Enabling Metallicity Measurements of Microlensing Lenses through Multi-band Lens Photometry
We present the photometric--microlensing metallicity method, which enables metallicity measurements of M-dwarf lenses out to bulge distances by combining their multi-band photometry with the angular Einstein radius. The cool atmospheres of M dwarfs contain abundant molecules, whose broad absorption bands make their positions in an optical--NIR color--absolute magnitude diagram sensitive to metallicity. The angular Einstein radius provides the mass--distance constraint needed to infer the lens absolute magnitude, while the intrinsic M-dwarf locus and reddening vector are non-parallel in color--color space, allowing the lens extinction and intrinsic color to be inferred simultaneously from its multi-band photometry, thereby recovering the lens intrinsic position in the metallicity-sensitive color--absolute magnitude diagram. The method requires three-band lens photometry spanning roughly the R, Z, and K bands, making it particularly well suited to Roman through its high-resolution F062, F087, and F213 imaging. With the planned Roman Galactic Bulge Time-Domain Survey (GBTDS) observations plus an additional $\sim$8 hr of F062 imaging per field ($\sim$40 hr in total) roughly a decade after Roman launch, host metallicities could be measured for $\sim$150 planetary systems under the GBTDS yield forecast, with a typical $1\sigma$ precision of $\sim$0.25 dex from our mock-recovery analysis. Applied homogeneously to GBTDS microlensing events with and without detected planets, the method would enable the first measurement of the occurrence--metallicity relation for cold low-mass planets beyond the snow line, constrain the low-metallicity cutoff for their formation, and extend occurrence--metallicity studies into the inner Galaxy.