The Detailed Forms of the LMC Cepheid PL and PLC Relations

Possible deviations from linearity of the LMC Cepheid PL and PLC relations are investigated. Two datasets are studied, respectively from the OGLE and MACHO projects. A nonparametric test, based on linear regression residuals, suggests that neither PL relation is linear. If colour dependence is allowed for then the MACHO PL relation is found to deviate more significantly from the linear, while the OGLE PL relation is consistent with linearity. These finding are confirmed by fitting "Generalised Additive Models" (nonparametric regression functions) to the two datasets. Colour dependence is shown to be nonlinear in both datasets, distinctly so in the case of the MACHO Cepheids. It is also shown that there is interaction between the period and colour functions in the MACHO data.Comment: 20 pages, 20 figures, MNRAS accepte

Testing the nonlinearity of the BVIcJHKs period-luminosity relations for the Large Magellanic Cloud Cepheids

A number of recent works have suggested that the period-luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids exhibits a controversial nonlinear feature with a break period at 10 days. Therefore, the aim of this Research Note is to test the linearity/nonlinearity of the PL relations for the LMC Cepheids in BVIcJHKs band, as well as in the Wesenheit functions. We show that simply comparing the long and short period slopes, together with their associate d standard deviations, leads to a strictly larger error rate than applying rigorous statistical tests such as the F-test. We applied various statistical tests to the current published LMC Cepheid data. These statistical tests include the F-test, the testimator test, and the Schwarz information criterion (SIC) method. The results from these statistical tests strongly suggest that the LMC PL relation is nonlinear in BVIcJH band but linear in the Ks band and in the Wesenheit functions. Using the properties of period-color relations at maximum light and multi-phase relations, we believe that the nonlinear PL relation is not caused by extinction errors.Comment: 6 pages, 5 figures and 2 tables, A&A accepte

Nonlinear Period-Luminosity Relation for the Large Magellanic Cloud Cepheids: Myths and Truths

In this paper, we discuss and examine various issues concerning the recent findings that suggested the observed period-luminosity (P-L) relation for the Large Magellanic Cloud (LMC) Cepheids is nonlinear. These include (1) visualizing the nonlinear P-L relation; (2) long period Cepheids and sample selection; (3) outlier removal; (4) issues of extinction; (5) nonlinearity of the period-color (P-C) relation; (6) nonlinear P-L relations in different pass-bands; and (7) universality of the P-L relation. Our results imply that a statistical test is needed to detect the nonlinear PL relation. We then show that sample selection, number of long period Cepheids in the sample, outlier removal and extinction errors are unlikely to be responsible for the detection of the nonlinear P-L relation. We also argue for the existence of a nonlinear P-L relation from the perspective of the nonlinear P-C relation and the non-universality of the P-L relation. Combining the evidence and discussion from these aspects, we find that there is a strong indication that the observed LMC P-L relation is indeed nonlinear in the optical bands (however the K-band LMC P-L relation is apparently linear). This could be due to the internal physical reasons or the external hidden/additional factors. Compared to the non-linear P-L relation, the systematic error in distance scale introduced from using the (incorrect) linear P-L relation is at most at a few per cent level. While this is small compared to other systematic errors, it will be important in future efforts to produce a Cepheid distance scale accurate to one per cent in order to remove degeneracies presented in CMB results.Comment: 22 pages, 8 figures, 1 table, ApJ accepte

The Hubble Constant from Type Ia Supernova Calibrated with the Linear and Non-Linear Cepheid Period-Luminosity Relation

It is well-known that the peak brightness of the Type Ia supernovae calibrated with Cepheid distances can be used to determine the Hubble constant. The Cepheid distances to host galaxies of the calibrating supernovae are usually obtained using the period-luminosity (PL) relation derived from Large Magellanic Cloud (LMC) Cepheids. However recent empirical studies provide evidence that the LMC PL relation is not linear. In this Letter we determine the Hubble constant using both the linear and non-linear LMC Cepheid PL relations as calibrating relations to four galaxies that hosted Type Ia supernovae. Our results suggest that the obtained values of the Hubble constant are similar. However a typical error of $\sim0.03$mag. has to be added (in quadrature) to the systematic error for the Hubble constant when the linear LMC PL relation is used, assuming that the LMC PL relation is indeed non-linear. This is important in minimizing the total error of the Hubble constant in the era of precision cosmology. The Hubble constants calibrated from the linear and non-linear LMC PL relation are H_0 = 74.92+-2.28(random)+-5.06(systematic) km/s/Mpc and H_0 = 74.37+-2.27(random)+-4.92(systematic) km/s/Mpc, respectively. Hubble constants calculated using the Galactic PL relations are also briefly discussed and presented in the last section of this Letter.Comment: 8 pages, 4 tables, ApJL accepte

Semi-Empirical Cepheid Period-Luminosity Relations in Sloan Magnitudes

In this paper we derive semi-empirical Cepheid period-luminosity (P-L) relations in the Sloan ugriz magnitudes by combining the observed BVI mean magnitudes from the Large Magellanic Cloud Cepheids (LMC) and theoretical bolometric corrections. We also constructed empirical gr band P-L relations, using the publicly available Johnson-Sloan photometric transformations, to be compared with our semi-empirical P-L relations. These two sets of P-L relations are consistent with each other.Comment: 4 pages, 2 tables and 2 figures, ApJ accepte

Period-Color and Amplitude-Color Relations in Classical Cepheid Variables - VI. New Challenges for Pulsation Models

We present multiphase Period-Color/Amplitude-Color/Period-Luminosity relations using OGLE III and Galactic Cepheid data and compare with state of the art theoretical pulsation models. Using this new way to compare models and observations, we find convincing evidence that both Period-Color and Period-Luminosity Relations as a function of phase are dynamic and highly nonlinear at certain pulsation phases. We extend this to a multiphase Wesenheit function and find the same result. Hence our results cannot be due to reddening errors. We present statistical tests and the urls of movies depicting the Period-Color/Period Luminosity and Wesenheit relations as a function of phase for the LMC OGLE III Cepheid data: these tests and movies clearly demonstrate nonlinearity as a function of phase and offer a new window toward a deeper understanding of stellar pulsation. When comparing with models, we find that the models also predict this nonlinearity in both Period-Color and Period-Luminosity planes. The models with (Z=0.004, Y=0.25) fare better in mimicking the LMC Cepheid relations, particularly at longer periods, though the models predict systematically higher amplitudes than the observations

Investigations of the Non-Linear LMC Cepheid Period-Luminosity Relation with Testimator and Schwarz Information Criterion Methods

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.Comment: 9 pages, 5 figures and 3 tables, PASP accepte