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

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5. Results

In Table 2 we report the results of our analysis for all stars of our sample for which the CORS method reached the convergence; from left we report in the order: name of the cepheid; period; radial velocity data source; photometric data source; radius obtained with the surface brightness method (Gieren et al. 1989); radius obtained with CORS (without [FORMULA] term); as before but with the [FORMULA] term.

These data are plotted in Fig. 4 were we present the Period-Radius relation as a result of CORS method in two cases, with and without [FORMULA] respectively; the solid lines superimposed represent a least square fit to our data that leads to the following Period-Radius relation (74 cepheids) without the [FORMULA] term in Eq. (13):

[EQUATION]

If we exclude from our fit X Lac (it shows a clear phase shift) and U Sgr (double star) we obtain a slightly better error:

[EQUATION]

Now, if we consider the [FORMULA] term in Eq. (13) for cepheids with BVRI photometric observations (65 stars) we obtain:

[EQUATION]

And excluding the large scattering YZ Sgr (poor radial velocity data) we obtain:

[EQUATION]

Our Period-Color relations are reported also in Table 3 in comparison with other selected results from the literature. We note that our P-R relations show a slope slightly shallower than either the more recent determinations via Baade-Wesselink methods, or theoretical determination.


[TABLE]

Table 3. Comparison of coefficients of Period-Radius relation [FORMULA] between this paper and selected other works available in literature.


Moreover the use of a second color (i.e. the inclusion of [FORMULA] in the determination of radius) goes in the sense to reduce further on the slope. Since we use (at least partially) the same data of Gieren et al. (1989) it is surprising to find such a different result. Anyway, in their recent paper, Laney and Stobie (1995) applied a Surface Brightness method to a set of 31 Cepheids, using different pairs of magnitudes and colors, from (V,B-V) to (K,J-K), and found a dependence of the P-R relation from the colors used, in the sense that the slope is shallower if "blue" colors are used instead of the infrared ones. This could partially explain our shallower slope in the P-R relations, since our two determinations of R depend either from two or three "blue" colors.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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