The next step in galaxy cluster strong lensing: modeling the surface brightness of multiply-imaged sources

Overcoming both modeling and computational challenges, we present, for the first time, the extended surface-brightness distribution model of a strongly-lensed source in a complex galaxy-cluster-scale system. We exploit the high-resolution Hubble Space Telescope (HST) imaging and extensive Multi Unit Spectroscopic Explorer spectroscopy to build an extended strong-lensing model, in a full multi-plane formalism, of SDSS J1029+2623, a lens cluster at $z = 0.588$ with three multiple images of a background quasar ($z = 2.1992$). Going beyond typical cluster strong-lensing modeling techniques, we include as observables both the positions of 26 pointlike multiple images from seven background sources, spanning a wide redshift range between 1.02 and 5.06, and the extended surface-brightness distribution of the strongly-lensed quasar host galaxy, over $\sim78000$ HST pixels. In addition, we model the light distribution of seven objects, angularly close to the strongly-lensed quasar host, over $\sim9300$ HST pixels. Our extended lens model reproduces well both the observed intensity and morphology of the quasar host galaxy in the HST F160W band (with a 0''.03 pixel scale). The reconstructed source shows a single, compact, and smooth surface-brightness distribution, for which we estimate an intrinsic magnitude of 23.3 $\pm$ 0.1 in the F160W band and a half-light radius of (2.39 $\pm$ 0.03) kpc. The increased number of observables enables the accurate determination of the total mass of line-of-sight halos lying angularly close to the extended arc. This work paves the way for a new generation of galaxy cluster strong-lens models, where additional, complementary lensing observables are directly incorporated as model constraints.