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\IBVShead{5619}{29 March 2005}

\IBVStitletl{There is No Third Body in the Eclipsing Binary System}{ HS Herculis}

\IBVSauth{\c{C}OLAK, T.$^1$; M\"{U}YESSERO\~{G}LU, Z.$^2$}

\IBVSinst{Ankara University Faculty of Sciences, Ankara, Turkey; e-mail: tcolak@science.ankara.edu.tr}
\IBVSinst{Ankara University Faculty of Sciences, Ankara, Turkey; e-mail: muyes@astro1.science.ankara.edu.tr}

\SIMBADobjAlias{HS Her}{HD 174714}
\IBVStyp{ EA }
\IBVSkey{photometry}

\IBVSabs{We present a complete period analysis of eclipsing binary system}
\IBVSabs{HS Herculis. In order to increase the number of minimum times,}
\IBVSabs{we observed five new minima in 2002 and 2003.}
\IBVSabs{Using all available minimum times, we analyzed the O-C diagram of}
\IBVSabs{HS Her and we confirmed an apsidal motion with a period of about}
\IBVSabs{77 years. According to the results of the detailed analysis,}
\IBVSabs{we determined that there is no third body in the system and the}
\IBVSabs{O-C curve can be explained with only apsidal motion.}


\begintext

\vspace*{-0.5cm}

\hspace*{-2mm}HS Herculis (HD\,174714, HIP\,92478, BD+24\deg 3552, $\alpha_{2000}=18\hr 50\mm 50\sec$, $\delta_{2000}=24\deg 43\arcm 12\arcs$) is a detached eclipsing binary 
system with an Algol-type light curve and period of 1\fday637434. It contains 
a B5-type primary and an A4-type secondary components. 
The variability of HS Herculis was first discovered by Martynov (1940) in 1934 and independently by Jacchia 
(1940) in 1940. The first spectroscopic study was published by Cesco \& Sahade 
(1945). Hall \& Hubbard (1971) published the first period analysis of 
HS Herculis and they found an apsidal motion with a period of 15.5 years 
in the system. 
Martynov \& Lavrov (1972), Todoran (1992) and Khaliullina \& Khaliullin (1992) 
confirmed the apsidal motion and 
computed the values of 110-130 years, 60 years, and 92 years for the period, 
respectively. On the basis of the same 
data as Todoran's, Bastian (1993) rejected the apsidal motion hypothesis and suggested a light-time effect with 
a period of 60 years. Todoran \& Agerer (1994) confirmed the apsidal motion and
rejected any assumption on the 
presence of a third body. Finally, Wolf et al. (2002) determined a period of 
78 years for the apsidal motion and, 
in addition to that, they proposed a light-time effect with a period of about 
85 years in the system.


The observations of HS Her were made with the 30 cm Maksutov telescope 
(equipped with a SSP-5A photometer 
containing a side-on R1414 Hamamatsu photomultiplier) of the Ankara University 
Observatory in 2002 and 2003. 
The observations are carried out using standard Johnson U, B and V filters. 
HD 343238 (HIP 92624) and HD 343123 
(PPM 107921) are used as comparison and check stars, respectively.


New minimum times of HS Herculis are given in Table 1. 
Note that the standard errors are given in parenthesis.


\begin{table}[!hb]
\centerline{\textbf{Table 1.} New minimum times of HS Herculis}
\vskip 3mm
\begin{center}
\begin{tabular}{lccc}
\hline
Min time HJD 		&Type	&Filter		&Observers \\ 
\hline
2452472.3943 (9)	& II	& UBV		& T\c{C} \& ET \\
2452513.3223 (22)	& II	& BV		& T\c{C} \& ET \\
2452833.4343 (5)	& I	& UBV		& OA \& MY \\	
2452842.4531 (16)	& II	& UBV		& T\c{C} \\
2452856.3594 (5)	& I	& UBV		& T\c{C} \& GG \\
\hline
\end{tabular}
\end{center}
Observers: T\c{C}: T.\c{C}olak, ET: M.E.T\"or\"un, GG: H.G.G\"okay, OA: O.Aksu, MY: M.Y\i lmaz
\end{table}


On the basis of 101 minimum times (including 33 secondary minima), we analyzed 
the $O-C$ curve of 
HS Herculis. The corresponding $O-C$ differences refer to the following linear ephemeris:

\begin{equation} 
{\rm Min\ I\  =\ HJD\ }2452856.3646 +  1\fday6374341\ {\rm E}  
\end{equation}


\IBVSfig{10cm}{5619-f1.eps}{The $O-C$ diagram of HS Herculis.}
\IBVSfigKey{5619-f1.eps}{HS Her}{O-C diagram}

\IBVSfig{10cm}{5619-f2.eps}{The $(O-C)_{II}$ diagram of HS Herculis.}
\IBVSfigKey{5619-f2.eps}{HS Her}{O-C diagram}


The $O-C$ values for the minimum times and the $(O-C)_{II}$ residuals from apsidal motion analysis are 
shown in Fig.~1 and Fig.~2 respectively. Primary and secondary minima are 
plotted as filled dots and open circles respectively. Larger symbols correspond
to more reliable points
(CCD, photoelectric and photographic data), smaller symbols correspond to less reliable visual 
estimates and to some photoelectric observations that have probable systematic errors. The weights used 
in the calculations are 1.0 for CCD and photoelectric minima, 0.5 for photographic minima and 0.1 for 
visual estimates. The theoretical fit curves are determined by using the apsidal motion analysis method 
described by Gim\'enez and Garc\'\i{}a-Pelayo (1983) and on equations revised by Gim\'enez and Bastero (1995).
Apsidal motion elements are computed adopting the orbital inclination of $i = 88\fdeg7$ which is derived by 
Hall \& Hubbard (1971) from light curve analysis. The full and dashed curves in Fig.~1 represent the 
fit curves of the primary and secondary minima, respectively. 


All the points except seven minima (which are located between Epoch $-$15000 and $-$14000 in Fig.~1 and Fig.~2) 
correspond to the theoretical apsidal motion curve. It is clear that these seven points could not be represented 
by the fit curve. However, these minima were obtained from visual observations and they have 
very low weights in the calculations. Since we know that visual observations have major errors and show 
very large scatters in general, in our opinion, it won't be suitable to hypothesize a light-time effect in 
the system, on the basis of them. Furthermore, the first and second minima not used in previous studies 
of HS Her, clearly deny a light-time hypothesis. These two minima obtained from photographic observations are 
relatively more reliable points then the visual estimates. Note that these two minima are published by Jacchia 
(1940) and Martynov (1985), respectively, and the first minimum time is also available on Dieter Lichtenknecker's 
database which is maintained by Dr. Walter (Paschke 2004). \\
As a result we find that the mechanism of the period variability can be only an apsidal motion with a period of about 
77 years and there is no evidence for presence of a third body in the system. Our results of apsidal motion 
analysis are given in Table 2.


\begin{table}
\centerline{\textbf{Table 2.} Apsidal motion parameters of HS Herculis}
\vskip 3mm
\begin{center}
\begin{tabular}{ll}
\hline
Parameters			& Value	\\
\hline
T$_0$ (HJD)			& 2452856.3646 $\pm$ 0.0002 \\
P$_s$ (days)			& 1.6374341 $\pm$ 0.0000001 \\
e				& 0.0205 $\pm$ 0.0010 \\	
$\omega$$_0$ (deg)		& 302.5 $\pm$ 4.0 \\
$\dot{\omega}$ (deg/cycle)	& 0.0210 $\pm$ 0.0010 \\	
P$_a$ (days)			& 1.6375296 $\pm$ 0.0000042 \\
U (years)			& 76.9 $\pm$ 3.4 \\
\hline
\end{tabular}
\end{center}
\end{table}

\newpage

\textit{Acknowledgements}: We are grateful to Dr. I. Ethem Derman for his supports on this research 
and we are thankful to Dr. Anton Paschke, Dr. Szil\'ard Csizmadia, Dr. Milos Zejda, Dr. Marek Wolf and 
Dr. Colin Scarfe for their help for collecting the data.

\vskip 0.5cm

\references

Bastian, U., 1993, {\it AN}, {\bf 314}, 39 

Cesco, C.U., Sahade, J., 1945, {\it ApJ}, {\bf 101}, 114

Gim\'enez, A., Garc\'\i{}a-Pelayo, J.M., 1983, {\it Ap\&SS}, {\bf 92}, 203  

Gim\'enez, A., Bastero, M., 1995, {\it Ap\&SS}, {\bf 226}, 99

Hall, D.S., Hubbard, G.S., 1971, {\it PASP}, {\bf 83}, 459 

Jacchia, L., 1940, \hspace{0.001 mm} {\it Harvard Bull.}, {\bf 912}, 20
\BIBCODE{1940BHarO.912Q..20J}

Khaliullina, A.I., Khaliullin, K.F., 1992, {\it Astron. Tsirk.}, {\bf 1552}, 15 

Martynov, D.J., 1940, {\it Bull. Ast. Obs. Eng.}, {\bf 18}, 38 

Martynov, D.J., 1985, {\it Astron. Tsirk.}, {\bf 1401}, 1 

Martynov, D.J., Lavrov. M.I., 1972, {\it Perem. Zvezdy}, {\bf 18}, 269

Paschke, A., 2004 (private communication)

Todoran, I., 1992, {\it AN}, {\bf 313}, 183

Todoran, I., Agerer, F., 1994, {\it AN}, {\bf 315}, 349

Wolf, M. et al., 2002, {\it A\&A}, {\bf 383}, 533

\endreferences


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