H. Cugier, M. Burghardt, D. Nowak and G. Polubek
Astronomical Institute of the Wroc
aw University,
Kopernika 11, 51-622 Wroc
aw, Poland,
E-mail:cugier
astro.uni.wroc.pl
Cephei stars. Two stars, 
Ceti
and 
Scorpii are considered. We found that stellar models obtained from
nonadiabatic observables fit other observational data very well. We also found
that stellar models calculated for OPAL opacities with X = 0.70, Y = 0.28 and Z
= 0.02 are in good agreement with observed properties of 
Cet and
Sco. On the other hand, OP models which predict higher effective
temperatures will result in a worse fit to the ground-based and UV
spectrophotometric observations. The basic mean stellar parameters are also
derived for 
Cet and 
Sco.
Keywords: 
Cephei stars, nonadiabatic observables, satellite
ultraviolet, mean stellar parameters, stellar opacities
Recent stability surveys for stellar models corresponding to 
Cephei
stars leave no doubt that 
--mechanism
is responsible for the origin of pulsation of these stars, cf. Dziembowski
(1995) and references cited therein.
Cugier, Dziembowski & Pamyatnykh (1994) compared the prediction of the
linear nonadiabatic theory
for the amplitude ratios and the phase differences---
the nonadiabatic observables---with multicolor photometry and radial
velocity data. The agreement is satisfactory and,
in most cases, the harmonic degree, l, of oscillations can be determined.
Furthermore, the effect of using
OP opacities (Seaton et al. 1994) instead of OPAL opacities
(Rogers & Iglesias 1992) demonstrates the usefulness of 
Cephei
stars to test stellar opacities.
This requires accurate 
and metal abundance values
obtained from spectroscopy.
In this paper we address these questions.
Both the nonadiabatic observables and mean stellar parameters are investigated
using 
photometric data and UV spectrophotometric observations
collected by the Goddard High-Resolution Spectrograph (GHRS) on the
Hubble Space Telescope (HST) and International Ultraviolet Satellite (IUE).
Cephei stars occupy a small part of the Main Sequence band
corresponding to stars with masses from 9 to 16 
.
About a dozen of them (including 
Ceti and 
Scorpii) were
observed by means of the IUE satellite and an extensive
observational material was collected by HST/GHRS for 
Scorpii and
Canis Majoris. Here we present results for
Cet and 
Sco, cf. Table 1.
In this table we also listed mean stellar parameters derived
from the Strömgren photometry and nonadiabatic observables as discussed
in Sect. 3.
IUE observational material of 
Cet consists of low and high
resolution spectra obtained in modes, which do not allow us to calibrate them
in the absolute units.
We, therefore, constructed the mean energy flux distribution
by co-adding all low resolution images for a given camera. Similarly, high
resolution images were used to construct a mean spectrum of 
Cet
because small pulsational effects for this star are not clearly seen in
0.2Å resolution IUE data.
Cet is a star pulsating in the radial mode, l=0, cf. e.g.,
Cugier et al. (1994a).
Figure 1 displays the diagram log g vs. log 
for stellar models
having unstable radial modes of 
and 
, with the period exactly the
same as observed for 
Cet, 
.
Figure: The diagram log g vs. log 
for stellar
models of M = 8--16 
during Main Sequence
phase of evolution (dotted lines). Models having unstable
radial modes with the period 
are shown as thick
lines (calculated with OP opacities) and thin lines with dots
(OPAL opacities), respectively. The line marked as UV shows
the best fit models to observed UV energy flux distribution.
Note that models corresponding to 
and 
are shifted in log g by
about 0.13 dex. Furthermore, the models calculated with OP opacities (thick
lines) indicate higher effective temperature by about 0.05 dex. than OPAL
(thin lines with dots) models. These model calculations are taken
from Dziembowski & Pamyatnykh (1993). From the numbers given above we can
conclude that knowledge of 
and log g with high precision
is needed to select the correct stellar model and oscillation mode from
observed period of pulsation.
An efficient method of estimating the atmospheric parameters of B-type stars
is based on the Strömgren-Crawford 
photometric system,
cf. Nowak & Cugier (1996) for details. We found log 
= 4.340
and log g = 3.84 from data published by Lindeman & Hauck (1973),
cf. Table 1. However, the observations given by Shaw (1975) lead to
log 
= 4.321 and log g = 3.54. The effective temperature in the
range log 
= 4.321--4.340 is in better agreement with OPAL
models than OP ones.
Next, we search for the best fit of the predicted UV radiation flux to the
observed flux, by adjusting the parameters: 
and log g. The
observed flux was dereddened by means of the mean extinction curve given by
Savage 
Mathis (1979) adopting E(B-V) = 1.26 E(b-y) + 0.007 = 0.017 mag.
(cf. Nowak & Cugier 1996). Figure 2 shows the best-fit solution, but almost
the same quality fits, in the sense of the 
--test, exist for a set of
models marked as UV in Fig. 1. Again, OPAL models for stellar pulsation are in
good agreement with UV flux distribution of 
Cet.
Figure: The best fit of the predicted flux of radiation
(points) to low resolution IUE images of 
Cet
(continuous line).
The nonadiabatic observables of 
Cet mentioned in Section 1 indicate
that only 
mode is able to describe all observables. The best fit
solution exists for OPAL stellar model with log 
= 4.347
and log g = 3.73, cf. Cugier et al. (1994a,b).
Finally, we used high resolution IUE images of 
Cet to study line
profiles of selected species, namely: H I 1216, C III 1175, 1247, Si III 1206,
1300 and Si IV 1400Å. The results plotted in Fig. 3 indicate solar
abundances of Carbon and Silicon. Moreover, the calculated photospheric line
profile of 
is slightly weaker than the observed profile
indicating interstellar absorption, cf. Fig. 3a. We found the Hydrogen column
density towards 
Cet to be N(H I) =
.
Figure: The high resolution IUE images of 
Cet are
compared with theoretical spectra. In Panel (a) the pure
photospheric spectrum is shown as dotted line, whereas the
continuum line includes the effect of the interstellar
absorption in 
.
The IUE observational material of 
Sco contains 62 images and a half
of them were obtained in the large entrance aperture mode. Both,
UV energy flux distribution and UV light curves are available for this star.
Table 2 shows the observed amplitudes and moments of the maximum light
at selected wavelength ranges adopting P = 
for the dominant
mode of pulsation according to Jerzykiewicz & Sterken (1984).
Table 2: Amplitudes and times of maximum lights of 
Sco.
The HST/GHRS observations of 
Sco consists 31
pieces of UV spectrum taken on 9 October 1992 at wavelength region from
1127Å to 2611Å. A few of them are obtained in the FP-SPLIT = DSFOUR
mode with 4 subexposures taken for different
grating (G160M and ECH-B) positions.
Both an intrinsic stellar spectrum and fixed pattern noise (FPN) are shifted
relative to each other by different amounts in subexposures.
We analyze these spectra using a tomographic technique already applied by
Lambert et al. (1994) and Lyu et al. (1995) for HST/GHRS data.
Figure 4 illustrates the raw data, FPN and reduced spectrum.
Figure: An example of the HST/GHRS observations of
Sco obtained in the FP-SPLIT=DSFOUR mode. There are 4
subexposures, FPN and intrinsic stellar spectrum.
FPN has an amplitude of about 0.5 percent and reveals two
narrow features (blemishes) near 1900 and 2000 data point numbers.
An analysis of the observed periods of oscillation and nonadiabatic observables
obtained from the Strömgren photometry made by Jerzykiewicz & Sterken
(1984) leads to the following stellar parameters: 
, log 
, 
, 
and l = 0 for the dominant mode of pulsation. These
values for log 
and log g differ markedly from the results
obtained from 
colors shown in Table 1. We found, however, that the
atmospheric model obtained from nonadiabatic observables fits best the HST/GHRS
observations. The essentially solar abundances of Carbon and Silicon is
indicated for 
Sco, cf. Fig. 5.
Figure: HST/GHRS observations of 
Sco (thin line)
in comparison with
spectra calculated for the photospheric model obtained from
nonadiabatic observables (see text).
Pulsation data for 
Cephei stars are an important source of information
about these objects. These data consist of periods of oscillations and
nonadiabatic observables. The latter quantities are related to the
eigenfunctions of nonadiabatic oscillations (cf. Cugier et al. 1994a).
In this paper we consider two well-known stars: 
Cet and 
Sco.
We find (cf. also Cugier et al. 1994b, where BW Vul is considered) that
stellar models derived from the oscillation parameters fit very well the
observed UV energy flux distributions as well as line profiles taken in the
high resolution mode. Figure 1 illustrates that these complementary
observations are useful to distinguish between stellar opacities used in the
nonadiabatic model calculations. We found that OPAL models with Z = 0.02 fit
best the observed properties of 
Cet and 
Sco. On the other
hand, OP models predict higher effective temperatures and will result in a
worse fit to the observations.
A correctly identified nonadiabatic model means that all basic stellar (mass,
age and chemical composition) parameters are known. Thus, the data on
individual 
Cephei stars may be used for precise determination of
distances and ages of stellar systems they live in.
Having determined dominant modes of oscillation and important constraints on
the mean stellar parameters, we could also derive of the chemical composition
of 
Cephei stars. This provides an independent test for stellar
opacities. We found essentially solar abundances for Carbon and Silicon in both
stars.
Finally, high signal-to-noise HST/GHRS data (cf. Figs. 4 and 5) can also be used to study dynamical effects due to stellar pulsations. Small discrepancies in the cores of the Si IV lines (cf. Fig. 5) are probably the result of such effects.
We would like to acknowledge ST-DADS and HST/ESO/CFHT Archive Services for the Space Telescope Data. STARCAT interface developed by ST-ECF, CADC and ESO has been installed on SPARCstation 2 computer at AI WrU. ESA IUE Observatory at VILSPA provided the IUE tapes. To them all we express our thanks.
This work was supported by the research grant No. 2 P03D 001 08 from the Polish Scientific Research Committee (KBN).
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