The distance of galactic Cepheids can be derived through the interferometric Baade-Wesselink method. The interferometric measurements lead to angular diameter estimations over the whole pulsation period, while the stellar radius variations can be deduced from the integration of the pulsation velocity. The latter is linked to the observational velocity deduced from lines profiles by the so-called projection factor p. The knowledge of p is currently an important limiting factor for this method of distance determination. In this context, an hydrodynamic model of the cepheid is required to study dynamical structure of its atmosphere together with the induced line profile.
We briefly introduce the theoretical framework developed to account for pulsation properties of radial variables, and in particular classical Cepheids. We also discuss intrinsic features and limits of the physical assumptions adopted to construct nonlinear, convective, hydrodynamical models. Finally, we outline the current status concerning the comparison between theoretical predictions and observations (photometry and spectroscopy).
The Period-Luminosity (P-L) relation of the Cepheids is the basis of the extragalactic distance scale, but its zero-point is still debated at a +/- 0.10 mag level. One classical way to calibrate the P-L relation is the Baade-Wesselink (BW) method where one combines photometry and radial velocity data to obtain the distance and radius of a Cepheid. A requirement of this method is a very accurate measurement of the Cepheid's effective temperature at all observed phases, in order to determine the angular diameter. Interferometry allows us to bypass this step and its associated uncertainties by measuring directly the variation of angular diameter during the pulsation cycle, but the combination of different types of data relies on strong hypotheses. In my presentation, I will summarize the strengths and weaknesses of the interferometric BW method, and present its practical application to the calibration of the P-L and Period-Radius relations.
The inclusion of turbulent convection in the Florida hydrodynamic code resulted in several new results, like the consistent modelling of double mode Cepheids and the Hertzsprung progression of s-Cepheids. Since this code uses an approximation of turbulent convection with several free parameters, we have not used the code to model individual stars, but the tendencies in a large ensemble of Cepheids. We describe our standard code and the results we obtained on Cepheid stars.
Recent nonlinear calculations of Cepheid pulsation are based on codes similar to Stellingwerf's code. The major differences are related to the treatment of envelop convection and radiation transfer. The model of turbulent convection is also a major shortcoming of these codes, since it is a 1D approximation. The real 3D modelling of stellar pulsation is still a dream, but hybrid codes (1D radial pulsation coupled with with 3D convection calculations) are expected in the near future. New developments are still expected in the purely 1D radial models. Our new code builder makes it possible to easily extend the pulsation code with additional equations (e.g. more complex model of convection or treatment of radiation transfer). These new developments will possibly result in more realistic theoretical models of observable variations.
With the exceptions of Sirius and Altair, direct interferometric limb-darkening observations (in the 2nd and higher lobes) have been limited to a small number of stars cooler than the Sun. I will describe an on-going observational program with the CHARA Array and FLUOR beam combiner to obtain 2nd lobe measurements of B- and A-type supergiants and F-type subgiants. I will also discuss the importance of multi-wavelength observations for testing theoretical limb-darkening predictions, a key to the atmospheric temperature structure and detailed tests of convection. I hope this work will provide context for similar studies of the brightest Cepheids.
I will talk about our efforts to produce time- and wavelength-dependent limb darkening corrections for Classical Cepheids. These corrections are derived by solving the full radiative transfer problem for pulsating atmospheres computed with a time-dependent hydrodynamic model. For each pulsational phase we compute the limb darkening profile in the UV, visible and near-IR, which can be used to directly fit interferometric data, or to correct uniform brightness diameter measurements obtained at specific wavelengths.
The state of the art method of modellization of the pulsating stellar atmospheres will be presented. The method allows to obtain not only the subphotospheric pulsating envelope but also the optically thin atmosphere, and the spectral line calculation. The model gives the light and velocity (in any desired line) curves and detailed line profile variations with time. Some important application to modern observations will be discussed.
After the first successes of cepheids observations by Long Baseline Interferometry, different ways are offered to us. We will discuss in this presentation the new possibilities that will be opened by the coming instrumentation in this field in terms of limiting magnitude or spectral resolution or spectral domain or angular resolution. Two main domains are of course in front of us: 1) the distance scale program will be developped first by increasing the accuracy on the measurements and secondly by accessing to more distant cepheids; 2) the atmospheric motion's studies will largely benefit from the increase in spectral resolution. It will be also interesting to develop this observing strategy to other kinds of stellar candles.
I will give a brief overview of the many uses of Cepheids' spectroscopy (abundance analyses, Galactic rotation, the Baade-Wesselink method and the projection factor, binarity). I will then focus on the structure and dynamics of Cepheids atmospheres, as can be studied through spectroscopy, with a particular emphasis on velocity fields and the effects of turbulence.
We present here recent results on the structure and dynamics of Cepheid atmospheres from Near-Infrared and high resolution spectroscopic measurements.
We briefly discuss the new possibilities to study unresolved radial pulsating in particular Classical Cepheids using Differential Interferometric techniques.
P. Fouqué, J. Storm, W. Gieren, T.G. Barnes, G. Pietrzynski
Pascal Fouqué, Observatoire Midi-Pyrénnées
Direct distances to Cepheids in the LMC: evidence for a universal slope of the PL relation up to solar abundance ?
slides 771 Ko
"We have applied the infrared surface brightness (ISB) technique to derive distances to twelve Cepheid variables in the LMC which span a period range from 3 to 42 days. From the absolute magnitudes of the variables calculated from these distances, we find that the LMC Cepheids define tight period-luminosity relations in V, I, W and K which agree very well with the corresponding Galactic PL relations derived from the same technique, but are significantly steeper than the LMC PL relations in these bands obtained by the Ogle-II project in V, I, W, and by Persson et al. (2004) in K.
We also find that the LMC Cepheid distance moduli we derive, significantly depend on the period of the stars. We identify as the most likely culprit of this fake effect a previously unrecognized strong variation with period of the p-factor, used to convert observed radial velocities of Cepheids into pulsational velocities. By demanding a zero slope in the tilt-corrected LMC distance moduli vs. period diagram, we find p = 1.595 - 0.164 log P, while we were using
a milder dependence of the p-factor with period in all our previous works since 1993, namely p = 1.39 - 0.03 logP, based on the models of Hindsley & Bell (1986). More modern atmosphere models are urgently needed to confirm these findings.
When we re-calculate the distances of the LMC Cepheids with the revised p-factor law, the slopes in the various LMC PL relations decrease to values now consistent with those reported by Ogle-II and Persson et al. Similarly, re-determined distances of Galactic Cepheids lead to Galactic PL relations also in agreement with the LMC ones, while the agreement with ZAMS-fitting distances is also slightly improved.
Our main conclusion from this ISB analysis of 12 LMC Cepheids is that there no longer seems to exist significant differences between the Galactic and LMC slopes of the PL-relations from V to K-band. Ogle-II results on more metal-poor Cepheids in IC 1613 lead to the conclusion that the slope of the PL-relation does not depend on metallicity, from [Fe/H] = -1 to solar values."
Thanks to the rich variety of pulsational characteristics associated with varying stellar parameters, cepheids grant potential remarkable insight and constraint on the internal structure and processes.
Cepheid interferometric and spectroscopic measurements may now be combined to offer unprecedented, quantitative detail concerning the cepheid appearance. However, cepheid observations are difficult to interpret, requiring substantial model support. Furthermore, extensive cepheid observing can be very expensive in telescope and instrument time. Cepheid modeling has attained an impressive level of sophistication - now including such complex physics that the modeling effort must be carefully focused on answerable questions. It is very timely to bring the observing and modeling efforts together, as each both benefits from and guides the other. An investment in cepheid star studies also promises to stimulate and enable improved understanding of other luminous stars - both non-variable and of other variability types. This summary collects a few highlights from the lectures and discussion .