Kiloparsec Mass/Light Offsets in the Galaxy Pair-Ly$\alpha$ Emitter Lens System SDSS\,J1011$+$0143

We report the discovery of significant mass/light offsets in the strong gravitational lensing system SDSS\,J1011$+$0143. We use the high-resolution \textsl{Hubble Space Telescope} (\textsl{HST}) F555W- and F814W-band imaging and Sloan Digital Sky Survey (SDSS) spectroscopy of this system, which consists of a close galaxy pair with a projected separation of $\approx 4.2$ kpc at $z_{\rm lens} \sim 0.331$ lensing a Ly$\alpha$ emitter (LAE) at $z_{\rm source} = 2.701$. Comparisons between the mass peaks inferred from lens models and light peaks from \textsl{HST} imaging data reveal significant spatial mass/light offsets as large as $1.72 \pm 0.24 \pm 0.34$ kpc in both filter bands. Such large mass/light offsets, not seen in isolated field lens galaxies and relaxed galaxy groups, may be related to the interactions between the two lens galaxies. The detected mass/light offsets can potentially serve as an important test for the self-interacting dark matter model. However, other mechanisms such as dynamical friction on spatially differently distributed dark matter and stars could produce similar offsets. Detailed hydrodynamical simulations of galaxy-galaxy interactions with self-interacting dark matter could accurately quantify the effects of different mechanisms. The background LAE is found to contain three distinct star-forming knots with characteristic sizes from 116 pc to 438 pc. It highlights the power of strong gravitational lensing in probing the otherwise too faint and unresolved structures of distance objects below subkiloparsec or even 100 pc scales through its magnification effect.