Period–luminosity and Period–luminosity–metallicity Relations for <i>δ</i> Scuti Stars

Abstract δ Scuti ( δ Sct) stars are potential distance tracers for studying the Milky Way structure. We conduct a comprehensive analysis of the period–luminosity (PL) and period–luminosity–metallicity (PLZ) relations for δ Sct stars, integrating data from the Zwicky Transient Facility, the Transiting Exoplanet Survey Satellite, Large Sky Area Multi-Object Fiber Spectroscopic Telescope, Apache Point Observatory Galactic Evolution Experiment, and Gaia. To mitigate the impact of the Gaia parallax zero point offset, we applied a correction method, determining the optimal zero point value to be zp ϖ = 35 ± 2 μ as. Using the three best bands, by varying the parallax error threshold, we found that the total error of the PLR zero point was minimized to 0.9% at a parallax error threshold of 6%. With this threshold, we derived the PL and PLZ relations for nine bands (from optical to mid-infrared) and five Wesenheit bands. Through our analysis, we conclude that the influence of metallicity on the PLR of δ Sct stars is not significant, and the differences across various bands are minimal.