---
abstract: 'We present new spectroscopic observations of the double-lined eclipsing binary V2653Oph. The photometric observations obtained by $ASAS$ were analysed and combined with the analysis of radial velocities for deriving the absolute parameters of the components. Masses and radii were determined for the first time as M$_p$=1.537$\pm$0.021 M$_{\odot}$ and R$_p$=2.215$\pm$0.055 R$_{\odot}$, M$_s$=1.273$\pm$0.019 M$_{\odot}$ and R$_s$=2.000$\pm$0.056 R$_{\odot}$ for the components of V2653Oph. We estimate an interstellar reddening of 0.15$\pm$0.08mag and a distance of 300$\pm$50pc for the system, both supporting the membership of the open cluster Collinder359. Using the out-of-eclipse photometric data we have made frequency analysis and detected a periodic signal at 1.0029$\pm$0.0019c/d. This frequency and the location of the more massive star on the HR diagram lead to classification of a $\gamma$ Dor type variable. Up to date only eleven $\gamma$ Dor type pulsators in the eclipsing binaries have been discovered. For six out of 11 systems, the physical parameters were determined. Although a small sample, we find empirical relations that $P_{puls}$ $\propto$ $P_{orb}^{0.43}$ and $P_{puls}$ $\propto$ $g^{-0.83}$. While the pulsation periods increase with longer orbital periods, they decrease with increasing surface gravities of pulsating components and gravitational pull exerted by the companions. We present, briefly, the underlying physics behind the correlations we derived.'
address: 'Ege University, Science Faculty, Astronomy and Space Sciences Dept., 35100 Bornova, İzmir, Turkey '
author:
- 'Ö. Çak[i]{}rl[i]{}'
- 'C. Ibanoglu'
title: 'V2653 Ophiuchii with a pulsating component and $P_{puls}$ - $P_{orb}$, $P_{puls}$ - $g$ correlations for $\gamma$-Dor type pulsators'
---

Stars: fundamental parameters – individual: V2653Oph – binaries: eclipses – –

INTRODUCTION  {#sec:intro}
=============

Main-sequence and subgiant stars of spectral type A to F in detached and semi-detached eclipsing binaries are very interesting targets for asteroseismic studies, i.e., the determination of the boundaries of instability strip by interpreting the observed oscillation characteristics. Indeed, eclipsing binaries containing A-F stars offer the possibility of determining accurate masses and radii for the components. Unique advantage is if the binary resides in a cluster, determination of the fundamental properties and, in particular for systems belonging to the open clusters, can be used to address relevant astrophysical issues, such as chemical compositions, age and the distance of two stars with accurate masses and radii, allowing a much more discriminating test of physical ingredients of theoretical models.

We present a study of the detached [*Algol*]{} type eclipsing binary, which is probably a member of the open cluster Collinder359 [@zejda]. We have obtained complete light curves from the photometry obtained by [*Hipparcos*]{} [@Perryman+97aa] and All Sky Automated Survey, ASAS, [@Poj02]. We have also obtained an extensive spectroscopy using the FRESCO [é]{}chelle spectrograph at the telescope of Catania Astrophysical Observatory.

[@och] measured the visual magnitude of 8.90 mag with a precision of one tenth of a magnitude and a color of G5 using “microfiche” photographic observations for V2653Oph. The eclipsing character of V2653Oph (HD162811;BD+03$^{o}$3514; HIP87511; V=9.49, B-V=0.60 mag) [^1] was discovered by the $Hipparcos$ satellite mission, the primary eclipse having an amplitude of 0.09mag. The depth of the secondary minimum is nearly equal to that of the primary one. The first eclipse light curve was roughly revealed by the $Hipparcos$ observations. @Kaz99 designated it as V2653Oph in the [74th Name-list of Variable Stars]{}, and classified it as an eclipsing binary. In recent years, large-scale photometric surveys, such as All Sky Automated Survey (ASAS) [@pojmanski], $MOST$[@wal], $CoRot$[@bag], $Kepler$ [@gil],etc. have been conducted with the main aim of looking for transiting exoplanets. The valuable by-product of this search has been the very large number of well sampled eclipsing binary light curves. One of the eclipsing binaries observed at the Las Campanas Observatory as part of the ASAS was V2653Oph. Yet the astrophysical parameters are not obtained for the system.

Observation and data reduction {#sec:observation}
==============================

The 91-cm telescope of the Istituto Nazionale di Astrofisica – Osservatorio Astrofisico di Catania (INAF–OACT) was used to carry out spectroscopy of the target. Details of the telescope and the echelle spectrograph are given by @or. Observations were carried out during eleven nights between 21 June - 05 July 2008. Exposure times were fixed for target star at 2400s.

The reduction of the spectra was done by using the NOAO/IRAF package[^2]. The [*Th-Ar*]{} emission line spectra were used to calibrate the wavelength references of each observations. The S/N ratio of the spectra was at least $\sim$90.

Photometric observations of the system obtained and published in ASAS-3 were used to construct the V-band light curve. For calculation of the orbital phases we tried to improve a better epoch and an orbital period for the system. An orbital period of about 4.394 days was estimated from the photometric observations of the system by the $Hipparcos$ mission. We searched for orbital period using data combined from the [*Hipparcos*]{} and ASAS surveys. Analysis of Variance (AoV) algorithm developed by @AoV89 and implemented in the VarTools light curve analysis program [@hartman08] was used for detection of sharp periodic signals. We obtained the period and [*False Alarm Probability*]{} of peaks which are significant at a level greater than 3$\sigma$. We detect significant peaks in the power spectra at periods between 2–5 days, the most significant being at 4.39days. We improved the light elements of the system using the Wilson-Devinney code [@Wil03]. The light and radial velocity curve of the system is phased with the following ephemeris and period:

$$T_{\mathrm{minI}} = 2453189.668(58) + 4^d.3942894(48)  \times E.$$

The orbital period is very close to that estimated by @ote. The radial velocities and photometric observations were phased using these light elements.

Spectroscopic data
==================

Radial velocity analysis {#sec:rv}
------------------------

Radial velocities (RV) of the components were derived with a standard cross correlation algorithm, IRAF’s tool FXCOR. We used the wavelength interval 4500 – 5000 Å, which is rich in metallic lines. As cross correlation template, we chose the nearby primary target $\iota$Psc (F7V) of similar spectral type and we used, for reference, as the RV standard. The radial velocities of the components were derived by fitting two Gaussian curves with the FXCOR function and presented in Table1. The radial velocities were analysed using the [RVSIM]{} software program [@Kan07]. The parameters are presented in Table2 and the fits are compared with the observations in Fig.1.

  ------------- --------- ------------- ---------- ------------- ---------- --
   HJD–2400000   Orbital                                                    
                  Phase     $V_{\rm P}$  $\sigma$    $V_{\rm S}$  $\sigma$  
   54638.34598   0.6729            84.2    0.6             -83.2    0.7     
   54639.33703   0.8984            44.2    0.9             -55.4    0.7     
   54640.33176   0.1248           -81.2    1.1              55.6    1.1     
   54641.34108   0.3545           -81.2    0.9              51.4    0.4     
   54642.34823   0.5837            50.1    1.1             -55.3    1.1     
   54643.35360   0.8124            81.5    1.0             -84.3    0.6     
   54644.38749   0.0477           -41.3    1.4              21.2    0.7     
   54647.37993   0.7287            92.4    0.7             -88.5    0.7     
   54649.36320   0.1800          -100.2    0.8              66.5    1.2     
   54651.35779   0.6339            71.4    0.8             -71.2    1.3     
   54654.34120   0.3129           -95.6    0.7              66.2    1.1     
  ------------- --------- ------------- ---------- ------------- ---------- --

  : Heliocentric radial velocities of V2653Oph. The columns give the heliocentric Julian date, orbital phase and the radial velocities of the two components with the corresponding standard deviations.

  -------------------------- --------------- --------------- -- -- -- -- -- -- --
  Parameter                                                                    
                                 Primary        Secondary                      
  $K$ (kms$^{-1}$)              $ 83\pm$1       $93\pm$1                       
  $V_\gamma$ (kms$^{-1}$)                                                      
  Average O-C (kms$^{-1}$)         0.5             0.9                         
  $a\sin i$ ($R_{\odot}$)                                                      
  $M\sin^3i$ ($M_{\odot}$)    1.50$\pm$0.10   1.25$\pm$0.18                    
  $e$                                                                          
  -------------------------- --------------- --------------- -- -- -- -- -- -- --

  : Results of the radial velocity analysis for V2653Oph.

Determination of the atmospheric parameters {#sec:class}
-------------------------------------------

The width of the cross-correlation function (CCF) is a good tool for the measurement of $v\sin i$ of a star. We used a method developed by @Pen96 to estimate the $v\sin i$ of each star composing the investigated double–lined eclipsing binary system from its CCF peak by a proper calibration based on a spectrum of a narrow-lined star with a similar spectral type. The rotational velocities of the components were obtained by measuring the FWHM of the CCF peak related to each component in five high-S/N spectra acquired near the quadratures, where the two spectra have the largest relative difference in radial velocity. The CCFs were used for the determination of $v\,sin\,i$ through a calibration of the full-width at half maximum (FWHM) of the CCF peak as a function of the $v\,sin\,i$ of artificially broadened spectra of a slowly rotating standard star ($\iota$Psc, $v\sin i \simeq$3kms$^{-1}$, e.g., @takeda) acquired with the same set up and in the same observing night as the target system. The limb darkening coefficient was fixed at the theoretically predicted values, 0.55 for the system [@Van93]. We calibrated the relationship between the CCF Gaussian width and $v\,sin\,i$ using the @Con77 data sample. This analysis yielded projected rotational velocities for the components of V2653Oph as $v_{\rm P}\sin i$=25 kms$^{-1}$, and $v_{\rm S}\sin i$=20 kms$^{-1}$. The mean deviations were 1 and 2 kms$^{-1}$, for the primary and secondary, respectively, between the measured velocities for different lines.

In Fig.2 we show the simulation of the spectrum of the system with that of broadened combination of the two standard spectra at phase 0.72 (HJD 54647.37993) using the derived rotational velocities. The spectral order at blue wavelength is displayed. The sum of residuals is also shown, as a function of $v\,sin\,i$, in the insets of Fig2.

  ------------------------ ---------------- --------------- -- -- -- -- -- -- --
  Parameter                                                                   
                               Primary         Secondary                      
  Spectral type             F(2$\pm$0.5)V    F(7$\pm$0.5)V                    
  $T_{\rm eff}$ (K)          6950$\pm$480    6350$\pm$650                     
  $\log~g$ ($cgs$)          4.07$\pm$0.02    4.22$\pm$0.06                    
  $v\sin i$ (kms$^{-1}$)       25$\pm$1        20$\pm$2                       
  $[Fe/H]$ (dex)            -0.11$\pm$0.08   0.07$\pm$0.09                    
  ------------------------ ---------------- --------------- -- -- -- -- -- -- --

  : Spectral types, effective temperatures, surface gravities, metallicity and rotational velocities of components estimated from the spectra of V2653Oph.

We also performed a spectral classification for the components of the system using the COMPO2, an IDL[^3] code for the analysis of high-resolution spectra of eclipsing binary systems originally written by @Frasca2006 and adapted to the [REOSC]{} spectra. This code searches for the best combination of two reference spectra able to reproduce the observed spectrum of the system. We give, as input parameters, the radial velocities and projected rotational velocities of the two components of the system, which were already derived. The code then finds, for the selected spectral region, the spectral types and fractional flux contributions that best reproduce the observed spectrum, i.e. which minimize the residuals in the collection of difference (observed$-$composite) spectra. For this task we used reference spectra taken from the @Val04 $Indo-U.S.\ Library\ of\ 
Coude\ Feed\ Stellar\ Spectra$ (with a a resolution of $\approx$1Å) that are representative of stars with spectral types from late-O type to early-M, and luminosity classes V, IV, and III. The atmospheric parameters of these reference stars were recently revised by @Wu2011.

We selected 198 reference spectra spanning the ranges of expected atmospheric parameters, which means that we have searched for the best combination of spectra among 39204 possibilities per spectrum. The observed spectra of V2653Oph in the $\lambda$4960–5000 spectral region were best represented by the combination of HD183085 (F0.5V) and $\iota$ Psc (F7V). However, we have adopted, for each component, the spectral type and luminosity class with the highest score in the collection of the best combinations of templates, where the score takes into account the goodness of the fit expressed by the minimum of the residuals. We have thus derived a spectral types for the primary and secondary component of V2653Oph as F2 and F7 main-sequence stars, with an uncertainty of about 0.5 spectral subclass. The effective temperature and surface gravity of the two components of the system are obtained as the weighted average of the values of the best spectra at phases near to the quadratures combinations of templates adopting a weight $w_i=1/\sigma_i^2$, where $\sigma_i$ is the average of residuals for the $i$-th combination. The standard error of the weighted mean was adopted for the atmospheric parameters. The atmospheric parameters obtained by the code and their standard errors are reported in Table3. The observed spectra of V2653Oph at phase near to the quadrature is shown in Fig.2 together with the combination of two reference spectra which gives the best match and their residuals.

Spectroscopic light ratio
-------------------------

For the detached eclipsing binaries, where the temperature of the two stars are closely similar, the light ratio can be calculated from the cross–correlation functions (CCF) of the various spectra. [@or] showed, by measuring the average fitted full width half maximum ([FWHM]{}) values of the echelle orders in the selected spectral domains, which include several photometric absorption lines. In this study we have disregarded very broad lines, such as H$_{\beta}$ and H$_{\alpha}$, because their broad wings affect the CCF and lead to large errors. Inspection of the CCFs showed that the two components are visible and well separated from each other near the quadratures. Following the method proposed by [@or], the two-Gaussian fits of the well–separated CCFs using the de-blending procedure in the IRAF routine SPLOT. The average fitted FWHMs are 120$\pm$2 and 65$\pm$3 [kms$^{-1}$]{}for the primary and secondary components. Fig.3 shows a sample of the double-Gaussian fit. Indeed, the shapes and velocities corresponding to the peaks of the CCFs are slightly changed. We estimated the intensity ratio $\ell_1$ /($\ell_{1}+\ell_{2}$)=0.649$\pm$0.032 from the two-Gaussian fits of the well-separated CCFs.

Light curve analysis {#sec:lc}
====================

The photometric data collected from the ASAS catalogue. We analyzed the light curve using the Wilson-Devinney code [hereafter WD; e.g., @Wil71; @Wil79; @Wil03; @Wil06] implemented into the software [phoebe]{} [@Prs05]. The WD code is widely used for determination of the orbital parameters of the eclipsing binaries. To run the code we need some initial parameters. The initial logarithmic limb-darkening coefficients were taken from the tables given by @Van93 as $x_1$=0.47 and $x_2$=0.48, and are automatically interpolated at each iteration by [phoebe]{}. The effective temperature of the primary star is taken as 6950 K and the ratio of the masses of two components $q$=0.84. We have started with $Mode-2$ meant for detached binary systems, keeping the temperature of the primary and the mass-ratio as fixed parameters. According to the WD code we adjusted the following parameters: $i$ (the orbital inclination), $\Omega_1$ (the potential for the primary), $\Omega_2$ (the potential for the secondary), $T_{\rm eff_2}$ (the effective temperature of the cool star), L$_1$ (the luminosity of the primary), and the zero-epoch offset. The luminosity of the secondary star, L$_2$, was constrained by the model. After a few numbers of runs of the Differential Correction program in $Mode-2$ the sum of residuals squared showed a minimum and the corrections to the adjustable parameters became smaller than their probable errors. The results are presented in Table4. The corresponding computed light curve is shown in Fig.4 as a continuous line.

            Parameters                 V2653Oph             
  ------------------------------- ------------------- -- -- --
              $i^{o}$               81.78$\pm$0.25          
        $T_{\rm eff_1}$ (K)           6950\[Fix\]           
        $T_{\rm eff_2}$ (K)          6540$\pm$160           
            $\Omega_1$              8.048$\pm$0.175         
            $\Omega_2$              7.717$\pm$0.183         
               $r_1$               0.1391$\pm$0.0034        
               $r_2$               0.1256$\pm$0.0035        
   $\frac{L_{1}}{(L_{1}+L_{2})}$    0.613$\pm$0.015         
          $\sum(O-C)^{2}$                0.188              

  : Final solution parameters for the detached model of V2653Oph.

Absolute dimensions
===================

Combining the results of radial velocities and light curve analysis we have calculated the absolute parameters of the stars. The separation between the components of eclipsing pair is calculated as $a$=15.98$\pm$0.07 R$_{\odot}$. The fundamental stellar parameters for the components such as masses, radii, luminosities are listed in Table5 together with their formal standard deviations. The standard deviations of the parameters have been determined by using the [JKTABSDIM[^4]]{} code, which calculates distance and other physical parameters using several different sources of bolometric corrections [@sou05]. The masses for the primary and secondary star are consistent with F2$\pm$0.5V and F7$\pm$0.5V stars.

  Parameter                               Primary          Secondary
  ---------------------------------- ----------------- -----------------
  Mass (M$_{\odot}$)                  1.537$\pm$0.021   1.273$\pm$0.019
  Radius (R$_{\odot}$)                2.215$\pm$0.055   2.000$\pm$0.056
  $T_{eff}$ (K)                        6950$\pm$480      6350$\pm$650
  $\log~(L/L_{\odot})$                1.014$\pm$0.122   0.820$\pm$0.175
  $\log~g$ ($cgs$)                    3.934$\pm$0.021   3.941$\pm$0.024
  $Sp.Type$                            F(2$\pm$0.5)V     F(7$\pm$0.5)V
  $M_{bol}$ (mag)                      2.21$\pm$0.31    2.69 $\pm$0.44
  $BC$ (mag)                               0.030             0.009
  $M_{V}$ (mag)                        2.18$\pm$0.33     2.69$\pm$0.48
  $(vsin~i)_{calc.}$ (km s$^{-1}$)     25.5$\pm$0.6      23.0$\pm$0.7
  $(vsin~i)_{obs.}$ (km s$^{-1}$)        25$\pm$1          20$\pm$2
  $d$ (pc)                              284$\pm$45        321$\pm$73

  : Absolute properties of the V2653Oph components[]{data-label="parameters"}

The distance determination depends, of course, on the total apparent visual magnitude and the observed colour of the system. The observed visual magnitude of the system was estimated by various authors in the range from 9.48 [@mendo] to 9.98mag. [@hanson]. Since the Tycho measurements include probable errors, e.g. $B_{T}$=10.224$\pm$0.030, $V_{T}$=9.568$\pm$0.024 mag, we adopt the apparent visual magnitude of 9.509$\pm$0.027mag and colour index of (B-V)=0.558$\pm$0.082mag for the system, transformed from Tycho to Johnson photometric system using the coefficients given by @hog. Taking into account the de-reddened colour index of the primary star as 0.35 mag for an F2V star and the light ratio of L$_2$ /L$_1$=0.63 we estimated de-reddened colour index for the system as 0.405 mag. Then we estimated the interstellar reddening of $E$(B-V)=0.15$\pm$0.08mag for the system. The bolometric corrections are adopted from @flo for the primary and secondary stars. The absolute bolometric magnitude of the Sun is taken as 4.74. The distance to the system is estimated as 300$\pm$50pc. The weighted mean distance calculated from the individual distances given in Table5 is 298$\pm$56pc, consistent with the distance estimated from total apparent visual magnitude and interstellar reddening of the system. As it is known that the distance measured by the $Hipparcos$ becomes inaccurate for d$>$100 pc.

V2653Oph is located, on the sky, very close to the centre of the Collinder359 open cluster. Recently [@zejda] presented the first new catalog of known variable stars in open cluster regions. They have proposed that V2653Oph is a probable member of the Collinder359. However, its membership to the Collinder359 is still uncertain. The systemic velocity of the V2653Oph, -8.4 [kms$^{-1}$]{}, is consistent with the measured cluster systemic velocities of @plasket, @nord and @gon. Interstellar reddenings for the stars in the cluster were estimated as of 0.16mag obtained by @kha and 0.191mag @zejda. The distance of the Collinder359 is still uncertain. Distance determination is in general based on isochrone fitting of early type stars. For Collinder359 listed 13 cluster members by [@col] and estimated a distance to the cluster ranging from 210pc to 290pc. Later, [@ruc] made UBVRI photometry and obtained a distance to the cluster about 436pc, rejecting half of the original members. Trigonometric parallaxes of five photometric members were measured by $Hipparcos$ satellite which yielded distances between 260pc and 280pc for Collinder359. The systemic velocity, interstellar reddening and distance of V2653Oph are in good agreement with those derived for the cluster. It seems highly probable that V2653Oph does belong to Collinder359.

The age determined for the Collinder359 has changed dramatically since the early determination by [@wi] of 20 to 50Myr. Later studies derived 30Myr [@abt]. Both results are in agreement and consistent with the more recent values range from 50Myr [@ba; @kha]. [@jef] put an upper limit of 100Myr on the age of Collinder 359 using the lithium test described by [@reb]. Comparison with the various evolutionary tracks indicates that the components of V2653Oph have an age of about 300($\pm$100)Myr, older than the cluster. If the binary is really a member of the cluster its age should be at least three times older than the values estimated up to date.

$\gamma$ Dor type variables in close binary systems
===================================================

Fig.4 shows that there is a considerable light variations at outside of eclipses. The $\gamma$ Dor type pulsating single stars and components in the eclipsing binaries were plotted in the logT$_{eff}$-logL/L$_{\odot}$ plane and shown in Fig.5. The empty symbols show the single stars taken from the catalog of @henry while the filled circles indicate the $\gamma$ Doradus type pulsators in the eclipsing binaries. The primary component of V2653Oph locates in the instability strip of $\gamma$ Doradus type variable stars. The known $\gamma$ Dor type pulsating variables in the eclipsing variables are: V551Aur, VZCVn, V2094Cyg, V404Lyr, Corot100866999, Corot102918586, Corot102937335, Corot102980178,KIC04544587, KIC11285625.

The $\gamma$ Doradus and $\delta$ Scuti type pulsators share a similar parameter space in the Hertzsprung-Russell (HR) diagram. While the $\delta$ Sct stars are believed to be mostly low-radial-order pressure mode pulsators [@bre00], the $\gamma$ Dor stars are high-radial-order gravity mode pulsators [@kaye]. [@handler02] showed that the $\delta$ Sct and $\gamma$ Dor type pulsating stars are separated by the values of their pulsation constants. While the $\delta$ Sct pulsators have pulsation constant of $Q\sim0.03$ days, the known $\gamma$ Dor pulsators all have $Q$ $>$ 0.23 days.

Therefore, we started to search any periodic light variations in the system. To investigate the intrinsic light variations of the components in eclipsing binary systems, the best-fit binary star model was subtracted from the light curve. This leaves the stellar pulsations, random noise, systematic calibration noise, and any slight mismatches between the model and actual binary star light curve. In these circumstances, frequency analysis was performed on the residuals of the system, in the region 0–3 d$^{-1}$, where the most of the dominant pulsation frequencies are found. In order to generate the frequency spectrum of residual data, shown in Fig.6, we used [Period04]{}[^5]. Figure6 displays the amplitude spectra in the frequency range from 0.6 to 2.0 d$^{-1}$, $\gamma$ Dor oscillation frequencies indeed are typically detected in this range [@balo].

The amplitude spectra after the analysis are presented in Fig.6. Clearly visible is the only a peak around 1.0 d$^{-1}$. The light variation is dominated with a frequency $f_1$=1.0029(19) and a full amplitude of about 60 mmag. The uncertainty of the frequency was derived according to [@kallinger]. No significant peaks are present in the region higher than 5 d$^{-1}$ and smaller than 0.6 d$^{-1}$. One sees that V2653Oph pulsates in the frequency range of $\gamma$ Dor type variables [@gri].

Investigation of $\gamma$-Dor type pulsating variables in close eclipsing binary systems is a relatively new area of the stellar astrophysics. The first $\gamma$ Dor type pulsation was discovered by [@iban] in the more massive primary star of the eclipsing binary system VZCVn. Following this discovery new $\gamma$-Dor pulsators were revealed by precise photometric studies. We collected the eclipsing binaries with $\gamma$-Dor pulsators and presented in Table6. So far, 11 eclipsing binary systems containing a $\gamma$-Dor type pulsating component have been discovered. Unfortunately, spectroscopic observations of only six systems have been made and precise radial velocities and, therefore, the orbital elements were determined. The number of $\gamma$-Dor type pulsators in the close binaries will be rapidly increased in a few years after the analyses of the huge precise data obtained by space missions such as $CoRot$, $Kepler$, etc.

A decade ago [@soy] suggested a linear relationship between the orbital and pulsation periods for the 20 $\delta$-Sct type pulsators in the classic Algol type systems. This relationship based on observations is confirmed and refined by [@lia] using the data almost quadruple than that of [@soy]. The correlation between the pulsation ($P_{puls}$) and orbital ($P_{orb}$) periods has been theoretically established by [@zhang]. In Table6 we present mass and radius (in solar units), mean density and surface gravity (in CGS units) and pulsation constant (in days) for the pulsating stars in the eclipsing binaries, for which precise photometric and spectroscopic observations are available. The dominant pulsation periods are taken into account and the pulsation constants were calculated using these periods and mean densities. The pulsation constants vary between 0.17 and 0.72, systematically larger than the value of 0.033 days for the radial fundamental modes [@bre; @sta].

In Fig.7 we plot the dominate pulsation periods against the orbital ones, where the periods are in days. Even with a small sample, 11 systems at present, we claimed sufficient evidence of a correlation. One possible explanation would be that according to this empirical correlation, the longer the orbital period of a binary, the longer the pulsation period of its pulsating primary. The $P_{puls}-P_{orb}$ relation appears to be a simple linear form, the following numerical relation was obtained by linear least squares method,

$$log P_{puls} = 0.425(\pm 0.016) \times \log P_{orb} - 0.355(\pm 0.087).$$

The correlation coefficient for this relationship is about 0.79, indicating its significance. The scatter appears to increase towards the shorter orbital periods.

Although the sample contains eleven pulsating primary stars and existence of a considerable scatter in the observed pulsation frequencies a connection between pulsation and orbital periods seems to exist in the $\gamma$-Dor type stars as pointed out by [@soy] for the $\delta$-Sct stars. The pulsation periods are proportional to the orbital periods as $P^{0.43}$. This relation indicates that the shorter orbital period the smaller pulsation period. For the $\delta$-Sct stars in close binaries [@lia] find a relationship as $P_{puls}$ proportional to $P_{orb}^{0.58}$.

Recently [@zhang] indicated that the upper limit of $P_{puls}/P_{orb}$ is about 0.09 for the $\delta$-Sct stars. All the stars given in Table6 have larger ratios than those of the $\delta$-Sct stars except CoRot102980178. It has the smallest ratio with 0.072. This star is not clearly classified yet. It was classified as a $\gamma$-Dor pulsator by [@sok], however, the classification as a [Slowly Pulsating B star]{} (SPB) could not be ruled out. There are some doubts about the classifications of V551 Aur and KIC04544587. Both the Q-values and period ratios lead to classification of $\gamma$-Dor type pulsation. The pulsational period is connected to the mean density in the pulsating variables. The period-mean density relationship can be written as:

$$P_{puls}= Q \sqrt{\rho_{\odot}/\rho}$$

where Q is the pulsation constant, $\rho$ and $\rho_{\odot}$ are the mean density of the star and the sun. The mean density is expressed by the mass and radius of the star. Then the above equation can be rearranged to the form:

$$P_{puls}= Q \sqrt{ \frac{R_{puls}^3}{M_{puls}} }$$

where R$_{puls}$ and M$_{puls}$ are the radius and mass of the pulsating star. Solving the Kepler’s Third law for the mass of the pulsator and inserting to the above equation we obtain,

$$P_{puls}= Q \times P_{orb} \times \bigg\{G \times \frac{R_{puls}^3} {4\pi^2 \times a^3}\bigg\}^{\frac{1}{2}} 
\times \bigg\{1-\frac{M_s}{M_{puls} + M_{s}}\bigg\}^{-\frac{1}{2}}$$

where P$_{orb}$ is the orbital period, $a$ is the semi-major axis of the eclipsing system’s orbit and M$_{s}$) is the mass of the secondary star and G is the Newton’s gravitational constant. This expression indicates that the pulsational period of a pulsator in an eclipsing binary is depended up on the orbital period.

We also plot the pulsation periods against the gravities of the pulsating stars in Fig.8, where the pulsational periods are in days and the gravities in CGS units. The open square in this figure shows V404Lyr for which no radial velocities exist, the gravity is estimated from the preliminary mass and radius determined only from the light curves. Therefore it was not used in the calculation of the correlation between the pulsational period and gravity. Gravities were calculated for only six $\gamma$-Dor type pulsators in the close binaries for which radial velocities and photometric light curves exist. A preliminary least squares analysis yields a relationship between the pulsational period and gravity as,

$$log P_{puls} = -0.828(\pm 0.076) \times \log g + 3.385(\pm 0.218)$$

with a correlation coefficient of 0.81. The pulsational periods are decreasing while the surface gravities are increasing, similar to the $\delta$-Sct stars (dot-dashed line in Fig.8) [@lia] and to those all radially pulsating variable stars (dashed line) [@fer]. While the slope is about -3.3 for the $\delta$-Sct stars, -0.88 for the radially pulsating variable stars. The pulsation periods of $\gamma$-Dor type pulsators seem to depend on the surface gravity similar to those radially pulsating variable stars proposed by [@fer].

The gravitational force applied to per gram matter on the surface of the pulsating component can be determined by

$$g =  G \times \frac{M_{puls}} {R_{puls}^2}.$$

Since P$_{puls}$ depends on the R$_{puls}$ and M$_{puls}$ as given in Eq.4 we can easily obtain,

$$P_{puls} = Q \times G^{\frac{1}{2}} \times R_{puls}^{ \frac{1}{2}} \times g^{-\frac{1}{2}}$$

The pulsational period is inversely proportional of the square root of the surface gravity of the pulsating star.

We also plot in Fig.9 the pulsational periods of the oscillating primary components against the gravitational pull exerted to the per gram of the matter on the surface of the pulsators by the less massive companions (in cgs units). The short orbital period binary VZ CVn appears to have longer pulsational period with respect to the gravitational pull of the companion. This star is significantly separated from the other stars. It has the greatest filling factor with 0.78 amongst the six stars (see Table6). Excluding VZ CVn, the linear least-squares fit gives the following relationship,

$$log P_{puls} = -2.021(\pm 0.012) \times \log (F/M_{puls}) + 2.093(\pm 0.098)$$

with a correlation coefficient of 0.83. The high-value of the correlation coefficient indicates that this empirical relationship is very significant. As the force per unit mass on the surface of the pulsating star applied by the companion star is increased the pulsational period is decreased. The force exerted to per gram matter on the surface of the pulsating star can be calculated as,

$$\frac{F} {M_{puls}} = \frac{GM_{s}} {(a-R_{puls})^2}.$$

Since $P_{puls}$ $\propto$ $R_{puls}^{3/2}$ we can obtain $P_{puls}$ $\propto$ $(\frac{F}{M_{puls}})^{-3/4}$. As the gravitational pull exerted on the per gram matter of the pulsator is increased the pulsational period is decreased, confirming the empirical relationship found.

Even with a small sample, pulsation periods of the $\gamma$-Dor type pulsators in the close binaries seem to depend on the orbital periods of the systems, to the surface gravities of the pulsating primaries, and also to the gravitational pull applied by their companions. These empirical relationships should, of course, be checked by increasing the number of the sample.

Although we are still at the beginning of understanding the whole extent of the $\gamma$ Doradus phenomenon, but the combination of the current observational results and theoretical models are expected to answer a lot of open questions. Verification of the present results, especially for the low amplitude frequencies, the detection of the multi-frequencies, and the derivation of the excitation modes are some open questions on the class of $\gamma$ Dor type asteroseismology. We strongly suggest that accurate photometric survey of these systems are needed for answering the listed open questions. Moreover, phase coverage of their light curves and radial velocities will provide their geometrical characteristics. Finally, high-resolution spectroscopy are also suggested not only for the pulsations, but also for the components’ radial velocity curves, which will lead us to calculate their absolute properties with high accuracy.

Conclusion
==========

V2653Oph is a detached eclipsing binary in the young open cluster Collinder359. It is composed of main sequence F type stars. We have derived the astrophysical parameters of the components and other properties for the first time, listed in Table5, by combining the results obtained from the analyses of light curve and radial velocities. The masses and radii of the stars were derived with accuracy of 2 and 6 percent, respectively. Both components are well inside their corresponding Roche lobes. Both components show nearly synchronized rotation. Taking into account the total apparent visual magnitude of the system, the light contribution of the stars and the bolometric corrections given by [@flo] and [@gir] we calculated a mean distance to V2653Oph as 300$\pm$50pc. The published parallax, measured by $Hipparcos$ satellite is very uncertain, $\pi$=3.72$\pm$1.28mas, corresponding to a formal distance of 269$_{-68}^{+141}$ pc. The distance we derived is in good agreement with that of $Hipparcos$, but is more accurately determined. Both the interstellar reddening of 0.15$\pm$0.08mag and a distance of 300pc are supporting the membership of the Collinder359.

After subtracting the binary model the residual light curve is obtained and analized for additional periodic signals. This analysis shows pulsation with a dominant frequency of about $f_1$=1.0029$\pm$19c/d, corresponding to 0.9971$\pm$0.0019 d. We calculate the pulsation constant as 0.479 days. The spectral type of the primary star, the dominant pulsation period and pulsation constant suggest that the more massive primary star is most probably a $\gamma$ Doradus type pulsator. As it is shown in Fig.5 the pulsating primary star locates well inside the $\gamma$ Dor instability strip of the Hertzsprung-Russell diagram. The primary star seems to pulsate in multiperiodic modes. Further continuous multi-band photometric observations are needed for a better determination of the pulsational periods and amplitudes.

We have suggested preliminary empirical relationships between the pulsation and orbital periods. In addition the pulsation periods of the primaries seem to correlate with their surface gravities and gravitational pull applied by their secondaries. We present some theoretical considerations which explain underlying physics behind these empirical relationships. Moreover, a physical interpretation of the empirical relations correlating the pulsation and orbital periods, and the location in the HR diagram with the evolutionary stage of the $\gamma$ Dor components in close binaries is certainly needed. Future theoretical pulsational mechanisms for pulsational behavior should take into account quantities such as mass, radius, radius expansion rate and dominant pulsation period. New observations of the binaries containing $\gamma$ Dor type components will increase the current example to better characterization of this type of asteroseismology.

  System                                       P$_{orb}$   P$_{puls}$    $q$     M$_p$/M$_{\odot}$   $r_p$,R$_{\odot}$   $\rho$   g, $\log$g   $r{_p}/r_{Roche}$    $Q$    M$_s$   $a$(R$_{\odot}$)   F/M$_p$           Ref
  ------------------------------------------- ----------- ------------ -------- ------------------- ------------------- -------- ------------ ------------------- ------- ------- ------------------ --------- ------------
  V551Aur ($\delta$ Sct?)                       1.1732      0.12892     0.725                              0.221         0.7500                      0.539                                                           [@Liu]
  VZCVn                                         0.84246     1.06876     0.778          1.83               0.3115         0.4985     16778            0.777         0.635   1.42         5.554          2663         [@iban]
                                                                                                           1.730                    4.225                                                                      
  V2094Cyg                                     8.485376      1.0995     0.4637         1.79               0.1024         0.1673      8045            0.229         0.379   0.83         24.13          48.5         [@caki]
                                                             1.0428                                        2.471                    3.906                          0.359                                       
  V404Lyr                                      0.730943     0.50643     0.385          1.35               0.4200         0.3500     12023                                                                            [@Lee]
                                                            4.47356                                        1.76                      4.08                                                                      
  V2653Oph                                      4.39429      0.9971     0.792          1.53               0.1192         0.3248     11879            0.299         0.479   1.292        15.98           178      This paper
                                                                                                           1.88                     4.075                                                                      
  CoRot100866999                                2.80889     0.62680      0.65                              0.158                                     0.378                                                           [@cha]
                                                            0.73210                                                                                                                                            
  CoRot102918586                                4.39138     0.81665     0.898          1.66               0.0992         0.5308     16936            0.256         0.501   1.49         16.53           184          [@mac]
                                                            0.88758                                        1.64                     4.229                          0.545                                       
  CoRot102937335                                3.97946      1.5772     0.3669                            0.1081                                     0.229                                                           [@dam]
                                                             1.5748                                                                                                                                            
  CoRot102980178 ($\gamma$Dor or SPB?)          5.0548       0.3637     0.206                             0.1068                                                                                                     [@sok]
  KIC04544587 ($\gamma$Dor or $\delta$Sct?)    2.189094     0.49721     0.808          1.98               0.1677         0.4633     16403            0.421         0.285   1.60         10.855          538          [@ham]
                                                             0.2883                                        1.82                     4.215                          0.165                                       
  KIC11285625                                  10.79049      1.7937     0.778          1.543              0.0737         0.2275      9376            0.184         0.720   1.200         28.8          46.6        [@debos]
                                                             1.7627                                        2.123                    3.972                          0.708                                       

Acknowledgments {#acknowledgments .unnumbered}
===============

This study is supported by Turkish Scientific and Technology Council under project number 112T263. The following internet-based resources were used in research for this paper: the NASA Astrophysics Data System; the SIMBAD database operated at CDS, Strasbourg, France.

[00]{} Abt H. A., Bollinger G., Burke E. W., Jr., 1983, ApJ, 272, 196 Baglin, A., Auvergne, M., Barge, P., et al. 2009, IAU Symposium, 253, 71 Balona L. A., Guzik J. A., Uytterhoeven K., Smith J. C., Tenenbaum P., Twicken J. D., 2011, MNRAS, 415, 3531 Baumgardt H., Dettbarn C., Wielen R., 2000, A&AS, 146, 251 Breger, M. 1990, DSSN, 2, 13 Breger, M. 2000, in Breger, M., Montgomery, M.H., eds., ASP Conf. Ser., 210, Delta Scuti and Related Stars, p.3 Chapellier, E., & Mathias, P. 2013, A&A, 556, A87 Collinder P., 1931, AnLun, 2, 1 Conti, P. S., & Ebbets, D., 1977, ApJ, 213, 438 ak[i]{}rl[i]{} [Ö]{}., 2015, NewA, 38, 55 ak[i]{}rl[i]{} [Ö]{}., Ibano[ǧ]{}lu C., Southworth J., Frasca A., Hernandez J., 2008, MNRAS, 389, 205 Damiani, C., Maceroni, C., Cardini, D., et al. 2010, Ap&SS, 328, 91 Debosscher, J., Aerts, C., Tkachenko, A., et al. 2013, A&A, 556, A56 Fernie, J. D. 1995, AJ, 110, 2361 Flower, P. J. 1996, ApJ, 469, 355 Frasca, A., Guillout, P., Marilli, E. 2006, A&A, 454, 301 Gilliland, R. L., Brown, T. M., Christensen-Dalsgaard, J., et al. 2010, PASP, 122, 131 Girardi, L., Bertelli, G., Bressan, A., et al. 2002, A&A, 391, 195 Gontcharov G. A., 2006, AstL, 32, 759 Grigahc[è]{}ne A., et al., 2010, ApJ, 713, L192 Hambleton, K. M.,Kurtz, D. W., Pr[š]{}a, A., et al. 2013, MNRAS, 434, 925 Handler, G., & Shobbrook, R. R. 2002, MNRAS, 333, 251 Hanson, R. B., Klemola, A. R., Jones, B. F., & Monet, D. G. 2004, AJ, 128, 1430

, J. D., [Gaudi]{}, B. S., [Holman]{}, M. J., [et al.]{} 2008, ApJ, 675, 1254 Henry G. W., Fekel F. C., Henry S. M., 2007, AJ, 133, 1421 H[ø]{}g, E., Fabricius, C., Makarov, V. V., et al. 2000, A&A, 355, L27 Ibano[ǧ]{}lu, C., Ta[ş]{}, G., Sipahi, E., & Evren, S. 2007, MNRAS, 376, 573 Jeffries R. D., Naylor T., 2001, ASPC, 243, 633 Kallinger, T., Guenther, D. B., Matthews, J. M., et al. 2008, A&A, 478, 497 Kane S. R., Schneider D. P., Ge J., 2007, MNRAS, 377, 1610 Kaye A. B., Handler G., Krisciunas K., Poretti E., Zerbi F. M., 1999, PASP, 111, 840 Kazarovets E. V., Samus N. N., Durlevich O. V., et al., 1999, IBVS, 4659, 1 Kharchenko N. V., 2001, KFNT, 17, 409 Lee, J. W., Kim, S.-L., Hong, K., Lee, C.-U., & Koo, J.-R. 2014, AJ, 148, 37 Lenz, P., & Breger, M., 2005, Communications in Asteroseismology, 146, 53 Liakos, A., Niarchos, P., Soydugan, E., & Zasche, P. 2012, MNRAS, 422, 1250 Liu, N., Zhang, X.-B., Ren, A.-B., Deng, L.-C., & Luo, Z.-Q. 2012, Research in Astronomy and Astrophysics, 12, 671 Maceroni, C., Montalb[á]{}n, J., Gandolfi, D., Pavlovski, K., & Rainer, M. 2013, A&A, 552, A60 Mendoza, E. E., Gomez, V. T., & Gonzalez, S. 1978, AJ, 83, 606 Nordstr[ö]{}m B., et al., 2004, A&A, 418, 989 Ochsenbein, F., 1980, Bull. Inf. CDS, 19, 74 Otero, S. A., Wils, P., & Dubovsky, P. A. 2005, IBVS, 5586 Penny, L. R., 1996, ApJ, 463, 737 , M. A. C., [Lindegren]{}, L., [Kovalevsky]{}, J., [et al.]{} 1997, A&A, 323, L49 Plaskett J. S., Pearce J. A., 1931, PDAO, 5, 1 Pojmanski, G. 1997, AcA, 47, 467

Pojmanski, G., 2002, AcA,52, 397 Prša A., Zwitter T., 2005, ApJ, 628, 426 Rebolo R., Martin E. L., Basri G., Marcy G. W., Zapatero-Osorio M. R., 1996, ApJ, 469, L53 Rucinski, S. M. 1987, PASP, 99, 487

Schwarzenberg-Czerny, A. 1989, MNRAS, 241, 153 Sokolovsky, K., Maceroni, C., Hareter, M., et al. 2010, Communications in Asteroseismology, 161, 55 Southworth J., Smalley B., Maxted P. F. L., Claret A. & Etzel P. B. 2005, MNRAS, 363, 529 Soydugan, E.,[İ]{}bano[ǧ]{}lu, C., Soydugan, F., Akan, M. C.,& Demircan, O. 2006, MNRAS, 366, 1289 Stankov, A., & Handler, G. 2005, ApJS, 158, 193 Takeda Y., Hashimoto O., Taguchi H., Yoshioka K., Takada-Hidai M., Saito Y., Honda S., 2005, PASJ, 57, 751 Valdes, F., Gupta, R., Rose, J. A., Singh, H. P., & Bell, D. J., 2004, ApJS, 152, 251 van Hamme, W., 1993, AJ, 106, 2096 Walker, G., Matthews, J., Kuschnig, R., et al. 2003, PASP, 115, 1023 Warner P. B., Kaye A. B., Guzik J. A., 2003, ApJ, 593, 1049 Wielen R., 1971, A&A, 13, 309 Wilson, R. E., & Devinney, E. J. 1971, ApJ, 166, 605 Wilson, R. E., 1979, ApJ, 234, 1054 Wilson, R. E., 2006, Astrophysics of Variable Stars, ASPC, 349, 71 Wilson, R. E., & van Hamme, W. 2003, [*Computing Binary Star Observables*]{}, Dept., University of Florida, Gainesville, FL 32611 Wu, Y., Singh, H. P., Prugniel, P., Gupta, R., & Koleva, M. 2011, A&A, 525, 71 Zejda M., Paunzen E., Baumann B., Mikul[á]{}[š]{}ek Z., Li[š]{}ka J., 2012, A&A, 548, AA97 Zhang X. B., Luo C. Q., Fu J. N., 2013, ApJ, 777, 77

![Radial velocities phased with the Eq.1 of the primary (open circles) and secondary (red filled circles) component of V2653Oph. Error bars are shown by vertical line segments, which are smaller than symbol sizes. The solid and dashed lines are the computed radial velocity curves for the component stars. []{data-label="rv"}](RV.ps){width="9cm" height="13cm"}

![image](ex.ps){width="17cm" height="7.5cm"}

![Sample of CCFs between V2653Oph and the RV template spectrum ($\iota$Psc) around the first and second quadratures. []{data-label="lightrat"}](ccfig1.ps){width="10cm" height="16cm"}

![image](lc.ps){width="16cm" height="20cm"}

![image](gen_eco.ps){width="13.5cm" height="17cm"}

![Periodogram of the detected frequency inside the $\gamma$ Dor frequency range for the system. The significance level (∼ 0.006 mag) is indicated. []{data-label="rv"}](zonk.ps){width="8.5cm" height="13cm"}

![Relation between the pulsational and orbital periods for $\gamma$ Dor type stars in eclipsing binaries. The solid line represents the best fit with an equation given in the text. ](puls7.ps){width="14cm" height="11cm"}

![Plot of the pulsational periods versus the gravity of the pulsating stars (filled squares). The solid line represents the best fit between two parameters. The open square symbol shows V404Lyr for which no spectroscopic observation exists. The relation, $P_{puls}$ - $g$ for the $\delta$-Sct stars (dot-dashed line) [@lia], and for radially pulsating variable stars (dashed line) [@fer] are also shown for comparison. The gravities for radially pulsating stars were shifted one dex for a better comparison. ](puls8.ps){width="14cm" height="11cm"}

![Relation between the pulsational period and the force on the surface of the pulsating star due to the companion per unit mass of the pulsating star for $\gamma$ Dor type stars in eclipsing binaries. The system VZ CVn (shown by empty circle) is considerably distinguished from the other five systems(see text). The solid line represents the best fit with an equation given in the text, excluding VZ CVn. ](puls9.ps){width="14cm" height="11cm"}

[^1]: adopted from the SIMBAD astronomical data base.

[^2]: IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc.

[^3]: Interactive Data Language, ITT 1997

[^4]: This can be obtained from http://http://www.astro.keele.ac.uk/$\sim$jkt/codes.html

[^5]: https://www.univie.ac.at/tops/Period04/
