
\documentstyle[epsf]{article}

\input ibvs2.sty

\begin{document}

\IBVShead{4563}{3 March 1998}

\IBVStitle{ON THE ORBITAL PERIOD CHANGES OF EG C\lowercase{ep}}

\IBVSauth{H.~ROVITHIS-LIVANIOU$^1$, P.~ROVITHIS$^2$, A.N.~KRANIDIOTIS$^1$, D.~CHOCHOL$^3$, T.~PRIBULLA$^3$}

\vskip 0.3cm plus 0.1cm minus 0.1cm

\IBVSinst{Section of Astrophysics, Astronomy \& Mechanics, Dept. of Physics,
 University of Athens, GR 15784 Zografos, Greece; e-mail: elivan@rigel.da.uoa.gr}
\IBVSinst{Astronomical Institute, The National Observatory of Athens,
 P.O.Box 20048, GR 11810 Athens, Greece} 
\IBVSinst{Astronomical Institute of the Slovak Academy of Sciences, SK 059 60 Tatransk\'a Lomnica, 
Slovakia}

\SIMBADobj{HD194089} 
\IBVStyp{ * } 
\IBVSkey{photometry}

\begintext

  EG Cep (BD +76$^{\circ }$790, HD 194089, V$_{max}$ = 9.36) was discovered by
Strohmeier (1958) as an eclipsing binary with the orbital period of 0.5446
days. The shape of the light curve is typical of the $\beta$ Lyr type with
the minima depth 0.87 mag and 0.29 mag in V light.

EG Cep is a poorly observed binary. Its light curves were presented by Geyer
(1961), Cochran (Wood, 1971), Van der Wal et al. (1972), Kaluzny \& Semeniuk
(1984) and Erdem et al. (1993). In the most comprehensive photometric study
of EG Cep Kaluzny \& Semeniuk (1984) determined the value of interstellar
extinction as E(B$-$V) = 0.035 and the distance {\it d} = 120 pc. They used
the intrinsic colour index (B$-$V)$_0$ = 0.197 to derive the spectral type A7
of the primary component, which is in disagreement with the spectral type A3
given in the HD catalogue. Etzel \& Olson (1993) measured the half-width of
the Mg 448.1 nm line and determined the projected rotational velocity of the
primary component as $v_1~\sin ~i$ = 146 km~s$^{-1}$. Other spectroscopic
observations of EG Cep are not available.

Photoelectric B and V light curves, analyzed by Kaluzny \& Semeniuk (1984)
with the Wilson \& Devinney method, led to the mass ratio {\it q} = (0.45 -
0.50) and a semi-detached configuration with the $M_1\sim $ 1.8~M$_{\odot }$
unevolved primary and evolved secondary component. Their analysis of the 
O$-$C diagram revealed a continuous orbital period increase. The
quadratic term of 0.820$\times$10$^{-10}$ days was explained by a mass transfer
rate $\dot{M}$~=~10$^{-7}$~M$_{\odot }$y$^{-1}$ from the secondary to the
primary component. Wolf \& Diethelm (1992) determined the quadratic term as
0.782$\times$10$^{-10}$ days and noted that omitting the secondary minima, which
are mentioned to be asymmetrical, two linear ephemeris are also suitable for
explanation of the O$-$C diagram. Erdem et al. (1993) found the
quadratic term to be 0.473$\times$10$^{-10}$ days.

The aim of this study is to present additional times of minimum light of EG
Cep, improve its ephemeris formula and examine its orbital period changes.

\vskip 0.3cm plus 0.1cm minus 0.1cm

  The first set of our photoelectric observations of EG Cep was performed in
1983-84 using a multi-mode, nebular-stellar photometer attached to the
1.22~m Cassegrain reflector at the Kryonerion Astronomical Station (KAS) of
the National Observatory of Athens, Greece. The B \& V filters used are in
close accordance to the standard UBV system. Estimated
uncertainties of a single observation taken at the KAS were 0.008 mag and
0.010 mag in B and V passbands, respectively. The stars BD +75$^{\circ }$737
(V = 9.5, sp. type A0) and BD +74$^{\circ }$857 (V = 10.7, sp. type A2)
served as a comparison and check star, respectively. The second set of EG
Cep observations was obtained in 1997 at the Skalnat\'e Pleso (SP) and
Star\'a Lesn\'a (SL) observatories of the Astronomical Institute of the
Slovak Academy of Sciences. In both cases 0.6~m Cassegrain telescope
equipped with a single-channel pulse-counting photoelectric photometer was
used. The accuracy of the SP and SL observations taken in B and V passbands
was two times higher in comparison with the KAS data. The stars BD +76$%
^{\circ }$791 (V = 9.2, sp. type K2) and BD +76$^{\circ }$789 (V = 9.6, sp.
type A0) served as a comparison and check star, respectively. Data
reduction, atmospheric extinction correction and the transformation to the
standard international system were carried out by usual way.

Our observations led to the determination of 11 new times of minimum light.
We have calculated the times of minima separately from B and V observations
using Kwee \& van Woerden's (1956) method (Table~1).

%\TeXButton{Table 1}
{\begin{table}
\centerline{Table~1. New times of minimum light of EG Cep.}
\centerline{The epochs were calculated using ephemeris (1)}
\vskip 2mm
\begin{center}
\label{t1}
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Epoch  & \multicolumn{2}{|c|}{B}& \multicolumn{2}{c|}{V}& Obs.\\
\hline
        & JD$_{hel}$  & $\sigma$& JD$_{hel}$  & $\sigma$&     \\
        &2\,400\,000+ & [days]  &2\,400\,000+ & [days]  &     \\
\hline
34266   & 45591.44113 & 0.00003 & 45591.43957 & 0.00010 & KAS \\
34268   & 45592.52767 & 0.00003 & 45592.52856 & 0.00034 & KAS \\
34269.5 & 45593.34637 & 0.00014 & 45593.34689 & 0.00017 & KAS \\
34914   & 45944.35676 & 0.00024 & 45944.35516 & 0.00028 & KAS \\
34916   & 45945.44566 & 0.00012 & 45945.44395 & 0.00006 & KAS \\
34919.5 & 45947.35141 & 0.00022 & 45947.34913 & 0.00010 & KAS \\
43588   & 50668.41219 & 0.00021 & 50668.41180 & 0.00017 & SL  \\
43599   & 50674.40330 & 0.00028 & 50674.40337 & 0.00034 & SP  \\
43714.5 & 50737.31060 & 0.00060 & 50737.31000 & 0.00040 & SL  \\
43744   & 50753.37367 & 0.00039 & 50753.37436 & 0.00017 & SL  \\
43794   & 50780.60460 & 0.00070 & 50780.60473 & 0.00030 & SP  \\ \hline
\end{tabular}
\end{center}
\end{table}
}

\IBVSfig{10cm}{4563-f1.ps}{The O$-$C diagram of EG Cep}


  In order to investigate the real period variations of EG Cep, we have
collected all available times of minima from the literature and added our 11
times of minima (BV averages). Complete list of minima times is given in the
paper by Chochol et al. (1998). They were used to construct the O$-$C
diagram (Figure 1) applying the following ephemeris:

\begin{equation}
\label{rm}{Min~I}=2426929.4376+0.5446216\times E. 
\end{equation}

\noindent To minimize the large scatter appearing in the observational
material, mean values were calculated for all kinds of the observational
data. Then, the period changes seen in the O$-$C diagram (Figure 1) are
examined using the {\it classical} parabola as well as the new method
proposed by Kalimeris et al. (1994). 

a) In the first case, we get the following improvement of the ephemeris:

\begin{equation}
\begin{array}{rrrlrl}
{\rm Min~I } = & {\rm JD_{hel}}~2\,426\,929.4575 & +~0.54461943 & \times E & 
+4.51 & \times 10^{-11}\times E^2. \\  
& \pm 12 & \pm 10 &  & \pm 19 &  \\  
&  &  &  &  &  
\end{array}
\end{equation}

The larger value of the quadratic term in the parabolic ephemeris given by
Kaluzny \& Semeniuk (1984) and Wolf \& Diethelm (1992), in comparison with
the value published by Erdem et al. (1993) and our ephemeris (1), was caused
by the fact that the first two authors omitted Strohmeier's (1958)
observations.

\IBVSfig{10cm}{4563-f2.ps}{The real period variation of EG
Cep}

b) Using Kalimeris et al. (1994) method, we described the O$-$C diagram of
EG Cep piecewise (Figure 1), using two fourth-order polynomials and
connecting their parts (descending and ascending branch) using a spline
interpolant (Kalimeris et al., 1995). Then, it is easy to find the way the
real orbital period P(E) of the system behaves. In Fig. 2, one can see the
variation of the real period P(E) of EG Cep for the last 70 years. It is
obvious from Figure 2 that a period jump of the order of $\Delta P=$$%
2.023\times 10^{-6}$ days  occurred at E=27200 cycles corresponding to the
year 1972.


The use of the {\it classical} parabola leads to a continuous increase of
the period of EG Cep. On the other hand, one could use two linear fittings
for the descending and ascending branches of the O$-$C diagram of the system
and see that a sudden period increase  occurred around the year 1972
(Chochol et al., 1998). The answer to what really happens is given using
Kalimeris et al.'s (1994) method, as was applied here. Comparing the
fittings of the O$-$C diagram of EG Cep we get from the parabola and from
the piecewise description, the great gain is not immediately seen. This
comes from the calculation of the real period P(E). Indeed, Kalimeris et al.
(1994) method permits us to compute it in a simple and accurate mathematical
way. Moreover, the jump in P(E), presented in Figure 2, does not only give
the answer (i.e. that really a sudden period change has occurred), but we can
also find when this has happened and how large it was. Finally, from a simple 
linear fitting --after period's jumping-- we get the following linear ephemeris:

\begin{equation}
\begin{array}{rrr}
{\rm Min~I } = {\rm JD_{hel}}~2\,426\,929.3987&+~0.54462272& \times E. \\
                                       \pm  20&      \pm  6&         \\
\end{array}
\end{equation}


{\bf Acknowledgements.} The authors are grateful to Dr. J. Grygar for careful
reading of the manuscript. This work was financially supported by the NATO
grant (No. 960322) and the VEGA grant 1282/97.
\vskip -4mm

\references

Chochol D., Pribulla T., Rovithis-Livaniou H., Rovithis P., Kranidiotis A.:
1998, {\it Contrib. Astron. Obs. Skalnat\'e Pleso}, {\bf 28} (submitted).

Erdem A., Kilinc B., Degirmenci O. L., G\"ulmen O., Sezer C. \& G\"ud\"ur N.:
1993, {\it Inf. Bull. Var. Stars}, No. 3915.

Etzel P. B. \& Olson E. C.: 1993, {\it Astron. J.}, {\bf 106}, 1200.

Geyer E.: 1961, {\it Z. f\"{u}r Astrophys.}, {\bf 51}, 79.

Kalimeris A., Rovithis-Livaniou H. \& Rovithis P.: 1994, {\it Astron. \&
Astroph.} 282, 775.

Kalimeris A., Mitrou C.K., Doyle J.G., Antonopoulou E. \& Rovithis-Livaniou
H.: 1995, {\it Astron. \& Astrophys.} 293, 371. 

Kaluzny J. \& Semeniuk I.: 1984, {\it Acta Astron.}, {\bf 34}, 433.

Kwee K. K. \& van Woerden H.: 1956, {\it Bull. Astron. Inst. Nether.}, {\bf 
12}, 327.

Strohmeier W.: 1958, {\it Kl. Ver\"{o}ff. Bamberg}, {\bf 21}, 22.

Van der Wal P.B., Nagel C., Voordes H.C., de Boer K.S.: 1972, {\it Astron.
Astrophys. Suppl.}, {\bf 6}, 131.

Wolf M., Diethelm R.: 1992, {\it Acta Astron.}, {\bf 42}, 363.

Wood D.B.: 1971, {\it Astron. J.}, {\bf 76}, 701.

\end{document}


