CDM and SIDM Interpretations of the Strong Gravitational Lensing Object JWST-ER1

van Dokkum et al. (arXiv:2309.07969) reported the discovery of JWST-ER1, a strong lensing object at redshift z≈2, using data from the James Webb Space Telescope. The lens mass within the Einstein ring is 5.9 times higher than the expected stellar mass from a Chabrier initial mass function, indicating a high dark matter density. In this work, we show that a cold dark matter halo, influenced by gas-driven adiabatic contraction, can account for the observed lens mass. We also derive constraints on dark matter self-interacting cross section per particle mass σ/m. For σ/m≳0.3  cm^2/g within a 10^13 M_⊙ halo, the density profile is too shallow to be consistent with the measured lens mass of JWST-ER1, while σ/m≈0.1  cm^2/g is well allowed. Intriguingly, self-interacting dark matter with σ/m≈0.1  cm^2/g can simultaneously explain the dark matter density profile of early-type galaxies at redshift z≈0.2, where adiabatic contraction is not observed overall.