Quantifying biases in stellar masses of JWST high-z quasar host galaxies caused by quasar subtraction

JWST has enabled dozens of high-$z$ quasar host galaxy detections. Many of these observations imply galaxies with black holes that are overmassive compared to their low-$z$ counterparts. However, the bright quasar point source removal can cause significant biases in recovered host magnitudes and stellar mass measurements due to the degeneracy in host galaxy and quasar light. We develop a statistical method to disentangle the quasar host galaxy stellar mass measurements from observational biases during the point source removal assuming the PSF is modelled perfectly. We use the BlueTides simulation to generate mock images and perform point source removal on thousands of simulated high-$z$ quasar host galaxies, constructing corrected host magnitude posteriors. We find that removing a bright quasar in JWST photometry tends to either correctly recover or modestly misestimate host magnitudes, with a maximum magnitude underestimate of 0.2 mag. With our corrected magnitude posteriors, we perform SED fitting on each quasar host galaxy and compare the stellar mass measurement before and after the correction. We find that stellar mass estimates are generally robust, or misestimated by <0.3 dex. We also find that the stellar masses of a subset of hosts (J0844-0132, J0911+0152, and J1146-0005) remain unconstrained, as key photometric bands provide only flux upper limits. Accounting for observational biases does not resolve the apparent mismatch between black hole and host galaxy growth at high-$z$, where some quasars appear to host overmassive black holes while others reside in relatively massive galaxies.