Figure 3: Colour-colour diagram of vs.
. Lines
of equal surface gravity
(in steps of
; dashed
lines) and equal effective temperature
(in steps of
; solid lines) are from corrected colours of Kurucz
models, calibrated with Hyades main-sequence stars (see text). The Hyades
main-sequence
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 , 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
and
values as functions of
and
were obtained from an empirically derived
main-sequence relation between
,
,
and
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
, 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
-
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,
) 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
and
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
and
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 ,
and E(V-B) were derived by
comparing their observed colours (
,
,
,
) 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 ,
and E(V-B) for all stars, as
listed in Table 2, their uncertainties and the uncertainties
on the theoretical colours
, have been
derived simultaneously by minimising
:
where and
are the observed colour and its
uncertainty, respectively. The uncertainties on the stellar parameters are
determined by the values where
equals the minimum
plus one,
and the uncertainties in the theoretical colours are determined by assuming
that the quadratic deviation between the observed and the theoretical colour
is on average equal to the sum of their quadratic
uncertainties
.
We find that for the present sample the uncertainties in the theoretical
colours are negligible in and
(compared to the
observational uncertainties). The uncertainty in the theoretical
is 0.013, and the uncertainty in the theoretical
is 0.015.
The uncertainties in the effective temperature, the surface gravity, and the
colour excess E(V-B), are typically (68%):
,
, and
, respectively. An extra (unknown)
uncertainty may occur if the stellar parameters are outside the range of the
parameters of the calibration stars (
between 6000 K and 8000 K;
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 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.