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
derived via photometric
calibrations
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.
