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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$^1$, ~M. ~K. ~K~a~m~i~\'n~s~k~a$^1$, ~K. B~a~k~o~w~s~k~a$^2$
\\ ~J.  ~T~o~k~a~r~e~k$^1$, ~M. ~P~a~w~{\l}~o~w~s~k~i$^1$, ~T. ~K~w~i~a~t~k~o~w~s~k~i$^1$}
{$^1$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}


\Received{December 15, 2020}
\end{Titlepage}

\Abstract{
We present a new spectroscopic measurements of the eclipsing binary V2080 Cygni. It is a dethached system with similar components
and periode 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.
The obtained masses of the eclipsing components are $M_1=1.190\pm 0.006$ and $M_2=1.139 \pm 0.005$ M$_{\odot}$.
%Our results agrees whith in errors with the previous two sudies. We obtain masses in about 1\% lower than the previous study.
We compared our two data sets with the results of three other investigations. We checked also the influence of the usage of different 
measurement technics: the cross correlation and broadening function method. We found that the obtained mases depends on the used
instrument or measurment technik in about 1-2\%, i.e. this is the level of the systematic errors that we could expect.
Aditionally we analysed the GAIA mission results. The V2080 Cygni A has a three visual companions, however
according to GAIA parallaxes and proper motions they cannot be dynamically connected with the eclipsing binary and they are background stars.}
{Stars: individual: V2080 Cygni - binaries: eclipsing}


\section{Introduction}
%First light curve of V2080 Cygni was obtained by Hipparcos.
Detached eclipsing binaries provide precize determination of stellar radii and mases. The modern photometric and spectroscopic observations 
allow us to reach accuracy of about 1\% or better for those absolute parameters.
The investigated star V2080 Cygni is a relatively bright 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 we can expect for similar almost spherical components.
The object is a relatively bright and close, i.e. it is a good candidate for precize determination of the absolute parameters.
Additionally, the spectral lines of both components are clearly seen.
First radial velocity measurements were presented in a short IBVS paper (Kurpinska-Winiarska et al. 2000). Autors yield the 
amplitudes of the radial velocity curves. They corrected the periode of the star, which is twice as long as the one given by Hipparcos.
Later two teams observe the star spectroscopically. First group collected thirteen 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 observe the star also 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 ELODIE spectrograph (Ali{\c c}avu{\c s} et al. 2019). 
For analysis they used spectral disentangling method. Atmospheric 
parameters were obtained as well. For modelling of the star autors used also 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 of both studies agrees within errors. The mass ratio is close to 1 and the obtained masses are 
$1.197\pm0.005$ and $1.173\pm0.004$ M$_{\odot}$.
Our spectroscopic observations complement the existing data and increase the number of all available observations in about four times.

\section{Visual companions}
As we mentioned in the introduction V2080 Cyg A have a three bright visual companions. They are listed in WDS and CCDM catalogs of visual doubles.
The latest results coming from GAIA mission yield the paralaxes and the proper motions of all four components  (Gaia Collaboration et al. 2016;
Lindgren et al. 2016).
The 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 sims to be also a background stars, their proper motions and paralaxes are small (Fig. 1).


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


\MakeTable{ccccccl}{12.5cm}{Proper motions and parallax for V2080 Cyg A and the potential companions from GAIA DR2.}
{\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.

First data set was obtained with 1.88 m telescope of the David Dunlap Observatory with the Cassegrain spectrograph.
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 a standard IRAF tasks.

%\MakeTable{ccc}{12.5cm}{Spectroscopic observations.}
%{\hline
%     &  DDO &  PST1   \\
%\hline\noalign{\smallskip}
% HJD            &  245             &     245     \\ 
% dates          &   0.0 &  0.0   \\ 
% n$_{obs}$      &   0.0 &  0.0  \\ 
% $\sigma_{RV}$  &   0.0 &  0.0   \\ 
%\noalign{\smallskip}\hline
%}


The second dataset was aquired on 0.5 m Poznan Spectrocopic Telescope (PST1). The instrument is smaller than the previous one but
its connected via fiber to an Echell\'{e} spectrograph (Baranowski et al. 2009). 
The system have very small light looses as the telescope parameters fit perfectly
the fiber requirements. The spectral range was 4500 - 9200 \AA~with dispersion of 0.11 \AA/pix. The exposure times were 1200 or 1800 s.
Two spectral regions are presented on the Fig 2. The split spectral lines of both components are clearly seen.


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{spec.eps}
\FigCap{Two spectral regions of the PST 1 spectrum near NaD and H$_{\alpha}$ lines.} %$
\end{center}
\end{figure}


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

For the radial velocity measurements we have used Broadening Function\footnote{http://www.astro.utoronto.ca/~rucinski/SVDcookbook.html} (BF) method and for comparison and tests we used also the 
Cross Correlation (CCF) method. Broadening Function was firstly described by S. Rucinski (1992, 2002). The method is resistant to the 
spectral line broadening and have higher resolution comparing to CCF. The typical BF is presented on the Figure 4. 
The Cross Correlation measurements was carried out with IRAF task FXCOR.


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


\begin{figure}%[htb]
\begin{center}
\includegraphics[width=0.9\textwidth]{BF.eps}
\FigCap{Broadening function for one of the our PST1 spectra. The solid line present the BF and the dashed line the fitted rotational profiles.
The BF is normalized to one and on the horizontal axis we have the relative velocity. The third peak is connected probably with the telluric lines.}
\end{center}
\end{figure}





\section{Results}

For the 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 sugests that 
the eclipsing pair could have a companion we fit the two data sets separatelly. For our fit we used a 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. 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 show some variation that are slightly higher than we could expect 
form the zero point shifts in different spectrographs. It could be also explained with the existence of third body and motion on the wide orbit.

First two collumns 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. The signal-to-noise ratio of the DDO spectra is higher but the PST1 echelle has wider spectral range. The dispersion of the RV measurements 
for the PST1 is smaler as we can expect for the spectrograph mounted in a termally stabilized room. The measured semi-major axis is in very good agreement 
but the mass ratio differs in about 1\%, which propagates in to a 1\% differences in masses.

The second and third collumns of Table 2 show the same PST1 dataset 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 yiels mass meaurements of eclipsing binaries with precision less than 1\%, however as we see in the Table 2 and 3
results, masses could differ in about 1-2\% depending on the used instrument or measurement method. Usually the listed errors of the obtained parameters 
are based on the dispersion of the RV/LC measurements and are not taking in to account the possible systematic errors.


\MakeTable{lccc}{12.5cm}{Fitting results 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 data. To achieve this we shifted up first data set in 1.1 $km~s^{-1}$. This is the diference 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 vary significantly. The masses for our result was calculated for inclination $86.\!\!^{\circ}009$ yilded by Ali{\c c}avu{\c s} et al. (2019). 
The {\. I}bano{\v g}lu et al. (2008) results were calculated for inclination of $86.\!\!^{\circ}20$ which is very close to 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 the newer papers we calculated rest of the values using
$i=86.\!\!^{\circ}009$. 

All our fitted moments of main eclipse or HJD$_0$ (Table 2 and 3) were fitted for 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 case of the {\. I}bano{\v g}lu et al. 2008 result listed in Table 3, the HJD$_0$ value present their best observed moment of the eclipse.
The latest paper K. Ali{\c c}avu{\c s} \& Ali{\c c}avu{\c s} (2019) present a non fitted value used for phasing of the 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. While our result yields the lowest value of the mass ratio of the eclipsing pair.


\MakeTable{lccccc}{12.5cm}{Comparison of the results}
{\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
}

If we compare 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 but we have six times more spectra.
One significant difference between our and Ali{\c c}avu{\c s} et al. 2019 results is that we fitted only RV data and they made a simultaneous 
fit of RV and LC data.
We performed the one of the botstrap 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 we fit the RV$_{12}$ curves. 
We calculated the stadart deviation of obtained values of the parameters.
Our formal errors listed in one before last collumn of Table 3 are in good agreement and slightly lower than the bootstrap errors listed
in the last collumn.




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




\section{Conclusions}
The investigated object V2080 Cyg is a well detached system, which provides posibility of precize 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 have three relatively bright visual companions however the 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 datasets 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 depends on usage of different instruments and different measurement methods. The influence of the systematic 
errors on the obtained mass is about 1-2\%.



%The analysis of BD-00~2862 system is based on our radial velocity observations, ASAS photometry and other measurements from the catalogs.
%The results reveal that the object is a triple star which consists of the main eclipsing binary and a farther, visual third component. 
%The star is not listed in the catalogs of visual binary stars, we started to use designations A and B for both components.
%The measured distance of component A, based on the trigonometric parallax method by Gaia and photometric parallax based on our model 
%are in very good agreement. 
%The latest GAIA DR2 results confirm that both A and B components have the same distance.
%The arguments for the dynamical connection between component A and B, except the small angular distance, are similar values of the 
%proper motions and the distances. 
%We used a Wilson-Devinney method to calculate the model of the close eclipsing pair. The spectroscopic detection of the secondary component was 
%on the limit of our telescope. Nevertheless, we were able to measure its velocities and to obtain radial velocity curves for both stars.
%We calculated the absolute parameters of the EB components with an accuracy of about 1 \% for radii and 3 \% for the masses.


\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 and Alexander Schwarzenberg-Czerny,
the founders of the Pozna\'{n} Spectroscopic Telescope project.
We thank the people who helped in observations and data reduction: 
Karolina Bakowska, Agata Ro\.{z}ek, Krystian Kurzawa, Anna Przybyszewska and Adrian Kruszewski.
%MP acknowledges the Polish National Science Center grant no. 2014/13/B/ST9/00902.
%N\.{Z} work was supported by the Polish National Science Centre (NCN) through the grant DEC-2014/15/N/ST9/05171.

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.}



% Reference do dodania 
% 2019MNRAS.488.5279K -  Mon. Not. R. Astron. Soc., 488, 5279-5289 (2019/October-1) KAHRAMAN ALICAVUS F. and ALICAVUS F. 
% 2008MNRAS.384..331I -  Mon. Not. R. Astron. Soc., 384, 331-342 (2008/February-2)  IBANOGLU C., EVREN S., TAS G., CAKIRLI O., BOZKURT Z., AFSAR M., FRASCA A., SIPAHI E., DAL H.A., OZDARCAN O., CAMURDAN D.Z. and CAMURDAN M. 
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