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3. Stellar parameters

  figure322
Figure 3: Colour-colour diagram of tex2html_wrap_inline1120 vs. tex2html_wrap_inline1284. Lines of equal surface gravity tex2html_wrap_inline1286 (in steps of tex2html_wrap_inline1288; dashed lines) and equal effective temperature tex2html_wrap_inline1290 (in steps of tex2html_wrap_inline1292; solid lines) are from corrected colours of Kurucz models, calibrated with Hyades main-sequence stars (see text). The Hyades main-sequence tex2html_wrap_inline1294 is plotted as a dotted line, and the adopted main-sequence for solar abundance as a thick solid line. Crosses denote the location of our sample stars, the error bars indicate the uncertainties as listed in Table 2

The effective temperature tex2html_wrap_inline1290, surface gravity g, and interstellar extinction E(V-B) (in the Walraven system) were derived for each star from a comparison of the observed Walraven colours with theoretical values. The theoretical tex2html_wrap_inline1120 and tex2html_wrap_inline1284 values as functions of tex2html_wrap_inline1290 and tex2html_wrap_inline1286 were obtained from an empirically derived main-sequence relation between tex2html_wrap_inline1290, tex2html_wrap_inline1286, tex2html_wrap_inline1120 and tex2html_wrap_inline1316 for the Hyades, combined with differential colour-colour vectors from a folding of the Walraven passbands with the spectral energy distributions for a grid of Kurucz (1992) model atmospheres. Both the empirical Hyades main-sequence and the differential vectors for the Kurucz model atmospheres were kindly provided by Pel (1991). The models used cover the effective temperature range from 5500 K to 8500 K and the surface gravity range 2.0 to 4.5. Chemical abundances range from 0.003 times the solar value to the solar value. We have converted the empirically derived Hyades main-sequence relation, with tex2html_wrap_inline1318, to a relation valid for solar abundances, and extrapolated it to lower surface gravity values, using differential vectors from Kurucz model atmospheres. The use of differential vectors bypasses possible systematic offsets in the colours derived from Kurucz model atmospheres. Figure 3 (click here) shows the resulting tex2html_wrap_inline1120 - tex2html_wrap_inline1284 diagram with lines of constant temperature and surface gravity, for solar abundances. Also, the location of the empirical Hyades main-sequence is indicated (dotted line, tex2html_wrap_inline1318) and the main sequence as converted to solar abundance (thick solid line), and the positions of the sample stars are plotted. For a subsample of stars with supposedly small interstellar reddening, preliminary values for the effective temperature and the surface gravity were derived by equating the observed tex2html_wrap_inline1120 and tex2html_wrap_inline1284 with the theoretical ones. The subsample was checked for consistency on the assumed interstellar reddening, after deriving the extinction for every star by comparing with the (corrected) theoretical Walraven colours. These preliminary values for the effective temperature and the surface gravity were used to calculate the expected theoretical colours tex2html_wrap_inline1122 and tex2html_wrap_inline1124 for the same subsample. The differences between observed and theoretical values were interpreted as a systematic error in the theoretical colours, and were used to correct the theoretical colours. The colour (B-L) is corrected using the corrections for (B-U) and (L-U).

After that, values for tex2html_wrap_inline1290, tex2html_wrap_inline1286 and E(V-B) were derived by comparing their observed colours (tex2html_wrap_inline1120, tex2html_wrap_inline1122, tex2html_wrap_inline1126, tex2html_wrap_inline1124) with the corrected theoretical ones. If any of the stars, used for calibration, had significant extinction the whole procedure was repeated, without these reddened stars.

The final values for tex2html_wrap_inline1290, tex2html_wrap_inline1286 and E(V-B) for all stars, as listed in Table 2, their uncertainties and the uncertainties tex2html_wrap_inline1360 on the theoretical colours tex2html_wrap_inline1362, have been derived simultaneously by minimising tex2html_wrap_inline1364:
equation811
where tex2html_wrap_inline1366 and tex2html_wrap_inline1368 are the observed colour and its uncertainty, respectively. The uncertainties on the stellar parameters are determined by the values where tex2html_wrap_inline1364 equals the minimum tex2html_wrap_inline1364 plus one, and the uncertainties in the theoretical colours are determined by assuming that the quadratic deviation between the observed and the theoretical colour tex2html_wrap_inline1374 is on average equal to the sum of their quadratic uncertainties tex2html_wrap_inline1376.

We find that for the present sample the uncertainties in the theoretical colours are negligible in tex2html_wrap_inline1120 and tex2html_wrap_inline1122 (compared to the observational uncertainties). The uncertainty in the theoretical tex2html_wrap_inline1124 is 0.013, and the uncertainty in the theoretical tex2html_wrap_inline1126 is 0.015.

The uncertainties in the effective temperature, the surface gravity, and the colour excess E(V-B), are typically (68%): tex2html_wrap_inline1388, tex2html_wrap_inline1390, and tex2html_wrap_inline1392, respectively. An extra (unknown) uncertainty may occur if the stellar parameters are outside the range of the parameters of the calibration stars (tex2html_wrap_inline1290 between 6000 K and 8000 K; tex2html_wrap_inline1286 between 3.4 and 4.4).

For five stars (HR 313, HR 7126, HR 8041, HR 8917 and HR 8935) we could not find consistent stellar parameters with this method, in the sense that the minimum tex2html_wrap_inline1364 for these stars is larger than 10. We can find no reason why these stars should deviate in their colour-colour behaviour. These stars are indicated in Table 2 with a colon after the values. No uncertainties are given for these stars.


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