sun (alpha < 0.352–0.372), finds results robust to various systematics, and concludes PBHs cannot be the dominant DM in this mass range, motivating lighter or subdominant DM scenarios. The work complements microlensing and other probes, and sets the stage for stronger constraints with larger SN catalogs in upcoming surveys.

Abstract

The nature of dark matter (DM) remains unknown despite very precise knowledge of its abundance in the universe. An alternative to new elementary particles postulates DM as made of macroscopic compact halo objects (MACHO) such as black holes formed in the very early universe. Stellar-mass primordial black holes (PBHs) are subject to less robust constraints than other mass ranges and might be connected to gravitational-wave signals detected by the Laser Interferometer Gravitational-Wave Observatory (LIGO). New methods are therefore necessary to constrain the viability of compact objects as a DM candidate. Here we report bounds on the abundance of compact objects from gravitational lensing of type Ia supernovae (SNe). Current SNe datasets constrain compact objects to represent less than 35.2% (Joint Lightcurve Analisis) and 37.2% (Union 2.1) of the total matter content in the universe, at 95% confidence-level. The results are valid for masses larger than $\sim 0.01M_\odot$ (solar-masses), limited by the size SNe relative to the lens Einstein radius. We demonstrate the mass range of the constraints by computing magnification probabilities for realistic SNe sizes and different values of the PBH mass. Our bounds are sensitive to the total abundance of compact objects with $M \lesssim 0.01M_\odot$ and complementary to other observational tests. These results are robust against cosmological parameters, outlier rejection, correlated noise and selection bias. PBHs and other MACHOs are therefore ruled out as the dominant form of DM for objects associated to LIGO gravitational wave detections. These bounds constrain early-universe models that predict stellar-mass PBH production and strengthen the case for lighter forms of DM, including new elementary particles.

Figures (9)

• Figure 1: Probability of lensing magnification $\Delta\mu$ (Eq. \ref{['eq:d_lum_magnified']}) and its dependence on SNe redshift $z$ and compact object abundance $\alpha ={\Omega_{\rm PBH}}/{\Omega_M}$. A sizable compact object population displaces the maximum of the PDF towards the empty-beam distance, compensated with a probability tail for high magnification. Both effects grow with redshift, we show only $z\geq 0.2$. Left panel: Probability density function (Eq. \ref{['eq:likelihood']}), normalized to unity. Histograms show to residuals of JLA (blue, solid) and Union 2.1 (green, dashed) data in the redshift ranges shown. Curves show theoretical predictions for negligible PBH (red, solid), 50% PBH (black, dotted) and PBH-only (black, dashed) universes at the mean redshift $\bar{z}$ of the subsample. A fiducial Gaussian scatter with typical SNe uncertainties $\sigma_\mu=0.15$ has been assumed to facilitate comparison of theory and data. Right panel: Tail distribution (cumulative) in logarithmic scale to highlight the enhanced probability of high-magnification in PBH models. Histograms are normalized to the number of SNe in each redshift interval and theory predictions are normalized to the number of JLA SNe. Horizontal lines correspond to 1-4 events and vertical lines mark where 3$\sigma_\mu$, 5$\sigma_\mu$ outliers are expected, relative to the SNe measurement uncertainty.
• Figure 2: Magnification PDF dependence on the PBH mass for extended SNe (compare with Fig. \ref{['fig:pdf_data']}). The curves for each PBH mass assume a SNe radius $R_S \approx 115 AU$ (see Supplemental Material Sec. \ref{['sec:finite_sources']}). Right panel: PDF without noise. For $M\lesssim 10^{-2}M_\odot$ the result converges the analytical fit used in the analysis Rauch:1991. Note that introducing realistic noise (as in Fig. \ref{['fig:pdf_data']}) would render both curves practically indistinguishable around the peak. Left panel: cumulative PDF, convolved with noise. The high-magnification tail decays faster than $(\Delta\mu)^{-3}$ but a significant fraction of highly magnified SNe are predicted even for low PBH masses.
• Figure 3: Bounds on the abundance of PBHs as a function of the mass (95 % confidence level). The analysis of SNe lensing using the JLA (solid) and Union 2.1 compilations (dashed) constrain the PBH fraction in the range $M\gtrsim 0.01 M_\odot$. This range includes the masses of black hole events observed by the Laser Interferometer Gravitational-Wave Observatory (gray), only weakly constrained by previous data including micro-lensing (EROS Tisserand:2006zx), the stability of stellar compact systems (Eridanus II Brandt:2016acoLi:2016utv) and CMB Ali-Haimoud:2016mbvBernal:2017vvn. The CMB excluded regions correspond to Planck-TT (solid), Planck-full (dotted) for the limiting cases of collisional (red) and photo-ionization (orange) (see Bernal:2017vvn for details).
• Figure S1: Lensing in a universe with compact objects. Right panel: Effects of the PBH fraction on the magnification probability density function (equation \ref{['eq:p_theory']}), including compact objects and cosmological large scale structure. Compact objects produce 1) a displacement of the maximum of the PDF towards a demagnified universe and 2) a larger probability of large magnifications. The cases shown correspond to no PBH (solid) and all of the dark matter (but not baryons) in PBH (dashed) at $z=1$. Also shown is the empty beam (vertical dotted line). We see that the probability of reaching empty beam values is negligible for LSS. Left panel: redshift dependence of the shift in the peak of the magnification PDF (equation \ref{['eq:friedman_mu']}) for different cosmologies, along with the SNe distribution. The effect is stronger at high redshifts where there are fewer supernovae (lower panel).
• Figure S2: Breakdown of the point-source approximation for type Ia supernovae. Right panel: Magnification as a function of the impact parameter Schneider87, normalized to the Einstein radius. The magnification saturates for $l/\xi\lesssim \eta$ for low impact parameter values $l\lesssim \eta$. Left panel: Maximum magnification of a source at $z_S = 1$ by a lens at $z_L$ (upper panel) for different values of the size parameter $\eta_0$ (corresponding lens mass in units of $M_\odot$). Horizontal lines show $\mu=1$ and $\bar{\mu}$ (equation \ref{['eq:friedman_mu']}), showing that SNe can be highly magnified even for very light PBHs, particularly at low redshift. The differential optical depth (lower panel) weights the effective contribution of lenses at different redshift $z_L$.