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The Cepheid period-luminosity (PL) relation is important in distance scale studies and stellar pulsation studies. This relation has been thought to be linear for a long time. However, recent work has strongly suggested that the PL relation for Large Magellanic Cloud (LMC) Cepheids is nonlinear: there are two relations, with a break at 10 days. In addition, the LMC periodcolor (PC) relation is also shown to be nonlinear. The main motivation for this dissertation is to investigate the nonlinearity of the LMC PL and PC relations and its implications for distance scale studies and for stellar structure, pulsation, and evolution. Due to the intrinsic dispersion of the PL relation and the relatively small number (∼100) of LMC Cepheids used in previous studies, the nonlinear nature of the LMC PL relation was not discovered until large numbers (∼1000) and high-quality LMC Cepheids became available from the OGLE (Optical Gravitational Lensing Experiment) and MACHO (Massive Compact Halo Objects) surveys. To test the existence of a nonlinear LMC PL relation, we apply a rigorous statistical test, the F-test, to the OGLE and MACHO data. After applying proper extinction corrections to both samples, the F-test results strongly suggested that the LMC PL relation is not linear in the VI bands (from OGLE data) and the VR bands (from MACHO data), with more than 99.5% confidence. A similar result from two totally independent samples suggested that the nonlinear LMC PL relation is real and is not due to artifacts of photometric reductions, extinction, or sample selections. The nonlinear nature of the LMC PL relation is further extended to the JH bands, but not the K band, with Two Micron All Sky Survey data. The fundamental reason that the LMC PL relation is nonlinear is that the LMC PC relation is also nonlinear. F-test results again strongly suggest that the LMC PC relation is nonlinear but that the Galactic PC relation is linear. This is because both the PL and PC relations follow the period-luminosity-color (PLC) relations for Cepheid variables; hence, understanding the nonlinear nature of the PC relation helps in understanding the nonlinear PL relation. Note that the PC relation here is actually the PC relation at mean light, which is the properties averaged over a pulsation cycle. Any “anomaly” of the color at certain phases of the pulsation (e.g., at maximum or minimum light) for some phase or period range would affect the mean-light properties of the PC relation and hence produce the observed break in the PC and PL relations. Consider that the relation , where V V ∝ log T log T T min max max min max and are the temperature at maximum and minimum light, Tmin respectively, which is directly related to the color and V min , is just the amplitude of the Cepheid. If versus period V log T max max has a flat slope for a given period range, then there is a relation between the amplitude and , hence the amplitude-color log Tmin relation, and vice versa. This flatness of the PC relation at maximum and/or minimum light could in principle influence the PC relation at mean light and produce the observed nonlinear PC (mean) relation. One mechanism that can produce a flat PC relation at maximum (and/or minimum) light is the interaction of the hydrogen ionization front (HIF) with the photosphere (defined at an optical depth of ), which halts the temperature of the photosphere 3 at some characteristic values that are independent of the global properties. Using stellar pulsation codes that include a recipe for turbulent convection, we constructed the Galactic and LMC Cepheid models to investigate this interaction. Comparing the “distance” as a function of period between the HIF and photosphere (in mass distribution) for these models, we found evidence that (1) the HIF-photosphere interaction for long-period LMC models occurs at maximum light, which is similar to the Galactic models, and (2) the same interaction for short-period LMC models occurs at minimum light, which is the opposite of Galactic models and behaves more like RR Lyrae stars. We believe that these different behaviors of the HIF-photosphere interaction between the longand short-period LMC models lead to the observed nonlinear PC (mean) and PL (mean) relations. In addition, we also constructed empirical multiphase PC relations from the LMC and Galactic Cepheids. The results show that the empirical LMC PC relations are nonlinear for most of the pulsation phases (especially near phase ∼0.8, where phase zero corresponds to maximum light), in contrast to the empirical Galactic multiphase PC relations. Cepheid distances were usually derived through a Wesenheit function (WF), a linear combination of the PL and PC relations. Although the LMC PL and PC relations are nonlinear, the WF for the LMC Cepheids is found to be linear, as the nonlinearities for both PL and PC relations cancel out when the WF is constructed. Comparisons of Cepheid distances obtained with the (correct) nonlinear PL and PC relations using the WF will only introduce a !0.07 mag (systematic) error in the distance modulus, or ∼4% in distance. However, a full understanding of the nonlinear nature of the Cepheid PL and PC relations is important in terms of stellar pulsation and evolutionary studies.

Investigating the Break in the Cepheid Period‐Luminosity Relation and Its Implications