The effect of metallicity on the Leavitt Law using phase-dependent properties of classical Cepheids

ABSTRACT The absolute calibration of period–luminosity (PL) relations of Cepheids in the Milky Way (MW) and its nearby galaxies has been a cornerstone in determining extragalactic distances and the current local expansion rate of the Universe. However, the universality of PL relations is still debated; in particular, the effect of metallicity on the Cepheid PL relation is not well understood. Due to the hydrogen ionization front and the stellar photosphere interactions in Cepheids, different period–colour relations at different phases can influence the corresponding period–luminosity relations at those phases. In this work, we have considered the PL relations at multiple pulsation phases as they capture the ensemble radiation hydrodynamic properties at those phases. We investigate the effect of metallicity on PL relations based on multiphase analysis of classical Cepheid light curves in the MW and its nearby satellite galaxies: the Large Magellanic Cloud and the Small Magellanic Cloud. Multiphase metallicity coefficients $(\gamma)$ are derived in five different photometric bands (V, I, G, $G_{\rm BP}$, $G_{\rm RP}$) and two Wesenheit indices ($W_{VI}$, $W_{G}$). We show that the coefficients of multiphase period–luminosity–metallicity relations vary dynamically as functions of Cepheid pulsation phases over a complete pulsation cycle. Significant differences in the metallicity effect are found between the short- $(0.4 \le \log {P} < 1)$ and long-period $(1 \le \log {P} < 2)$ Cepheids at multiple pulsation phases, in two bands, $G_{\rm RP}$ and $W_{G}$. The weighted averages of the multiphase $\gamma _{\lambda }$ values are found to be in good agreement with the latest results published in the literature. Our methods and results provide new insights into understanding the metallicity effect on the Leavitt law, which can be useful in constraining pulsation models as well as show that the metallicity effect on mean-light PL relations can be recovered from the phase-dependent nature of the metallicity effect found in this study.