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Astron. Astrophys. 318, 797-804 (1997)

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6. Conclusions

We have presented a method for computing Cepheid radii, which merges the CORS and the Surface Brightness method into a single, easy to use method applicable to observations in different photometric systems.

An interesting feature of this method is its independence from the knowledge of the reddening corrections, at least within the limits of an assumption that the derivative of [FORMULA] is the same as the one of [FORMULA].

In this first implementation, we have shown that the method is efficient and gives coherent results; we were able to compute radii for 74 Cepheids with a rather straightforward procedure. However, the improvements in the P-R relation are almost negligible with respect to previous works at least in terms of the scatter of the data. This scatter can be explained by the fact that our [FORMULA] is only an approximation to the correct [FORMULA] of the CORS method; however, its presence gives the right trend to the slope of the P-R relation, which is lower with [FORMULA] than without [FORMULA], as found also with the correct [FORMULA] (see Sollazzo et al. 1981). The fact that we always use three bands (B,V,R in this paper) should also give more consistency to the results.

We have actually to warn the reader that, as stated in the introduction, the method illustrated here represents a step backward with respect to the original CORS method, in the sense that the usage of Eq. (4) is a simplification which avoids using the proper photometric calibration, but also gives lower intrinsic precision to the derived radius. In other words, whenever possible the complete CORS method, with the full [FORMULA] term, should be used, because the method presented here gives a first order approximation to [FORMULA], which is better than neglecting [FORMULA], but worst than the second order approximation of the CORS method, i.e. the determination of [FORMULA] by mean of theoretical model atmosphere. The advantage is the very quick computation, namely a couple of minutes at the terminal for each star.

Further work is needed to improve the approximation, but the basis of the method seems now well laid. A possible idea, which we will work on, is in computing [FORMULA] as a sum of two terms, one based on the observations (like in the present paper) and one based on theoretical computations from Kurucz's models (like the original CORS method did, but only for a particular photometric system). We are also working on a method to compute statistically meaningful errors on the radii, based on the quality of the observations, rather than on the purely numerical errors of the fitting procedure.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998