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\IBVShead{4572}{23 March 1998}

\IBVStitle{B\lowercase{a} II line as Cepheid luminosity indicator. I}

\IBVSauth{S.M. ANDRIEVSKY}
\IBVSinsto{Dept of Astronomy, Odessa State University, Shevchenko Park, 270014 Odessa, Ukraine}
\IBVSinsto{e$-$mail: SCAN@deneb.odessa.ua}

\IBVStyp{ Cepheids }
\IBVSkey{spectroscopy}
\IBVSabs{Ba II lines are proposed as luminosity indicators for yellow supergiants.}
\IBVSabs{In particular, it is shown that equivalent width of BaII 5853.6 \AA}
\IBVSabs{line is well correlated with $M_{v}$ for s$-$Cepheids.}

\begintext
\vskip -5mm

Absolute magnitudes of the supergiant stars are the values of paramount
importance for stellar evolution theory and investigation of galactic
structure. The period$-$luminosity relation for pulsating stars,
which is frequently used for rapid $M_{v}$ determination, has nevertheless
two limiting factors: it cannot be applied in case of the non-variable
supergiants and, at least for galactic Cepheids, it does not allow
to find an accurate absolute magnitude if we do not know exactly about the
excited pulsational mode of the investigated star. In particular, such a problem
arises in connection with so-called galactic s-Cepheids.

Spectroscopic luminosity indicators (provided they are reliably calibrated),
in this sense, are more universal tool of $M_{v}$ determination for various
kinds of supergiant stars. For example, Sorvari (1974) and Baker (1974)
applied O I 7774 \AA~ line (triplet) as a luminosity indicator for F-supergiants.
\vskip 3mm

\centerline{Table 1. Ba II line equivalent widths in spectra of program stars}
\vskip 1mm
\begin{center}
\small
\begin{tabular}{ccccccc}
\hline
Star              &Period   & Phase &W(5853),m\AA~ &$M_{v}$ \\
\hline
V473 Lyr          &   1.4908& 0.899 &  244         &$-$2.25 \\
                  &         & 0.095 &  251         &      \\
                  &         & 0.793 &  247         &      \\
                  &         & 0.559 &  253         &      \\
                  &         & 0.136 &  248         &      \\
EU Tau            &   2.1025& 0.758 &  183         &$-$2.69 \\
IR Cep            &   2.1141& 0.137 &  175         &$-$2.69 \\
DT Cyg            &   2.4991& 0.774 &  222         &$-$2.90 \\
V526 Mon          &   2.6750& 0.674 &  191         &$-$2.99 \\
SZ Tau            &   3.1484& 0.501 &  217         &$-$3.19 \\
                  &         & 0.573 &  239         &      \\
                  &         & 0.577 &  228         &      \\
$\alpha$ UMi$^{1}$&   3.9696& 0.516 &  275         &$-$3.49 \\
                  &         & 0.775 &  256         &      \\
                  &         & 0.015 &  239         &      \\
                  &         & 0.775 &  228         &      \\
V1162 Aql         &   5.3761& 0.273 &  267         &$-$3.87 \\
V924 Cyg          &   5.5715& 0.702 &  266         &$-$3.91 \\
V440 Per          &   7.57  & 0.080 &  283         &$-$4.30 \\
                  &         & 0.534 &  310         &      \\
FN Aql            &   9.4816& 0.464 &  320         &$-$4.58 \\
                  &         & 0.525 &  315         &      \\
                  &         & 0.841 &  317         &      \\
SZ Cas            &  13.6377& 0.047 &  315         &$-$5.04 \\
Y Oph             &  17.1269& 0.530 &  342         &$-$5.33 \\
\hline
\end{tabular}
\end{center}
\vskip 1mm
\small
\centerline{Remarks: 1 $-$ W values are from Sanval et al. (1988)}
\large
\eject

In this paper another luminosity indicator is proposed. In contradiction
to near-infrared O I triplet, its location in the spectrum is more favourable
for spectroscopic observations. Below it will be shown that Ba II 5853.6 \AA~
line appears to be a rather sensitive indicator of the luminosity
of supergiants. Its equivalent width depends upon luminosity of the star as
a result of the increasing of non-LTE effects in stellar atmosphere with the
luminosity increase.


At the first step of the study, an existence of the possible relation
between equivalent width of Ba II 5853.6 \AA~ line and $M_{v}$
was investigated only for small-amplitude s-Cepheids. Equivalent widths measured
in the spectra of the program stars are listed in Table 1.


To investigate a possible dependence between Ba II line equivalent
width and luminosity (or absolute magnitude $M_{v}$) we first calculated
$M_{v}$ for program Cepheids using recent results by Gieren \& Fouqu\'{e} (1993):
\begin{equation}
M_{v} = -2.9 \times log P -1.30
\end{equation}

\noindent
Pulsational periods were selected from Fernie et al. (1995) catalogue.
The s-Cepheids are assumed to be overtone pulsators.
Therefore for those stars we used observed period as the first overtone one
$P_{1}$. Period of the fundamental mode $P_{0}$ for each s-Cepheid was
determined using a period ratio $P_{1}/P_{0}$=0.7 (see Szabados, 1997).

Equivalent width of barium line was precisely measured for all the
program stars using the spectra collected with an echelle spectrometer LYNX
on 6-m telescope (Special Astrophysical Observatory of the Russian Academy
of Sciences, Russia, Northern Caucasus; the detailed description of the
spectrometer is given by Panchuk et al., 1993), AURELIE spectrograph (Gillet
et al., 1994) on the 1.52m telescope of Haute Provence Observatory (France) and
with ELODIE, a fibre-fed echelle spectrograph installed on the 1.93m telescope
of Observatoire de Haute-Provence, France (Baranne et al., 1996 give detailed
descriptions of the spectrograph). Some of the collected spectra were previously
analysed (for determination of elemental abundances) in several papers by
Andrievsky et al. (1996), Kovtyukh et al. (1996), Andrievsky et al. (1998).
The necessary information about the spectra of program stars (telescope,
spectrograph, resolving power, S/N ratio), as well as information concerning
the procedure of the equivalent width measurements, can be found in the
above mentioned works. The internal accuracy of the equivalent widths is of
the order of 5\%. This estimate is based on the comparison of values derived
from the lines presented in two overlapping spectral orders.\\
Note also, that in none of those works the Ba II lines were used for abundance
determination. The main problem is connected with their large equivalent widths
that completely excludes an application of LTE approach for abundance analysis.\\

The relation $M_{v}-W(Ba II~5853.6~\AA)$  is shown in Fig. 1 for program s-Cepheids.
Very clear dependence between visual absolute magnitude and equivalent width
of Ba II 5853.6 \AA~ line is seen.

\IBVSfig{10cm}{4572-f1.ps}{ $M_{v}$ vs. Ba II 5853.6 \AA\ line equivalent width for s-Cepheids. Horizontal lines indicate  $\sigma$ values}
\vskip 3mm

Taking into account that s-Cepheids are small-amplitude pulsators, one can
expect that equivalent width variations during the pulsational cycle will be
small (it is confirmed, e.g. by V473 Lyr data, see Table 1).

The least squares fit for $M_{v}-W(Ba II~5853.6~\AA)$ relation is following:
\begin{equation}
M_{v} = -0.016 \times W(5853) + 0.28
\end{equation}

\noindent
The unusual Cepheid V473 Lyr strongly deviates from the least squares fit found for s-Cepheids. Even supposing that it pulsates in the second overtone (see Andrievsky
et al., 1998), we can not adjust its calculated absolute magnitude with
the predicted one from the sample of investigated s-Cepheids.\\
A careful investigation of the possible relations between equivalent widths of
Ba II 5853.6 \AA~ and 6141.7 \AA~ lines and absolute magnitude for a sample of
classical Cepheids and non-variable F$-$G supergiant will be a subject of the next
paper.\\
Of course, the relations between $M_{v}$ and equivalent width of Ba II 5853.6 \AA~
will not substitute a dependence between absolute magnitude and pulsational
period for Cepheids which is usually used by the specialists. Nevertheless, the
found relation given in Eq.(2) can be considered as a complementary one, allowing to reveal in some
cases unusual Cepheids (pulsating in high overtones) and to determine absolute
magnitudes for non-variable supergiants using, in particular, spectra collected
for those stars during previous years.

The author is grateful to Drs. V. Kovtyukh and I. Usenko for the help with
spectra reducing and to Dr. L. Szabados for providing the new data on some
Cepheids.
This work was supported, in part, by the International Soros Science Education
Program through grant No APU072001.

\references

Andrievsky, S.M., Kovtyukh, V.V., Usenko, I.A., 1996,
{\it Astron. Astrophys.}, {\bf 305}, 551

Andrievsky, S.M., Kovtyukh, V.V., Bersier, D., Luck, R.E., Gopka, V.P.,
Yushchenko, A.V., Usenko, A.V., 1998, {\it Astron. Astrophys.},
{\bf 329}, 599

Baker, P.W., 1974, {\it Publ. Astron. Soc. Pacif.}, {\bf 86}, 33

Baranne, A., Queloz, D., Mayor, M., Adrianzyk, G., Knispel, G., Kohler, D.,
Lacroix, D., Meunier, J.$-$P., Rimbaud, G., Vin, A., 1996,
{\it Astron. Astrophys. Suppl. Ser}, {\bf 119}, 373

Fernie, J.D, Beattie, B., Evans, N.R., Seager, S., 1995, {\it IBVS}, No.\,4148

Gieren, W.P, Fouqu\'e, P., 1993, {\it Astron. J}, {\bf 106}, 734

Gillet, D., Burnage, R., Kohler, D., Lacroix, D., Adrianzyk, G., Baietto, J.C.,
Berger, J.P., Goillandeau, M., Guillaume, G., Joly, C., Meunier, J.P., Rimbaud, G., Vin, A., 1994, {\it Astron. Astrophys. Suppl. Ser}, {\bf 108}, 181

Kovtyukh, V.V., Andrievsky, S.M., Usenko, I.A., Klochkova, V.G., 1996,
{\it Astron. Astrophys.}, {\bf 316}, 155

Panchuk, V.E., Klochkova, V.G., Galazutdinov, G.A., Ryadchenko, V.P.,
Chentsov, E.L., 1993, {\it Sov. Astron. Lett.}, {\bf 19}, 11

Sanval, B.B., Rautela, B.S., Joshi, G.C., 1988, {\it Astrophys. Space Sci.},
{\bf 140}, 131

Sorvari, J.M., 1974, {\it Astron. J.}, {\bf 79}, 1416

Szabados, L., 1997, {\it Proc. ESA Symp. ``Hipparcos$-$Venice 97", ESA SP$-$402},
657
 

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