Biases in galaxy spectral analysis from strong lensing differential magnification effect and correction methods

Abstract

Strong gravitational lensing has significantly advanced the study of high-redshift galaxies, but the differential magnification effect inevitably introduces biases in the spectral analysis of source galaxies. This work investigates these biases using mock lensing systems from MaNGA survey data and IllustrisTNG simulations. We analyze the impact of lensing effect on several spectral properties, including stellar age, metallicity, H$\alpha$ flux, and optical emission line ratios. Our results show significant biases in all properties after lensing. The values of quantities can be either over- or under-estimated, except for the consistently enhanced H$\alpha$ flux. The bias varies with lensing configurations and always arises when part of the source galaxy falls into the strong lensing regime. We evaluate two correction methods to recover the intrinsic source properties: the average magnification factor ($\bar{\mu}$) and full ray-tracing. While both methods reduce the overestimated H$\alpha$ flux, the $\bar{\mu}$ method shows a much larger discrepancy. For stellar population properties and emission line ratios, the $\bar{\mu}$ method fails whereas the ray-tracing method proves effective. Applying these two methods to a statistical sample of mock systems further shows their strong dependence on lens modeling accuracy. As a demonstrative study, our results highlight the importance of spatially resolved spectroscopic observations and precise lens modeling for reconstructing spectra of strongly lensed galaxies. While our conclusions are based on a specific source and lens galaxy, further studies with a statistical sample of realistic mock lensing systems are needed for understanding any systematic differences between the two correction methods.