Semi-Analytic Predictions for Strong-Lensing Perturbers in Cold and Self-Interacting Dark Matter
Strong gravitational lensing is sensitive to the abundance and internal structure of dark matter halos, providing a probe of gravothermal evolution in self-interacting dark matter (SIDM). We combine semi-analytic cold dark matter (CDM) subhalo histories with a model for gravothermal evolution in SIDM to generate CDM and SIDM subhalo populations across SIDM parameter space. We predict their projected enclosed masses and deflection-based projected density slopes and compare them with three perturbers inferred through gravitational imaging in PJ011646, SDSS J0946+1006, and JVAS B1938+666. For SIDM model parameters $σ_0/m_χ=147.1$ cm$^2$/g and $w=120$ km/s, SIDM subhalos reproduce all three perturbers more often than CDM subhalos. For PJ011646, we find ~0.6 cored SIDM subhalos per host matching the perturber, compared with ~0.002 in CDM, while core-collapsed subhalos are too steep. For SDSS J0946+1006, we find ~3 core-collapsed and ~0.004 cored SIDM subhalos per host, compared with none in 900 CDM realizations, although baryons, neglected here, may matter for such massive subhalos. For "detection V" in JVAS B1938+666, we find ~220 core-collapsed and ~20 cored SIDM subhalos per host within the $2σ$ posterior region, compared with ~0.2 in CDM; the CDM candidates require exceptionally early accretion, at median redshift $z\sim13$. Simultaneously reproducing all three perturbers requires $w\gtrsim10^2$ km/s, so that the massive (~$5.6\times10^{10}M_\odot$) progenitors of SDSS J0946+1006 candidates can collapse, and is achieved for $σ_0/m_χ\gtrsim10^2$ cm$^2$/g in the parameter sets studied. Our results show how semi-analytic models can quantify how often subhalos reproduce individual perturbers in different dark matter models, and our modular framework can be readily updated as models of tidal stripping and late-stage gravothermal evolution in SIDM improve. (abridged)