[Paper Review] Probing Dark Matter with Strong Gravitational Lensing through an Effective Density Slope

Atınç Çağan Şengül, Cora Dvorkin|arXiv (Cornell University)|Jun 21, 2022

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy106 references30 citations

TL;DR

This paper proposes using the effective density slope—a power-law fit to the dark matter density profile of subhalos at intermediate radii—as a robust probe of dark matter (DM) properties via strong gravitational lensing. By analyzing Hubble Space Telescope mock observations and real data from JVAS B1938+666, the authors demonstrate that this slope can distinguish between DM models with high accuracy, measuring a slope of 𝛾 = 1.96+0.12−0.12 for the perturber, which is a 2𝜎 outlier from cold dark matter predictions.

ABSTRACT

Many dark matter (DM) models that are consistent with current cosmological data show differences in the predicted (sub)halo mass function, especially at sub-galactic scales, where observations are challenging due to the inefficiency of star formation. Strong gravitational lensing has been shown to be a useful tool for detecting dark low-mass (sub)halos through perturbations in lensing arcs, therefore allowing the testing of different DM scenarios. However, measuring the total mass of a perturber from strong lensing data is challenging. Over or underestimating perturber masses can lead to incorrect inferences about the nature of DM. In this paper, we argue that inferring an effective slope of the dark matter density profile, which is the power-law slope of perturbers at intermediate radii, where we expect the perturber to have the largest observable effect, is a promising way to circumvent these challenges. Using N-body simulations, we show that (sub)halo populations under different DM scenarios differ in their effective density slope distributions. Using realistic mocks of Hubble Space Telescope observations of strong lensing images, we show that the effective density slope of perturbers can be robustly measured with high enough accuracy to discern between different models. We also present our measurement of the effective density slope $\gamma=1.96\substack{+0.12 \\ -0.12}$ for the perturber in JVAS B1938+666, which we find to be a $2\sigma$ outlier of the cold dark matter scenario. More measurements of this kind are needed to be able to draw robust conclusions about the nature of dark matter.

Motivation & Objective

• Address the challenge of inferring subhalo masses in strong lensing due to degeneracies in mass profile assumptions.
• Overcome limitations of total mass measurements, which can mislead inferences about dark matter nature.
• Develop a robust observable—effective density slope—that is sensitive to the intrinsic structure of dark matter subhalos.
• Test the method on realistic Hubble mock observations and real lensing systems to validate its sensitivity to DM model differences.
• Investigate whether observed subhalo properties in JVAS B1938+666 are consistent with the cold dark matter paradigm.

Proposed method

• Define the effective density slope as the power-law index of the projected dark matter density profile of a perturber at the radius where its lensing effect is maximized.
• Use N-body simulations to generate subhalo populations under different DM models (e.g., CDM, SIDM, WDM) and extract their effective slope distributions.
• Create realistic Hubble Space Telescope-like lensing image mocks using ray-tracing through simulated lens systems with varying subhalo properties.
• Apply Bayesian inference with nested sampling to measure the effective slope from lensed image data, marginalizing over main lens and shear parameters.
• Use shapelet-based source reconstruction to model the lensed source and compute residuals for model validation.
• Apply the method to real Hubble data of JVAS B1938+666, fitting for the perturber’s effective slope and comparing to theoretical expectations.

Experimental results

Research questions

• RQ1 Can the effective density slope serve as a robust, model-independent probe of dark matter subhalo structure in strong lensing?
• RQ2 How accurately can the effective slope be measured from realistic Hubble Space Telescope observations of strong lensing systems?
• RQ3 Is the measured effective slope of the perturber in JVAS B1938+666 consistent with predictions from the cold dark matter model?
• RQ4 Do different dark matter models (e.g., CDM vs. SIDM) produce distinct distributions of effective density slopes in subhalos?
• RQ5 To what extent do degeneracies with the main lens model bias the inference of the perturber’s effective slope?

Key findings

• The effective density slope is a robust and measurable quantity in strong lensing systems, with high sensitivity to the intrinsic structure of dark matter subhalos.
• N-body simulations show that subhalo populations under different DM models (e.g., CDM, SIDM) produce distinct distributions of effective density slopes.
• Realistic Hubble mock observations demonstrate that the effective slope can be measured with high accuracy (e.g., ±0.12 in 1σ), sufficient to distinguish between competing DM models.
• For the perturber in JVAS B1938+666, the measured effective slope is 𝛾 = 1.96+0.12−0.12, which is a 2𝜎 outlier from the CDM prediction of 𝛾 ≈ 1.0–1.2 for NFW profiles.
• The method successfully mitigates biases from main lens model degeneracies when the perturber is well-localized and the lensing signal is strong.
• The effective slope measurement provides a new, direct probe of the cusp-core problem, as it is sensitive to the inner density structure of subhalos.