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Register a new userThe Cepheid Distance Scale: recent progress in fundamental techniques
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Thomas G. Barnes III
Publication date
2009
fields
Physics
and research's language is
English
Authors
Thomas G. Barnes III
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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.
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Through an innovative combination of multiple observing techniques and mod- eling, we are assembling a comprehensive understanding of the pulsation and close environment of Cepheids. We developed the SPIPS modeling tool that combines all observables (radial velocimetry, photometry, angular diameters from interferometry) to derive the relevant physical parameters of the star (effective temperature, infrared ex- cess, reddening,...) and the ratio of the distance and the projection factor d/p. We present the application of SPIPS to the long-period Cepheid RS Pup, for which we derive p = 1.25 +/- 0.06. The addition of this massive Cepheid consolidates the existing sample of p-factor measurements towards long-period pulsators. This allows us to conclude that p is constant or mildly variable around p = 1.29 +/- 0.04 (+/-3%) as a function of the pulsation period. The forthcoming Gaia DR2 will provide a considerable improvement in quantity and accuracy of the trigonometric parallaxes of Cepheids. From this sample, the SPIPS modeling tool will enable a robust calibration of the Cepheid distance scale.
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.
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.
The determination of pulsation mode and distance for field Cepheids is a complicated problem best resolved by a luminosity estimate. For illustration a technique based on spectroscopic luminosity discrimination is applied to the 4.47d s-Cepheid FF Aql. Line ratios in high dispersion spectra of the variable yield values of <Mv>=-3.40+-0.02 s.e.(+-0.04 s.d.), average effective temperature Teff=6195+-24 K, and intrinsic color (<B>-<V>)o = +0.506+-0.007, corresponding to a reddening of E(B-V)=0.25+-0.01, or E(B-V)(B0)=0.26+-0.01. The skewed light curve, intrinsic color, and luminosity of FF Aql are consistent with fundamental mode pulsation for a small amplitude classical Cepheid on the blue side of the instability strip, not a sinusoidal pulsator. A distance of 413+-14 pc is estimated from the Cepheids angular diameter in conjunction with a mean radius of <R>=39.0+-0.7 Rsun inferred from its luminosity and effective temperature. The dust extinction towards FF Aql is described by a ratio of total-to-selective extinction of Rv=Av/E(B-V)=3.16+-0.34 according to the stars apparent distance modulus.
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