Effects of a central dark matter core on time-delay cosmography with galaxy clusters

Abstract

The central dark matter distribution probes the nature of dark matter and baryon physics, yet its impact on time-delay cosmography is not fully explored. We update previous analyses of the cluster-lensed quasar SDSS J1004+4112 and the supernova Refsdal in MACS J1149.5+2223 by replacing the main halo density profile from an elliptical Navarro-Frenk-White (NFW) profile to a cored elliptical NFW profile and investigating the impact of the central dark matter core on the Hubble constant $H_0$. We jointly infer $H_0$ and the dimensionless core size parameter $\beta =r_{\mathrm{c}}/r_{\mathrm{s}}$, while the Brightest Cluster Galaxy (BCG) is either tied to the scaling relation of cluster member galaxies or modeled separately, with its mass left free or assigned a Gaussian prior from the stellar mass estimate for a Chabrier or Salpeter initial mass function (IMF). For SDSS J1004+4112, constraints on both $\beta$ and $H_0$ strongly depend on the treatment of the BCG. A large core is implied when no prior is added to the BCG stellar mass, while a reasonable assumption on the BCG mass prefers a nearly cuspy halo with $\beta \sim 10^{-3}$. For MACS J1149.5+2223, a large core of $\beta \sim 0.5$ is obtained with no prior, while a modest core of $\beta =0.0410_{-0.0276}^{+0.0865}$ is preferred when the Salpeter IMF is assumed. The constraint on $H_0$ from MACS J1149.5+2223 is stable against the BCG treatment, supporting its robustness. For the Salpeter-prior case, we obtain $H_0=65.9_{-3.4}^{+3.5}\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$, and different BCG assumptions change the median $H_0$ by less than $1\sigma$. The core size constraints are translated into the self-interacting dark matter cross section, giving a 95% upper limit of $\sigma /m<0.035{\mathrm{cm}}^2{\mathrm{g}}^{-1}$ from SDSS J1004+4112 and the 68% range of $\sigma /m=0.071_{-0.045}^{+0.15}{\mathrm{cm}}^2{\mathrm{g}}^{-1}$ from MACS J1149.5+2223.

arXiv comment15 pages, 4 figures, submitted