The mass and radius of the M-dwarf companion in the double-lined eclipsing binary T-Cyg1-01385
aa r X i v : . [ a s t r o - ph . S R ] M a r The mass and radius of the M-dwarf companion in thedouble-lined eclipsing binary T-Cyg1-01385 ¨Om¨ur C¸ akırlı a, ∗ , Cafer Ibanoglu a , E. Sipahi a a Ege University, Science Faculty, Astronomy and Space Sciences Dept., 35100 Bornova,˙Izmir, Turkey.
Abstract
We observed spectroscopically the eclipsing binary system T-Cyg1-01385 inorder to determine physical properties of the components. The double-linednature of the system is revealed for the first time and the radial velocitiesare obtained for both stars. We have derived masses, radii and luminosi-ties for both components. Analyses of the radial velocities and the Kepler-Cam and the T r ES light curves yielded masses of M =1.059 ± M ⊙ andM =0.342 ± M ⊙ and radii of R =1.989 ± R ⊙ and R =0.457 ± R ⊙ . Locations of the low-mass companion in the mass-radius and mass-effective temperature planes and comparison with the other low-mass starsshow that the secondary star appears just at the transition from partially tofully convective interiors for the M dwarfs. When compared to stellar evolu-tion models, the luminosities and effective temperatures of the componentsare consistent with Z=0.004 and an age of about 6 Gyr. A distance to thesystem was calculated as d=355 ± Keywords: binaries; eclipsing - stars: fundamental parameters; individual ∗ Corresponding author
Email address: [email protected], Tel:+90 (232) 3111740,Fax:+90(232) 3731403 ( ¨Om¨ur C¸ akırlı)
Preprint submitted to New Astronomy August 10, 2018 ethod: spectroscopy
1. Introduction
The lower-mass stars of the main-sequence of the Hertzsprung-Russelldiagram are known as M-dwarfs. They constitute the majority of stars inthe solar neighbourhood. They are intrinsically faint since they are coolerand smaller than the other stars . Because of their faintness photometric andspectroscopic observations could be obtained for a limited number M-dwarfs.Chabrier (2003) suggests that at least 70 per cent of all stars in the spherewith a radius of 10 pc about the Sun are M-dwarfs. Therefore, detailedstudies of these faint but numerous low-mass stars are critical importance toevaluate a model of the galactic evolution and present status. Moreover theM-dwarfs are particularly needed in the understanding of evolution of main-sequence stars towards the lower-mass regime. The evolutionary calculationsof low-mass stars allow us to define not only the transition from partly tofully convection but also to define a limit between stars and brown dwarfs.As pointed out by Shulyak et al. (2011) around spectral type M3.5 stars be-come fully convective and thus the dynamo mechanism must be different incooler stars because they do not posses tachocline layer with strong differ-ential rotation. However, Reiners & Basri (2007) have concluded from themeasurements of Stokes parameter about tens of stars spanning the whole M-dwarfs that no significant change in the average magnetic field strengths oc-curs when stars become fully convective. Later on Reiners, Basri,& Browning(2009) could reveal the rotation- magnetic field relation in which magneticfield strengths increase towards short rotation periods.2ow-mass M-dwarfs are generally faint objects because of their small radiiand low temperatures. Due to their faintness the M-dwarfs have limited thenumber of high-resolution, high signal-to-noise spectroscopic studies. In ad-dition, the optical spectrum of these cool stars is mostly covered by molec-ular bands which hide and blend the atomic lines used in spectral analysis.These dominant molecular bands make it difficult to measure the atomic linestrengths which are needed for metallicity determination. The physical pa-rameters, such as mass, radius and luminosity as well as age and rotationalperiod could only be derived if a M-dwarf is a member of a close binary or amultiple system. In a binary or a multiple system the components are mostlikely coeval and their spin axes are perpendicular to the orbital plane.Numerous photometric observations of binary stars were recently gath-ered by the surveys of like the T r ES (Alonso et al. , 1996), NSVS (Wozniak et al.,2004), SuperWASP (Christian et al., 2006), Kepler (Borucki, Koch, & Kepler Science Team,2010), etc. Despite the main aim of these surveys is to search gamma-ray bursters, and especially extra-solar planetary transits many binary sys-tems are discovered and light curves of many systems could be obtained.Therefore, the tremendous photometric datasets containing unknown or lit-tle known binary systems are presented for the use of astronomers.Light variability of T-Cyg1-01385 was announced by Devor (2008) andDevor et al. (2008) in the list of 773 eclipsing binaries found in the Trans-Atlantic Exoplanet Survey. It was classified as an ”ambiguous” binary intheir list. Mass and radius of the components were estimated for the firsttime by Fernandez et al. (2009) combining the spectroscopic orbital elementsobtained from the primary star’s radial velocities with a high-precision transit3 igure 1: The residuals between the observed times of minimum light and computed withthe new ephemeris. light curve obtained by the KeplerCam. The results obtained up-to-datepoint out that the fainter component of T-Cyg1-01385 is so close to the fullyconvective M-dwarfs. Therefore we planned new spectroscopic observationsof the system to refine the masses, radii and effective temperatures of bothstars.
2. Period determination
The catalog information for T-Cyg1-01385 was given in Table 1. Firstwe collected the times for mid-light minimum obtained by various automaticand robotized telescopes and surveys. These times of minima are given inTable 2 as averaged for the filters used. A linear least-squares fit to the datayields the following ephemerisMin I = HJD 2453926 . d . × E where the bracketed quantity is the uncertainty in the last digit(s) of thepreceding number. All uncertainties quoted in this work are standard errors.The residuals of the fit are plotted in Fig. 1 and show no indication of anyform of period change in about ten years.4 able 1: Catalog information for T-Cyg1-01385. Source Catalog Parameter Value2MASS a α (J2000) 20 h m s δ (J2000) +48 ◦ ′ ′′ PPMX b V mag 10.92 ± c B mag 11.68 ± V mag 11.02 ± d B T mag 11.68 ± V T mag 11.02 ± J mag 9.834 ± H mag 9.593 ± K s mag 9.513 ± e B mag 11.520 ± V mag 10.956 ± R mag 10.580 ± f r ′ mag 10.892 ± g B mag 11.565 ± V mag 10.920 ± h B mag 11.680 ± V mag 11.016 ± i V mag 11.103 ± I mag 10.363 ± j B mag 11.741 ± V mag 10.997 ± r ES k Identification T-Cyg1-01385SB9 l Identification 3018SWASP m Identification 1SWASP J201521.94+481714.1UCAC4 µ α , µ δ (mas yr − ) -9.2 ± ± µ α , µ δ (mas yr − ) -8.4 ± ± µ α , µ δ (mas yr − ) -8.77 ± ± µ α , µ δ (mas yr − ) -10 ±
1, -20 ± µ α , µ δ (mas yr − ) -7.8 ± ± a Two Micron All Sky Survey Catalog (Skrutskie et al., 2006), b PPMX
Position and Proper Mo-tions Catalog, (R¨oser et al., 2008), c GSC2.3
Guide Star Catalog, version 2.3.2 (Morrison et al., 1999), d TYCHO
Tycho Catalog, (Perryman & ESA, 1997), e NOMAD
NOMAD Catalog, (Zacharias et al.,2005), f CMC14
Carlsberg Meridian Catalog 14 (Copenhagen University et al., 2006), g ASCC-2.5V3
All-Sky Compiled Catalog of 2.5 Millon Stars, (Kharchenko & Roeser, 2009), h ACT
Astrographic Catalog,(Urban, Corbin, & Wycoff, 1997), i TASS
The Amateur Sky Survey (TASS) Catalog, (Droege et al., 2006), j UCAC
High density, Highly Accurate, Astrometric Catalog, (Urban et al., 2004), k T r ES Trans EclipsingBinary Catalog, (Devor et al., 2008), l SB th Catalog of Spectroscopic Binary Orbits, (Pourbaix et al.,2009). m SuperWASP (Christian et al., 2006) . able 2: Times of minimum light for T-Cyg1-01385. The O-C values refer to the differencebetween the observed and calculated times of mid-eclipse. Minimum time Cycle number O-C Ref.(HJD-2 400 000)51263.5000 -406.0 0.0983 153198.6330 -111.0 -0.0041 253205.1940 -110.0 -0.0032 253208.4730 -109.5 -0.0043 253211.7550 -109.0 -0.0023 253926.6737 0.0 -0.1367 353926.6743 0.0 -0.1361 353926.6755 0.0 -0.1349 353926.6761 0.0 -0.1343 353926.8104 0.0 0.0000 354661.5413 112.0 -0.00126 4Ref: (1) (Copenhagen University et al., 2006), (2) Devor (2008), (3)Fernandez et al. (2009), (4) Christian et al. (2006)
3. Echelle Spectroscopy
Optical spectroscopic observations of the T-Cyg1-01385 were obtainedwith the RTT150 using the R ∼ ≤ λ ≤
900 nm. These observations wereused to resolve the components of T-Cyg1-01385 and get individual radialvelocity measurements for each star in the system. Eleven spectra wereobtained using 60 minute integrations on 8 nights in July, 2010 with typicalsignal-to-noise ratios of ∼
120 at 6563 ˚A.The spectra were processed in the standard way for cross-dispersed Echelle http://tug.tug.tubitak.gov.tr/rtt150 tfosc.php T ¨UB˙ITAK National Observatory (Turkey) fxcor package in IRAF. The routine processes the data usingbiases and halogen lamp observations taken at the beginning of the night,median combines three individual images while performing cosmic ray rejec-tion, extracts the individual orders from the combined image and performsthe wavelength solution on each order using a FeAr arc lamp taken eitherbefore or after each set of science exposures.A total of 11 orders are used each night to derive radial velocities viacross-correlation with a standard template. We use the bright ι Psc (F7 V)and 50 Ser (F0 V) as the heliocentric radial velocity standard stars. Eachspectral order is cross-correlated separately, then an iterative 3- σ clippingis performed prior to performing a weighted average to obtain a final radialvelocity measurement for each night. The components are identified eachnight via the peak and width of each feature in the cross correlated functions.The typical radial velocity precisions ranged from 2 to 13 km s − for thevarious components. To derive the radial velocities, the eleven spectra obtained for the systemare cross-correlated against the template spectra of standard stars on anorder-by-order basis using the fxcor package in IRAF (Simkin, 1974).The majority of the spectra showed two distinct cross-correlation peaksin the quadratures, one for each component of the binary. Thus, both peaksare fitted independently with a
Gaussian profile to measure the velocitiesand their errors for the individual components. If the two peaks appearblended, a double Gaussian was applied to the combined profile using de-blend function in the task. For each of the eleven observations we then7etermined a weighted-average radial velocity for each star from all orderswithout significant contamination by telluric absorption features. Here weused as weights the inverse of the variance of the radial velocity measurementsin each order, as reported by fxcor .The heliocentric radial velocities for the primary (V p ) and the secondary(V s ) components are listed in Table 3 , along with the dates of observa-tions and the corresponding orbital phases computed with the new ephemerisgiven in the previous section. The velocities in this table have been cor-rected to the heliocentric reference system by adopting a radial velocity valuefor the template stars. The radial velocities are plotted against the orbitalphase in Fig. 2. The radial velocities of the more massive star measured byFernandez et al. (2009) are also plotted as circles in the same figure. Thereis no systematic difference between the measurements.We analysed the radial velocities for the initial orbital parameters us-ing the RVSIM software program (Kane, Schneider, & Ge, 2007). Figure 2shows the best-fit orbital solution to the radial velocity data. The resultsof the analysis are as follow: γ = -9 ± − , K =31 ± K =96 ± − with circular orbit. Using these values we estimate the projected or-bital semi-major axis and mass ratio as: a sin i =16.46 ± R ⊙ and q = M M =0.323 ±
4. Light curves and their analyses
Photometric observations of T-cyg1-01385 were obtained by automaticand robotised telescopes. The first complete light curve was obtained bythe T r ES wide-angle transiting planet survey (Alonso et al. , 1996). Addi-8 igure 2: Radial velocities for the components folded on a period of 6.5587 days. Symbolswith error bars (error bars are masked by the symbol size in some cases) show the radialvelocity measurements for the components of the system (primary: filled circles, secondary:open squares). The velocities measured by Fernandez et al. (2009) are shown by emptycircles. able 3: Heliocentric radial velocities of T-Cyg1-01385.The columns give the heliocentric Julian date, the or-bital phase (according to the ephemeris in § HJD 2400000+ Phase Star 1 Star 2 V p σ V s σ N o r m a li z ed F l u x Phase
Figure 3: Unbinned phase-folded light curve of T-Cyg1-01385 obtained by the T r ES in the
Sloan r -passband and the best-fit model. The very shallow secondary eclipse is detectableat around phase 0.5. tional photometric data, especially in the primary eclipse, were obtained bythe NSVS (Wozniak et al., 2004), SuperWASP (Christian et al., 2006), and
Kepler
Cam(Borucki, Koch, & Kepler Science Team, 2010). Since the datagathered by the SuperWASP have too large scatters we do not include theminto the analysis for the orbital parameters. In Fig. 3 we plotted the T r ESdata against orbital phase. The observations obtained by the T r ES and the
Kepler
Cam within the primary eclipse are shown in Fig.4.We may constrain the effective temperature and spectral type of the pri-mary star using the B T , V T , J, H, and K magnitudes which are already given11n Table 1. We have derived V=10.96, B-V=0.56, J-H=0.241 and H-K=0.08mag. Comparing the color indices with color-spectral type calibrations givenby Drilling & Landolt (2000) and Tokunaga (2000) we estimated a spectraltype of F8 sub-giant for the primary star. Thus, an effective temperature of T eff = 6 250 ± phoebe code of Prˇsa & Zwitter (2005). In order to obtain the physical parameters ofthe component stars we, first analysed the T r ES data. The code needs someinput parameters, which depend upon the physical structures of the com-ponent stars. The values of these parameters can be estimated from globalstellar properties. Therefore, we adopted the linear limb-darkening coeffi-cients from van Hamme (1993), the bolometric albedos from Lucy (1967)and the gravity brightening coefficients as 0.32 for both components. Therotational velocities of the components are assumed to be synchronous withthe orbital one.The adjustable parameters in the light curves fitting were the orbital in-clination, the surface potentials of the two stars, the effective temperatureof the secondary, and the color-dependent luminosity of the hotter star, thezero-epoch offset, semi-major axis of the orbit, the mass-ratio and the sys-temic velocity. A detached configuration (Mode 2) with coupling betweenluminosity and temperature was used for solution. The iterations were car-ried out automatically until convergence, and a solution was defined as theset of parameters for which the differential corrections were smaller than theprobable errors. Our final results are listed in Table 4. The uncertainties12
TrES
KeplerCam
Phase R e l a t i v e F l u x Figure 4: Eclipse light curves of T-Cyg1-01385 obtained by the T r ES at the
Sloan r -passband and the
Kepler
Cam at the z-passband. The continuous lines show the bestfits. able 4: Results of the simultaneous analyses of the T r ES and the
Kepler
Cam light curvesfor T-Cyg1-01385.
Parameters Adopted i o ± eff (K) 6 250[Fix]T eff (K) 2 940 ± ± ± r ± r ± L ( L + L ) (T r ES-r) 0.9993 ± L ( L + L ) ( Kepler -z) 0.9996 ± χ assigned to the adjusted parameters are the internal errors provided directlyby the code. The computed light curve corresponding to the simultaneouslight-velocity solution is compared with the observations in the Fig. 3 and 4.The fundamental stellar parameters for the components such as masses,radii, luminosities were calculated and listed in Table 5 together with theirformal standard deviations. The standard deviations of the parameters havebeen determined by JKTABSDIM code, which calculates distance and otherphysical parameters using several different sources of bolometric corrections(Southworth et al., 2005). The mass for the primary of M A = 1.06 ± ⊙ and secondary of M B = 0.34 ± ⊙ are consisting of an evolved lateF-star and mid M-dwarf (Drilling & Landolt , 2000).There is no measured trigonometric parallax available for the system.From the B- and V-passband measurements of Tycho and the JHK magni- ∼ jkt/codes.html able 5: Fundamental parameters of T-Cyg1-01385 Parameter Primary SecondarySpectral Type F8( ± ± a (R ⊙ ) 16.49 ± V γ (km s − ) -9 ± i ( ◦ ) 86.36 ± q ± ⊙ ) 1.059 ± ± ⊙ ) 1.989 ± ± T eff (K) 6 250 ±
100 2 940 ± L/L ⊙ ) 0.736 ± ± g ( cgs ) 3.866 ± ± vsin i ) calc. (km s − ) 15 ± ± d (pc) 355 ± tudes given in the 2MASS catalog we estimated an interstellar reddening of E ( B − V ) ≃ .
04 mag. Then we estimated an average distance to the systemas 355 ±
5. Comparison with models and other low-mass stars
Using the radii and effective temperatures we computed the luminositiesof the components as L = 5.4 ± ⊙ and L = 0.009 ± ⊙ for theprimary and secondary, respectively. In Fig. 5 we compare the positions of thestars in the L − T eff diagram. The isochrones for 5, 6, and 7 Gyr obtainedby Y models ((Yi et al., 2001), (Demarque et al., 2004)) for Z=0.004 arealso plotted. The primary star appears to an evolved F-star with an age ofabout 6 Gyr. This comparison with the theoretical models indicates that theprimary star should have poor metal abundance.For the first time Ribas (2003) and Ribas (2006) called attention aboutthe significant difference of low-mass stars’ radii between measured and pre-15 Gyr6 Gyr7 Gyrz= 0.004
Figure 5: The primary component of T-Cyg1-01385 compared with Y models for Z=0.004.For comparison the evolutionary tracks for 1 and 1.1M ⊙ and isochrones for 5, 6 and 7 Gyrare shown. ⊙ have radii and effective temperatures which areconsistent with those of models. However, larger mass stars, above 0.3 M ⊙ ,begin to deviate from the theoretical predictions in the M − R diagram. Theobserved radii are significantly larger than that of models. In contrary, theirobserved effective temperatures are significantly lower than those models, i.e.they appear as below-shifted from the theoretical M − T eff relation. The dis-crepancies in radii and effective temperatures could neither be explained bychanging the ratio of mixing-length to pressure scale height nor metallicity(Demory et al., 2009). As an alternative explanation the magnetic activity,which is responsible for the observed larger radii but cooler effective temper-atures, was adopted by Mullan & MacDonald (2001), Torres et al. (2006),Ribas (2006) and Cakirli et al. (2013). Due to high magnetic activity infast-rotating dwarfs, because of spin-orbit synchronization, their surfaces arecovered by dark spots. Faster rotation enhances solar-type activity whichresults in larger radius and lower effective temperature.Fig. 6 shows locations of the low-mass stars in the in M − R and M − T eff ⊙ . Theempirical M − R diagram shows that the stars with masses lower than about0.3 M ⊙ do not deviate from that predicted by the models. However, largestdeviations both in M − R and M − T eff occur just at the mass higherthan 0.34 M ⊙ . This mass may be taken as transition from partly convectiveatmospheres to the fully convective stars.
6. Conclusions
Spectroscopic observations of T-Cyg1-01385 are obtained and the radialvelocity curves of both components are revealed for the first time. Analy-sis of the radial velocities and the T r ES at the
Sloan r -passband and the
Kepler
Cam at the z-passband light curves yielded the physical parametersof the components. Our analysis indicates that the eclipsing binary consistsof an F8 subgiant and an M4 dwarf.
The radius of the less massive M-dwarf is larger about 26 percent but the effective temperature 18percent cooler than those estimated from the models.