The Cluster AgeS Experiment (CASE). Analysis of the Detached Eclipsing Binary V15 in the Metal-Rich Open Cluster NGC 6253
M. Rozyczka, J. Kaluzny, I.B. Thompson, A. Dotter, W. Pych, W. Narloch
aa r X i v : . [ a s t r o - ph . S R ] O c t The Clusters AgeS Experiment (CASE)Analysis of the detached eclipsing binary V15 inthe metal-rich open cluster NGC 6253 ∗ M. R o z y c z k a , J. K a l u z n y , I. B. T h o m p s o n ,A. D o t t e r W. P y c h and W. Narloch Nicolaus Copernicus Astronomical Center, ul. Bartycka 18, 00-716 Warsaw,Polande-mail: (jka, mnr, wp)@camk.edu.pl The Observatories of the Carnegie Institution of Washington, 813 SantaBarbara Street, Pasadena, CA 91101, USAe-mail: [email protected] Research School of Astronomy and Astrophysics, Australian NationalUniversity, Canberra, Australiae-mail: [email protected]
ABSTRACTWe present the first detailed analysis of the detached eclipsing binary V15 in the super-metal rich open cluster NGC 6253. We obtain the following absolute parameters: M p =1 . ± .
006 M ⊙ , R p = 1 . ± .
03 R ⊙ , L p = 2 . ± .
10 L ⊙ for the primary, and M s =1 . ± .
006 M ⊙ , R s = 1 . ± .
02 R ⊙ , L s = 2 . ± .
06 L ⊙ for the secondary. Based onDartmouth isochrones, the age of NGC 6253 is estimated to be 3.80 – 4.25 Gyr from themass-radius diagram and 3.9 – 4.6 Gyr from color-magnitude diagram (CMD) fitting. Bothof these estimates are significantly higher than those reported so far. The derived apparentdistance modulus of 11.65 mag agrees well with the range of 10.9 – 12.2 mag derived by otherauthors; however our estimated reddening (0.113 mag) is lower than the lowest published value(0.15 mag). We confirm earlier observations that model atmospheres are not accurate enoughto account for the whole CMD of the cluster, with the largest discrepancies appearing onthe subgiant and giant branches. Although age estimation from the mass-radius diagram is arelatively safe, distance- and reddening-independent procedure, our results should be verifiedby photometric and spectroscopic observations of additional detached eclipsing binaries whichwe have discovered, at least two of which are proper-motion members of NGC 6253. binaries: close binaries: spectroscopic open clusters: individual (NGC 6253) stars: indi-vidual (V15-NGC 6253) NGC 6253 is an attractive research target for several reasons. Because it is an ex-ceptionally metal-rich and evolutionary advanced open cluster, it offers a uniqueopportunity to verify predictions of stellar evolution codes in the high-metallicityregime (Claret 2007). As a high metallicity environment favors planet forma-tion, it is of special interest in the search for exoplanets (Montalto et al. 2011)and for the development of the theory of planetary systems. Finally, it is animportant benchmark for scenarios of the chemical evolution of the Galacticdisk (Montalto et al. 2011) and an ideal sample to study the dependence ofevolutionary alterations of the chemical abundances in metal-rich stars (Sestitoet al. 2007; Mikolaitis et al. 2012). ∗ Based on data obtained with the Magellan, du Pont, and Swope telescopes at Las Cam-panas Observatory.
The cluster has been the subject of several photometric surveys, brieflyrevieved by Kaluzny et al. (2014, hereafter Paper I), a proper-motion anal-ysis (Montalto et al. 2009), and a radial velocity survey (Montalto et al.2011). Metallicity determinations based on high resolution spectra range from[Fe / H] = +0 .
46 (Carretta et al. 2007; Anthony-Twarog et al. 2010) through[Fe / H] = +0 .
36 (Sestito et al. 2007) to [Fe / H] = +0 .
19 (Montalto et al. 2012).The latter value is based on observations of just two red giants while the samplesof Carretta et al. (2007), Anthony-Twarog et al. (2010) and Sestito et al. (2007)included 4, 15, and 4 stars, respectively. The rms errors range from 0.03 (Car-retta et al. 2007; Anthony-Twarog et al. 2010) to 0.13 (Montalto et al. 2012).Only Carretta et al. (2007) give an estimate of the systematic uncertainty(0.08). There is no evidence that [ α/ Fe] = 0 . / H] = +0 .
46 and [ α/ Fe] = 0 . BV system. Another problem is the interstellarreddening, which essentially all authors attempted to determine simultaneouslywith the age of the cluster by means of isochrone fitting. Additional complica-tions arise from the poorly defined red giant branch of NGC 6253 and a highcontamination of the cluster field by background and foreground stars. Theastrometric study by Montalto et al. (2009) provided a list of likely clustermembers; however it also demonstrated that on the vector-point diagram themembers are poorly separated from the field population.In Paper I, we reported the results of an extensive photometric survey ofNGC 6253 as part of a search for variable stars. Two new detached eclipsingbinaries were discovered at the turnoff region of the cluster, and another one onthe subgiant branch. These systems can be used to independently determinethe age and distance modulus of NGC 6253 as proposed by (Paczy´nski 1997).We also obtained good phase coverage for another turnoff binary, discovered byMontalto et al. (2011). This object, their star Our photometric observations of V15 consist of two data sets secured at LasCampanas Observatory. BV observations collected with the 1.0-m Swope tele-scope and the SITE3 CCD camera are described in detail in Paper I. Additional BV data were obtained on the 2.5-m du Pont telescope equipped with the SITE2camera providing a scale of 0.26 arcsec/pixel. Profile photometry was extractedwith the Daophot/Allstar utility (Stetson 1987). Since the field of NGC 6253 isonly moderately crowded, the quality of the profile photometry was comparableto that obtained with the image subtraction technique. Moreover, the profilephotometry practically eliminated any zero-point differences measured betweenthe du Pont and Swope data. The instrumental magnitudes were transformedto the standard values using stars observed by Sagar et al. (2001). A detailedjustification for this choice of secondary standards is given in Paper I.The light curves of V15 turned out to be unstable; most likely due to chro-mospheric activity. Such instabilities are common for short period binariescomposed of low-mass stars with convective envelopes. We detected varia-tions both in and out of the eclipses, with amplitudes reaching 0.03 mag in V . Upon averaging over seasonal light curves we found V = 14 . ± .
05 magand B − V = 0 . ± .
007 mag at quadratures.Altogether, 13 eclipses of V15 were observed between 2007 August 7 and2013 September 13. However, only for a few of these were both ingress andegress covered, which would allow for precise timing. This prevented us froma classical period study based on the determination of individual moments ofeclipses and the O-C technique. We began by assuming P =2 . V light curve includingdata from all seasons and both telescopes was used, with seasonal light curvesadjusted in magnitude to assure a consistent level of the maximum light. Thecombined curve was fitted with the JKTEBOP code † (Southworth et al. 2004),allowing only for variations of P and the moment of primary eclipse T . Mode8 of the code was used, which enabled a robust determination of the errors ofthe two parameters with the help of a Monte Carlo algorithm. We obtained thelinear ephemeris HJD min = 2455691 . . × E (1)where numbers in parentheses are the uncertainties of the last significant digits.This refined period was then used to calculate updated geometric parameters.These turned out to be insignificantly different from those reported in Section 3.No evidence for any variability of P was found. The refined period is 65.7 sshorter than that found by Montalto et al. (2011). Their result was based onfour eclipses, all only partially covered during the ingress. This difference islarge enough to cause a profound dephasing of seasonal light curves when theirperiod is used. Our radial velocity data are based on observations obtained with the blue chan-nel of the MIKE Echelle spectrograph (Bernstein et al. 2003) on the MagellanClay telescope between 2010 June 7 and 2011 July 29 (UT). Most of the ob-servations consisted of two 1200 s exposures interlaced with an exposure of aTh/Ar lamp (depending on observing conditions, some exposures were shorteror longer). For all observations a 0 . × . × λ = 440 nm the resolution was ∼ λ was 45. The spectra wereprocessed using a pipeline developed by Dan Kelson following the formalism ofKelson (2003).A total of 15 spectra were used for the analysis. The velocities were measuredusing software based on the TODCOR algorithm of Zucker & Mazeh (1994),kindly made available by Guillermo Torres. Synthetic echelle-resolution spectrafrom the library of Coelho et al. (2005) with [Fe / H] = +0 .
46 and [ α /Fe]=0.0were used as velocity templates. The templates were Gaussian-smoothed to † match the resolution of the observed spectra. All velocities were measured onthe wavelength range 400 – 460 nm. Results of the measurements are presentedin Table 1. A nonlinear least-squares fit to the observed velocity curves of V15 was obtainedwith the help of code kindly made available by Guillermo Torres. Since thesecondary minimum occurs at phase 0.5, the orbital eccentricity was fixed atzero while fitting. Observations and orbital solutions are shown in Fig. 1, andthe derived orbital parameters are listed in Table 2 together with formal errorsreturned by the fitting routine. The table also lists standard deviations fromthe orbital solution σ p and σ s which are a measure of the precision of a singlevelocity measurement. We note that the derived systemic velocity γ of V15agrees well with the mean radial velocity of NGC 6253, which according toMontalto et al. (2011) is equal to 29 . ± .
85) km/s.For the photometric analysis we selected six seasonal curves distinguished bylow dispersion and relatively high symmetry. The analysis was performed withthe PHOEBE implementation (Prˇsa & Zwitter 2005) of the Wilson-Devinneymodel (Wilson & Devinney 1971; Wilson 1979) which offers the possibility ofsimultaneous fitting of V and B light curves. Linear limb darkening coefficientswere interpolated from the tables of Claret (2000) with the help of the JKTLDcode. ‡ .The color of V15 remains nearly constant at all phases, indicating nearlyequal temperatures of the components. The map of galactic extinction bySchlafly & Finkbeiner (2011) predicts E ( B − V ) = 0 .
316 mag at the locationof NGC 6253. However, the amount of foreground extinction is not known(Anthony-Twarog et al. 2010), and values ranging from E ( B − V ) = 0 .
23 mag(Bragaglia et al. 1997) to E ( B − V ) = 0 .
15 mag (Montalto et al. 2009) can befound in the literature. Thus a direct estimation of the temperature from thedereddened color is not feasible. Our procedure, based on Dartmouth isochrones(Dotter et al. 2008) fitted to the CMD of the cluster (see Section 4), yields5830 K and this is the value we adopt for both the primary and the secondary, T p and T s , at the start of the PHOEBE iterations.The eclipses of V15 are partial, moderately deep ( ∼ T p fixed and iterating for T s , orbitalinclination i and surface potentials (Ω p , Ω s ) we obtained a range of equallygood fits for which the sum of the component radii was nearly constant at3 . ± .
009 R ⊙ . A pair of such fits is shown in Fig. 2. Photometric solutionswith 3 . < R p + R s < .
165 R ⊙ occupy a stripe signified by the grey coloredregion in Fig. 3.To remove the degeneracy we calculated a series of synthetic spectra ofV15, again using the library of Coelho et al. (2005). The spectra retrievedfrom the library were rotationally broadened (a synchronous rotation of bothcomponents was assumed) and Doppler-shifted to the velocities of the primaryand secondary listed in Table 1. These pairs of spectra corresponding to agiven phase were then combined in various proportions and compared to theobserved spectrum taken at the same phase. The comparison was performedseparately for 15 different spectral ranges between 408 and 496 nm, each 3 nm ‡ long (we decided to compare short segments of the spectra rather than the wholeavailable range in order to account for the varying mean intensity). For eachphase and each segment the best value of the total secondary-to-primary lightratio was found by minimizing the sum of squared differences in synthetic andobserved spectrum intensity. For further analysis the mean value of light ratiosthus obtained, q l = 0 . ± . q l one can derive the ratio ofthe radii of the components of the binary R s /R p = q q l β ( T p ) /β ( T s ) , where β ( T ) = Z B ν ( T ) s ( ν ) dν,B ν ( T ) is the Planck function and s ( ν ) is the spectral sensitivity of MIKE’s bluearm. Since the difference between T s and T p is small, we can write R s /R p = √ q l (1 − T s − T p ) /T s ) . We found that the correction introduced by the temperature factor was smallerthan 0.005 and could be neglected. Thus, the spectroscopic data impose acondition R s /R p = 0 . ± .
014 which on the ( R p , R s ) plane defines a stripemarked with the light grey color in Fig. 3. The best solution is defined by theintersection of lines R p + R s = 3 .
156 R ⊙ and R s /R p = 0 . R p = 1 . ± .
018 R ⊙ and R s = 1 . ± . R ⊙ , where the errors aredefined by the corners of the dark-grey quadrangle in Fig. 3. The remainingparameters of the best photometric model of V15 can be found in Table 3, andthe final fits to the observed light curves are shown in Fig. 4. The errors of i , T s , ( L p /L s ) V and ( L p /L s ) B given in Table 3 are based on 20,000 Monte Carlosimulations performed with the help of a procedure written in PHOEBE-scripterafter that outlined in the description of the JKTEBOP code (Southworth et al.2004, and references therein). Upon combining data from Tables 2 and 3 weobtained the absolute parameters of V15 listed in Table 4.We finish this Section with a word of caution. One should be very carefulwhen dealing with light curves similar to that of V15, as accepting the firstsolution found may lead one completely astray. The problem becomes especiallyacute when automatic light-curve solvers are applied. Fig. 5 shows the color-magnitude diagram of NGC 6253 to which Dartmouthisochrones with [Fe/H] = +0.46 and [ α /Fe]=0.0 are fitted. Simultaneous fittingof unevolved main sequence, turnoff region, subgiant branch and giant branchturned out to be impossible. Similar problems had been encountered earlier byAnthony-Twarog et al. (2007), Montalto et al. (2009), and Anthony-Twarog etal. (2010). Since uncertainties of stellar models grow larger with evolutionarytime, we decided to assign the largest weight to main sequence and turnoff. Wefound the latter to be nearly entirely contained between isochrones for 3.9 and4.6 Gyr, with that for 4.25 Gyr running through its center (Fig. 5). The meanturnoff temperature obtained from the three curves amounts to 5830 K withthe caveat that the fit yields E ( B − V ) = 0 .
113 mag, i.e. a value lower thanthe lowest used so far. Keeping this in mind, we performed a consistency checkusing dereddended color index of the cluster and color-temperature calibrationof Sousa et al. (2011) which is valid for − . < [Fe/H/] < +0 .
5, 0 . < B − V < . < T < B − V ) = 0 .
724 mag yields T = 5797 K – a value consistent with the assumedone within the 1- σ range of the calibration, equal to 52 K.Fig. 5 also shows the location of V15 and its components on the CMD of thecluster. Both the primary and the secondary are located at the turnoff, withthe primary being slightly more evolved. The activity of V15 suggests that itscomponents might be cooler and larger than inactive stars of the same massand at the same evolutionary phase (see e.g. Morales et al. 2008). However,there are good reasons to believe that they are quite normal. First, none ofour spectra shows emission in Ca II H & K or the Balmer lines. Second, bothcomponents are located close to the blue edge of the turnoff, whereas one wouldexpect them to be shifted to the red if their sizes and temperatures are affectedby the activity.The apparent distance modulus obtained from the isochrone fit is 11.65 mag.This is nearly the mean of values found by the other authors, which range from10.9 mag (Sestito et al. 2007) to 12.2 mag (Twarog et al. 2003).Almost all ages reported so far for NGC 6253 range from 2.5 Gyr (Anthony-Twarog et al. 2007) to 3.5 Gyr (Montalto et al. 2009), the sole exception isan age of 5 Gyr found by Piatti et al. (1998). Our attempts to fit Dartmouthisochrones for those ages failed completely. For the younger ages the discrep-ancy between theoretical turnoff temperature and temperature obtained fromthe calibration was too large, while for the older ages the reddening becameunreasonably small ( < .
08 mag). Further support for our CMD fit comes fromthe mass-radius diagram shown in Fig. 6, where error boxes of both componentsare contained between isochrones for 3.8 Gyr and 4.25 Gyr. As the mass-radiusrelation is free from uncertainties in distance and extinction that plague agesderived via isochrone fitting, we regard this estimate as very reliable. The dataare also compatible with 3.8 Gyr and 4.25 Gyr isochrones in the mass-luminositydiagram (Fig. 6) , but because of the way the temperature was estimated thisresult cannot be regarded as an independent verification.The recently published BT-Settl model atmospheres (Allard 2014) producebluer isochrones than those from the Dartmouth database. We obtained severalsuch isochrones and repeated CMD and mass-radius fitting. The age derivedfrom the mass-radius diagram did not change; essentially the same age as before(3.8-4.5 Gyr) was also derived from the CMD fit. However, the distance modulusand reddening changed to 11.45 mag and 0.13 mag, respectively. The overallagreement of isochrones with the data did not improve. While most objects onthe subgiant branch fell within the area bordered by 3.8 Gyr and 4.5 Gyr lines(as opposed to Fig. 5, where most of them lie above the 3.9 Gyr line), all BT-Settl isochrones missed the ”blue clump” composed of seven stars surroundingthe location of the binary. The O-C discrepancy on the giant branch remainedas large as before, however the theoretical colors were bluer than the observedones.Brogaard et al. (2012) extensively discuss problems related to the theoreticalrelation between colours and effective temperatures, which are a major uncer-tainty when comparing observations to stellar models in the CMD. The problembecomes especially acute at high metallicities, where a significant contributionto opacity comes from metals with poorly known abundances. Brogaard et al.(2012) explicitly warn that a good match between models and the observedCMD is likely to be more of a coincidence than a reflection of reality. Obvi-ously, the same may be true regarding age estimation based on CMD fitting.Indeed, the agreement between ages derived for V15 from CMD and mass-radiusdiagram is so good that a suspicion arises it might be spurious. Although agedetermination from the mass-radius diagram is a relatively safe procedure, it isclear that our results should be verified.In Paper I we reported a discovery of additional three detached eclipsingbinaries in NGC 6253, two of which are proper motion members of the cluster(PM data are missing for the third one). All these systems are bright enough( V m ax < . Based on photometric and spectroscopic observations of the detached eclipsingbinary V15 in NGC 6253 we derived absolute parameters of its components.Both the primary and the secondary are located at the turnoff of the cluster,making them suitable for an age estimate from the mass-radius diagram. UsingDartmouth isochrones we find NGC 6253 to be 3.80 – 4.25 Gyr old - a rangeof ages compatible with 3.9 – 4.6 Gyr derived from CMD fitting. Both theseestimates are significantly higher than those reported so far, which with oneexception do not exceed 3.5 Gyr. The apparent distance modulus found fromCMD fitting amounts to 11.65 mag and it agrees well with 10.9 – 12.2 magderived by other authors; however the reddening (0.113 mag) is lower thanthe lowest published value (0.15 mag). We confirm earlier conclusions thatmodels of metal-rich atmospheres are not accurate enough to account for thewhole CMD of the cluster, with the largest discrepancies appearing at advancedevolutionary phases. Although age estimation from the mass-radius diagramis a relatively safe, distance- and reddening-independent procedure, we stressthe need to verify our results by photometric and spectroscopic observations ofthree detached eclipsing binaries discovered by Kaluzny et al. (2014), at leasttwo of which are proper-motion members of NGC 6253.
Acknowledgements.
JK, WN, WP and MR were partly supported by thegrant DEC-2012/05/B/ST9/03931 from the Polish National Science Center.
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Table 1: Radial velocity observations of V15HJD v p v s Phase ( O − C ) p ( O − C ) s -2450000 [km/s] [km/s] [km/s] [km/s]5354.59687 56.61 -120.07 0.840 -0.72 -0.155354.81742 17.45 -77.63 0.925 0.18 -0.185355.62665 -130.44 78.70 0.240 -0.18 -0.255388.72531 -91.68 38.97 0.107 0.27 0.645389.51319 -81.33 27.85 0.413 0.27 0.495457.55448 49.27 -110.26 0.863 0.97 0.095458.47928 -129.19 77.62 0.223 -0.20 0.025459.48720 37.94 -100.56 0.615 -0.50 -0.665763.64679 51.86 -115.00 0.854 -0.34 -0.525764.61295 -129.86 77.45 0.229 -0.25 -0.805770.73991 37.08 -97.38 0.611 0.39 0.665836.49309 -118.38 67.40 0.172 0.10 0.946096.58400 -128.34 77.07 0.280 0.36 -0.226096.80512 -103.62 51.89 0.366 1.13 -0.016097.66008 67.25 -131.80 0.698 -0.42 -0.92Table 2: Orbital parameters of V15Parameter Value Error γ (km s − ) -28.73 0.011 K p (km s − ) 101.61 0.20 K s (km s − ) 108.06 0.19 q e a σ p (km s − ) 0.51 σ s (km s − ) 0.54Derived quantities: A sin i (R ⊙ ) 10.657 0.015 M p sin i (M ⊙ ) 1.2662 0.0055 M s sin i (M ⊙ ) 1.1906 0.0056 a Assumed in fit0Table 3: Photometric parameters of V15Parameter Value Error i (deg) 82.14 0.06 R p R s e a T p (K) 5830 a T s (K) 5842 10( L p /L s ) V L p /L s ) B σ rms ( V ) (mmag) 7 σ rms ( B ) (mmag) 7 V p (mag) 15.297 0.012 b V s (mag) 15.665 0.016 b B p (mag) 16.137 0.012 b B s (mag) 16.497 0.016 b ( B − V ) p (mag) 0.840 0.017 b ( B − V ) s (mag) 0.832 0.023 ba Assumed. b Includes errors from photometric solution and profile photometry.Table 4: The physical properties of V15Parameter Value Error M p (M ⊙ ) 1.303 0.006 M s (M ⊙ ) 1.225 0.006 R p (R ⊙ ) 1.714 0.018 R s (R ⊙ ) 1.441 0.018 T p (K) 5830 a T s (K) 5842 10 L bolp (L ⊙ ) 3.05 0.10 L bols (L ⊙ ) 2.17 0.06 A (R ⊙ ) 10.758 0.017 P (d) 2.5724149 3 × − Assumed.1Figure 1: Velocity curve of V15. Top panel: observed velocities (filled circles:primary; open circles: secondary) and PHOEBE fits (lines). Bottom panel:residuals to the orbital fits.Figure 2: Illustration of the degeneracy of photometric solutions for V15. Fromtop to bottom: O − C from the V light curve for the solution with ( R p , R s ) =(1.600,1.556) R ⊙ ; the same for the solution with ( R p , R s ) = (1.750,1.406) R ⊙ ;difference between the two solutions.2Figure 3: Photometric fits (grey) and spectroscopic solutions (light-grey) forV15. The black dot marks the best model of the system.Figure 4: Top panel: final fits to light curves of V15 (the B light curve is shiftedupwards by 0.6 mag). Middle panel: V residuals. Bottom panel: B residuals.3Figure 5: The color-magnitude diagram of NGC 6253 with fitted Dartmouthisochrones. The apparent distance modulus and E ( B − V ) resulting from thefit are equal to 11.65 mag and 0.113 mag, respectively. Labels indicate ages inGyr. Large dots show locations of V15 and its components (errors in V are toosmall to be visualized on this scale). Only proper motion and radial velocitymembers of the cluster are plotted, following Montalto et al. (2009; 2011).4Figure 6: Dartmouth isochrones for [Fe/H] = +0.46, [ αα