[Paper Review] A Stringent Upper Limit on Dark Matter Self-Interaction Cross Section from Cluster Strong Lensing

Kevin E Andrade, Jackson Fuson+5 more|arXiv (Cornell University)|Dec 11, 2020

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy120 references88 citations

TL;DR

This study uses strong gravitational lensing in 8 massive galaxy clusters to constrain the self-interaction cross section of dark matter (DM), finding σ/m = 0.082+0.027−0.021 cm²/g at 68% credibility and σ/m < 0.13 cm²/g at 95% confidence. The method combines lens modeling with a self-interacting dark matter (SIDM) halo profile, inferring DM density profiles from image positions and fitting them to an analytic SIDM model, yielding one of the tightest constraints to date on DM self-interactions using only strong lensing data.

ABSTRACT

We analyze strongly lensed images in 8 galaxy clusters to measure their dark matter density profiles in the radial region between 10 kpc and 150 kpc, and use this to constrain the self-interaction cross section of dark matter (DM) particles. We infer the mass profiles of the central DM halos, bright central galaxies, key member galaxies, and DM subhalos for the member galaxies for all 8 clusters using the Qlens code. The inferred DM halo surface densities are fit to a self-interacting dark matter (SIDM) model, which allows us to constrain the self-interaction cross section over mass $\sigma$/m. When our full method is applied to mock data generated from two clusters in the Illustris-TNG simulation, we find results consistent with no dark matter self-interactions as expected. For the eight observed clusters with average relative velocities of $1458_{-81}^{+80}$ km/s, we infer $\sigma$/m = $0.082_{-0.021}^{+0.027}$ cm$^2$/g and $\sigma$/m < 0.13 cm$^2$/g at the 95% confidence level.

Motivation & Objective

• To constrain the self-interaction cross section of dark matter (σ/m) using strong gravitational lensing in massive galaxy clusters.
• To test whether strong lensing alone can yield robust constraints on self-interacting dark matter (SIDM) by modeling DM and baryonic mass distributions in cluster centers.
• To assess systematic biases in concentration and halo shape from line-of-sight projections and model assumptions in lensing-based DM profile inference.
• To validate the method using mock data from the Illustris-TNG simulation, ensuring consistency with no self-interactions.

Proposed method

• The QLens code is used to model the total mass distribution in 8 relaxed galaxy clusters, including contributions from dark matter halos, bright central galaxies (BCGs), member galaxies, and DM subhalos.
• Strong lensing images are used to infer surface mass density profiles, with image positions and multiple images serving as constraints in the lens modeling.
• An analytic SIDM halo model is applied, where the outer profile follows an NFW form and the inner region becomes isothermal due to self-interactions, with the transition radius determined by σ/m.
• The halo is allowed to be elongated along the line of sight using a cosmological prior to regulate axis ratios, reducing biases from projection effects.
• The inferred σ/m values from all clusters are combined with a common systematic error to derive a global constraint, accounting for modeling uncertainties.
• The method is validated on two mock clusters from the Illustris-TNG simulation, confirming consistency with zero self-interactions.

Experimental results

Research questions

• RQ1 Can strong gravitational lensing alone provide a stringent constraint on the self-interaction cross section of dark matter (σ/m)?
• RQ2 How do halo elongation and line-of-sight projections affect the inference of DM concentration and σ/m in lensing models?
• RQ3 To what extent do baryonic components, particularly the BCG, influence the inferred DM density profile and σ/m in high-mass clusters?
• RQ4 How do the inferred DM halo parameters compare to expectations from ΛCDM and SIDM simulations?
• RQ5 What is the impact of systematic errors in lens modeling on the final σ/m constraint?

Key findings

• The analysis yields a 68% credible interval constraint of σ/m = 0.082+0.027−0.021 cm²/g for the self-interaction cross section per unit mass of dark matter.
• At 95% confidence, the upper limit is σ/m < 0.13 cm²/g, representing one of the tightest constraints on SIDM from cluster-scale lensing.
• The mean relative velocity of DM particles in the clusters is 1458+80−81 km/s, which is relevant for velocity-dependent cross sections.
• The median offset between the BCG and DM halo center is 4 kpc in projection, consistent with expectations for low σ/m scenarios (σ/m ≪ 1 cm²/g).
• The method successfully reproduces image positions with RMS errors between 0.′′32 and 1.′′07, with only one outlier image in MACS2129.
• Systematic error from modeling is estimated at 0.27 dex, indicating potential biases from imperfect halo or baryonic profile assumptions.