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Register a new userA Bayesian Analysis of the Cepheid Distance Scale
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Thomas G. Barnes III
Publication date
2003
fields
Physics
and research's language is
English
Authors
T. G. Barnes III
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We develop and describe a Bayesian statistical analysis to solve the surface brightness equations for Cepheid distances and stellar properties. Our analysis provides a mathematically rigorous and objective solution to the problem, including immunity from Lutz-Kelker bias. We discuss the choice of priors, show the construction of the likelihood distribution, and give sampling algorithms in a Markov Chain Monte Carlo approach for efficiently and completely sampling the posterior probability distribution. Our analysis averages over the probabilities associated with several models rather than attempting to pick the `best model from several possible models. Using a sample of thirteen Cepheids we demonstrate the method. We discuss diagnostics of the analysis and the effects of the astrophysical choices going into the model. We show that we can objectively model the order of Fourier polynomial fits to the light and velocity data. By comparison with theoretical models of Bono et al. (2001) we find that EU Tau and SZ Tau are overtone pulsators, most likely without convective overshoot. The period-radius and period-luminosity relations we obtain are shown to be compatible with those in the recent literature.
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In a previous paper (Maoz et al. 1999), we reported a Hubble Space Telescope (HST) Cepheid distance to the galaxy NGC 4258 obtained using the calibrations and methods then standard for the Key Project on the Extragalactic Distance Scale. Here, we reevaluate the Cepheid distance using the revised Key Project procedures described in Freedman et al. (2001). These revisions alter the zero points and slopes of the Cepheid Period-Luminosity (P-L) relations derived at the Large Magellanic Cloud (LMC), the calibration of the HST WFPC2 camera, and the treatment of metallicity differences. We also provide herein full information on the Cepheids described in Maoz et al. 1999. Using the refined Key Project techniques and calibrations, we determine the distance modulus of NGC 4258 to be 29.47 +/- 0.09 mag (unique to this determination) +/- 0.15 mag (systematic uncertainties in Key Project distances), corresponding to a metric distance of 7.8 +/- 0.3 +/- 0.5 Mpc and 1.2 sigma from the maser distance of 7.2 +/- 0.5 Mpc. We also test the alternative Cepheid P-L relations of Feast (1999), which yield more discrepant results. Additionally, we place weak limits upon the distance to the LMC and upon the effect of metallicity in Cepheid distance determinations.
This review examines progress on the Pop I, fundamental-mode Cepheid distance scale with emphasis on recent developments in geometric and quasi-geometric techniques for Cepheid distance determination. Specifically I examine the surface brightness method, interferometric pulsation method, and trigonometric measurements. The three techniques are found to be in excellent agreement for distance measures in the Galaxy. The velocity p-factor is of crucial importance in the first two of these methods. A comparison of recent determinations of the p-factor for Cepheids demonstrates that observational measures of p and theoretical predictions agree within their uncertainties for Galactic Cepheids.
Uncertainty in the metal abundance dependence of the Cepheid variable period- luminosity (PL) relation remains one of the outstanding sources of systematic error in the extragalactic distance scale and Hubble constant. To test for such a metallicity dependence, we have used the WFPC2 camera on the Hubble Space Telescope (HST) to observe Cepheids in two fields in the nearby spiral galaxy M101, which span a range in oxygen abundance of 0.7+-0.15 dex. A differential analysis of the PL relations in V and I in the two fields yields a marginally significant change in the inferred distance modulus on metal abundance, with d(m-M)/d[O/H] = -0.24+-0.16 mag/dex. The trend is in the theoretically predicted sense that metal-rich Cepheids appear brighter and closer than metal-poor stars. External comparisons of Cepheid distances with those derived from three other distance indicators, in particular the tip of the red giant branch method, further constrain the magnitude of any Z-dependence of the PL relation at V and I. The overall effects of any metallicity dependence on the distance scale derived with HST will be of the order of a few percent or less for most applications, though distances to individual galaxies at the extremes of the metal abundance range may be affected at the 10% level.
We present the modeling tool we developed to incorporate multi-technique observations of Cepheids in a single pulsation model: the Spectro-Photo-Interferometry of Pulsating Stars (SPIPS). The combination of angular diameters from optical interferometry, radial velocities and photometry with the coming Gaia DR2 parallaxes of nearby Galactic Cepheids will soon enable us to calibrate the projection factor of the classical Parallax-of-Pulsation method. This will extend its applicability to Cepheids too distant for accurate Gaia parallax measurements, and allow us to precisely calibrate the Leavitt laws zero point. As an example application, we present the SPIPS model of the long-period Cepheid RS Pup that provides a measurement of its projection factor, using the independent distance estimated from its light echoes.
The Hubble Space Telescope is being used to measure accurate Cepheid distances to nearby galaxies with the ultimate aim of determining the Hubble constant, H_0. For the first time, it has become feasible to use Cepheid variables to derive a distance to a galaxy in the southern hemisphere cluster of Fornax. Based on the discovery of 37 Cepheids in the Fornax galaxy NGC 1365, a distance to this galaxy of 18.6 +/- 0.6 Mpc (statistical error only) is obtained. This distance leads to a value of H_0 = 70 +/- 7 (random) +/- 18 (systematic) km/sec/Mpc in good agreement with estimates of the Hubble constant further afield.
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