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\begin{document}
\IBVShead{4300}{29 February 1996}
\title{TIMES OF MINIMA OF FIVE ECLIPSING BINARIES}
\begintext
We report photoelectric times of minima of double-lined detached eclipsing
binaries derived from photometric observations made with a six channel
Str\"omgren photometer attached to the 0.9m reflector at Observatorio de
Sierra Nevada (Granada, Spain), and a single channel Str\"omgren photometer
attached to the 1.52m reflector at Observatorio Astron\'omico Nacional
(Calar Alto, Almer\'{\i}a, Spain). The observations, performed
in $u$, $v$, $b$, $y$, ${H_{\beta}}_{w}$ and ${H_{\beta}}_{n}$ filters in
the case of PV Cas, V442 Cyg and V477 Cyg, and in ${H_{\beta}}_{w}$ and
${H_{\beta}}_{n}$ in the case of CW Cep and U Oph, were corrected for system
deadtime and atmospheric extinction. The adopted heliocentric times of minima
were computed from the weighted average over all filters, which were in all
cases concordant. Uncertainties in the times of minima are
the standard deviation of the computed values for the various filters used.
PV~Cas, CW~Cep, V477~Cyg and U~Oph have been included in a published
list of eccentric eclipsing binaries to be eclipse monitored (Gim\'enez, 1995).
In order to compute the values O$-$C we have selected precise ephemeris
especially because the observed systems are detached and some of them
eccentric, showing a substantial amount of apsidal motion.
In general, the rotation of the apsidal line, considering only secular terms,
produces a sinusoidal displacement of both primary and secondary eclipse
with respect to linear predictions. The most general expression to
compute times of minima taking into account this effect, considers an
infinite Fourier series as a function of the true anomaly. The coefficients
of the series can be computed by means of the eccentricity, the
orbital inclination and the anomalistic period. In fact, a
fifth order equation is usually sufficient regarding the precision of the
photoelectric measurements, since it includes powers of eccentricity up
to 5. This fifth order equation gives the times of minima of the eclipsing
binary as a function of a reference time $T_0$, the sidereal period $P_s$, the
anomalistic period $P$, the periastron longitude $\omega$, the orbital
inclination $i$ and the eccentricity $e$. Light curve analysis provides
good values of $e$ and $i$, and times of minima can be used to
obtain the rest of parameters. A detailed discussion about
the determination of nonlinear ephemeris can be found in
Gim\'enez \& Garc\'{\i}a-Pelayo (1983).
For three of the observed systems, complete studies of apsidal motion have
been performed, leading to more accurate expressions than linear ephemeris.
\vskip .2in
The ephemerides were adopted as follows:
\vfill \eject
\centerline{2}
\vskip 2mm
\underline{PV Cas}:
\[T_{min,j}=HJD\;2441729.2905+P_{s} E+0.5(j-1)P+0.01795(2j-3)\cos \omega+
0.00022 \sin 2\omega \]
\vskip 3mm
With $P_{s} = 1.750470$ d, $P = 1.750562$ d and $\omega=197.0+0.0189\;E$ in
degrees. The index $j$ is $1$ for primary eclipses and $2$ for secondaries.
The ephemeris was taken form the apsidal motion study performed by
Gim\'enez \& Margrave (1982), and the obtained parameters are in excellent
agreement with those computed in the recent studies of Barembaum \& Etzel (1995) and Wolf (1995). The adopted expression was tested with recent times
of minima, showing a low dispersion ($\simeq 0^{d}\!\!.0015$) and no
systematic deviations.
\vspace{3mm}
\underline{CW Cep}:
\[T_{min,j}=HJD\;2441669.5722+P_{s} E+0.5(j-1)P+0.02581(2j-3)\cos \omega+
0.00029 \sin 2\omega \]
With $P_{s} = 2.729139$ d, $P = 2.729588$ d and $\omega=201.6+0.0593\;E$ in
degrees. The index $j$ is $1$ for primary eclipses and $2$ for secondaries.
The apsidal motion parameters for this system were obtained by
Gim\'enez {\em et al.} (1987) and the final expression was computed using
the previously described method (Gim\'enez \& Garc\'{\i}a-Pelayo, 1983).
\vspace{3mm}
\underline{V442 Cyg}:
\vspace{3mm}
\noindent Min I $=$HJD\,2444919.561+2.3859437 $\times$ E \hfill (Lacy \& Frueh, 1987)
\vspace{3mm}
\noindent The secondary minimum was assumed to be at phase 0.5.
\vspace{3mm}
This system is known to be eccentric although no detailed studies of apsidal
motion have been performed. The adopted linear ephemeris does not show a very
good agreement with recent times of minima, although the value O$-$C in
our case is outstandingly low.
\vskip 5mm
\centerline{Table 1}
\begin{table}[h]
\begin{center}
\begin{tabular}{lllrl}
\hline
\multicolumn{1}{c}{System}&\multicolumn{1}{c}{Type of}&\multicolumn{1}{c}{HJD}&
\multicolumn{1}{c}{O$-$C}&\multicolumn{1}{c}{Comparison} \\
&\multicolumn{1}{c}{eclipse}&\multicolumn{1}{c}{($-$2400000)}&
\multicolumn{1}{c}{(days)}&\multicolumn{1}{c}{Stars} \\
\hline
PV Cas & Secondary & $50048.4031$ & $-.0012$ & HD\,$220760$ \\
& &\hfill $\pm 0.0003$& & BD\,$+60$\degr$2509$ \\
CW Cep & Primary & $50045.2793$ & $.0029$ & HD\,$218342$ \\
& &\hfill $\pm 0.0007$& & HD\,$217035$ \\
V442 Cyg & Secondary & $50043.3757$ & $.0006$ & BD\,$+31$\degr$3924$\\
& &\hfill $\pm 0.0025$& & HD\,$188725$ \\
V477 Cyg & Secondary & $50043.3598$ & $-.0144$ & BD\,$+31$\degr$3924$ \\
& &\hfill $\pm 0.0019$& & HD\,$188725$ \\
U Oph & Secondary & $49905.5077$ & $.0060$ & HD\,$156208$ \\
& &\hfill $\pm 0.0006$& & HD\,$154445$ \\
\hline
\end{tabular}
\end{center}
\end{table}
\vfill \eject
\centerline{3}
\vskip 1mm
\underline{V477 Cyg}:
\[T_{min,j}=HJD\;2439762.6724+P_{s} E+0.5(j-1)P+0.22986 (2j-3)\cos \omega+
0.02698 \sin 2\omega\]
\[ -0.00380 (2j-3) \cos 3\omega - 0.00054 \sin 4\omega
+0.00008 (2j-3) \cos 5\omega \]
With $P_{s} = 2.3469768$ d, $P = 2.3470199$ d and $\omega=145.6+0.00661\;E$ in
degrees. The index $j$ is $1$ for primary minima and $2$ for secondaries.
The most recent apsidal motion study of this system was undertaken by
Gim\'enez \& Quintana (1992), and we adopted the nonlinear ephemeris proposed
in that work. The agreement with recent times of minima is
not very good, showing O$-$C significantly negative for secondary
minima. The same trend is shown in our observation presented in Table 1.
\vskip 3mm
\underline{U Oph}:
\vspace{3mm}
\noindent Min I $=HJD\;2440484.6890+1.67734598\; \times E$ \hfill
(GCVS, Kholopov, 1985-87)
\vspace{3mm}
\noindent The secondary minimum was assumed to be at phase 0.5.
\vspace{3mm}
This system is known to be eccentric and shows apsidal motion, but the
adopted linear ephemeris shows a better agreement with recent times of minima
than the nonlinear ephemeris computed from the apsidal motion parameters
given in K\"amper (1986).
\vskip 1cm
\beginauthors
C. JORDI and I. RIBAS
Dept. d'Astronomia i Meteorologia
Universitat de Barcelona
Avda. Diagonal, 647
E-08028 Barcelona
Spain
\authorsrightcol
J.M. GARC\'IA
Dpto. de F\'{\i}sica Aplicada E.U.I.T.I.
Universidad Polit\'ecnica de Madrid
Ronda de Valencia, 3
E-28012 Madrid
Spain
\endauthors
\references
Barembaum, M.J., Etzel, P.B., 1995, {\it Astron. J.}, {\bf 109}, 2680
Gim\'enez, A., 1995, {\it Experimental Astronomy}, {\bf 5}, 91
Gim\'enez, A., Garc\'{\i}a-Pelayo, J.M., 1983, {\it Astrophys. Space Sci.},
{\bf 92}, 203
Gim\'enez, A., Kim, C.H., Nha, I.S., 1987, {\it Mon. Not. R. Astron. Soc.},
{\bf 224}, 543
Gim\'enez, A., Margrave, T.E., 1982, {\it Astron. J.}, {\bf 87}, 1233
Gim\'enez, A., Quintana, J.M., 1992, {\it Astron. Astrophys.}, {\bf 260}, 227
K\"amper, B., 1986, {\it Astrophys. Space Sci.}, {\bf 120}, 167
Kholopov, P.N., editor 1985-87, {\it General Catalog of Variable Stars},
Fourth Edition, Nauka Publishing, Moscow
Lacy, C.H., Frueh, M.L., 1987, {\it Astron. J.}, {\bf 94}, 712
Wolf, M., 1995, {\it Mon. Not. R. Astron. Soc.}, {\bf 277}, 95
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