Breaking the mass-sheet degeneracy in strong lensing mass modeling with weak lensing observations

The Hubble constant ($H_0$), a crucial parameter in cosmology, quantifies the expansion rate of the universe so its precise measurement is important to understand the fundamental dynamics of our evolving universe. One of the major limitations of measuring $H_0$ using time-delay cosmography is the presence of the mass-sheet degeneracy (MSD) in the lens mass modeling. We propose and quantitatively assess the use of galaxy-galaxy shear measurements to break the MSD in the strong lensing mass modeling. We use stacked galaxy-galaxy lensing profiles and corresponding covariance matrices from Huang et al. (2022) to constrain the MSD in lens mass modeling with a highly flexible mass profile. Our analyses show that if ideally all galaxy-galaxy lensing measurements from the Hyper Suprime-Cam (HSC) survey can be used to constrain the MSD, we can achieve $\sim 10\%$ precision on the MSD constraint. We forecast that galaxy-galaxy lensing measurements from LSST-like surveys can in general constrain the MSD with $\sim 1-3\%$ precision. Furthermore, if we push weak lensing measurements to a lower angular scale of $\sim 0.04$ $\rm Mpc$, a survey like LSST can provide $\sim 1\%$ precision on the MSD constraint, enabling a measurement of $H_0$ at the $1\%$ level. We demonstrate that galaxy-galaxy weak lensing can robustly constrain the MSD independent of stellar kinematics of the deflector, with wide-field survey data alone.