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Astron. Astrophys. 364, 102-136 (2000)

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7. Stellar parameters

7.1. Stellar parameters from Strömgren photometry

The stellar parameters [FORMULA] and [FORMULA] were found from the observed Strömgren indices after de-reddening (as discussed in Sect. 5) by interpolation in the [FORMULA] synthetic grids. The adopted indices are those listed in boldface in Table 1. Dereddened indices were obtained both from [FORMULA] values derived from the SFD whole sky map (Table 6, Column 6) and from the [FORMULA] derived from the UVBYLIST program of Moon (1985) (Table 6, Column 8). The reddening relations given in Sect. 5.2 were used in both cases.

When [FORMULA][FORMULA]8 500 K and [FORMULA][FORMULA], the (c, [FORMULA]) grid does not give an unambigous determination of the parameters and the (a, r) grid (Strömgren 1966) is to be preferred. It should be noted that different values for the reddening may be derived for a star by the two methods, so that it may lie in the (a, r) plane according to one reddening determination, and in the (c, [FORMULA]) plane according to the other.

For each star, we started by selecting, from among the available grids of colour indices, the one which had the metallicity closest to that given in the literature or from a preliminary estimate based on the strength of the [FORMULA]4481 Mg II  line (KSK). After a new metallicity was found from the model atmosphere analysis, it was used to determine, by interpolation, the colour grid which corresponded to this new metallicity. New parameters were then redetermined. We found that the stellar parameters were, in practice, relatively insensitive to the value used for the metallicity. For this reason, the stellar parameters found from the Strömgren indices and listed in the first two (or three) lines of Table 7 are those relative to the approximate metallicity listed in Column 6. At this stage, we also adopted a microturbulent velocity of [FORMULA]= 2.0 km s[FORMULA] for all the stars. In Table 7, the data on the first line for each star correspond to the [FORMULA] derived from the SFD whole sky-map (Table 6, Column 6), while the data on the second line correspond to the [FORMULA] derived using Moon's program (Table 6, Column 8). The reddening [FORMULA]=[FORMULA]/0.73 is given in Column 3 of Table 7. The specific Strömgren indices that we used to obtain [FORMULA] and [FORMULA] for each star are given in the second column of Table 7. The errors in the parameters were calculated by assuming an uncertainty of [FORMULA] 0.015 mag for all Strömgren indices except [FORMULA] for which [FORMULA] 0.005 mag was adopted. The actual error in [FORMULA] may well be larger than this for some stars as noted in Table 1 and in Sect. 3.

7.2. Stellar parameters from spectrophotometry in the visible

Spectrophotometric observations are available (Philip & Hayes 1983; Hayes & Philip 1983) for some of our candidate BHB stars. Stellar parameters were derived for these stars by fitting the observed energy distribution to the fluxes of that grid, among those available to us, which had the closest metallicity either to that given in the literature, or to that obtained from a preliminary estimate based on the strength of the [FORMULA]4481 Mg II  line, or to that given in a preliminary abundance analysis. The observed energy distribution was dereddened as described in Sect. 5.3. The fitting procedure is that described by Lane & Lester (1984) in which the entire energy distribution is fitted to the model which yields the minimum rms difference. The search for the minimum rms difference is made by interpolating in the grid of computed fluxes. The computed fluxes are sampled in steps of 50 K or 100 K in [FORMULA] depending whether [FORMULA][FORMULA] 10000 K or [FORMULA][FORMULA]10000 K, and in steps of 0.1 dex in [FORMULA]. The fluxes are actually given in steps of 250 K or 500 K in [FORMULA] and in steps of 0.5 dex in [FORMULA], so the finer sampling was obtained by linear interpolation.

The parameters derived from the energy distributions are given on the "En. Distr." line in Table 7 and the adopted metallicity is that listed in Column 6. The errors in the parameters were estimated from the ranges in [FORMULA] and [FORMULA] for which rms=rms(min)+50% rms(min). Lane & Lester note that the point-to-point scatter that determines the value of rms may be less important in their data than the calibration errors over large ranges of wavelength. In our data the main uncertainty in deriving [FORMULA] and [FORMULA] from the energy distribution probably comes from the spectrophotometric observations being available at relatively few wavelengths. This makes it difficult to get accurate results when they are fitted to the computed spectra.

7.3. Stellar parameters from H[FORMULA]

For stars cooler than about 8000 K, the H[FORMULA] profile is a good temperature indicator because it is almost independent of gravity, while for hotter stars with [FORMULA] between 8000 K and 10 000 K it depends on both [FORMULA] and [FORMULA]. Above 10 000 K, H[FORMULA] becomes a good gravity indicator, because it is almost independent of temperature.

In order to derive the stellar parameters from the H[FORMULA] profiles given by the KPNO spectra, we fitted the observed profiles (normalized to the continuum level) to the grids of profiles computed with the BALMER9 code (Kurucz 1993a). For each star, we used the grid computed for a microturbulent velocity [FORMULA] = 2 km s[FORMULA] and the metallicity closest to that derived for the star in a preliminary abundance analyses. We found that the fit was insensitive to the adopted value of [FORMULA].

We used an interactive routine to omit all the lines of other elements which affect the H[FORMULA] profile, and by linear interpolation, we derived the residual intensities [FORMULA](i) of H[FORMULA] for each [FORMULA](i) sampled in the observed spectrum. We then used the same fitting procedure as that used to derive the parameters from the energy distributions. For each star, the parameters [FORMULA] and [FORMULA] are those which give the minimum rms difference.

For stars cooler than 8000 K, this procedure gives [FORMULA], but not [FORMULA], because the H[FORMULA] profile is not sensitive to gravity for these temperatures. Therefore, to derive [FORMULA] for these stars, we adopted the average [FORMULA] from the Strömgren photometry and UV colours, since small differences in [FORMULA] do not change the value of [FORMULA].

For stars with [FORMULA] between 8000 K and 10000 K both [FORMULA] and [FORMULA] can be obtained by the fitting procedure, but the situation is less satisfactory because some ambiguity occurs in this range. For example, for [M/H] = -1.5, the H[FORMULA] profile is almost the same for [FORMULA] = 8800 K, [FORMULA] = 3.0 as for [FORMULA] = 9500 K, [FORMULA] = 3.4. This means that very small differences in the reduction procedure may give very different values for the parameters. Therefore, when the parameters derived from the fitting procedure were in reasonably agreement with other determinations, we have given both [FORMULA] and [FORMULA]. Otherwise we fixed either [FORMULA] or [FORMULA] and calculated the other parameter. The stellar parameters found in this way are given on the "H[FORMULA]" line in Table 7. We give in parenthesis the parameters that were fixed in advance. As for the energy distribution, the errors in the parameters were estimated from the ranges in [FORMULA] and [FORMULA] for which rms = rms(min)+50% rms(min).

The main error in deriving [FORMULA] and [FORMULA] from H[FORMULA] comes from the uncertainty in the normalization of the KPNO spectra; this is largely because of a small non-linear distortion in the spectra which means that it is not a straightforward task to decide where the wings of H[FORMULA] start. The uncertainty in [FORMULA] produced by the extraction procedure of the unblended H[FORMULA] profile is of the order of 50 K.

7.4. Stellar parameters from IUE data

As we discussed in Sect. 5, the parameters derived from the ultraviolet fluxes are those which lead to the most consistent values of reddening when one compares the observed [FORMULA] colours and also the observed [FORMULA] vs. [FORMULA] colours with the corresponding theoretical values. The parameters found in this way are on the "UV" lines in Table 7.

As a further check, we compared the whole UV-observed energy distributions, for the stars that have both short- and long-wavelength IUE data, with model energy distributions computed with the adopted parameters given in Table 7. We did not find systematic discrepancies between the models and the observed data at 1 600 Å and shorter wavelengths, as was found by Huenemoerder et al. (1984) and Cacciari et al. (1987) using the 1979 Kurucz models. For more than half of these stars (HD 2857, HD 4850, HD 13780, HD 14829, HD 31943, HD 74721 and HD 93329) the observed and calculated energy distributions match rather well over the entire IUE wavelength range. For three stars (HD 78913, BD +00 0145 and HD 130201), the UV data suggest hotter temperatures than those adopted in Table 7. For three other stars (HD 8376, HD 60778 and HD 252940), the discrepancies may be caused by incorrect values of the adopted stellar parameters and/or uncertainties in the IUE and Strömgren photometry. A detailed investigation, that compares the observed and synthetic UV energy distributions using the latest model atmospheres, would be of interest but is beyond the scope of this paper. Meanwhile, we are confident that the use of the [FORMULA] colour index gives results for the reddening and physical parameters which are consistent with and give the same degree of uncertainty as those that would be derived by using the entire IUE energy distributions.

7.5. The effective temperatures from [FORMULA]

The ([FORMULA]) colours are available for nine of our candidate BHB stars (Arribas & Martinez Roger 1987). These ([FORMULA]) colours are listed in Table 1. For seven of these stars, ([FORMULA]) colours had previously been given by Carney (1983). The mean difference between these two sets of colours (Carney minus Arribas & Martinez Roger) is 0.016[FORMULA]0.005; this corresponds to a temperature difference of [FORMULA]50 K; presumably the systematic error in these colours is of this order. The largest source of error in deriving temperatures in this way is likely to come from the correction for reddening. We assumed that [FORMULA] = 2.72 [FORMULA] (Cohen et al. 1999) and took the [FORMULA] to be the mean of the [FORMULA] derived from the other methods given in Column 3 of Table 7. We assumed the mean [FORMULA] from the other determinations, and derived [FORMULA] by interpolation in the [FORMULA][FORMULA] and [FORMULA] grid. These temperatures are given in Table 7 and their errors are scaled from the estimated errors in [FORMULA]; they were not used in deriving the mean [FORMULA] but gave a useful independent check on the temperatures obtained by other methods (see Table 7). We see that the systematic difference between our adopted mean [FORMULA] and the [FORMULA] derived from ([FORMULA]) is only slightly larger than that expected from the likely systematic errors in the ([FORMULA]) colours.

7.6. The comparison of the stellar parameters determined by the different methods

Table 7 gives, for each star, the straight means of [FORMULA], [FORMULA], and [FORMULA] together with the errors of the means. In nearly all cases, the extinction derived from the SFD maps exceeds that derived by using the Moon UVBYLIST program (Table 6) and the use of the SFD extinctions with the [FORMULA] data gives higher [FORMULA] than those found by other methods. This difference is most pronounced for low-latitude stars (HD 252940, HD 60778, HD 78913, HD 130095, HD 130201, HD 139961, HD 161817 and HD 180903) whose computed extinction depends upon an uncertain model of the local distribution of the interstellar extinctions. We have therefore felt justified in rejecting the stellar parameters that were derived using the SFD maps for these low-latitude stars. We also excluded the parameters determined from the Strömgren indices according to the Moon UVBYLIST program for the stars HD 117880 and HD 130095, because of the excessive difference betwen the reddening derived from the Moon code and that from the other determinations. These excluded parameters (and those derived from ([FORMULA])) are enclosed in square brackets in Table 7.

The differences from these straight means were then computed for each method. The average of these differences ([FORMULA]) for [FORMULA] are given for each method in Table 8. The dispersions given in Column 4 of Table 8 are of the same order as the error estimates of the [FORMULA] given in Column 4 of Table 7 but there are significant differences. Thus the Energy Distribution method has among the smallest errors in Table 7 but has one of the largest dispersions in Table 8. This, together with the undoubted presence of systematic errors associated with each method has stopped us from using the error estimates for any attempt at weighting the [FORMULA] in Table 7; we have therefore adopted the straight means for the parameters given in this table.


[TABLE]

Table 8. Systematic differences ([FORMULA]) from mean of [FORMULA] obtained by different methods.
Notes:
[FORMULA]) Omitting HD 117880, HD 130095 & HD139961.
1) [FORMULA] taken from SFD map (Table 6, Column 6).
2) [FORMULA] taken from Strömgren colours using Moon (1985) UVBYLIST program (Table 6, Column 8).


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© European Southern Observatory (ESO) 2000

Online publication: December 15, 2000
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