The Clusters AgeS Experiment (CASE). III. Analysis of the Eccentric Eclipsing Binary V32 in the Globular Cluster NGC 6397
aa r X i v : . [ a s t r o - ph ] A p r The Clusters AgeS Experiment (CASE). III.Analysis of the Eccentric Eclipsing Binary V32 in the GlobularCluster NGC 6397 J. Kaluzny , I. B. Thompson , S. M. Rucinski , W. Krzeminski , ABSTRACT
We present spectroscopic and photometric observations of the eclipsing binaryV32 located in the central field of the globular cluster NGC 6397. The variableis a single-line spectroscopic binary with an orbital period of 9.8783 d and alarge eccentricity of e = 0 .
32. Its systemic velocity ( γ = 20 . − ) andmetallicity ([Fe/H] ∼ -1.9) are both consistent with cluster membership. Theprimary component of the binary is located at the top of the main-sequenceturn-off on the cluster color-magnitude diagram. Only a shallow primary eclipseis observed in the light curve. Based on stellar models for an age of 12 Gyr and themass-function derived from the radial velocity curve, we estimate the masses tobe M p = 0 .
79 M ⊙ and M s = 0 .
23 M ⊙ . The light curve of V32 can be reproducedby adopting R p = 1 .
569 R ⊙ and R s = 0 .
236 R ⊙ for the radii and i = 85 .
44 degfor the system inclination. The system geometry precludes observations of thesecondary eclipse. The large eccentricity of the orbit is puzzling given that formetal poor, halo binaries the transition from circular to eccentric orbit occursat an orbital period of about 20 days. We suppose that the orbit of V32 wasmodified relatively recently by dynamical interaction with other cluster star(s).An alternative explanation of the observed eccentricity calls for the presence ofa third body in the system.
Subject headings: binaries: spectroscopic – stars: individual (V32-NGC 6397) Copernicus Astronomical Center, Bartycka 18, 00-716 Warsaw, Poland; [email protected] Carnegie Observatories, 813 Santa Barbara St., Pasadena, CA 91101-1292; [email protected] David Dunlap Observatory, Department of Astronomy and Astrophysics, University of Toronto, P.O.Box 360, Richmond Hill, ON L4C 4Y6, Canada; [email protected] Las Campanas Observatory, Casilla 601, La Serena, Chile; [email protected] This paper utilizes data obtained with the 6.5-meter Magellan Telescopes located at Las CampanasObservatory, Chile.
1. INTRODUCTION
Little is known about the properties of main-sequence binary stars in globular clusters.These systems offer the potential for measurements of cluster age and distance independentof cluster main-sequence fitting (see, for example, Paczy´nski 1997; Thompson et al. 2001),and as testbeds for theories of the stellar evolution of Population-II stars.The eclipsing binary V32-N6397 (hereafter V32) was discovered by Kaluzny et al. (2006)during a survey for variable stars in the central field of the globular cluster NGC 6397. Theyobserved only one shallow eclipse event with a depth of about 30 mmag. With V max = 16 .
2. SPECTROSCOPIC AND PHOTOMETRIC OBSERVATIONS
Spectroscopic observations of V32 stars were carried out with the MIKE echelle spectro-graph (Bernstein et al. 2003) on the Magellan II (Clay) telescope at Las Campanas Obser-vatory. The data were collected during several observing runs between 2005 May and 2007August. For this analysis we use data obtained with the blue channel of MIKE coveringthe wavelength range 3350 ˚A to 5000 ˚A at a resolving power of λ/ ∆ λ ≈ , . × . × ≃ . . Eachof the final individual spectra typically consisted of two 300 s exposures interlaced with anexposure of a thorium-argon lamp. We obtained 16 spectra of V32.Velocities were measured with the IRAF FXCOR package. For the template we used asingle MIKE spectrum of the metal-poor subgiant HD 193901 ([Fe / H] = − .
22, Tomkin et al.1992) with an adopted radial velocity of −
172 km s − . The velocity measurements weremade over the wavelength range 4000 ˚A – 5000 ˚A with the Balmer lines masked out of the IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Asso-ciation of Universities for Research in Astronomy, Inc., under cooperative agreement with the NSF. T is the moment of periastronpassage and the remaining quantities have their standard meaning. The solution with 6 freeparameters implies that a superior conjunction occured at HJ D = 2453109 . ± . HJ D = 2453109 . P = 9 . T = 2453899 . P = 9 . T = 2453899 . P and T fixed at these values is listed in the thirdcolumn of Table 2. The corresponding velocity curve and observed velocities are plotted inFig. 1.At the beginning of the 2007 observing season we had in hand an approximate ephemerisfor V32 and further photometric observations of a few predicted eclipses of the binary wereobtained. The observations were made with the TEK5 camera on the 2.5m du Pont telescopeat Las Campanas Observatory. The instrumental setup and reduction methods were the sameas these described in Kaluzny et al. (2006). These observations were mostly hampered bypoor weather but on one of the nights we obtained some useful data covering the phasesimmediately preceding the predicted ingress into primary eclipse. These observations helpedto constrain the spectroscopic solution as described above. The V -band light curve based onall available observations of V32 is shown in Fig. 2 for the region of the light curve near theobserved eclipse. It is phased with the spectroscopic ephemeris listed in the third columnof Table 2. The continuous line shows the synthetic light curve corresponding to the modelpresented in the next section. The full V -band observation data set is given in Table 3.The V /B − V color-magnitude diagram for NGC 6397 based on the du Pont photometricobservations is presented in Fig. 3. 4 –
3. Properties of V32
A direct determination of the absolute parameters of the components of V32 is hamperedby the lack of velocity observations of the secondary. In the following analysis we assumethat the variable is a member of the globular cluster NGC 6397. This conclusion is based onfour arguments. First, the systemic velocity of V32 ( γ = 20 . ± .
19 km s − ) agrees with themean velocity of the cluster determined by Meylan & Mayor (1991), V rad = 18 . ± . − with a central velocity dispersion of 4.5 km s − . Second, on the V /B − V diagram shown inFig. 3 the binary is located at the top of the cluster turnoff, the primary is apparently justbeginning to evolve onto the cluster sub-giant branch. Third, the variable is located on thesky only 51 arcsec from the projected center of NGC 6397. The cluster itself has a half-lightradius of r h = 140 arcsec (Harris 1996). Finally, we have estimated the metallicity of V32.We shifted the individual spectra of V32 to zero velocity, and averaged these shifted spectrato produce a mean spectrum for V32. We measured the equivalent widths of 10 Fe I linesselected from Thompson et al. (2008) in this mean spectrum, and compared these to theequivalent widths measured in a grid of alpha-enhanced synthetic spectra from Coelho et al.(2005) linearly interpolated at T eff = 6400 and log g = 4.3 for metallicities of [Fe/H] = -2.4,-2.0, -1.6, and -1.2. From this comparison we obtain [Fe/H] = -1.9 ± / H] = − . α -element enhancement of[ α/ H] = +0 .
34. Recent estimates of the age of NGC 6397 span a range of 11 . ± .
47 Gyr(Hansen et al. 2007) to 13 . ± . . ± . . ± . / H] = − . α/ H] = +0 .
4, thelocation of the primary of V32 on the cluster
V / ( B − V ) diagram implies a primary mass of M p = 0 . ± .
009 M ⊙ . Assuming for the moment an orbital inclination of i = 90 deg, weuse the measured mass function to derive a secondary mass of M s = 0 . ± . M ⊙ . TheDotter et al. (2007) models then suggest a secondary radius of R s = 0 . R ⊙ .We fit the light curve of V32 using the PHOEBE code (Prˇsa & Zwitter 2005) which isbased on the models of Wilson & Devinney (1971) and Wilson (1979). Two free parameterswere fit: the inclination i and the radius of the primary. The remaining parameters were fixedas follows: The orbital elements were adopted from the 3rd column of Table 2. The effectivetemperature of the primary was set at T p = 6490 K based on an unreddened ( B − V ) p = 0 . E ( B − V ) = 0 . T s = 3874 usingthe Dotter et al. (2007) models. The solution converged to i = 84 .
96 deg and R p = 1 . R ⊙ .We then made one more iteration of the above procedure starting with i = 84 .
96 deg, M s =0 . M ⊙ and R s = 0 . R ⊙ . The solution converged to i = 85 .
03 deg and R p = 1 . R ⊙ .The calculated luminosity ratio in the V -band is L p /L s = 664. In the middle of the primaryeclipse the entire disk of the secondary is projected against disk of the primary – the eclipseis a transit. The secondary (occultation) eclipse is not observable. The estimated radiusof the primary is consistent with its location above the main-sequence turnoff on the color-magnitude diagram of the cluster. For a mass of 0 . M ⊙ and an age of 12 Gyr the modelsof Dotter et al. (2007) predict a radius of r = 1 . R ⊙ . For the same age the radius reaches r = 1 . R ⊙ for a mass of 0 . M ⊙ . Given the approximate nature of our analysis weconsider the derived solution to be self-consistent.Clearly the limited data make a direct and accurate determination of the absoluteparameters for components of V32 impossible. The light curve lacks a secondary eclipseand the photometric coverage of the primary eclipse is not complete. However, the deducedparameters of V32 reproduce well its observed radial velocity and light curves, and areself-consistent with evolutionary models of low mass stars.
4. Discussion
The properties of V32 are consistent with membership in the globular cluster NGC 6397.The system is composed of two main-sequence stars with an age of about 12 Gyr. The orbitshows a large eccentricity with e = 0 .
32. Such an eccentricity is unexpected is since tidalforces should circularize the orbit of the binary on a short time scale. The theoreticaland observational aspects of the circularization of binary orbits for solar mass binaries arediscussed in some detail in Meibom & Mathieu (2005). They estimate, based on results ofLatham et al. (2002), that halo binaries with periods shorter than 15 . +2 . − . d should havecircular orbits. For the old open clusters NGC 188 (age ≈ ≈ < P <
10 days were detected in the central part of47 Tuc in the HST/WFPC2 survey by Albrow et al. (2001) using photometric observations.All of these have presumed circular orbits although observations do not cover the full orbital 6 –cycle for two of the systems with the longest periods. Extensive ground base surveys of47 Tuc (Weldrake et al. 2004) and ω Cen (Kaluzny et al. 2004; Weldrake et al. 2007) led tothe detection of two eclipsing binaries with orbital periods exceeding 10 days. Follow upobservations conducted by our group show that 47 Tuc-V69 and ω Cen-V406 have eccentricorbits with P = 29 d and P = 71 d, respectively (Thompson et al. 2008, in preparation).All of the other cluster eclipsing binaries reported so far have orbital periods less than 10days and show circular orbits.The eccentric orbit of V32 can possibly be due to a relatively recent dynamical interac-tion of the binary with other cluster star(s). NGC 6397 has a “collapsed” core (Djorgovski & King1986) containing a population of about 20 X-ray sources including 9 candidate cataclysmicvariables, a millisecond pulsar and several candidate BY Dra-type close binaries (Grindlay et al.2001). Kaluzny et al. (2006) reported the detection of 9 eclipsing binaries and 6 candidatesfor ellipsoidal binaries located in the central part of the cluster. A dynamical interactioncapable of transforming the circular orbit of V32 into a highly eccentric one would also likelysignificantly disturb the systemic velocity of the binary. Our data show that the radial ve-locity of V32 is not unusual for an object from the central part of the cluster. Unfortunately,the transverse velocity is V32 is unknown as the binary is not included in the recent propermotion survey of NGC 6397 conducted by Kalirai et al. (2007).As an alternative explanation of the eccentric orbit of V32 we consider the possibilitythat the system is in fact a hierarchical triple. The third component located on the outerorbit is capable of generating eccentricity in the inner binary. Extensive reviews of theevolution of the orbits of binary stars have been presented by Eggleton (2006) and Mazeh(2008). Numerical simulations of stellar clusters predict dynamical formation of triple stars,especially in the presence of primordial binaries (McMillan et al. 1990; Heggie & Aarseth1992). Examples of known triple stars in globular clusters include the pulsar PSR B1620-26 in M4 (Thorsett et al. 1993) and possibly the ultracompact X-ray binary 4U 1820-303(Zdziarski et al. 2007). The hypothesis that V32 is a triple can be tested by spectroscopicobservations aimed at detection of variability of the systemic velocity of the putative innerbinary. We see no systemic velocity residuals from the orbit give in Table 3 over the 2.2 yearduration of our velocity observations.Finally we comment on possibility that the eccentric orbit of V32 is related to its ratherlow mass ratio q = M s /M p ≈ .
30. According to Mathieu & Mazeh (1988) the time scaleof circularization of a binary is related to q by the relation: τ circ ∝ q / (1 + q − ) / . Thiscorresponds to an increase of τ circ of a factor of 1.6 as the mass ratio ranges from q = 1 to q = 0 .
3. For low values of q the contribution of the secondary to the circularization processbecomes negligible (Mazeh 2008). At the same time τ circ is a strong function of the orbital 7 –period P , with τ circ ∝ P / (Zahn 1977). The net result is that the circularization periodwill lengthen as the mass ratio decreases from for q = 1 and q = 0 .
3, especially for longperiod systems. It is appropriate to note at this point that that the sample of halo starspresented by Latham et al. (2002) consists entirely of single line binaries and hence objectswith mass ratios noticeably lower than unity. More globular cluster binaries with periodof the order of 10 days have to be detected and analyzed before V32 can be called a trulyunusual system. The CASE group is in a process of collecting data which can shed morelight on the relation between eccentricity and orbital period for binaries in globular clusters.JK and WK were supported by the grant 1 P03D 001 28 from the Ministry of Science andHigher Education, Poland. Research of JK is also supported by the Foundation for PolishScience through the grant MISTRZ. IBT was supported by NSF grant AST-0507325. Sup-port from the Natural Sciences and Engineering Council of Canada to SMR is acknowledgedwith gratitude. It is a pleasure to thank Willy Torres for sharing his code with us.
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10 –Table 1. Velocity Observations of V32
HJD V rad σ (- 2450000) km s − km s −
11 –Table 2. Orbital Parameters for V32Parameter Value Value P (days) 9.8783 ± a T (HJD-245 0000) 3899.832 ± a γ ( km s − ) 20.67 ± ± K p ( km s − ) 23.92 ± ± e ± ± ω (deg) 72.7 ± ± O − C ) rms ( km s − ) 0.60 0.62Derived quantities: f ( M ) sin i ( M ⊙ ) 0.01192 ± ± A p sin ( i ) ( R ⊙ ) 3.079 ± ± a Fixed based on photometry. 12 –Table 3. V -band Photometric Observations of V32 HJD
V σ V (- 2450000)2765.8121 16.128 0.0082765.8209 16.134 0.0082765.8277 16.128 0.0082765.8371 16.126 0.0082765.8677 16.125 0.0082765.8894 16.129 0.0082765.8966 16.122 0.0082765.9061 16.129 0.0082765.9128 16.127 0.0082765.9294 16.131 0.008Note. — This Table is pub-lished in its entirety in the elec-tronic addition of the Astro-nomical Journal . A portionhere is shown for guidance re-garding its form and content.