It is firmly established that the Balmer lines are optimum indicators for because of their virtually null gravity dependence (Smalley & Dworetsky 1993; Furhmann et al. 1994). In this work, effective temperatures for La Palma observations have been obtained from the comparisons, using a least-squares fitting technique, between the observed H profile and a grid of synthetic profiles generated using ATLAS8 (Kurucz 1979a). The gravity and metallicity were fixed to and [M/H]=0.0 respectively. Previous to any comparison it was necessary to convolve the synthetic spectra with the instrumental and rotational profiles. The instrumental profile was calculated from the Thorium-Argon calibration spectra taken every night whereas the rotational profile was derived for each spectra by using Eq. (1), where was calculated following the method described in the previous section. A step of 100 K was assumed between models.
Likewise, we tried to apply this method to McDonald observations. However, the spectral range covered by the order where appears was not wide enough to embrace the wings of the line. This produced a continuum indetermination giving rise large errors in . An alternative method based on the variations in intensity of the wings of at two wavelengths (, ) was proposed. The selection of the wavelengths was done in such a way that they lie in the region of the profile with the greatest dependency with temperature. Using the set of non-variable stars and variable stars with (which would correspond to a variation in temperature of , that is, the assumed step in ) observed in McDonald and whose temperatures were determined using from La Palma spectra, we obtained a linear relationship between the intensity ratio and temperatures (Fig. 3.1 (click here)). An error of was assumed for La Palma spectra and for McDonald observations.
Table 5: Influence of the limb-darkening coefficient for different rotation velocities
Effective temperatures of the observed stars are displayed in Tables 6, 7. The effective temperature of UZ Lyn was not calculated using since the photometric calibrations indicate a temperature : at these temperatures, Balmer lines also depend on surface gravity and they cannot be used. Moreover, the effective temperature of CY Aqr has not been calculated using due to the low signal-to-noise ratio which prevented us from deriving its projected rotation velocity. Also, some McDonald spectra have no using due to problems in the flatfields of one of the nights.
The most natural way of checking the method of calculating based on Balmer lines would be to use it for standard stars with accurate values of . Code et al. (1976) and Hayes (1978) gave a list of stars with fundamentally determined values of . Three stars from Code et al. (1976) were also observed by us (Table 8): no systematic differences were found between the derived from and those given in Code et al. (1976).
Table 8: Comparison between the effective temperatures given in Code et al. (1976) and those derived using . An error of was assumed for the measurements
The temperatures obtained using have been compared with those obtained from the following photometric calibrations: Petersen & Jørgensen (1972) (PJ72), Philip & Relyea (1979) (PR79), Moon & Dworetsky (1985) (MD85), Lester et al. (1986) (LGK86a,b) and Balona (1994) (B94). Except for PJ72 which relies on the scale of temperatures (Popper et al. 1970) together with the relation (Crawford & Perry 1966), the remaining calibrations use the ATLAS8 code (Kurucz 1979a) to generate the synthetic indices and colours except for LGK86b who also used a different version of ATLAS8 (Kurucz 1979b) with a modified treatment of convection (Lester et al. 1982). Temperatures provided by the Petersen & Jørgensen (1972) and Balona (1994) calibrations have been derived using an interpolation formulae whereas temperatures calculated with the rest of photometric calibrations have been derived from grids assuming a step of 50 K. All calibrations use as the temperature indicator except PR79 who use (b-y). The and (b-y) values of the Sct stars have been taken from Rodríguez et al. (1994) except for UZ Lyn which does not appeared in this catalogue and its values were taken from García et al. (1993). For the sample of non-variable stars the and (b-y) were taken from the catalogue of Hauck & Mermilliod (1990). Both for variable and for non-variable stars, the dereddened indices were obtained using the dereddening law given by Philip & Relyea (1979). A comparison between the values of derived using and the photometric calibrations given above appears in Fig. 4.2 (click here). Those stars with variations in amplitude which would correspond to variations along the pulsation cycle were not considered.
PJ72 calculated effective temperatures which are, on average, 196 K higher than the values. These differences can be interpreted in terms of the old relationships and the few stars which this calibration is based on. In fact, these systematic differences disappear when a more modern calibration with more complete bolometric corrections and more numerous and precise angular diameters is applied (Bohm-Vitense 1981). The effective temperatures derived from PR79 are, on average, 155 K hotter than the H temperatures, this difference being larger when is hotter which can be attributed to the fact that only one star, Vega, with well outside of our range of temperatures (9 400 K), has been used in the transformation from synthetic to observed colors. MD85 provides the closest values to temperatures with a mean difference of 22 K and a standard deviation of , consistent with the error of adopted in the values whereas the mean difference between LGK86a and is with a standard deviation of . Although this difference is not significant with respect to the assumed error in the temperatures (), Fig. 4.2 (click here) illustrates that the difference tends to be greater in the region of lower temperature. This trend can be again caused by the lack of calibration stars in our range of temperatures (only one, Procyon, and just in the edge of the interval ( K)). The differences are even more relevant when the LGK86b is used (, ). Finally, the mean difference between B94 and is 96 K with a standard deviation of 164 K. This difference shows a similar trend to LGK86a which is reasonable since B94 is based on the synthetic colours derived by Lester et al. (1986a). Moreover, the greatest differences, which appear in the interval , can be explained in terms of how the calibration was defined: B94 used three different calibrations for three different intervals of : ; ; . In this last group the calibrating stars have , which means that effective temperatures in the range were calculated by extrapolation and thus the error being greater. Moreover, we see that, for , when a new calibration is used, the differences are much less significant.