In order to make an in‐depth comparison between theory and observations, we analyse the light and velocity curves of various hydrodynamical models simulating RRab stars. The observations are represented by empirical formulae, derived in this and our earlier papers. It is shown that the overwhelming majority of the models tested do not follow the empirical relations regarding the shape of the light curves and the physical parameters. In almost all cases the luminosities predicted from the model light curves are significantly lower than the corresponding model values. The overall discrepancy of the models is an important indication of the limitation of the applicability of the present theoretical light and velocity curves in the determination of the physical parameters of these stars. In transforming the theoretical data to the observed light curves in V colour and in computing the observed radial velocities, it is shown that both bolometric correction and tracing the line‐forming regions have considerable effects on the evaluation of the observed quantities. In an effort to resolve the discrepancy between theory and observations, it is suggested that a proper evaluation of the bolometric correction and radial velocity based on complete dynamical atmosphere models may be a useful step in this direction.

Using Spitzer archival data from the SAGE (Surveying the Agents of a Galaxy's Evolution) program, we derive the Cepheid period-luminosity (P-L) relation at 3.6, 4.5, 5.8, and 8.0 m for Large Magellanic Cloud (LMC) Cepheids. These P-L relations can be used, for example, in future extragalactic distance scale studies carried out with the James Webb Space Telescope. We also derive Cepheid period-color (P-C) relations in these bands and find that the slopes of the P-C relations are relatively flat. We test the nonlinearity of these P-L relations with the F-statistical test and find that the 3.6, 4.5, and 5.8 m P-L relations are consistent with linearity. However, the 8.0 m P-L relation presents possible but inconclusive evidence of nonlinearity.

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.

In this Letter, we analyse period–colour and amplitude–colour relations at minimum, mean and maximum V‐band light for 6391 RRab stars in the Large Magellanic Cloud obtained by the MACHO project. Specifically, we find that colour and amplitude are nearly independent of period at minimum light, but that there exists a definite relation between period and colour and amplitude and colour at maximum light. These two properties are consistent with earlier work suggesting that these observed properties are, at least to some extent, explained by the application of the Stefan–Boltzmann law and the interaction of the photosphere and hydrogen ionization front at minimum light. When we examine the slope of the period–colour relation as a function of phase, we find that the slope varies significantly with phase and is small for a wide range of phases around minimum light. This suggests that another factor that needs to be considered when trying to understand RR Lyrae observed properties is their behaviour at different phases during a pulsation cycle.

In this paper we discuss the evidence for a period-luminosity (PL) relation and periodluminosity-colour (PLC) at maximum light for Mira variables. We confirm the existence of such relations in the J, H and K bands, and also based on bolometric magnitudes, for oxygen-rich (O) and carbon-rich (C) Miras in the LMC. We demonstrate that in the J and H bands the maximum light PL relations have a significantly smaller dispersion than their counterparts at mean light, while the K band and bolometric PL relations have a dispersion comparable to that at mean light. In the J, H and K bands the fitted PL relations for the O Miras are found to have smaller dispersion than those for the C Miras, at both mean and maximum light, while the converse is true for the relations based on bolometric magnitudes. The reduction in dispersion between mean and maximum light is generally found to be more significant in the J, H and bolometric bands than in the K band -in which the mean PL relations display the smallest dispersion. The inclusion of a non-zero log period term in the regression fits is found to be highly significant in all cases except that of the C Miras in the J band, for which the data are found to be consistent with having constant absolute magnitude. Moreover, if we consider only C Miras with periods in excess of 250 days, then the data are also substantially more consistent with constant absolute magnitude at mean and maximum light in the H, K and bolometric wavebands. This suggests the possibility of employing C Miras as standard candles.We suggest both a theoretical justification for the existence of Mira PL relations at maximum light and a possible explanation of why these relations should have a smaller dispersion than at mean light. The existence of such maximum light relations offers the possibility of extending the range and improving the accuracy of the Mira distance scale to Galactic globular clusters and to other galaxies.