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\begin{document}
\IBVShead{5695}{5 April 2006}
\IBVStitle{V380 Cygni - Request for new observations}
\IBVSauth{Roman, R.$^1$; Roman, S. A.$^2$}
\IBVSinst{Astronomical Observatory, Cluj-Napoca, Romania.
e-mail: rroman@math.ubbcluj.ro}
\IBVSinst{Northeastern University, Boston, MA, USA.
e-mail: roman.s@neu.edu}
\SIMBADobj{V380 Cyg}
\IBVSabs{The problem of apsidal motion for V380 Cygni is reviewed. From}
\IBVSabs{the existing observations it is difficult to determine an accurate}
\IBVSabs{apsidal period. We argue that further observations are needed.}
\begintext
The eclipsing binary system V380 Cygni is considered as having a long periodic apsidal
motion. Semeniuk (1968) and Battistini et al. (1974) have
determined U=2019 and U=1470 years, respectively, for the apsidal
period. Therefore, in this case a sudden change in the longitude
of periastron, $\omega$, must be postulated. In the last time,
Guinan et al. (2000), based on ,,a linear fit to observed time
differences between primary and secondary minima'' have
reconsidered the apsidal motion for V380 Cygni, their result being
U=1490 years. Nevertheless, nothing is said about an eventual
variation of the apsidal motion. Consequently, before we can draw
some important conclusions concerning the predictions of an
independent test for stellar models, we have to re-examine the
corresponding result.
Now we consider that a combination of the photometric and
spectroscopic observations could help us with a greater number of
observed values for the longitude of periastron, $\omega$. With
this in mind we performed the following two tables, where the
epoch E is referring to the linear formula:
$$Min.hel.\;I=J.D. 2441255.973+12\fday425612 \times E.$$
\begin{table}[htpb]
\begin{center}
\caption{ Photometric observations}
\smallskip
\smallskip
\begin{tabular}{lclcc}\hline
\\
{\bf T$_{II}$-T$_I$}& {\bf E}& $\omega$&{\bf w} &{\bf References}\\
\\
\hline
$ 5\fday381\pm0\fday008 $ & $-$1422 & $ 117\deg\pm2\fdeg9 $&3.4&Guinan et al. (2000), p. 417\\ \hline
$ 5\fday199\pm0\fday0115$ & $-$240 & $ 124\deg\pm4\fdeg1 $&2.4&Guinan et al. (2000), p. 417\\ \hline
$ 5\fday079\pm0\fday0035$ & 0 & $ 129\deg\pm1\fdeg26 $&7.9&Guinan et al. (2000), p. 417\\ \hline
$ 5\fday004\pm0\fday010 $ & +204 & $ 133\deg\pm3\fdeg6 $&2.8&Guinan et al. (2000), p. 417\\ \hline
$ 4\fday995\pm0\fday005 $ & +506 & $ 133\deg\pm1\fdeg8 $&5.6&Guinan et al. (2000), p. 417\\ \hline
$ 4\fday908\pm0\fday005 $ & +706 & $ 138\deg\pm1\fdeg8 $&5.6&Guinan et al. (2000), p. 417\\ \hline
\end{tabular}
\end{center}
\end{table}
In order to obtain the values of $\omega$ from the difference
$T_{II}-T_I$ we have used Eq.(6) from Todoran (1972). We have adopted
the following ,,constant'' orbital parameters: $e=0.22$, $i=82\deg 24\arcm$,
$P=12\fday4257$.
\begin{table}[htpb]
\begin{center}
\caption{ Spectroscopic observations}
\smallskip
\smallskip
\begin{tabular}{clcl}\hline
\\
{\bf E} &$\omega$& {\bf w}&{\bf References}\\
\\
\hline
$-$1740 & $115\fdeg8 \;\;- $ & 0 &Batten, (1962), p. 100\\ \hline
$-$1680 & $121\deg\pm3\fdeg0 $ & 3.33&Popper and Guinan, (1998), p. 573\\ \hline
$-$1524 & $120\fdeg1\pm2\fdeg0 $ & 5.0&Batten, (1962), p. 103\\ \hline
$-$1524 & $116\;\;- $ & 0 &Popper, (1949), p. 105\\ \hline
$-$1333 & $118\fdeg5\pm3\fdeg3$ & 3&Batten, (1962), p. 103\\ \hline
$-$737 & $118\deg\pm9\fdeg0 $ & 1.1&Popper and Guinan, (1998), p. 573\\ \hline
$-$732 & $118\deg\pm6\fdeg0 $ & 1.7&Batten, (1962), p. 100\\ \hline
$-$306 & $127\fdeg2\pm2\fdeg1$ & 4.8&Batten, (1962), p. 100 \\ \hline
$-$306 & $129\fdeg0\pm3\fdeg8$ & 2.6&Popper and Guinan, (1998), p. 573\\ \hline
+663 & $133\fdeg2\pm3\fdeg2$ & 3&Popper and Guinan, (1998), p. 573\\ \hline
\end{tabular}
\end{center}
\end{table}
\IBVSfig{12cm}{5695-f1.eps}{The nonlinear dependence $\omega =
f(E)$. With squares are represented the photometric observations
and with circles the spectroscopic observations.}
\IBVSfigKey{5695-f1.eps}{V380 Cyg}{}
The function $\omega =f(E)$ is illustrated in Figure 1.
\medskip
Here we can put in evidence the following three possible situations:
a) We can divide the points into two series: for $-1740\leq E\leq -1333$, and $-737\leq E\leq 706$. Then the functions:
$$(i)\;\;\;\omega = 104.473-0.009880 \times E$$
$$(ii)\;\;\omega =128.927+0.010751 \times E$$
obtained with the least squares method, are fitted well the points. These lines are represented in Figure 1 by dot-line and dash-dot-line. But, in such a case, a sudden change in the function $\omega =\omega (E)$ must be postulated, even if the corresponding reason, nowadays, cannot be interpreted.
b) If we accept a periodic function for $\omega = \omega (E)$, the existence of a third body could be assumed and the corresponding perturbations could be investigated. But for such a distinguished problem, we must be sure of the existence of the corresponding periodicity. In Figure 1 the curve:
$$\omega = 9.773 \times sin(0.001256 \times E)+1.644 \times cos(0.001256 \times E)+127.355$$
obtained with the least squares method, is used to fit all the points (the solid curve).
c) If the first series of observations ($-1740\leq E \leq -1333$) is ignored, then, from the second series of observations ($-737\leq E\leq 706$) it would be possible to determine an apsidal period, but, even in such a case, we must be sure that the relationship ($ii$) remains also valuable even if
$E>706$. In addition, we do not have a well-founded reason to ignore the first series of observations.
Therefore, in our days, it is very difficult to speak about a habitual apsidal motion in the binary system V380 Cygni. This is why we are considering that, very likely, a new series of observations could help us to solve such an ambiguous problem.
\references
Batten, A. H., 1962, Publ. Dom. Astrophys. Obs., 12, 91
Battistini, P., Bonifazi, A., Guarnieri, A., 1974, Astrophys. Space
Sci., 30, 163
Guinan, E. F., Ribas, I., Fitzpatrick, E. L.,
Gim\'{e}nez, A., Jordi, C., McCook, G. P., Popper, D. M., 2000,
Astrophys. J., 544, 409
Popper, D. M., 1949, Astrophys. J., 109, 100
Popper, D. M., Guinan, E. F., 1998, PASP, 110, 572
Semeniuk, I., 1968, Acta Astronomica, 18, 1
Todoran, I., 1972, Astrophys. Space Sci., 15, 229
\endreferences
\end{document}