Weighing Galaxies Inside-Out: Small-Scale Lensing and the Stellar Mass Problem

Small-scale galaxy-galaxy weak lensing provides an independent way to probe the stellar initial mass function by constraining the matter distribution within galaxies. We forecast the potential of upcoming $\mathit{\text{Euclid}}$ observations using realistic mock catalogues designed for a DESI-like Bright Galaxy Survey, which is expected to cover approximately $9000{\mathrm{d}\mathrm{e}\mathrm{g}}^2$ of the $\mathit{\text{Euclid}}$ wide survey area. We assess the impact of foreground lens light, which introduces significant scale-dependent biases in source detection, photometry, and shape measurements. Subtracting the lens light with $\text{textsc}Galfit$ reduces these biases by nearly an order of magnitude at scales down to four times the half-light radius. We model the predicted lensing signal around central galaxies with stellar masses between $9.5\le \log (M_{\ast }\mathrm{/}{h}^{-2}{M}_{\odot })\le 11.5$ over projected separations of $10$ to $100h^{-1}\mathrm{k}\mathrm{p}\mathrm{c}$. The resulting signal-to-noise ratios reach $\sim 150$ for intermediate-mass galaxies. Assuming an NFW profile for the dark matter contribution, we constrain the stellar mismatch parameter $\alpha$ to a precision of approximately $8.5$ percent for the full sample and $8.6$ percent for massive galaxies. These results highlight the potential of small-scale galaxy–galaxy weak lensing as a robust probe of the IMF and the connection between stellar and dark matter in galaxies using upcoming $\mathit{\text{Euclid}}$ data.