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; particularly, the metallicity effect on the Cepheid PL relation. Due to the HIF-stellar photosphere interactions in Cepheids, different period-color (PC) relations at different phases can influence the corresponding PL relations at those phases.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, Large Magellanic Cloud (LMC) and Small Magellanic Cloud (SMC). Multiphase metallicity coefficients $(γ)$ 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 (PLZ) relations vary dynamically as functions of Cepheid pulsation phases over a complete pulsation cycle. We find significant differences in the $γ_λ$ values between the short- $(0.4 \leq \log{P} < 1)$ and long-period $(1 \leq \log{P} < 2)$ Cepheids at multiple phases, in two bands, $G_{\rm RP}$ and $W_{G}$. The weighted averages of the multiphase $γ_λ$ values are found to be in good agreement with the latest results published in the literature. Our methods and results provide new insights into the metallicity effect on the Leavitt law, which can be useful in constraining pulsation models. Additionally, this study shows that the metallicity effect on mean-light PL relations can be recovered from its phase-dependent nature found in this study.

Figures (16)

• Figure 1: Distribution of the sample of LMC (left panel) and SMC (right panel) Cepheids overplotted on gray-scale Digitized Sky Survey 2 (DSS2) blue-filter images of the LMC and SMC, respectively. These images are obtained using the Aladin virtual observatory tool. Cepheids plotted as colour-coded dots represent the sample before applying any selection criterion. The colour of the dots represents distances of individual Cepheids in both galaxies. Dashed circular boundaries in both panels denote the regions within $3^{\circ}$ and $0.6^{\circ}$ angular radii from the adopted LMC and SMC centres, respectively. The LMC and SMC centres are denoted by yellow coloured circles with RA-Dec coordinates: $(\alpha_{0, \rm LMC}, \delta_{0, \rm LMC}) = (80.05^{\circ}, -69.30^{\circ})$, and $(\alpha_{0, \rm SMC}, \delta_{0, \rm SMC}) = (12.54^{\circ}, -73.11^{\circ})$, respectively. Cyan coloured star symbols represent detached eclipsing binaries from pie19 and grac20, respectively.
• Figure 2: Distribution of the Fourier parameter $R_{21}$ as a function of the logarithm of the pulsation period $(\log{P})$ for LMC and MW Cepheids in the $V$-band, respectively. LMC Cepheids are already classified by the OGLE survey, which are shown in the left panel. The purple colored box in the both panels represents the region in which the FO mode outliers are located in the period range $0.4 \leq \log{P} < 0.7$. MW Cepheids located inside this region in the $R_{21}-\log{P}$ plane in the right panel are rejected from the sample. The dashed vertical line represents the $\log{P} =0.4$ period cut-off taken in sampling the Cepheids.
• Figure 3: Number of Cepheids in the MW, LMC and SMC before (clear bar charts) and after (striped bar charts) the application of selection criterion in all five photometric bands: $G_{\rm BP}, V, G, G_{\rm RP}, I$ and two Wesenheit indices: $W_{VI}$ and $W_{G}$. The final numbers of Cepheids used for fitting the PL relations after removing the $3\sigma$ outliers are shown as dotted bar charts.
• Figure 4: Top panel shows the Fourier fitted $V$-band light curve of the MW Cepheid VW-CAS and the bottom panel shows residuals of the Fourier fit. The light curve has 15 epoch of observed data and is fitted well with a Fourier series of order $N=4$, represented by the red coloured solid line. The blue coloured points represent the interpolated points.
• Figure 5: PL slopes of Cepheids in the LMC as a function of pulsation phases in five photometric bands: $G_{\rm BP}$, $V$, $G$, $G_{\rm RP}$, $I$, and two Wesenheit indices: $W_{VI}$ and $W_{G}$, respectively. Pulsation periods of the Cepheid sample used to determine the multiphase PL slopes are within the range: $0.4 \leq \log{P} < 2$. The dashed horizontal lines overplotted on the figure represent the PL slopes obtained using mean magnitudes in respective bands. The median uncertainties denote the typical uncertainties of the multiphase PL slopes.