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\IBVShead{4571}{23 March 1998}

\IBVStitle{Pulsating AGB star in the symbiotic nova PU Vulpeculae}

\IBVSauth{D.~CHOCHOL$^1$, T.~PRIBULLA$^1$, S.~TAMURA$^2$}

\vskip 0.3cm plus 0.1cm minus 0.1cm

\IBVSinst{Astronomical Institute of the Slovak Academy of Sciences, SK 059 60 Tatransk\'a Lomnica,
Slovakia}
\IBVSinst{Astronomical Institute, Faculty of Sciences, Tohoku University,
 Aoba-ku, Sendai, Miyagi 980, Japan}

\SIMBADobj{PU Vul} 
\IBVStyp{ * } 
\IBVSkey{photometry}

\begintext



PU Vul is well known very slow eclipsing symbiotic nova, which exhibited
   outburst in 1979. The nova reached its maximum in 1983 (B = 8.9, V = 8.33). From
   that time the nova fades. The light-curve of the nova exhibited two minima
   in 1980-2 and 1993-4, explained by Vogel \& Nussbaumer (1992) and Nussbaumer
   \& Vogel (1996) as eclipses of an outbursted white dwarf by a red
   M4-6 giant. The pre-outburst B light curve of PU Vul taken in years
   1898-1956 showed brightness fluctuations between 14 and 15 mag (Liller
   \& Liller, 1979). Its period analysis confirmed the presence of eclipses on the
   4900 day orbit and revealed another significant period {\it P} = 231.5 days
   (Chochol et al., 1997). The same period, found by Chochol et al. (1997)
   in J,H,K postoutburst photometry taken by Belyakina et al. (1985, 1990) and
   Kenyon (1986), was explained by pulsations of the AGB variable. Its
   bolometric luminosity $M^{bol}_c$ = $-$4.29 ($L_c$ = 4100 L$_{\odot}$)  can
   be easily derived using the empirical period-luminosity relation of Hughes
   and Wood (1990) valid for AGB variables (Miras and SRa's).

Chochol et al. (1997) proposed that PU Vul is a triple system. The inner binary
   with an orbital period of 760 days consists of an outbursted white dwarf
   (its luminosity during the F5 supergiant mimicry stage was $L_{h}$ = 23900
   L$_{\odot}$) and the AGB or bright M giant with luminosity $L_{c}^{inn}$ =
   5100 L$_{\odot}$. The third component is an M type AGB variable
   ($L_{c}^{out}$ = 4100 L$_{\odot}$) on 4900 days outer orbit. The
   luminosities of the cool components were determined from the primary
   and secondary eclipse in an outer orbit using the infrared K passband
   observations. The distance of PU Vul determined from the luminosity
   of the hot component and $E$(B-V) = 0.39 (Belyakina et al., 1985) is
   $d$ = 5.3 kpc.

The aim of our paper is to give an independent proof of the presence of the
   AGB variable in PU Vul using the photoelectric observations in V and R
   passbands and to show, that in 1995-8 the period of pulsations
   was {\it P} = 217 days.

Photoelectric U,B,V,R observations of PU Vul were obtained in 1995 - 98 at
   the Skalnat\'e Pleso (SP) and Star\'a Lesn\'a (SL) observatories of the
   Astronomical Institute of the Slovak Academy of Sciences. In both cases
   0.6~m Cassegrain telescope equipped with a single-channel pulse-counting
   photoelectric photometer was used. The stars HD 193706~=~BD +21$^{\rm
   o}$4167 (V = 7.84, B = 9.48, U = 11.46, sp. type K5) and BD +21$^{\rm
   o}$4165 (V = 9.23, B = 9.80, U = 9.79, sp. type F8) served as a comparison
   and check star, respectively. The data reduction, atmospheric extinction
   correction and transformation to the standard international system were
   carried out by the usual way. The photoelectric light-curves in U,B,V and R
   passbands are plotted in Fig. 1.

\IBVSfig{9cm}{4571-f1.ps}{U,B,V  and R light-curves of PU Vul since January 1993.
The data till January 1995 were taken from Hric et al. (1994, 1996),
Skopal et al. (1995) and Kolotilov et al. (1995). The observations taken at SP
and SL are denoted by large symbols. The brightness maxima in V and R
passbands are marked by arrows}


\IBVSfig{9cm}{4571-f2.ps}{The power spectrum of our V observations taken
since 1995}
\IBVSfig{9cm}{4571-f3.ps}{The spectral window corresponding to the
power spectrum}


It is clearly seen that the light-curve variability of PU Vul increases
   from U to R colour, so the source of variations is the cool component.
   The Fourier  analysis of the V data in the interval 100 - 1000 days
   revealed the most significant period at 217$\pm$20 days (Figs.~2 and 3).
The  mean error was determined from the halfwidth of the
spectral window.
   Corresponding phase diagram of the pulsating AGB component is displayed
   in Fig. 4. The brightness maxima can be predicted using the following
   ephemeris:

\begin{equation}
   JD_{max} = 2\,449\,860~+~217\times E.
\end{equation}

The luminosity of the AGB variable can be derived using the period-luminosity
   relation of Hughes and Wood (1990):

\begin{equation}
  M^{bol}_c = -4.39 - 2.91(\log~P - 2.4),
\end{equation}

   valid for $P~{\leq}$ 450 days. Period of pulsations {\it P} = 217 days
   gives $M^{bol}_{c}$ = $-$4.205 or $L_{c}$ = 3820 L$_{\odot}$
   (supposing $M^{bol}_{\odot}$ = 4.75 (Allen, 1976)). The effective temperature
   of the M4 Mira star, corresponding to the period of pulsation 217 days, is
   $T_{eff}~{\approx}$ 2700 K (Allen, 1976). Its radius and mass can be
   determined using the Stephan-Boltzmann law and the standard pulsation
   equation (e.g. Feast, 1996)

\begin{equation}
    \log P = 1.5\log R - 0.5\log M + \log Q,
\end{equation}

   \noindent where stellar radius $R$ and mass $M$ are in solar units and $Q$ is
   the pulsation
   constant, taken to be 0.04, a value appropriate for overtone pulsation.
   These relations give $R_{c}$ = 282 {\it R}$_{\odot}$ and ${\it M}_{c}$ =
   0.76 M$_{\odot}$.

\IBVSfig{7cm}{4571-f4.ps}{V and R phase diagrams for $P$ = 217 days
constructed from our observations since 1995}

Acknowledgements. This work was financially supported by the VEGA grant
 5038/98.

\eject

\references

Allen C.W.: 1976, {\it Astrophysical Quantities}, The Athlone Press, London

Belyakina T.S., Bondar N., Gershberg R.E. et al.: 1985, {\it Bull.
   Crim. Astr. Obs.}, {\bf 72}, 3

Belyakina T.S., Bondar N., Gershberg R.E. et al.: 1990, {\it Bull.
   Crim. Astr. Obs}, {\bf 81}, 28

Chochol D., Pribulla T., Tamura S. et al.: 1997, in J. Mikolajewska (ed.):
   {\it Physical Processes in Symbiotic Binaries}, CFPA, Warszawa, 127

Feast M.W.: 1996, {\it Mon. Not. R. Astron. Soc.}, {\bf 278}, 11

Hric L., Skopal A., Chochol D. et al.: 1994, {\it Contrib. Astron. Obs.
     Skalnat\'e Pleso}, {\bf 24}, 31

Hric L., Skopal A., Urban Z. et al.: 1996, {\it Contrib. Astron. Obs.
     Skalnat\'e Pleso}, {\bf 27}, 121

Hughes S.M.G., Wood P.R.: 1990, {\it Astron. J.}, {\bf 99}, 784

Kenyon S.J.: 1986, {\it Astron. J.}, {\bf 91}, 563

Kolotilov E.A., Munari U., Yudin B.F.: 1995, {\it Mon. Not. R. Astron. Soc.},
     {\bf 275}, 185

Liller M.H., Liller W.: 1979, {\it Astron. J.}, {\bf 84}, 1357

Nussbaumer H. \& Vogel M.: 1996, {\it Astron. Astrophys.}, {\bf 307}, 470

Skopal A., Hric L., Chochol D. et al.: 1995, {\it Contrib. Astron. Obs.
     Skalnat\'e Pleso}, {\bf 25}, 53

Vogel M. \& Nussbaumer H.: 1992, {\it Astron. Astrophys.}, {\bf 259}, 525

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