Probing Dark Matter Substructure with Image Number Anomaly in Strong Lensing Systems

TL;DR

This study uses gravitational lensing image number anomalies to constrain dark matter substructure, setting upper limits on primordial black holes and fuzzy dark matter based on null detection in simulated data.

Contribution

It introduces a novel method leveraging image number anomalies in strong lensing to place constraints on dark matter substructure, including PBHs and FDM.

Findings

Upper limits on PBH abundance are set at 0.125%, 0.08%, and 0.04% for different angular resolutions.

Constraints exclude FDM particle masses below 0.4, 0.6, and 3.5 x 10^{-22} eV at corresponding resolutions.

Potential to constrain PBH abundance to 0.9% at 0.5'' resolution with LSST observations.

Abstract

Gravitational lensing observables, including anomalies in image positions, flux ratios, and time delays, serve as usual probes of dark matter (DM) substructure. When dark matter substructure possesses sufficient perturbations, it may lead to the formation of extra images in otherwise canonical doubly or quadruply imaged systems. With the advent of increasingly precise observational instruments, previously undetectable images may become measurable and image number anomalies therefore could be an increasingly viable method. In this paper, we utilize the gravitational lensing phenomenon of image number anomaly to derive constraints on dark matter substructure. We present the extra images induced by distinct forms of DM substructure, specifically primordial black holes (PBHs) and fuzzy dark matter (FDM) and show that higher angular resolution observations increase the probability of detecting additional lensed images. Based on a null detection of image number anomalies in a sample of 3500 lens systems generated from the \textit{Strong Lensing Halo model-based mock catalogs} (SL-Hammocks), we derive upper limits on the abundance of PBHs. At the 95\% confidence level, the PBH abundance is constrained to $\lesssim 0.125\%$, $0.08\%$, and $0.04\%$ for PBH masses in the range $\sim 10^{7}$--$10^{9}~M_{\odot}$, corresponding to angular resolutions of $0.1''$, $0.05''$, and $0.01''$, respectively. Similarly, we exclude particle masses below $0.4$, $0.6$, and $3.5 \times 10^{-22} \ \mathrm{eV}$ for FDM at the same confidence level for the respective resolutions. Furthermore, the abundance of PBHs $\lesssim 0.9\%$ could be constrained at an angular resolution of $0.5''$ for the Legacy Survey of Space and Time (LSST) Observations. Finally, we discuss methodologies for identifying image number anomalies in special cases and demonstrate feasibility using a fitting procedure.