Measuring the Stellar-to-Halo Mass Relation at $\sim {10}^{10}$ Solar masses, using forthcoming space-based imaging of galaxy-galaxy strong lenses

The stellar-to-halo mass relation (SHMR) is central to understanding the co-evolution of galaxies and their host dark matter haloes, yet it remains weakly constrained for dwarf galaxies owing to their faintness, especially beyond the Local Group. Strong gravitational lensing offers a unique probe of the SHMR at sub-galactic scales and cosmological distances, as the masses of subhalos within the main lens can be inferred from the perturbations they imprint on lensed images. Anticipating the discovery of $\sim {10}^5$ galaxy–galaxy strong lenses by forthcoming facilities such as $\mathit{\text{Euclid}}$, we perform an end-to-end simulation to forecast $\mathit{\text{Euclid}}$'s constraints on the SHMR at the halo mass scale of $\sim {10}^{10}{\mathrm{M}}_{\odot }$. We generate mock $\mathit{\text{Euclid}}$ VIS images of lens systems hosting a fiducial $3\times {10}^{10}{\mathrm{M}}_{\odot }$ subhalo and vary its properties to assess the robustness of mass inference. We find that $\mathit{\text{Euclid}}$'s angular resolution cannot break the intrinsic mass–concentration degeneracy of subhaloes, nor deblend the light of satellite galaxies (when present) associated with them, leading to biased inferred halo masses. These limitations are overcome with high-resolution follow-up imaging from facilities such as the $\mathit{\text{Hubble}}\mathit{\text{Space}}\mathit{\text{Telescope}}$, enabling accurate halo-mass measurements. We forecast that a statistical sample of $\sim 100$ such systems, combining lensing-derived halo masses with stellar masses from photometric SED fitting, can constrain the SHMR at dwarf-galaxy scales with a precision of $\sim 0.05$~dex in halo mass and $\sim 0.03$~dex in stellar mass, enabling powerful tests of galaxy formation theories.