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Register a new userNon-Linear Cepheid Period-Luminosity Relation and the Interaction of Stellar Photosphere with Hydrogen Ionization Front
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C. Ngeow
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The Cepheid period-luminosity (P-L) relation is regarded as a linear relation (in log[P]) for a wide period range from ~2 to ~100 days. However, several recent controversial works have suggested that the P-L relation derived from the Large Magellanic Cloud (LMC) Cepheids exhibits a non-linear feature with a break period around 10 days. Here we review the evidence for linear/non-linear P-L relations from optical to near infrared bands. We offer a possible theoretical explanation to account for the nonlinear P-L relation from the idea of stellar photosphere - hydrogen ionization front interaction.
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Recent evidence has emerged that the Cepheid PL relation in the LMC is nonlinear in the sense that the existing data are more consistent with two lines of differing slope with a break at a period of 10 days. We review the statistical evidence for this, the implications for the extra-galactic distance scale and CMB independent estimations of Hubbles constant and briefly outline one possible physical mechanism which could cause this nonlinearity.
Period-colour and amplitude-colour (PCAC) relations can be used to probe both the hydrodynamics of outer envelope structure and evolutionary status of Cepheids and RR Lyraes. In this work, we incorporate the PCAC relations for RR Lyraes, BL Her, W Vir and classical Cepheids in a single unifying theory that involves the interaction of the hydrogen ionization front (HIF) and stellar photosphere and the theory of stellar evolution. PC relations for RR Lyraes and classical Cepheids using OGLE-IV data are found to be consistent with this theory: RR Lyraes have shallow/sloped relations at minimum/maximum light whilst long-period ($P>10$ days) Cepheids exhibit sloped/flat PC relations at minimum/maximum light. The differences in the PC relations for Cepheids and RR Lyraes can be explained based on the relative location of the HIF and stellar photosphere which changes depending on their position on the HR diagram. We also extend our analysis of PCAC relations for type II Cepheids in the Galactic bulge, LMC and SMC using OGLE-IV data. We find that BL Her stars have sloped PC relations at maximum and minimum light similar to short-period ($P<10$ days) classical Cepheids. W Vir stars exhibit sloped/flat PC relation at minimum/maximum light similar to long-period classical Cepheids. We also compute state-of-the-art 1D radiation hydrodynamic models of RR Lyraes, BL Her and classical Cepheids using the radial stellar pulsation code in MESA to further test these ideas theoretically and find that the models are generally consistent with this picture. We are thus able to explain PC relations at maximum and minimum light across a broad spectrum of variable star types.
Period-color (PC) relations may be used to study the interaction of the stellar photosphere and the hydrogen ionization front (HIF). RR Lyraes (RRLs) and long period classical Cepheids (P > 10d) have been found to exhibit different PC behavior at minimum and maximum light which can be explained by the HIF-photosphere interaction based on their location on the HR diagram. In this work, we extend the study to include type II Cepheids (T2Cs) with an aim to test the HIF-photosphere interaction theory across a broad spectrum of variable star types. We find W Vir stars and BL Her stars to have similar PC relations as those from long period and short period classical Cepheids, respectively. We also use MESA to compute RRL, BL Her and classical Cepheid models to study the theoretical HIF-photosphere distance and find the results to be fairly consistent with the HIF-photosphere interaction theory.
In this paper, we investigate the linearity versus non-linearity of the Large Magellanic Cloud (LMC) Cepheid period-luminosity (P-L) relation using two statistical approaches not previously applied to this problem: the testimator method and the Schwarz Information Criterion (SIC). The testimator method is extended to multiple stages for the first time, shown to be unbiased and the variance of the estimated slope can be proved to be smaller than the standard slope estimated from linear regression theory. The Schwarz Information Criterion (also known as the Bayesian Information Criterion) is more conservative than the Akaike Information Criterion and tends to choose lower order models. By using simulated data sets, we verify that these statistical techniques can be used to detect intrinsically linear and/or non-linear P-L relations. These methods are then applied to independent LMC Cepheid data sets from the OGLE project and the MACHO project, respectively. Our results imply that there is a change of slope in longer period ranges for all of the data sets. This strongly supports previous results, obtained from independent statistical tests, that the observed LMC P-L relation is non-linear with a break period at/around 10 days.
We have assessed the influence of the stellar iron content on the Cepheid Period-Luminosity (PL) relation by relating the V band residuals from the Freedman et al (2001) PL relation to [Fe/H] for 68 Galactic and Magellanic Cloud Cepheids. The iron abundances were measured from FEROS and UVES high-resolution and high signal-to-noise optical spectra. Our data indicate that the stars become fainter as metallicity increases, until a plateau or turnover point is reached at about solar metallicity. This behavior appears at odds both with the PL relation being independent from iron abundance and with Cepheids becoming monotonically brighter as metallicity increases (e.g. Kennicutt et al 1998, Sakai et al 2004).
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