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Astron. Astrophys. 327, 207-214 (1997)

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5. Conclusions

Using a sample of 53 stars belonging to 30 detached double-lined eclipsing binaries with accurate ([FORMULA] 1-2%) determinations of masses and radii, we present photometric calibrations for the mass, radius and surface gravity of single stars in terms of Strömgren-Crawford photometric indices. The calibrations are based on those suggested by Andersen (1991) and have a similar formal expression to Crawford's (1975, 1978, 1979) absolute magnitude calibrations. Basically, a ZAMS reference relation and two photometric indices, one related to [FORMULA] and another related to evolution, were used to build such calibrations.

We considered the separation of the stars in the sample into three different photometric regions and both a ZAMS relation and a calibration depending on suitable indices were considered for each region. Due to the lack of unevolved stars in the sample to define a purely observational ZAMS relation, we used that of SSMM evolutionary models, which was related to the photometric indices by means of the MD grids and NSW interpolation. Additionally, a simulation using SSMM evolutionary tracks was performed in order to consider a set of synthetic stars spread over a wide range of evolutionary stages within the main sequence, for a better definition of the linear calibrations attempted. The agreement between real and synthetic stars was excellent in all photometric regions. An additional linear term in [FORMULA] was considered in the calibrations of the late region to account for abundance effects. Although a similar treatment may also be necessary for the intermediate region, the lack of real stars in this region prevented an equivalent correction.

Thus, Eqs. (2), (3) and (4), together with Tables 3, 4 and 5 constitute the biparametric calibrations proposed in this work, applicable to main sequence stars with 7000 K [FORMULA] 20000 K. For both cooler and hotter stars, a suitable definition of the ZAMS relation and, accordingly, of the calibrations was not possible, as quoted in Paper I, due to the inaccuracies in the model atmospheres used to relate the phometric indices to [FORMULA] and [FORMULA]. The mean residuals obtained for the real stars are very similar to those given by a more complex algorithm using MD grids and SSMM stellar evolutionary models, and better than those from single-parameter calibrations by a factor of about three.

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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