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\begin{document}


\begin{Titlepage}
\Title{A new mass determination of an eclipsing binary V2080 Cygni\footnote{Based on the spectroscopic data obtained with Pozna\'n Spectroscopic Telescope 1 
and David Dunlap Observatory 1.88 m telescope.}}

\Author{W. ~D~i~m~i~t~r~o~v$^1$, ~K. ~K~a~m~i~\'n~s~k~i$^1$, ~K. B~\k{a}~k~o~w~s~k~a$^2$,\\ ~M. ~K. ~K~a~m~i~\'n~s~k~a$^1$,
 ~J.  ~T~o~k~a~r~e~k$^1$, ~M. ~P~a~w~{\l}~o~w~s~k~i$^1$, ~P. ~B~a~r~t~c~z~a~k$^1$\\ ~T. ~K~w~i~a~t~k~o~w~s~k~i$^1$, ~A. ~S~c~h~w~a~r~z~e~n~be~r~g -- C~z~e~r~n~y$^3$}
{$^1$Astronomical Observatory Institute, Faculty of Physics,\\ Adam Mickiewicz University, ul. S{\l}oneczna 36, 60-286 Pozna\'{n}, Poland\\
e-mail: dimitrov@amu.edu.pl\\
$^2$Institute of Astronomy, Faculty of Physics, Astronomy and Informatics,\\ Nicolaus Copernicus University, ul. Grudzi\k{a}dzka 5, 87-100 Toru\'{n}, Poland\\
$^3$Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw, Poland}

\Received{January 30, 2021}
\end{Titlepage}

\Abstract{
We present new spectroscopic measurements of the eclipsing binary V2080 Cygni. It is a detached system with similar components
and period of 4.9 d.
We collected data with two instruments, 1.88 m DDO telescope equipped with Cassegrain spectrograph and 0.5 m PST1 connected to a fiber
fed echell\'{e} spectrograph. We collected 127 measurements for each component, 
which significantly increase the number of available radial velocity measurements for the V2080 Cygni system.
Obtained masses of the eclipsing components are $M_1=1.190\pm 0.006$ and $M_2=1.139 \pm 0.005$ M$_{\odot}$.
We compared both our data sets with the results of three other investigations. We also checked the influence of the usage of different 
measurement techniques: the cross-correlation and the Broadening Function method. We found that the obtained masses depend on the
instrument used or measurment technique in about 1-2\%, i.e. this is the level of the systematic errors that we could expect.
Additionally, we analysed the GAIA mission results. V2080 Cygni A has three visual companions, however
according to GAIA parallaxes and proper motions, they cannot be dynamically connected with the eclipsing binary and therefore are background stars.
The possible existence of third body in the system could be cause of light-time effect.
We collected multicolor photometry and calculated new times of minima. The $O-C$ diagrams 
indicate variation, which requires more recent data in order to be confirmed.}
{Stars: individual: V2080 Cygni - binaries: eclipsing}


\section{Introduction}
Detached eclipsing binaries provide precise determination of stellar radii and masses. Modern photometric and spectroscopic observations 
allow us to reach the accuracy of about 1\% or better for those absolute parameters.
The investigated star V2080 Cygni is a relatively bright F5 eclipsing binary with a visual magnitude of 7.4. 
Other designations of the object are HD 183361 and BD+49 3012. The object is listed as a visually multiple star in
Catalog of the Components of Double and Multiple Stars (CCDM; Dommagnet \& Nys 1994) and 
Washington Double Star Catalog (WDS; Mason et al. 2001).
The eclipsing nature of the main A star was detected by Hipparcos satellite mission. The light curve has flat maxima and 
minima with comparable depth, as can be expected for similar, almost spherical components.
The object is relatively bright and close, i.e. it is a good candidate for precise determination of absolute parameters.
Spectral lines of both V2080 Cygni components are clearly seen.
First radial velocity measurements were presented in a short IBVS paper (Kurpinska-Winiarska et al. 2000). Authors provided the 
amplitudes of radial velocity curves. They corrected the orbital period of the star, which is twice as long as the one given by Hipparcos.
Later two teams observed the star spectroscopically. The first group collected 13 spectra at TUBITAK National Observatory and 
Catania Astrophysical Observatory ({\. I}bano{\v g}lu et al. 2008). The velocities were measured with the cross-correlation method.
The authors also observed the star photometrically and acquired UBV light curves. They obtained a model of the system using 
the Wilson-Devinney method. Authors mentioned the existence of third light in the system of about 3\%.
The second team obtained 8 spectra with the ELODIE spectrograph (Ali{\c c}avu{\c s} et al. 2019). 
For analysis they used the spectral disentangling method. Atmospheric 
parameters were obtained as well. For modelling of the star authors also used earlier radial velocity measurements of the first team
and SuperWASP light curve. Authors detected third light of about 8\% in both light curve modelling and spectrum disentangling.
The results for masses from both studies agree within errors. The mass ratio is close to 1 and the obtained masses are 
$1.197\pm0.005$ M$_{\odot}$ for the primary component and $1.173\pm0.004$ M$_{\odot}$ for the secondary.



\section{Visual companions}
As was mentioned in the introduction, V2080 Cyg A has three bright visual companions. They are listed in WDS and CCDM catalogs of visual doubles.
The latest results coming from GAIA mission\footnote{https://gea.esac.esa.int/archive/} yield the parallaxes and the proper motions of all four components  (Gaia Collaboration et al. 2016;
Lindgren et al. 2016).
GAIA DR2 results are presented in Table 1. Both DR1 and DR2 results are in good agreement and show that the all components
have different parallaxes and proper motions and they are not connected dynamically.
The fainter stars in the close neighbourhood also seem to be background stars, their proper motions and parallaxes are small (Fig. 1).


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.7\textwidth]{F1.eps}
\vspace{2mm}
\FigCap{Proper motions of V2080 Cyg A neighbourhood stars (GAIA DR2).}
\end{center}
\end{figure}


\MakeTable{ccccccl}{12.5cm}{Proper motions and parallax for V2080 Cyg A and its potential companions from GAIA DR2 catalogue.}
{\hline
 comp.  &  phot. g & sep.    & $\mu_{\alpha}$ & $\mu_{\delta}$ &  parallax   \\
 WDS    & (mag)    & (arcsec)&    (mas/yr)    &     (mas/yr)   &   (mas)     \\
\hline\noalign{\smallskip}
 A & 7.24  & -  &    55.50 $\pm$ 0.07   & 75.01  $\pm$ 0.07   &  11.70  $\pm$ 0.03      \\    %zacmieniowa
 C & 14.08 & 14 &   -2.97  $\pm$ 0.04   & -5.94  $\pm$ 0.04   &  0.48   $\pm$ 0.03      \\
 D & 11.49 & 36 &   -6.21  $\pm$ 0.06   & -13.51 $\pm$ 0.05   &  0.57   $\pm$ 0.03      \\
 B & 8.57  & 73 &    2.36  $\pm$ 0.13   & 10.41  $\pm$ 0.11   &  2.55   $\pm$ 0.05      \\     %jasny towarzysz
\noalign{\smallskip}\hline
}


\section{Spectroscopy and measurements}
%We have two datasets obtained on a different instruments. So we can compare results of both telescopes
%as well as with the data from the literature. 
Each of the two spectroscopic data sets used in the present study has been obtained with a different instrument.
Both was analysed independantly and compared with each other, as well as with the data from the literature. 
Our spectroscopic observations complement the existing data and increase fhe number of all available observations in about four times.

The first data set was obtained with 1.88 m telescope of the David Dunlap Observatory with the Cassegrain spectrograph
between April 21$^{st}$ and November 10$^{th}$ 2006.
Two different detectors were used 1024x1024 Thomson CCD, and later 2048x512  Jobin Yvon Horiba CCD.
The exposure times were 1200 s, and we observed the Mg spectral region near 5184 \AA. The typical signal--to--noise 
ratio was in the range of 100 -- 150. Data reduction was carried out using standard IRAF tasks.

%\MakeTable{ccc}{12.5cm}{Spectroscopic observations.}
%{\hline
%     &  DDO &  PST1   \\
%\hline\noalign{\smallskip}
% HJD$_{start}$            &  245 3847   &     245 4268     \\ 
% HJD$_{end}$              &  245 4050   &     245 4388     \\ 
% Start date               &   0.0       &     0.0   \\ 
% End date                 &   0.0       &     0.0   \\ 
%\noalign{\smallsk ip}\hline
%\vspace{2mm}
%}


The second dataset was acquired with 0.5 m Poznan Spectrocopic Telescope (PST1) 
between June 16$^{th}$ and October 14th 2007. 
This instrument is smaller than the previous one, however
it is connected via fiber to an echell\'{e} spectrograph (Baranowski et al. 2009). 
The system has very small light losses, as the telescope parameters fit perfectly
the fiber requirements. 
The spectrograph is equipped with Andor DZ 436 CCD with 5 stage peltier plus liquid cooling.
The spectral range was 4500 - 9200 \AA~with dispersion of 0.11 \AA/pix. The exposure times were 
1200 or 1800 s and the typical signal--to--noise ratio is 25--125.
Two spectral regions are presented in Fig 2. 
The split spectral lines of both components are clearly seen.


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{spec.eps}
\vspace{2mm}
\FigCap{Two spectral regions of a PST 1 spectrum: near NaD (top) and H$_{\alpha}$ (bottom) lines.} %$
\end{center}
\end{figure}


We searched for traces of the third star, mentioned by the previous authors, 
in the cross correlation function.
To enhance the signature of this component we used low temperature templates. 
We have not found any significant traces (Fig 3.).


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{ccf.eps}
\FigCap{Cross correlation function for PST 1 spectrum.}
\end{center}
\end{figure}


For radial velocity measurements we have used the Broadening Function\footnote{http://www.astro.utoronto.ca/~rucinski/SVDcookbook.html} 
(BF) method and for comparison and tests we also used the 
cross correlation (CCF) method. Broadening Function was first described by S. Rucinski (1992, 2002). The method is resistant to the 
spectral line broadening and has higher resolution compared to CCF. Typical BF for V2080 Cygni spectra is presented in Fig. 4. 
The cross correlation measurements were carried out with IRAF task FXCOR.


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.75\textwidth]{BF.ps}
\vspace{3mm}
\FigCap{Broadening function for one of the PST1 spectra. Solid line represents the BF 
and dashed line the fitted rotational profiles.
The BF is normalized to 1. The horizontal axis represents the relative radial velocity. 
The third peak, near 0, is probably related to the telluric lines.}
\end{center}
\end{figure}



\section{Mass determination}

For fitting of the radial velocity curves we have employed the PHOEBE SVN code (Pr{\v s}a \& Zwitter 2005).
The program is based on the Wilson-Devinney method (Wilson \& Devinney 1971). As the results of the previous investigations sugest that 
the eclipsing pair could have a companion, we fitted the two data sets separately. For our fit we used the period of 4.933588(28) d 
given by {\. I}bano{\v g}lu et al. (2008) and 
surface potentials and inclination presented by Ali{\c c}avu{\c s} et al. (2019). 
We fitted four parameters: semi-major axis, mass ratio, systemic velocity and $HJD_0$. 
%The moment of minimal radial velosities was fitted for the middle of the period of RV observations. 
$HJD_0$ was selected in the middle of the time span of RV observations.
As there is a potential third body
in the system we could expect light-time effect and possible phase shifts with respect to the ephemeris.
That was the reason to leave this parameter free. The systemic velocity shows some variation that are slightly 
higher than what could be expected 
from zero point shifts in different spectrographs. It could be explained with the existence of third body and system's 
motion on the wide orbit.

First two columns of Table 2 present the influence of the usage of different instruments on the obtained results. 
In both cases Broadening Function method was used for the measurements. 
%We compared the 1.88 m DDO telescope equipped with cassegrain spectrograph and the 0.5 m PST1 telescope with a fiber fed echele spectrograph. 
We compared data from 1.88 m DDO telescope and 0.5 m PST1 telescope.
The signal-to-noise ratio of the DDO spectra is higher, however the PST1 echell\'{e} has a wider spectral range. The dispersion of the RV measurements 
for PST1 is smaller as can be expected for the spectrograph mounted in a thermally stabilized room. The measured semi-major axis 
of V2080 Cygni is in very good agreement, 
but the mass ratio differs by about 1\%, which propagates into 1\% differences in masses.

The second and third column of Table 2 show the same PST1 data set measured with two methods -- BF and CCF. The mass ratio is in very good agreement, 
but the semi-major axis is slightly lower for the CCF results and that causes less than 1\% lower masses. 

The modern radial velocity measurements yield mass meaurements of eclipsing binaries with precision below 1\%, however, as can be seen in the Table 2 and 3
results, masses could differ by about 1-2\% depending on the instrument or measurement method used. Usually the listed errors of obtained 
parameters are based on the dispersion of the RV/LC measurements and do not take into account possible systematic errors.


\MakeTable{lccc}{12.5cm}{Comparison of BF and CCF fitting results for V2080 Cygni parameters 
based on our spectroscopic observations.}
{\hline
Instrument  &  DDO &  PST1 & PST1 \\
Method      &   BF &  BF   & CCF  \\
\hline\noalign{\smallskip}
 a $($R$_{\odot})$               &  $16.16 \pm 0.02$  & $16.15 \pm 0.02$  &  $16.12  \pm 0.02$  \\ %&  $16.118 \pm 0.012$   
 q                               &  $0.953 \pm 0.003$ & $0.965 \pm 0.002$ &  $0.964  \pm 0.002$ \\ %&  $0.965  \pm 0.001$   
 $V_{\gamma}$~(km~s$^{-1}$)      &  $1.76  \pm 0.09$  & $2.86  \pm 0.06$  &  $2.65   \pm 0.06$  \\ %&  $2.72   \pm 0.04$    
 $HJD_0 - 2450000$               &  $3944.7883$       & $4329.6078$       &  $4329.6072$        \\ %&  $4329.6069$         
                                 &  $\pm 0.0012$      & $\pm 0.0008$      &  $\pm 0.0008$       \\ %&  $\pm 0.0006$        
                              &&&\\                                                           
 $M_1$ $($M$_{\odot})$           &  $1.193 \pm 0.006$ & $1.183 \pm 0.006$ & $1.177  \pm 0.006 $ \\ %&   $1.176  \pm 0.003 $
 $M_2$ $($M$_{\odot})$           &  $1.137 \pm 0.006$ & $1.142 \pm 0.005$ & $1.135  \pm 0.005 $ \\ %&   $1.135  \pm 0.003 $
                              &&&\\                                                           
 $\sigma_{RV}$~(km~s$^{-1}$)     &  1.08              & 0.59              &  0.57               \\ %&  0.40                
 $n_{obs}$                       &  80                & 47                &  47                 \\ %&  45                  
\noalign{\smallskip}\hline
}



\subsection{Simultaneous fit}
In this section we present the simultaneous fit for all our spectroscopic data. To achieve this we shifted up the first data set (DDO) by 1.1 $km~s^{-1}$. 
This is the difference between the systemic velocities for both data sets. We compared the results with three other investigations (Table 3). 
Most of the results are in good agreement, only the systemic velocity values vary significantly. The masses for our result were calculated for the 
inclination of $86.\!\!^{\circ}009$ provided by Ali{\c c}avu{\c s} et al. (2019). 
The {\. I}bano{\v g}lu et al. (2008) results were calculated for the inclination of $86.\!\!^{\circ}20$, which is very close to the upper one, therefore 
the results could be directly compared without recalculation of semi-major axes and masses. 
The earliest paper (Kurpi\'nska-Winiarska et al. 2000) did not present neither inclination nor semi-major 
axis values. The error bars were not presented as well. To compare those results with most recent literature, we calculated the rest of the values using
$i=86.\!\!^{\circ}009$.

All our moments of main eclipse, or HJD$_0$, (Table 2 and 3) were fitted to our RV data 
for the middle of the period of observation for each data set.
The HJD$_0$ given by Kurpi\'nska-Winiarska et al. (2000) is based on their radial velocity and photometric observations (Tab. 3).
In the case of the {\. I}bano{\v g}lu et al. (2008), result listed in Table 3, the HJD$_0$ value presents their best observed moment of the eclipse.
The latest paper, K. Ali{\c c}avu{\c s} \& Ali{\c c}avu{\c s} (2019), presents a value based on their RV data.

We collected four times more measurements than all the previous investigations together. 
Our primary mass value is close to the one obtained by {\. I}bano{\v g}lu et al. (2008), while the secondary is about 2\% lower. Mases obtained 
by Ali{\c c}avu{\c s} et al. (2019) are 
the highest among all results. Our result yields the lowest value of the mass ratio of the eclipsing pair.


\MakeTable{lccccc}{12.5cm}{Comparison of V2080 Cygni parameters obtained in this work 
with values from the literature.}
{\hline
                         & Kurpi\'nska-Winiarska  & {\. I}bano{\v g}lu & K. Ali{\c c}avu{\c s} \&  &   PST1 \& DDO        &  bootst. \\
                         & et al. 2000            & et al. 2008        & Ali{\c c}avu{\c s} 2019   &   (this paper)       &  err.    \\
\hline\noalign{\smallskip}
 a $($R$_{\odot})$               &  $16.16$  & $16.20 \pm 0.07$  &  $16.254 \pm 0.019$  &  $16.16  \pm 0.02$   & 0.026   \\ 
 q                               &  $0.974$  & $0.971 \pm 0.009$ &  $0.982  \pm 0.002$  &  $0.957  \pm 0.002$  & 0.002   \\ 
 $V_{\gamma}$~(km~s$^{-1}$)      &  $3.2 $   & $1.0  \pm 0.4$    &  $1.17   \pm 0.32 $  &  $2.88   \pm 0.06$   & 0.08    \\ 
 $HJD_0$                         &  $1053.705  $  & $3895.4534 $ &  $2504.186        $  &  $4117.4638 $        &         \\
 $- 2450000$                     &  $\pm 0.001 $  &$\pm 0.0008$  &  $  -             $  &  $\pm 0.0009$        & 0.0011  \\
                              &&&&&\\
 $M_1$ $($M$_{\odot})$           &  $1.180 $ & $1.191  \pm 0.017$  & $1.197  \pm 0.005 $   & $1.190  \pm 0.006 $  & 0.007 \\
 $M_2$ $($M$_{\odot})$           &  $1.149 $ & $1.157  \pm 0.017$  & $1.173  \pm 0.004 $   & $1.139  \pm 0.005 $  & 0.007 \\
                              &&&&&\\
 $n_{obs}$                       &  11   & 13  &  21 &  127 &    \\
method                           &  -    & CCF & CCF &  BF  &    \\
% $\sigma_{RV}$                  &  0.0 & 0.0  &  0.0 &  \\
\noalign{\smallskip}\hline
}

Comparing the error bars of our and Ali{\c c}avu{\c s} et al. (2019) results listed in Table 3, we could mention that the authors have slightly 
smaller estimations of the errors. It is surprising because the quality of the RV data is comparable in both cases,
while our analysis was carried out using six times more spectra.
One significant difference between our and Ali{\c c}avu{\c s} et al. (2019) results is that we only fitted RV data and they made a simultaneous 
fit of RV and LC data.
We performed one of the bootstrap method variants to check our error estimations. We randomly draw N measurements from N observations with 
possible value repetitions. This way we obtained ten data sets for both components, and fitted RV$_{12}$ curves. 
We calculated the standard deviation of obtained values of the parameters.
Our formal errors listed in one before last column of Table 3 are in good agreement and slightly lower than the bootstrap errors listed
in the last column.


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=1.0\textwidth]{rv1.eps}
\vspace{1mm}
\FigCap{Radial velocity curves of V2080 Cygni. Green dots represent DDO measurements shifted up 
by 1.1 $km~s^{-1}$. Black dots represent measured PST1 velocities while the straight lines -- 
synthetic RV curves based on the model listed in the one before last column of Table 3.}
\end{center}
\end{figure}



\section{Photometry}


\subsection{Observations and data reduction} 



\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.6\textwidth]{Fig1.ps}
\vspace{5mm}
\FigCap{Finding chart of V2080 Cyg. The variable is marked as V1.  
Positions of the three comparison stars C1, C2 and C3 are also shown. 
The field of view is about 17.0'$\times$25.5'. North is up, east is to the left.}
\end{center}
\end{figure}


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{Fig2.ps}
\FigCap{The observed light curves in the I, R and V band  passes for V2080 Cyg.}
\end{center}
\end{figure}




Observations of V2080 Cyg were obtained during 41 nights between September 7$^{th}$ to October 1$^{st}$ 2011 at the Pozna\'{n} 
Astronomical Observatory located in Poland. For observations we used a 200 mm, F/4.5 Newton reflector, equipped with 
SBIG ST-7 XME camera and a set of Bessel BVRI filters. The camera provided $17.0' \times 25.5'$ field of view. 

All observations were carried out in the V, I and R filters with the exposure times of 10, 8 and 6 seconds, respectively. 
In total, we obtained 50699 exposures of V2080 Cyg during 108.59 hours. Table 4 presents a full journal of our CCD observations. 

We determined relative unfiltered magnitudes of V2080 Cyg by taking the difference between 
the magnitude of the object and the mean magnitude of three comparison stars. 
In Fig. 6 the sky region is displayed with V2080 Cygni marked as V1 and the comparison 
stars as C1, C2 and C3, respectively. The equatorial coordinates and the brightness of 
comparison stars C1 (RA$=19^h26^m41^s.246$, Dec$=+50^o09^{'}18^{"}.274$, $8.56$ mag in V filter), 
C2 (RA=$19^h27^m00^s.870$,\\ Dec=$+50^{o}14^{'}04^{"}.884$, $8.98$ mag in V filter), 
and C3 (RA=$19^h27^m16^s.991$,\\ Dec=$+50^{o}16^{'}10^{"}.986$, $10.08$ mag in V filter) 
were taken from the Tycho-2 Catalogue (H\o{}g et al. 2000).

CCD frames were reduced with the $STARLINK$\footnote{The Starlink software is currently
supported by the East Asian Observatory} package (Currie 2014). 
Corrections for bias, dark current and flat-field were applied and the aperture photometry was conducted.

In Fig. 7 we present the resulting light curves of V2080 Cygni in I, R and V filters. We used the value of $4.9335$ days 
as an orbital period to phase the data. 

\begin{table*}
 \centering
 \begin{small}

  \caption{The journal of the CCD observations of V2080 Cyg.}
  \vspace{0.25cm}
  \begin{tabular}{@{}lcccccc@{}}
  \hline
   Year     & Start date & End date &  Number of nights      & Exposure & Number of & Filter \\
            &            &          &                        & time [sec]& frames    &         \\
\hline
    2009  & September 7 & November 21 & 19                  & 10 & 6306        & V       \\
          &             &             &                     & 8  & 7248        & I       \\
          &             &             &                     & 6  & 9550        & R       \\          
    2010  &  October 17 & October 31  & 5                   & 10 & 1726        & V       \\
            &            &            &                     & 8  & 2141        & I       \\
            &            &            &                     & 6  & 3012        & R       \\
    2011    & May 23     & October 1  & 17                  & 10 & 5515        & V       \\
            &            &            &                     & 8  & 6888        & I       \\
            &            &            &                     & 6  & 8313        & R       \\
\hline
Total:      &     -      &   -        & 41                  &-   & 50699        & -       \\
\hline
\end{tabular}
 \end{small}
\end{table*}


\subsection{$O-C$ diagrams for eclipses}

To check the stability of the orbital period and determine its value, the $O-C$ analysis was conducted. 
First, we used the timings of 5 eclipses from our 2009-2011 observing season and the following ephemeris of the minima was derived: 

\begin{equation}
{\rm HJD_{\rm min}} = 2455094.3114(2) + 4.933550(2) \times E,
\label{Eq1}
\end{equation} 

\noindent
which gives the orbital period of $P_{orb1} = 4.933550(2)$ days. The resulting $O-C$ diagram for the moments of minima is shown in Fig. 8.

To obtain the best possible value of the orbital period we combined our 5 timings of eclipses from September 2009 - September 2011 observations, 
the SuperWASP\footnote{https://wasp.cerit-sc.cz} June-July 2008 data set, and the date presented in \.{I}bano\v{g}lu et al. (2008). 
Based on this, we calculated the following ephemeris of the minima:

\begin{equation}
{\rm HJD_{\rm min}} = 2455094.31027(9) + 4.9335701(4) \times E,
\label{Eq2}
\end{equation} 

\noindent
and this corresponds to the orbital period of $P_{orb2}=4.933701(4)$ days. In Fig. 9 we show the resulting $O-C$ diagram for the moments of eclipses for 1998-2011 time span.

In Table 5 we present the timings of eclipses with errors, cycle numbers $E$ and $O-C$ values. As Type I and II are marked the primary and the secondary eclipses observed in V2080 Cyg, respectively.    

The decreasing trend of the orbital period shown in Fig. 9 was confirmed by calculations of the second-order polynomial fit to the moments of minima. The following ephemeris was obtained:


\begin{equation}
{\rm HJD_{\rm min}} = 2455094.31054(9) + 4.9335634(6) \times E - 2.7(2) \times 10^{-8} \times E^{2}.
\label{Eq3}
\end{equation}

In Fig. 9 the solid line corresponds to the ephemeris given by Eq. 3.

After this investigation, we suggest that the orbital period might have not been stable between August 1998 and September 2011 and it can be described by a decreasing trend with a rate of \textit{\.{P}}$=-2.7(2) \times 10^{-8}$. It should be noted that the observed change in the orbital period, presented in Fig. 9, was calculated based on the only one point of data from 1998 given by \.{I}bano\v{g}lu et al. (2008). Hence, this time span of observations and the amount of available data are insufficient for any conclusive statement pertaining to the changes in the orbital period of V2080 Cyg.    




\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.8\textwidth]{Fig3.ps}
\FigCap{The $O-C$ diagram of the moments of eclipses observed in V2080 Cyg 
during our 2009-2011 campaign.}
\end{center}
\end{figure}


\begin{figure}[htb]
\begin{center}
\includegraphics[width=0.8\textwidth]{Fig4.ps}
\FigCap{The $O-C$ diagram of the moments of eclipses in V2080 Cyg based on data 
collected between 1998 and 2011 from both literature and our measurements. 
Black circles represent our dataset, data taken 
from the SuperWASP is marked with red triangles, and blue squares correspond to 
data provided by \.{I}bano\v{g}lu et al. (2008).}
\end{center}
\end{figure}






\begin{small}
\begin{table*}[!h]
\caption{Times of minima in the light curves of V2080 Cyg observed since August 1998 until September 2011.}
\vspace{0.1cm}
\begin{center}
\begin{tabular}{lccccc}
\hline
$E$ & ${\rm HJD}_{\rm min} - 2450000$ & Error & $O-C$    & Type & Reference \\
    &                                 &       & [cycles] &      & \\
\hline
-819   & 1053.7050 & -      &  -0.00230221  &  II  & \.{I}bano\v{g}lu et al. (2008) \\ 
-318   & 3525.4317 & 0.0008 &  -0.00066447  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-259   & 3816.5114 & 0.0006 &  -0.00085417  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-250.5 & 3858.4507 & 0.0003 &  -0.00005269  &  I   & \.{I}bano\v{g}lu et al. (2008) \\
-243   & 3895.4534 & 0.0001 &   0.00013467  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-227   & 3974.3903 & 0.0006 &   0.00089732  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-184   & 4186.5310 & 0.0003 &  -0.00048071  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-168   & 4265.4713 & 0.0006 &   0.00016353  &  II  & \.{I}bano\v{g}lu et al. (2008) \\
-94    & 4630.5586 & 0.0005 &   0.00079444  &  II  & SuperWASP \\
-93    & 4635.4923 & 0.0008 &   0.00082077  &  II  & SuperWASP \\
-87.5  & 4662.6265 & 0.0005 &   0.00073248  &  I   & SuperWASP \\
-85.5  & 4672.4834 & 0.0006 &  -0.00134313  &  I   & SuperWASP \\
0      & 5094.3114 & 0.0002 &   0.00022904  &  II  & This work \\
81.5   & 5496.3957 & 0.0002 &  -0.00010807  &  I   & This work \\
82.5   & 5501.3293 & 0.0003 &  -0.00010201  &  I   & This work \\
149    & 5829.4103 & 0.0003 &  -0.00038814  &  II  & This work \\
150    & 5834.3439 & 0.0004 &  -0.00038208  &  II  & This work \\
\hline
\end{tabular}
\end{center}
\end{table*}
\end{small}

%\bibitem{Hog} E. H\o{}g et al., 2000, {\it A\&A}, 355, L27-L30
%\bibitem{Ibanoglu} C. \.{I}bano\v{g}lu et al., 2008, {\it MNRAS}, 384, 331-342



%000000000000000000000000000000000

\newpage
\section{Conclusions}
The investigated object V2080 Cyg is a well detached system, which provides the posibility of precise measurements of 
absolute parameters. The star is bright and the spectral lines of both components are clearly resolved. 
The lines of both components are blended only near the eclipse phases.
The binary has three relatively bright visual companions however GAIA proper motion and parallax results reveal that they are 
not connected with the EB as well as the dimmer background stars.
We analysed our two radial velocity data sets obtaining a new mass determination based on a significantly 
higher number of measurements than the previous investigations. Comparing our and literature data we show that 
results depend on the usage of different instruments and different measurement methods. The influence of systematic 
errors on the obtained mass is about 1-2\%.
Additionally, we collected photometric data and calculated new times of minima.
The analysis of eclipse times show possible variation of the orbital period, which must be 
confirmed with new measurements. Those variations could be related to a third body and the 
light-time effect in the system.


\Acknow{We would like to thank Slavek M. Rucinski and DDO staff for generous hospitality. 
In particular, our team wants to express appreciation to the observers Heide DeBond and Jim Thomson.
We are grateful to our engineer Roman Baranowski the co-founder of the Pozna\'{n} Spectroscopic Telescope project.
We thank the people who helped in observations: 
Agata Ro\.{z}ek, Krystian Kurzawa, Anna Przybyszewska and Adrian Kruszewski.
WD, TK, KK and ASC were supported by the Polish grant KBN 1 P03D 025 29.

This work has made use of data from the European Space Agency (ESA)
mission {\it Gaia} (http://www.cosmos.esa.int/gaia), processed by
the {\it Gaia} Data Processing and Analysis Consortium\\ (DPAC, 
http://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding
for the DPAC has been provided by national institutions, in particular
the institutions participating in the {\it Gaia} Multilateral Agreement.}


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