A photometric study of two neglected eclipsing binaries
RResearch in Astronomy and Astrophysics manuscript no.(L A TEX: ms0398.tex; printed on February 22, 2021; 1:32)
A photometric study of two neglected eclipsing binaries
V. Kudak , M. Fedurco , V. Perig , ˇS. Parimucha Laboratory of space researches, Uzhhorod National University, Uzhhorod, Daleka Str., 2A, 88000,Ukraine; e-mail: [email protected] Institute of Physics, Faculty of Science, University of P.J. ˇSaf´arik, Koˇsice, Park Angelinum 9, 04001,Slovakia; e-mail: [email protected]
Received 20xx month day; accepted 20xx month day
Abstract
We present the first BVR photometry, period variation, and photometric light-curveanalysis of two poorly studied eclipsing binaries V1321 Cyg and CR Tau. Observations werecarried out from November 2017 to January 2020 at the observatory of Uzhhorod NationalUniversity. Period variations were studied using all available early published as well as ourminima times. We have used newly developed ELISa code for the light curve analysis and de-termination of photometric parameters of both systems. We found that V1321 Cyg is a closedetached eclipsing system with a low photometric mass ratio of q = 0 . which suggeststhat the binary is a post mass transfer system. No significant period changes in this systemare detected. CR Tau is, on the other hand, a semi-detached system where the secondarycomponent almost fills its Roche lobe. We detected a long-term period increase at a rate of . × − d/y , which support mass transfer from lower mass secondary component to themore massive primary. Key words: binaries: close — binaries: eclipsing — stars: individual (V1321 Cyg, CR Tau)
Eclipsing binaries are an important group of variable stars, where both components are obscured for theobserver during their mutual motion around a common centre of mass. They exhibit features in their lightcurves, which are specific and well recognized among all variable stars. The shape of their light curvesdepends on the physical properties of the components and geometrical configuration (Hilditch 2001; Prˇsa2019). Analysis of light-curves of eclipsing binaries can reveal, among others, relative dimensions of stars,their effective temperatures, orbital inclination, the eccentricity of the orbit, and potential spots. Togetherwith radial velocities obtained from spectroscopic observations, we can determine masses of the compo-nents, their distances, and radii.The shapes of components in binary stars are described by Roche geometry (Prˇsa 2019). Accordingto this, three configurations of binary systems are possible, detached (both components are in their Roche a r X i v : . [ a s t r o - ph . S R ] F e b V.I. Kudak et al. lobes), semi-detached (one component fill its Roche lobe), and contact, where both components overfilltheir Roche lobes. All this is reflected in the light curves and have also other observational consequenceslike a period change due to mass transfer, angular momentum loss (e.g., Yang et al. 2009) and/or magneticbraking (Applegate 1992).In this paper, we present photometry, period, and light-curves analysis of two neglected detached bina-ries, which were not up to now, studied in more details in literature:
V1321 Cyg (NSVS 5731097) was for the first time mentioned as eclipsing variable in Romano (1967).In the database of Kreiner (2004), the period of the system is listed as P = 0.3640924 days. Otero et al.(2006) redefined system as Algol-type binary with the orbital period P = 0.72818 days. In the catalogue ofAvvakumova et al. (2013), the orbital period of the system was again set to half of the previous value. Thedistance to the system is 735 ±
12 pc according to GAIA DR2 release (Bailer-Jones et al. 2018).
CR Tau (GSC 01862-01633) was discovered by Hoffmeister (1949) who also determined ephemerisfrom minima times from photographic plates. The system was neglected till the paper from Agerer(1999), who presented the first CCD light-curve of the system and determined new ephemeris with pe-riod P = 0.6827035 days. It is included in catalogue of Algol-type eclipsing binaries from Budding et al.(2004) and in the catalogs Malkov et al. (2006) and Avvakumova et al. (2013). This eclipsing binary wasalso monitored by the OMC instrument (The Optical Monitoring Camera) on-board INTEGRAL satellitewhich provided photometry measurements in the Johnson V-band (Alfonso-Garz´on et al. 2012). The dis-tance to the system was established to 796 ±
26 pc according to GAIA DR2 release (Bailer-Jones et al.2018).
Observations of all studied eclipsing binary systems were carried out at Derenivka Observatory of UzhhorodNational University, Ukraine (Lat: 48.563417 N; Long: 22.453758 E). Measurements were collected fromNovember 2017 to January 2020. For our observation, we have used a Newton-type telescope with a diam-eter of 400 mm and a focus of 1750 mm. It is accompanied by FLI PL9000 CCD camera (array 3056x3056,pixel size 12 µm ) with Johnson BV R photometric filters. The field of view of such configuration of thesystem is 1.21 ◦ x 1.21 ◦ . The journal of our CCD observation is given in Table 1.The CCD images were reduced in the usual way (bias and dark subtraction, flat-field correction) usingsoftware package CoLiTecVS (Savanevych et al. 2017; Parimucha et al. 2019). This package was also usedfor aperture photometry, calculation of differential magnitudes according to artificial comparison star aswell as calibration to the standard photometric system. The comparison stars used for the determination ofartificial ones were selected manually according to the similarity of the studied binaries (brightness, distanceon the sky). This approach significantly improves the quality of photometric measurements. Due to not astable night-to-night observing conditions, the average precision of our measurements reached ∼ ∼ ∼ ∼ photometric study of two neglected eclipsing binaries 3 Table 1: The journal of CCD photometric observations. Phase is calculated accordingto ephemeris determined in Section 3.
System Date Time(UT) Phase Filters
V1321 Cyg Nov 05 18 16:27 - 23:22 0.047 - 0.442 B, V, RNov 06 18 16:32 - 19:55 0.426 - 6.618 B, V, RNov 15 18 19:59 - 21:31 0.977 - 0.053 B, V, ROct 15 19 17:09 - 23:56 0.500 - 0.882 B, V, ROct 17 19 16:39 - 00:19 0.213 - 0.635 B, V, ROct 22 19 16:54 - 01:02 0.093 - 0.544 B, V, ROct 27 19 16:57 - 18:47 0.961 - 0.068 B, V, RJan 15 20 16:40 - 20:04 0.808 - 0.971 B, V, RCR Tau Nov 30 18 18:31 - 04:31 0.945 - 0.562 B, V, ROct 25 19 23:13 - 03:24 0.146 - 0.401 B, V, ROct 27 19 20:45 - 04-02 0.927 - 0.371 B, V, RNov 30 19 20:05 - 03:07 0.688 - 0.117 B, V, RJan 16 20 19:37 - 21:43 0.503 - 0.634 B, V, R
The resulting light-curves of all eclipsing binaries are depicted in Fig. 1. The light-curves were phasedaccording to ephemeris determined from O-C variations analyzed in the next chapter.
The study of period changes of both systems was carried out using their O-C diagrams. In our analysis wehave used all available published minima times as can be found in the O-C gateway , minima times deter-mined from our observations (weighted averages from B,V,R light curves), minima times determined fromavailable SuperWASP data (Pollacco et al. 2006) and INTEGRAL-OMC observations (Alfonso-Garz´onet al. 2012). Our new minima times were calculated using the phenomenological method described in http://var2.astro.cz/ocgate/ Table 2: Comparison stars used for a determination of artificial comparison stars. BVRmagnitudes are taken from the NOMAD Catalogue (Zacharias et al. 2004, 2005)
System Comparison stars Coordinates B V RNOMAD α (2000) δ (2000) V1321 Cyg 1315-0399331 20:23:35.66 +41:32:52.8 14.780 14.330 15.2401315-0399475 20:23:48.84 +41:31:36.3 12.590 12.380 11.4601314-0397913 20:23:33.94 +41:27:56.5 14.190 13.680 14.2401315-0399386 20:23:41.82 +41:35:23.5 13.160 12.810 13.380‘ 1315-0399546 20:23:55.19 +41:30:28.6 15.140 14.520 14.950CR Tau 1140-0090488 05:51:17.48 +24:04:56.1 12.456 12.072 10.951140-0090531 05:51:21.78 +24:04:31.5 12.500 12.178 11.911140-0090614 05:51:32.65 +24:04:55.0 14.813 14.101 13.411141-0092118 05:51:38.19 +24:06:58.2 14.642 13.073 11.77 V.I. Kudak et al.
Fig. 1: Phased light curves of V1321 Cyg (top) and CR Tau (bottom) systems in B,V,R passbands by datesof observations.Mikul´aˇsek (2015). This method gives a realistic and statistically significant error in determining minimatimes. Newly calculated minima times are listed in Tab. 3.O-C diagram of V1321 Cyg compiled from archived CCD and newly determined ones contains a totallyof 88 times of minima. We have omitted old photographic minima times obtained before 1968 because oftheir large scatter. We also excluded visual observations. The precision of CCD minima times is in the rangeof − days. A weighted least-squares solution using all minima (weights were calculated as /σ , where σ is an error of the minimum) leads to the following linear ephemeris of the system (errors of parametersare given in parenthesis): Min I = HJD 2458428 . d . × E. (1) photometric study of two neglected eclipsing binaries 5 Table 3: New times of minima of studied objects. BVR - weighted average from our B,V,R light curves,SWASP - SuperWasp minima, OMC - INTEGRAL-OMC minima. The errors of minima times are given inparenthesis.
HJD(2400000+) Filter HJD(2400000+) Filter HJD(2400000+) Filter
V1321 Cyg
CR Tau
This ephemeris was used to create the O-C diagram displayed in Fig. 2 (left). Despite the fact that we usedonly CCD observations, quite a large scatter in the resulting diagram is apparent in the range of about 10minutes. But no significant period changes in this system are detected.O-C diagram of CR Tau contains 48 CCD times of minima, including archival and new points. Weagain excluded old photographic minima times obtained by Hoffmeister (1949), because of their very largescatter (up to 2 hours on O-C diagram). The precision of CCD minima times is in the range of − days.As in the previous case, we performed a weighted least-squares solution using all minima and determinedthe following linear ephemeris of the system: Min I = HJD 2452500 . d . × E, (2)which was used to create the O-C diagram depicted in Fig. 2 (right). Unlike the previous case, there is somevisible variation on O-C of CR Tau. Because of the lack of minima times and insufficient coverage we canonly speculate about their nature. The first explanation can be a mass transfer between components in thesystem. We made a weighted least-squares solution of residuals and obtained quadratic ephemeris: Min I = HJD 2452500 . d . × E + 1 . × − × E . (3)This solution is depicted in Fig. 3 (left). According to ephemeris (3), a long-term period increase at a rateof . × − d/y is detected. The second possible explanation of the O-C diagram is the presence ofthe rd body in the system, which we do not directly see. It causes a light-time effect, a shifting of minimatimes according to the movement of the visible binary around the common center of mass (Hilditch 2001).We have used code from Gajdoˇs & Parimucha (2019) to test this hypothesis. Our best solution (shown inFig. 3 right) led to the high eccentric e = 0 . orbit of the body with almost 28 years orbital period. V.I. Kudak et al.
Fig. 2: O-C diagrams of V1321 Cyg (left) and CR Tau (right) systems determined from linear ephemeris(1) and (2). Primary minima are denoted by filled circles and secondary ones by blank circles.Fig. 3: The fit (red line) of the O-C diagram of CR Tau systems according to a quadratic ephemeris (left)and 3 rd body (right), with residuals at the bottom. For the analysis of light curves of both systems, we have used ELISa code ( ˇCokina et al. 2021). It is a newlydeveloped cross-platform Python software package dedicated to modeling close eclipsing binaries includingsurface features such as spots and pulsations. ELISa utilizes modern approaches to the EB modeling withan emphasis on computational speed while maintaining a sufficient level of precision to process a ground-based and space-based observation. In this paper, we utilize its capability to model the light curves of closeeclipsing binaries with the built-in capability to solve an inverse problem using the Least Squares (LS) andMarkov Chain Monte-Carlo (MCMC) methods.Observations in all passbands were normalized according to flux in the maxima and were simultaneouslyfitted by the LS method to find initial approximate solutions. Subsequently, MCMC sampling was usedto produce 1 σ confidence intervals of the fitted system parameters. Each system was fitted with model https://github.com/mikecokina/elisa photometric study of two neglected eclipsing binaries 7 − − − N o r m a li z ed f l x Generic.Bessell.BGeneric.Bessell.VGeneric.Bessell.R − − − − R e s i d a l s Fig. 4: The synthetic model fitted on observational data of V1321 Cyg (left) and the results of the MCMCsampling displayed in form of the corner plot (right). − − − N o r m a li z ed f l x Generic.Bessell.BGeneric.Bessell.VGeneric.Bessell.R − − − − R e s i d a l s Fig. 5: The synthetic model fitted on observational data of CR Tau (left) and the results of the MCMCsampling displayed in form of the corner plot (right).containing 6 free parameters: orbital inclination i , photometric mass ratio q , surface potentials of bothcomponents Ω and Ω and effective temperatures of the primary and secondary component T eff and T eff . In case of V1321 Cyg, T eff was kept during fitting procedure within ± K of the value 6770 Kobtained from LAMOST spectra (Qian et al. 2018). On the other hand, T eff of CR Tau was constrainedwithin ± K interval from the value 8200 K provided by the 2 nd GAIA data release (Gaia Collaborationet al. 2018).For the components with convective envelopes (effective temperatures bellow ∼ A , A of components were set to 0.6 (Ruci´nski 1969) and gravity darkening factors, g and g to 0.32(Lucy 1967). In the case of radiative envelope (above ∼ /σ , where σ is the standard error of pointderived during photometric measurement. Initially, the LS algorithm was used with suitable initial param-eters to find an approximate solution and then the parameter space near the solution was explored with V.I. Kudak et al.
Fig. 6: 3D models with the most likely surface temperature distributions of V1321 Cyg (left) and CR Tau(right) binary systems based on parameters obtained from LC fitting listed in Tab. 4. The displayed temper-ature distributions take into account gravity darkening and the reflection effect using standard techniquesbased on Wilson-Devinney code (Wilson & Devinney 1971).Table 4: Parameters of the V 1321 Cyg and CR Tau systems derived from multi-color photometry usingELISa code. The description of parameters is given in text. Goodness of the obtained fits are provided inthe form of coefficient of determination R . Parameter V1321 Cyg CR Tau
Primary Secondary Primary SecondaryP [HJD] 0.7281849 a a T [HJD] 2458428.879 a a i [deg] . +0 . − . . +0 . − . q (M /M ) . +0 . − . . +0 . − . T [K] +40 − +30 − +190 − +87 − Ω 3 . +0 . − . . +0 . − . . +0 . − . . +0 . − . Ω crit . +0 . − . . +0 . − . . +0 . − . . +0 . − . R eqiv [SMA] . +0 . − . . +0 . − . . +0 . − . . +0 . − . Periastron radii [SMA] r polar . +0 . − . . +0 . − . . +0 . − . . +0 . − . r backward . +0 . − . . +0 . − . . +0 . − . . +0 . − . r side . +0 . − . . +0 . − . . +0 . − . . +0 . − . r forward . +0 . − . . +0 . − . . +0 . − . . +0 . − . R Notes: a - adopted values of period and epoch from linear ephemerides MCMC sampler with 500 walkers and 500 iterations with prior 300 iterations discarded as it belonged tothe thermalization stage of the sampling. The resulting and derived parameters of both systems, like a criti-cal potential Ω crit , corresponding radius R eqiv , and periastron radii in SMA are listed in Tab. 4. The best-fitmodels with observed LCs and resulting flat chains displayed in the form of the corner plot are shownin Fig. 4 and 5. On the Fig. 6 we also display 3D models of the systems with a temperature distribution,corresponding to a best fitting solution listed in Tab. 4. photometric study of two neglected eclipsing binaries 9 In our study we have presented the first multi-color
BV R photometry of two, so far neglected eclipsingbinaries V1321 Cyg and CR Tau. We have analyzed their period variations using archival and our newminima times as well as we performed a photometric analysis of their light-curves.The analysis of our multi-color photometric observations demonstrates that V1321 Cyg is a close de-tached binary with a low photometric mass ratio of q = 0 . +0 . − . . Such a low value of q combined witha secondary potential Ω = 2 . +0 . − . being relatively close to the critical potential Ω crit, = 2 . +0 . − . suggests that V1321 Cyg is a post mass transfer system, where a significant portion of the secondary com-ponent’s mass was transferred onto the primary component. We detected no significant period changes inthis system and it also supports the idea that the system is detached. We found two viable solutions, how-ever only one was located within the temperature range derived by the LAMOST spectra while the seconddiscarded solution contained much colder primary component with ≈ K , well below the expectedvalue.On the other hand, a photometric analysis of the light curves of CR Tau revealed that the system is asemi-detached system where the secondary component almost fills its Roche lobe, as detected in some othernear-contact systems, like EG Cep (Zhu et al. 2009) or BF Vir (Zhu et al. 2012) The main consequence ofsuch configuration is a mass transfer from the secondary to the primary component, which is reflected onthe O-C diagram as a parabolic variation according to the epoch. If the mass is transferred from a lessmassive star to a more massive one, we detect period increase, as observed in our data (see Fig. 3 - left).So we can conclude that the most probable explanation of O-C variations of CR Tau is a mass transfer andfurther observations should confirm that.Subtraction of the best fit from the observed multi-colour data (Fig. 5 - left) uncovered phase correlatedresiduals centered around the primary eclipse. This can be also explained by the mass transfer from the lessmassive and much cooler secondary component onto the heavier primary component. The surface of theprimary component is obscured by the fraction of the relatively cold stream of matter from the secondarycomponent. A slight shift in the position of residuals to the beginning of the eclipse can be explained bythe Coriolis force acting on the falling stream of matter. Additionally, it is worth to mention other observedproximity effects such as the deformation and heating of secondary component of CR Tau on the part of thesurface facing the primary component due to the close proximity of the components and large temperaturedifference between the component’s surfaces. Acknowledgements
This work was supported by national grant 0119U100236 and by the Slovak Researchand Development Agency under contract No. APVV-15-0458. The research of M.F. was supported by theinternal grant No. VVGS-PF-2019-1392 of the Faculty of Science, P. J. ˇSaf´arik University in Koˇsice.
References
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