Filter Design for Estimating the Stellar Metallicity of Metal-poor Stars from Gaia XP Spectra

The estimation of stellar atmospheric parameters for large-scale samples, particularly metal-poor stars, is a cornerstone of Galactic archaeology. In this work, we optimized a photometric filter design tailored to measuring stellar metallicities for very metal-poor stars with [Fe/H]$<-1$.The optimal configurations consist of a central wavelength $\lambda_{\rm c}$ = 3960 Angstrom with a bandwidth $\Delta\lambda$ = 80 Angstrom for giant stars, and $\lambda_{\rm c} $= 3920 Angstrom with $\Delta\lambda$ = 80 Angstrom for dwarf stars. By applying these optimized filters to synthetic photometry derived from Gaia XP spectra, we inferred metallicities for both populations. Both internal and external validations demonstrate high precision across a wide metallicity range: 0.18-0.19 dex for $-2 \le \rm [Fe/H] \le -1$, 0.23-0.33 dex for $-3 \le \rm [Fe/H] \le -2$, and approximately 0.39 dex for the most metal-poor regime, successfully extending down to $\rm [Fe/H] \approx -4$ for giant stars, $\rm [Fe/H] \approx -3.3$ for dwarf stars. Finally, we present a catalog of approximately 14.5 million metal-poor stars with robust $\rm [Fe/H]$ measurements, along with more than ten thousand red giant ultra metal-poor candidates with $\rm [Fe/H]<-4.0$, providing a valuable resource for exploring the early formation and chemical evolution of the Milky Way.