Towards Understanding the Nature of Young Detached Binary System HD 350731
F. Soydugan, F. Alicavus, S. Bilir, E. Soydugan, C. Puskullu, T. Senyuz
aa r X i v : . [ a s t r o - ph . S R ] J un Towards Understanding the Nature ofYoung Detached Binary System HD 350731
F. Soydugan and F. Ali¸cavu¸s Department of Physics, Faculty of Arts and Sciences, C¸ anakkale Onsekiz Mart University,TR-17100 C¸ anakkale, Turkey [email protected]
S. BilirDepartment of Astronomy and Space Science, Faculty of Science, ˙Istanbul University,TR-34119, University-Istanbul, TurkeyandE. Soydugan , C¸ . P¨usk¨ull¨u and T. S¸eny¨uz Department of Physics, Faculty of Arts and Sciences, C¸ anakkale Onsekiz Mart University,TR-17100 C¸ anakkale, TurkeyReceived ; acceptedNot to appear in Nonlearned J., 45. Astrophysics Research Center and Ulupınar Observatory, C¸ anakkale Onsekiz Mart Uni-versity, TR-17100, C¸ anakkale, Turkey 2 –
ABSTRACT
The young binary system HD 350731 is a noteworthy laboratory for study-ing early-type binaries with similar components. We present here the analy-sis of differential multi-color photometric and spectroscopic observations for thedouble-lined detached system. Accurate absolute parameters were determinedfrom the simultaneous solution of light and radial velocity curves for the firsttime. HD 350731 consists of two B8V-type components having masses and radiirespectively of M = 2 . ± .
13 M ⊙ , M = 2 . ± .
14 M ⊙ , R = 2 . ± .
05 R ⊙ and R = 2 . ± .
05 R ⊙ . The effective temperatures were determined based onanalysis of disentangled spectra of the components and derived to be 12000 ± ±
300 K for the primary and secondary components, respectively.The measured projected rotational velocities, 69.2 ± − for primary and70.1 ± − for secondary, were found closer to the pseudo-synchronous ve-locities of the components. Comparison with evolutionary models suggests an ageof 120 ±
35 Myr. Kinematic analysis of the unevolved binary system HD 350731revealed that it belongs to the young thin-disc population of the Galaxy.
Subject headings: stars: fundamental parameters — stars: binaries: eclipsing — stars:individual: HD 350731 — Techniques: photometric, spectroscopic.
1. Introduction
Precise knowledge of the absolute parameters of stars (mass, radii, etc.) is a meansto better understand the structure and evolution of galaxies. Eclipsing binary stars arethe most important objects for determining these basic parameters of stars. In order toderive the mass, radius, temperature and other physical parameters of eclipsing binarystars, spectroscopic, photometric -and interferometric data are required. In particular, thequality of the observational data plays crucial role in determining the absolute parametersof the component stars precisely. Among the eclipsing binary stars, detached double-linedspectroscopic binaries are the best sources for acquiring more accurately the main physicalproperties of stars (e.g. Southworth 2013, Lacy et al. 2015). Well measured detachedeclipsing binaries have been recently listed and studied based on distributions of theirabsolute parameters by Torres et al. (2010) and Eker et al. (2014).HD 350731 (BD+20 4323, GSC 01624-00493, V = 9 m .60) was identified as an eclipsingbinary system with eccentric orbit by Otero et al. (2004). In the AGK3 catalogue, thespectral type of the system is given as A0 by Heckmann (1975) based on the Henry Draper(HD) catalogue (Pickering and Cannon 1918-1924). However, Nesterov et al. (1995)suggested it was B9 using the extension charts of HD catalogue. The first photometricstudy, based on BV R c I c light curves, was conducted by Kleidis et al. (2008) in which, inaddition to preliminary photometric analysis, it was suggested that HD 350731 indicatesapsidal motion.In this study, the first detailed photometric and spectroscopic analysis was carried out,based on newly-obtained data. After descriptions of the spectroscopic and photometricobservations, Section 3 presents spectral analysis, which contains radial velocitymeasurements of the components, preliminary orbit solution, spectroscopic light ratio,spectral disentangling and model atmosphere application. Analysis of multi-color light 4 –and radial velocity curves is given in Section 4, followed by apsidal motion analysis. Theabsolute parameters and kinematic properties of the system are detailed in Sect. 6. Finally,we conclude the study with the results and discussions.
2. Observations
New multi-color photometric observations of HD 350731 were performed at C¸ anakkaleOnsekiz Mart University Ulupınar Observatory, Turkey over 11 nights in August andSeptember 2012. Observations were carried out with a 60 cm Cassegrain telescope equippedwith SBIG STL1001E CCD camera. One secondary minimum was also observed with a 122cm Cassegrain-Nasmyth telescope incorporating Apogee Alta U42 CCD camera. The datawere collected using Bessell B , V and R c filters. HD 350730 (A0) and HD 350727 (F5)were used as comparison and check star, respectively. CCD frames were reduced in thestandard way: bias and dark frames were subtracted from the frames and then corrected forflat-fielding. Such reduced images were used to extract the differential magnitudes of HD350731. C-Munipack code was used for these processes. Standard deviation of variationsbetween the observed comparison and check stars was determined to be about 0 m .01 for allpassbands.Spectroscopic observations of HD 350731 were made using the Cassegrain spectrographinstalled on the 1.85 m Plaskett telescope at Dominion Astrophysical Observatory (DAO),British Columbia, Canada. The spectrograph has a spectral resolving power of about R = 9000. A back-illuminated SITe CCD of 1752 ×
532 pixels (size 15 µ m) was used torecord spectra spanning from about 4370 to 4630 ˚A. During the observations, twenty onespectra for HD 350731 and several spectra for 21 Peg were taken. The spectra of the http://c-munipack.sourceforge.net/ 5 –reference star 21 Peg were used to measure the radial velocities of the components. Allspectral data were acquired between 6 August and 6 September 2012. Spectroscopic datareduction was handled using the appropriate tasks of IRAF package with the followingsteps: background subtraction, division by flat field spectrum, wavelength calibration usingFe-Ar lamp, and normalization to the continuum.
3. Spectroscopic Analysis3.1. Radial Velocities and Preliminary Orbital Solution
In order to determine the orbital parameters of HD 350731, the radial velocities (RVs)of the components must be measured. Taking into account the spectral type of the system,given as B9 by Nesterov et al. (1995), 21 Peg (B9.5V, V r = − . − ) was chosen as theRV standard star for both components. The cross-correlation technique (CCT) was usedfor determination of RVs of the components. Simkin (1974) reported an useful descriptionof CCT which are widespread, especially for RV measurements of binary stars (e.g. Hill1993, Gunn et al. 1996, Frasca et al. 2002, Soydugan et al. 2007). The CCT was appliedby FXCOR routine in the IRAF package which was developed based on the standard Tonry& Davis (1979) algorithm. The weights of RVs and their standard errors were calculatedaccording to the usual formulas given by Topping (1972) and Tonry & Davis (1979). Themeasured RVs of both components are given in Table 1 together with their standard errors,which are between 4-9 km s − for the components.As can be seen in the light curves of the system, the secondary minimum is notlocated at the 0.5 orbital phase and indicates a displacement comparing primary minimum.Therefore, most probably HD 350731 has an eccentric orbit and this must be taken into http://iraf.noao.edu/ 6 –Table 1: Radial velocity measurements of components of HD 350731. HJD Orbital V V
24 50000+ Phase (km s − ) (km s − )6173.8976 0.0773 -72.9 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Spectroscopic line ratios ensure us constraints on the luminosity ratios of thecomponents determined from the light curve solutions at similar wavelengths, as reportedin the study of Petrie (1939) and applied in many studies (e.g. Andersen et al. 1983,Southworth & Clausen 2007, Garcia et al. 2014). This also helps us to reduce thedegeneracy, which occurs in the light curve solutions of eclipsing binaries with similarcomponents for the radii of the components, if the binary are partially eclipsing system. Inthis study, we have derived spectroscopic light ratio for the system using the spectral lineof MgII at 4481 ˚A. Equivalent widths ( EW ) of MgII lines for the both components weremeasured using SPLOT task in the IRAF package on seven spectra taken at the phasesout of the eclipses. The weighted mean ratio was found to be EW /EW = 0.953 ± In order to derive the atmospheric parameters of the components of HD 350731,individual spectrum for each component is required. The method of spectral disentangling 8 –Table 2: Orbital elements of HD 350731.
Parameter Value T (HJD) 2454631.4603 P orb (day) 1.635135 V γ (km s − ) -10.4 ± K (km s − ) 157.2 ± K (km s − ) 162.7 ± e ± ω (degree) 23.5 ± a sin i (10 km) 3.52 ± a sin i (10 km) 3.64 ± M sin i (M ⊙ ) 2.79 ± M sin i (M ⊙ ) 2.70 ± q (=M /M ) ± Kleidis et al. (2008) V γ ) could be determined with KOREL. However, the radial velocities of the componentsderived from KOREL are not independent as noted by Lehmann et al. (2013). Therefore,we used the orbital properties listed in Table 2 as input data for KOREL application.Finally, we derived the radial velocity amplitudes ( K and K ) from two different methods,which are compatible within better than 2 km s − . The fractional light contribution ofthe components determined from spectroscopic analysis was used for the application. Atthe end of the process, separate spectra of the primary and secondary components wereobtained. Some observed composite spectra of the system at different orbital phases,together with the model spectra and decomposed spectrum of the components calculatedby KOREL in the wavelength range 4450-4500 ˚A, are shown in Figure 1. The physical parameters of the components of HD 350731 can be derived from analysisof the radial velocities of the components and light curves. On the other hand, if one 10 –Fig. 1.— Fits calculated by KOREL (thick lines) to observed spectra (thin lines) at differentorbital phases (a), and disentangled spectra of primary and secondary components (b) inwavelength range 4450-4500˚A. 11 –can obtain decomposed spectra of the components, their atmospheric parameters can befound by line-profile fitting. The advantages of spectral disentangling method for thespectroscopic analysis of the eclipsing binaries’ components are presented in the studies ofHensberge et al. (2000) and Pavlovski & Hensberge (2005). Therefore, we obtained theindividual spectrum of the components of HD 350731 considering these previous studies tomake spectral analysis. The SME (Spectroscopy Made Easy) code, which enabled us todetermine the basic atmospheric parameters of the components by matching the computedspectrum to the observed one was used for the analysis. SME was developed by Valenti &Piskunov (1996) and includes several model atmospheres to compute synthetic spectra. Thecode uses Levenberg-Marquardt algorithm to fit an observing spectrum with a syntheticone. The code has been applied in many studies to determine the atmospheric properties ofstars (e.g. Torres et al. 2012, Soydugan et al. 2013). For the application, Kurucz (1993)model atmospheres were used and the atomic data for the spectral lines were taken fromthe Vienna Atomic Line Database (Piskunov et al. 1995; Kupka et al. 1999).The disentangled spectrum of both components in the wavelength region 4375-4575˚Aincluded Mg II at 4481 ˚A and He I at 4471 ˚A spectral lines. These data were used tocompute of the model atmospheres. The microturbulent velocities for the componentswere adopted to be 3 km s − , which is an appropriate value for late-type B stars (e.g.Adelman 1996, Usenko et al. 2000). The surface gravities of both components were fixedat the dynamical values determined from solution light and radial velocity curves (seeTable 8). After preparing SME code to fit the spectrum of the components of HD 350731,atmospheric parameters, namely T eff and v sin i adjusted during the analysis have beendetermined assuming solar abundance taken from Asplund et al. (2009). The resultedparameters and their uncertainties estimated using the ∆ χ min = 1 method as described byLampton et al. (1976) are listed in Table 3 . In Fig. 2, the decomposed spectra of thecomponents and the synthetic spectra calculated by the best model parameters in Table 12 –3 are compared. The figure also shows the observed composite spectrum of HD 350731together with the computed spectrum, which was calculated by the model atmosphereparameters in Table 3, taking into account light contributions at the orbital phase of 0.2.The synthetic composite binary spectrum in Fig. 2 was calculated by using BinMag IDLvisualization code (developed by O. Kochukov). As seen in Fig. 2, the synthetic spectraagree well with the composite binary spectrum and individual spectra of the components.Table 3: Model atmosphere parameters of the components of HD 350731. Primary SecondaryParameter Value Value T eff (K) 12000 ±
250 11830 ± g (cgs) 4.25 v sin i (km s − ) 69.2 ± ± Dynamical values adopted from analysis of light and radial velocity curves.
13 –Fig. 2.— Disentangled spectra of components with best model atmosphere fits. Compari-son between observed composite binary spectrum and computed spectrum calculated withparameters in Table 3. 14 –
4. Analysis of Light and Radial Velocity Curves
The
BV R c light curves and radial velocities of the components of HD 350731 have beenmodeled using the version v34 of JKTEBOP code (Southworth et al. 2004, Southworthet al. 2005a, Southworth 2013). The code is based on the EBOP program, which wasdeveloped by P. Etzel (Etzel 1981, Popper & Etzel 1981). It was written in FORTRAN77by J. Southworth and uses Levenberg-Marquardt algorithm to reach the best model.We preferred JKTEBOP code since it was stable, and very fast and includes variouserror-estimate algorithms. This code is also very useful for well-detached eclipsing binariesas tested in several studies (e.g. Ratajczak et al. 2010, Debosscher et al. 2013, Lehmann etal. 2013).HD 350731 is a partially eclipsing binary with almost identical components. In thatcase, the degeneracy may occur in determination of the radii of the components. Therefore,we used spectroscopic line ratio as given in the Section 3.2 to constrain the range of theratio of the radii ( k ). As the first step, the luminosity ratio was adopted at 0.953 asdetermined from the spectroscopy during the analysis of B light curve since MgII line at4481 ˚A was used to derive spectroscopic light ratio. Thus, the k value was found to be0 . ± . k value and also examine the distributions of k valuesagainst to surface brightness ratio of the components ( J /J ), these two parameters werescanned corresponding χ values of each solution. Then, χ values of the solutions weremapped into contours which indicate the uncertainties in Fig. 3. As shown in the figure, the k value of 0.993 can be seen around the lowest χ value. After that, the resulted k = 0 . V and R c light curves. The third light contribution( l ) was assumed to be 0.0 after several iterations since it did not vary significantly. Wehave used the linear limb darkening coefficients as adopted parameters for the components J /J ), sum of the fractional radii ( r + r ), ratio of fractional radii ( k ) for only B filter, orbital inclination ( i ), eccentricity ( e sin ω , e cos ω ), phase shift, radial velocityamplitudes of the components ( K and K ) and the systemic velocity ( V γ ). 16 – (cid:19)(cid:17)(cid:19)(cid:19)(cid:19)(cid:17)(cid:19)(cid:21)(cid:19)(cid:17)(cid:19)(cid:23)(cid:19)(cid:17)(cid:19)(cid:25)(cid:19)(cid:17)(cid:19)(cid:27)(cid:19)(cid:17)(cid:20)(cid:19)(cid:19)(cid:17)(cid:20)(cid:21)(cid:19)(cid:17)(cid:20)(cid:23)(cid:19)(cid:17)(cid:20)(cid:25)(cid:19)(cid:17)(cid:20)(cid:27)(cid:19)(cid:17)(cid:21)(cid:19)(cid:19)(cid:17)(cid:21)(cid:21)(cid:19)(cid:17)(cid:21)(cid:23)(cid:19)(cid:17)(cid:21)(cid:25)(cid:19)(cid:17)(cid:21)(cid:27)(cid:19)(cid:17)(cid:22)(cid:19)(cid:19)(cid:17)(cid:22)(cid:21)(cid:19)(cid:17)(cid:22)(cid:23)(cid:19)(cid:17)(cid:22)(cid:25)(cid:19)(cid:17)(cid:22)(cid:27)(cid:19)(cid:17)(cid:23)(cid:19)(cid:19)(cid:17)(cid:23)(cid:21)(cid:19)(cid:17)(cid:23)(cid:23)(cid:19)(cid:17)(cid:23)(cid:25) (cid:21)
Fig. 3.— Contour map indicating the distribution of the results from B light curve analysisfor the correlated parameters of surface brightness ratio ( J /J ) and ratio of fractional radii( k ) of the components. The position of the plus symbol in the figure represents minimum χ value. 17 –In order to determine uncertainties for the solutions, we used task 9 of JKTEBOPcode and calculated 1 σ errors with Monte Carlo algorithm. The resulted parameters arepresented in Table 4 together with their uncertainties for B, V and R c filters. The adoptedphotometric parameters, which are the weighted mean of the solutions in each filter, arelisted in Table 5. In this table, the final orbital parameters and also their uncertaintiescalculated by JKTEBOP are also given. A comparison between observed and computedlight curves is presented in Fig. 4 together with the residuals of the observational data fromthe best fits, while the RVs of the components together with the best fits are shown in Fig.5.
5. Apsidal Motion Analysis
The apsidal motion of HD 350731 was indicated for the first time by Kleidis et al.(2008). In order to establish a preliminary estimation of the apsidal motion elements basedon the commonly-used method of O − C data analysis, we collected published minima timesand determined two primary and two secondary minima times from our observations, aslisted in Table 6. In total, 15 minima times were achieved.The analysis was made using code written by Zasche et al. (2009), which was developedbased on the mathematical methods reported by Gim´enez & Garcia-Pelayo (1983). For theanalysis, the orbital inclination and eccentricity were adopted as i = 81 ◦ .
70 from the lightcurve analysis and e =0.079 from the orbital analysis. The resulting preliminary apsidalmotion parameters are given in Table 7, while the O − C diagram with theoretical fits isshown in Fig. 2. The changing rate in longitude of the periastron is ˙ ω = 0 . ± . − , which corresponds to an apsidal motion period of U =92 yr. As seen inTable 7, the errors of the parameters are high and the parameters are not sensitive since 15minima times, which cover only 9 yr, were used for the analysis. However, the results can 18 –Table 4: Parameters of HD 350731 obtained from analysis of multi-color light curves andradial velocities of components. Parameters
B V R c r + r ± ± ± k ± r ± ± ± r ± ± ± i ( ◦ ) 81.83 ± ± ± J /J ± ± ± e sin ω ± ± ± e cos ω ± ± ± Fixed during the analysis.
Table 5: Final values of photometric and spectroscopic parameters for HD 350731.
Parameters Value r ± r ± i ( ◦ ) 81.703 ± L /L ( B ) 0.952 ± L /L ( V ) 0.961 ± L /L ( R c ) 0.961 ± e ± ω ( ◦ ) 24.63 ± K (km s − ) 157.44 ± K (km s − ) 163.14 ± V γ (km s − ) -10.29 ±
19 –Fig. 4.— Observed and theoretical light curves of HD 350731 in
BV R c filters (a) and theresiduals from the best fits (b). 20 –Fig. 5.— RV curves of components of HD 350731 plotted versus orbital phase. Filled andopen circles represent RVs of primary and secondary components, respectively. Solid linerepresents orbital solution for primary component and dashed line for secondary component.The residuals are indicated below. 21 –be accepted for a preliminary estimation of the apsidal motion properties and improved byadding new times of minima.
6. Absolute Properties and Kinematic Behavior
Analysis of the light curve of HD 350731 and the radial velocities of its componentsled to acquisition of its accurate absolute dimensions and physical properties for the firsttime. In order to calculate absolute parameters and their uncertainties except effectivetemperatures, which were determined from spectral analysis, we used the JKTABSDIMcode, which is developed by Southworth et al. (2005b). In this code, the uncertaintiesare calculated with very robustly and a complete error budget is found for every outputparameter. Derived fundamental parameters are listed in Table 8. The physical constantsused for the calculations are given by Southworth (2011).The accuracy of the masses is better than 5%, while radii values of the componentsare good to about 2.5%. We calculated E ( B − V ) color excess for HD 350731 from thedust maps of Schlafly & Finkbeiner (2011). Because the system is relatively close tothe sun, the color excess value from Schlafly & Finkbeiner (2011) needed to be reducedaccording to the distance. The J band absolute magnitude of the system was calculatedusing the color-luminosity relation of Bilir et al. (2008). Then, the calculated colorexcess E ( B − V ) = 0 .
157 mag was reduced using the equation of Bahcall & Soneria(1980). The color excess value is consistent with the position of HD 350731 in the MilkyWay. The interstellar absorption value ( A v ) has been calculated to be 0.49 mag from thecommonly-accepted formula A v = 3 . × E ( B − V ). The distance of the system was found tobe 703 ±
34 pc based on apparent system magnitude, light ratio of the system’s components,and interstellar extinction values. The temperatures of the components determined fromspectroscopic analysis are consistent with the spectral types of B8V+B8V, according to 22 –Table 6: List of minima times of HD 350731.
HJD Error Filter Epoch Ref.24 50000+3594.4279 – I -646.5 13612.4138 0.0001 R c -635.5 23653.2919 0.0001 R c -610.5 24002.3133 0.0001 R -397.0 14299.9065 0.0002 V -215.0 34340.7838 0.0002 V -190.0 34345.6896 0.0001 V -187.0 34628.5684 0.0002 BV R c I c -14.0 34642.5482 0.0002 BV R c I c -5.5 34651.4605 0.0004 BV R c I c BV R c I c BV R c BV R c BV R c V R c Br´at et al. (2007), Zejda et al. (2006), Kleides et al. (2008).
23 –Table 7: Apsidal motion elements of HD 350731.
Parameter Value T (HJD) 2454651.5008 ± P s (day) 1.63511 ± e a ω (degree) 3.4 ± d ω /dt (degree cycle − ) 0.0170 ± U (yr) 92 ± P a (day) 1.63519 ± a : Adopted from orbital analysis.
500 0 500 1000 1500 2000 2500 O C ( da ys ) O C ( P e r i od ) Fig. 6.— O − C diagram for HD 350731 obtained with parameters given in Table 7. Primaryand secondary minima times are indicated by filled and open circles, respectively. 24 –calibrations given by Sung et al. (2013).The components of the system have similar properties since the temperature differencebetween the components was found to be ∆ T =170 K which is smaller than 1 σ uncertaintiesfor the effective temperatures of both components (see Table 3). Furthermore, the massesand radii values were very close, as seen in Table 8. From the photometric analysis, thesystem was found to be detached and the Roche lobe filling ratios were calculated to be63% and 64% for the primary and secondary components, respectively.In order to analyze the kinematical properties of HD 350731, we used the system’scenter of mass velocity, distance and proper motion values. The proper motion data ( µ α cos δ , µ δ )=(1.0 ± ± − were taken from the Fourth US Naval ObservatoryCCD Astrograph Catalog (UCAC4; Zacharias et al. 2013), whereas the center of massvelocity V γ = − . ± . − and distance d=703 ±
34 pc were obtained in this study.The system’s space velocity was calculated using Johnson & Soderblom’s (1987) algorithm.To obtain the space velocity precisely, first-order galactic differential rotation correctionwas taken into account (Mihalas & Binney 1981). The differential rotation corrections werecalculated as 16.23 and 0.89 km s − and applied to U and V space velocity components,respectively. The W velocity is not affected in this first-order approximation. As forthe local standard of rest correction (LSR), Co¸skuno˜glu et al.’s (2011) values ( U , V , W )=(8.50, 13.38, 6.49) km s − were used and the total space velocity of HD 350731 wasobtained as S tot = 15 . ± − . The corrected space velocity components are ( U , V , W )=(6.10 ± ± ± − . The total space velocity and spacevelocity component values are in agreement with young-disc stars (Leggett, 1992).To determine the population type of HD 350731, we used Dinescu, Girardi & vanAltena’s (1999) N-body code and obtained the galactic orbit of the system. In this code,the timescale in generating the orbits was assumed to be 3 Gyr, and the calculation steps 25 –Table 8: Astrophysical properties of HD 350731.Parameter Primary SecondaryMass (M ⊙ ) 2.91 ± ± ⊙ ) 2.11 ± ± ±
250 11830 ± L (L ⊙ ) 1.92 ± ± g (cgs) 4.25 ± ± ± × − Orbital separation (R ⊙ ) 10.43 ± ± − ) -10.1 ± ± V (mag) 9.60 a M Bol (mag) -0.05 ± ± BC (mag) -0.66 b -0.62 b M V (mag) 0.61 ± ± v sin i (km s − ) 69.2 ± ± v sin i (km s − ) 67.5 ± ± v sin i (km s − ) 65.4 ± ± ± a :SIMBAD Database, b : Sung et al. (2013)
26 –were 2 Myr. The 3 Gyr timescale was assumed so that precise orbits would be created,even though this is longer than the nuclear time scale of early-type stars. The orbits of HD350731 on the X − Y and X − Z planes around the galactic center are shown in Fig. 7.The system’s apogalactic ( R max ) and perigalactic ( R min ) distances obtained were 7.72 and7.09 kpc, respectively. According to N-body code, the maximum vertical separation fromthe galactic plane of the system is | z max | =100 pc. The following formulae were used toderive the planar ( e p ) and vertical ( e v ) eccentricities: e p = R max − R min R max + R min , (1) e v = ( | z max | + | z min | ) R m , (2)where R m is the mean of R min and R max . The planar and vertical eccentricities werecalculated as e p = 0 .
04 and e v = 0 .
01, respectively. These eccentricities show that HD350731 is in a circular orbit around the mass center of the Galaxy and that it belongs tothe young thin-disc population.
7. Discussion and Conclusion
Double-line detached eclipsing binaries (DBs) are valuable sources for determining theprecise fundamental properties (mainly masses and radii) of stars. A recent catalogue ofthis type of binaries was published by Eker et al. (2014). It consists of 257 DBs; their388 component stars have better than 5% accuracy in their masses and radii. When oneexamines the basic properties of the DBs in the catalogue (especially mass ratio, mass,radius and temperatures of components), it can be seen that there is no detached eclipsingbinary system which has absolute properties similar to HD 350731. The spectral type 27 – (cid:42)(cid:68)(cid:79)(cid:68)(cid:70)(cid:87)(cid:76)(cid:70)(cid:38)(cid:72)(cid:81)(cid:87)(cid:85)(cid:72)
Fig. 7.— Orbital motion of HD 350731 on projections of X − Y (a) and X − Z (b) planesaround galactic center for 3 Gyrs. 28 –of the system was determined to be B8V+B8V, while the masses were derived to be M = 2 . ± .
13 M ⊙ and M = 2 . ± .
14 M ⊙ for the primary and secondary components,respectively. Therefore, DBs with mass ratio in the range of 0.95-1.0 and spectral type Oand/or B need to be further studied in order to fill the gap in this parameter range. This isnecessary to understand the evolution and structure of early-type stars.The mass-luminosity relation (MLR) was updated recently by Eker et al. (2015) usingDBs data. In this study, they identified four mass domains and derived MLRs for thesemass ranges. For comparison, using the MLR given in the mass range of 2.4 M ⊙ and 7 M ⊙ ,we calculated luminosity values on a logarithmic scale to be 1.96 L ⊙ and 1.89 L ⊙ , for theprimary and secondary components, respectively. The predicted values from the updatedclassical MLR agree with the values derived from Stefan-Boltzmann law (see Table 8).Spectral data enables us to find temperatures and projected rotational velocities ofthe components. For the model atmosphere application, the disentangled spectra of thecomponents obtained from KOREL analysis were used. As a results the temperature of theprimary and secondary components was found to be 12000 K and 11830 K, respectively.The surface gravity values (log g , ) calculated from the masses and radii of the componentswere adopted during spectral analysis. The projected rotational velocities ( v sin i ) ofthe components were measured to be 69.2 km s − and 70.1 km s − for the primary andsecondary components, respectively. Within errors the measured v sin i values agree withthe pseudo-synchronous velocities of the components in Table 8, which were calculated onthe basis of the formulations by Hut (1981).The orbit of the system is slightly eccentric determined from the orbital solution andalso an analysis of the multi-color light curves and radial velocities of the components. Thesecondary minimum can be seen to have shifted from the orbital phase of 0.5. This is anindication of apsidal motion in the system. We collected 15 minima times together with 29 –newly-measured eclipse times to study the apsidal motion by means of O − C analysis. Theapsidal motion parameters could not be determined accurately since the observed eclipsetimes were not-well covered. The apsidal motion was found at a rate of ˙ ω = 0 . ± . − , which corresponds to an apsidal motion period of about 92 yr.The locations of the components of HD 350731 are seen in the Hertzsprung-Russell(HR) diagram and plane of M − R in Fig. 8. Zero Age Main Sequence (ZAMS) andthe evolutionary tracks for the exact masses of the components, and isochrones for solarchemical composition, are taken from the Yonsei–Yale (Y ) series of Yi et al. (2001). Asseen in Fig. 8, the components are a bit away from the ZAMS line and the age of thesystem was estimated to be 120 ±
35 Myr from Y isochrones. Kinematic analysis indicatedthat the system leaves the galactic plane just about 100 pc during its movement on galacticorbit. This is evidence for membership of the thin-disc population by HD 350731. Thepositions of the components in the HR diagrams are in agreement with the evolutionarytracks for the masses of 2.91 M ⊙ and 2.80 M ⊙ .As a general conclusion, we can mention that the photometric and spectroscopicanalysis of HD 350731 leads us to extend the database of DBs with intermediate masscomponents having similar properties. This is important since in the catalogue of DBsby Eker et al. (2014) there are only a few systems with a mass ratio close to q = 1 . ⊙ (e.g. η Mus, V799 Cas, V906 Sco).The unevolved binary system HD 350731 belongs to the young thin-disc population of theGalaxy with an estimated age of 120 ±
35 Myr. In order to make abundance analysis indetail, and also verify population type of the system, more high resolution spectroscopicdata is needed. New eclipse times are also required to enlarge the time interval for betteranalysis and to confirm the apsidal motion parameters.This research was supported by the Scientific and Technological Research Council of 30 –Fig. 8.— Locations of primary and secondary components of HD 350731 in log L - log T eff (a) and log M -log R planes (b). Evolutionary tracks for masses of 2.91 M ⊙ and 2.80 M ⊙ (solidlines), isochrones for ages of 80 Myr, 120 Myr and 150 Myr (dashed lines), and ZAMS forsolar chemical composition adopted from Yi et al. (2001). 31 –Turkey (T ¨UB˙ITAK, Grant no. 111T224). The authors would like to thank the anonymousreferee for valuable suggestions and comments which helped us to improve the study. Wethank C¸ anakkale Onsekiz Mart University Astrophysics Research Center and UlupınarObservatory together with ˙Istanbul University Observatory Research and ApplicationCenter for their support and allowing use of T122 and IST60 telescopes. The project wassupported partly by National Planning Agency (DPT) of Turkey (project DPT-2007K120660carried out at C¸ anakkale Onsekiz Mart University) and the Scientific Research ProjectsCoordination Unit of Istanbul University (project no. 3685). We gratefully acknowledgethe support of the NRC (Canada) Herzberg Institute of Astrophysics. The authors wouldespecially like to thank Dr. D. Bohlender and Dr. D. Monin for their hospitality andallowing telescope time for observations at the Dominion Astrophysical Observatory,Canada. This research has made use of the SIMBAD and NASA Astrophysics Data SystemBibliographic Services. 32 – REFERENCES