A Constraint on Dark Matter Self-Interaction from Combined Strong Lensing and Stellar Kinematics in MACS J0138-2155

Abstract

Self-Interacting Dark Matter (SIDM) represents a compelling alternative to collisionless dark matter, with diverse phenomenological signals from dwarf galaxy to galaxy cluster scales. We present new constraints on the SIDM cross section from the galaxy cluster MACS J0138-2155, host to the strongly lensed supernovae Requiem and Encore. Our analysis combines strong gravitational lensing with spatially resolved stellar kinematics of the central galaxy, employing several methodological advances over previous cluster-scale SIDM studies. The result is a self-consistent measurement of the density profile of MACS J0138-2155 across two orders of magnitude in radius. Our lensing and kinematics analyses individually yield highly consistent results, and from their combination we report a 95% confidence upper limit on the SIDM cross section of $σ/m < 0.613$ cm$^2$/g, at an interaction velocity of $\langle v_\text{pair}\rangle < 2090$ km/s. This constraint, derived from the most detailed single-system analysis to date, is competitive with previous cluster-scale limits while demonstrating the power of combining complementary gravitational probes. The methodology developed here advances precision cluster lens modeling and will inform future studies of dark matter physics, as well as time-delay cosmography in this unique strong lensing system. Additionally, our results imply SN Requiem will reappear sooner than previously reported, with a 1$σ$ CL between January 2027 and November 2028 at H$_0 = 67.7$ km s$^{-1}$ Mpc$^{-1}$.

Figures (18)

• Figure 1: Analysis Outline: High-level overview of the analysis done in this work. Pieces of this analysis were presented in Flowers.ODonnell.ea2025. Lens modeling is accomplished with PyAutoLensNightingale2018Nightingale2019. Kinematics modeling in this work uses vorbinvorbin to spatially segment the MUSE observations into regions, ppxfCappellari.Emsellem2004Cappellari2017 to model the spectrum of each region and extract stellar kinematics, MGEFitMGEFit to produce a Gaussian expansion approximating the stellar luminosity of the BCG, and JAMCappellari2008Cappellari2012 to forward model the observed kinematics.
• Figure 2: SIDM Analysis: Illustration of how the SIDM-modified dark density profile is translated into lensing and kinematics observables. In all figures, an unmodified NFW profile is shown for reference in black, and the SIDM-predicted dark density profile is shown in red. Left: First, the isothermal Jeans equation is solved to compute the predicted SIDM-modified density profile, as described in Section \ref{['sec:methods_sidm_model']} and Appendix \ref{['appendix:jeans']}. Middle: The SIDM-modified density profile is approximated by a sum in a particular basis suitable for each observable. For lensing, we use CSEs, and for kinematics we use an MGE. In both cases, the approximation is accurate to within 1.5% across the radii shown. Right: The model is fit to data. See Sections \ref{['sec:methods_strong_lensing']} and \ref{['sec:methods_stellar_kinematics']} for details.
• Figure 3: JWST NIRCam imaging of MACSJ0138. All galaxies labeled here included as components of the strong lensing mass model. Red-sequence galaxies are shown in green, emission-line galaxies are in cyan. All circles have radius 0.5". Several cluster members outside this FOV are also included in the mass model. In this RGB image, the blue, green, red channels show the F115W, F150W, and F200W NIRCam filters, respectively.
• Figure 4: Lensing position constraints: The positions of lensed features used to constrain the strong lens model, using the likelihood described in Section \ref{['sec:lensing_constraints']}. The RGB color bands and scaling are the same as Figure \ref{['fig:members']}. Three fields are shown here, showing lensed features of the quiescent source in the South, West, and North-East. In each field, a compass in displayed showing North and East; both segments of the compass are 1" long for scale.
• Figure 5: The central galaxy of MACSJ0138, and the LOS stellar velocity dispersions measured in this work. Left: MUSE color imaging of the central galaxy, with the Voronoi bins used in this work overlaid in green. Upper Right: The LOS stellar velocity dispersion in each bin, in km/s. Lower Right: The correlation matrix of the LOS velocity dispersion in all 25 spatial bins, displayed in a symlog scaling with a linear threshold of 0.2.