Detecting dark matter substructure with lensed quasars in optical bands

TL;DR

This work demonstrates that optical flux ratios of strongly lensed quasars, despite contamination from stellar microlensing, can be used to probe dark matter substructure by leveraging a Kolmogorov–Smirnov test. The authors simulate a representative sample of 100 systems (90 doubles, 10 quads) with both CDM subhalos and FDM-induced fluctuations, and they show that quads offer the strongest constraint power, with tens to a few hundred independent flux ratio measurements being sufficient to distinguish substructure models from microlensing plus noise. They also show that multi-band flux ratios can substantially reduce the required sample size. The approach broadens the wavelength range for flux-ratio studies and highlights the practical potential of upcoming wide-field surveys to constrain dark matter properties in the near future.

Abstract

Flux ratios of multiple images in strong gravitational lensing systems provide a powerful probe of dark matter substructure. Optical flux ratios of lensed quasars are typically affected by stellar microlensing, and thus studies of dark matter substructure often rely on emission regions that are sufficiently extended to avoid microlensing effects. To expand the accessible wavelength range for studying dark matter substructure through flux ratios and to reduce reliance on specific instruments, we confront the challenges posed by microlensing and propose a method to detect dark matter substructure using optical flux ratios of lensed quasars. We select 100 strong lensing systems consisting of 90 doubles and 10 quads to represent the overall population and adopt the Kolmogorov--Smirnov (KS) test as our statistical method. By introducing different types of dark matter substructure into these strong lensing systems, we demonstrate that using quads alone provides the strongest constraints on dark matter and that several tens to a few hundred independent flux ratio measurements from quads can be used to study the properties of dark matter substructure and place constraints on dark matter parameters. Furthermore, we suggest that the use of multi-band flux ratios can substantially reduce the required number of quads. Such sample sizes will be readily available from ongoing and upcoming wide-field surveys.

Figures (12)

• Figure 1: Probability density curve of the Einstein radii for all the selected strong lensing systems, obtained with a Gaussian kernel density estimator. The black dashed line indicates the median Einstein radius.
• Figure 2: Probability density curve of the Einstein radii for the selected quads, obtained with a Gaussian kernel density estimator. The black dashed line indicates the median Einstein radius.
• Figure 3: Redshift distribution of all strong lensing systems, with green and red dots representing doubles and quads, respectively. The black dashed lines mark the median lens and source redshifts. The upper and right panels show the probability density estimates of the lens and source redshift distributions, obtained with a Gaussian kernel density estimator.
• Figure 4: Cumulative number of CDM subhalos generated by SASHIMI-C for a strong lensing system with a host halo mass of $M_{200} = 10^{12.35}\,\mathrm{M}_\odot$, concentration parameter $c_{200} = 9.5$, lens redshift $z_l = 0.789$, and source redshift $z_s = 1.74$.
• Figure 5: Surface mass density and critical curve maps for a strong lensing system with a host dark matter halo of $M_{200} = 10^{12.35}\,\mathrm{M}_\odot$, $c_{200} = 9.5$, lens redshift $z_l = 0.789$, and source redshift $z_s = 1.74$. The left panel shows the smooth mass model without any substructure. The middle panel includes CDM subhalos with a mean substructure mass fraction of $\bar{f}_\mathrm{sub} \approx 0.04$, modeled with a TNFW profile. The right panel includes FDM-induced fluctuations corresponding to an ultra-light boson mass of $m_{\psi} = 10^{-22}\,{\mathrm{eV}}$.