\documentstyle[epsf]{article}

\input ibvs2.sty

\begin{document}

\IBVShead{4522}{3 October 1997}

\IBVStitletl{RADII OF LOW-AMPLITUDE CEPHEIDS}{ AND THEIR PULSATION MODE}

\IBVSauth{M.E. SACHKOV}

\IBVSinsto{Institute of Astronomy of Russian Acad. Sci.,
48, Pyatnitskaya Str.,
Moscow 109017, Russia\\
{\sl e-mail:\/} sachkov@sai.msu.su; sachkov@inasan.rssi.ru}

\IBVSabs{Based on the period-radius relation of classical cepheids,}
\IBVSabs{it is shown that both fundamental ard first overtone pulsators}
\IBVSabs{occur among the low-amplitude cepheids}

\IBVStyp{ DCEPS }



\begintext

Low-amplitude Cepheids (DCEPS in GCVS, 1985) are a specific group of pulsating
stars. In contrast to ordinary Cepheids, these stars have small light amplitudes
($0\fmm5\ V$ and lower) and practically sinusoidal light curves. It is
usually assumed
that
such stars pulsate in the first overtone, whereas ordinary Cepheids,
in the fundamental tone (GCVS, 1985). Theory of stellar pulsations gives the ratio
of periods of the first overtone $P_1$ to the fundamental tone $P_0$,
for galactic Cepheids, equal to
0.71 (see, for instance, Alcock et al., 1995).

For 13 Cepheids (see Table 1) classified as DCEPS in the GCVS, we have long sets of precise
observations of radial velocity. Our radial velocity
observations were made with A. Tokovinin's correlation spectrometer in 1987--1997.
The majority of these observations were included in our two catalogues
(Gorynya et al., 1992, 1996b).


We used these spectroscopic data together with photoelectric data
(brightnesses $V$ and
color indices $B-V$) from the Sternberg Institute database (Berdnikov,
1995) to estimate the radii
of such Cepheids using a nonlinear modification of the method
described by Balona (1977). Note that Balona's method is,
in principle, free from any significant influence of interstellar extinction.

\vfil

\begin{center}
\begin{tabular}{lccrc}
\hline
Star & $ \log P $ & $ R/R_\odot $ & $ \sigma_R $ &  Pulsation mode  \\
\hline
    FN Aql &  0.9768 &  80  &  12  & $P_1$ \\
 V1162 Aql &  0.7305 &  60  &  14  & $P_1$ \\
    BY Cas &  0.5080 &  40  &  10  & $P_1$ \\
    SU Cas &  0.2899 &  33  &   8  & $P_1$ \\
 V1726 Cyg &  0.6271 &  55  &   5  & $P_1$ \\
     X Lac &  0.7360 &  61  &   7  & $P_1$ \\
    EU Tau &  0.3227 &  35  &   5  & $P_1$ \\
    SZ Tau &  0.4982 &  43  &   6  & $P_1$ \\
    EV Sct &  0.4901 &  46  &  14  & $P_1$ \\
    FF Aql &  0.6503 &  34  &   7  & $P_0$ \\
  V636 Cas &  0.9231 &  46  &   5  & $P_0$ \\
  V532 Cyg &  0.5163 &  31  &   8  & $P_0$ \\
     Y Oph &  1.2335 &  71  &  10  & $P_0$ \\
\hline
\end{tabular}
\end{center}



Table 1 gives the Cepheid radii and their formal r.m.s.\ errors. For
calculations of
radii of spectroscopic binaries SU Cas, FF Aql and V532 Cyg, we used
pulsational radial velocity curves (after taking into account
orbital motion, with elements from Gorynya et al., 1996a).




In the period--radius diagram, all stars fall into two groups with
different period--radius relations (Fig.\ 1):

     {\sl        Group 1: FF Aql, V636 Cas, V532 Cyg, and Y Oph}

{\sl             Group 2: FN Aql, V1162 Aql, BY Cas, SU Cas, V1726 Cyg,
                     X Lac, EV Sct, EU Tau, and SZ Tau}


\IBVSfig{8cm}{4522-f1.ps}{
The period--radius diagram. Open circles, Group 1; crosses,
Group 2}



This segregation can be explained if we assume that stars of the two groups
pulsate in different
modes: group 1, in the fundamental tone; group 2, in the first overtone.
Taking into account that $P_0=P_1/0.71$, one can write:

$$\log R = {1.21\atop\pm.03} + {0.51\atop\pm.04} 
\log P_0 \qquad  \mbox{for group 1}\; $$

$$\log R = {1.36\atop\pm.02} + {0.57\atop\pm.04} 
\log P_1 \qquad \mbox{for group 2}\; $$

\noindent or

$$\log R = {1.27\atop\pm.03} + {0.57\atop\pm.04} 
\log P_0 \qquad \mbox{for group 2}\; $$

With this assumption, the relations can be considered the same.  This
relation agrees well with that for single-mode Cepheids (Ripepi et al.,
1997, Sachkov et al., 1997) and for double-mode Cepheids (Sachkov,
1997).  Low-amplitude Cepheids have the same period--luminosity
relation as the ordinary ones (Berdnikov et al., 1996). Therefore, the
period--radius relations for low-amplitude and ordinary Cepheids must
be the same.

\pagebreak

The author is grateful to Drs.\ A.S. Rastorgouev, N.N. Samus, L.N. Berdnikov,
and N.A. Gorynya for helpful discussions.

This work was partially supported by the Russian Foundation for Basic Research
through grant 96-02-18491.


\references

Alcock, C., Allsman, R.A., Axelrod, T.S., et al., 1995,
{\sl A.J.}, {\bf 109}, 1653

Balona, L.A., 1977, {\sl M.N.R.A.S.}, {\bf 178}, 231

Berdnikov, L.N., 1995, {\sl ASP Conference Series}, {\bf 83}, 349

Berdnikov, L.N., Vozyakova, O.V., and Dambis, A.K., 1996,
{\sl Astronomy Letters}, {\bf 22}, 936

Gorynya, N.A., Irsmambetova, T.R., Rastorgouev, A.S.,
and Samus, N.N., 1992, {\sl Sov.\ Astron.\ Lett.}, {\bf 18}, No.5

Gorynya N.A., Rastorgouev, A.S., and Samus, N.N., 1996a,
{\sl Astronomy Letters}, {\bf 22}, 38

Gorynya N.A., Samus, N.N., Rastorgouev, A.S., and Sachkov, M.E., 1996b,
{\sl Astronomy Letters}, {\bf 22}, 175

Ripepi, V., Barone, F., Milano, L., and Russo, G., 1997,
{\sl Astron.\ and Astrophys.}, {\bf 318}, 797

Sachkov, M.E., 1997, {\sl Inf.\ Bull.\ Var.\ Stars}, No. 4484

Sachkov, M.E., Rastorgouev, A.S., Gorynya, N.A., and Samus, N.N., 1997,
{\sl Astronomy Letters}, in preparation

\end{document}
