385 research outputs found
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 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
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