photometric monitoring of open clusters. ii. a new m dwarf eclipsing ...

The Astronomical Journal, 131:555–561, 2006 January # 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.

PHOTOMETRIC MONITORING OF OPEN CLUSTERS. II. A NEW M DWARF ECLIPSING BINARY SYSTEM IN THE OPEN CLUSTER NGC 1647 Leslie Hebb,1 Rosemary F. G. Wyse,1 Gerard Gilmore,2 and Jon Holtzman3 Received 2005 June 20; accepted 2005 September 8

ABSTRACT We have discovered a new M dwarf eclipsing binary system in the open cluster NGC 1647. Unlike field binaries, accurate age and metallicity estimates for the system are potentially available through an analysis of the brighter cluster members. This information will ultimately allow a detailed and robust comparison with the appropriate stellar evolution models. Analysis of our spectroscopic radial velocity data and photometric light-curve data gives an orbital period of 0:618790
0:000005 days and the following properties for the individual stellar components: M1 ¼ 0:47
0:05 M , M2 ¼ 0:19
0:02 M , R1 ¼ 0:57
0:02 R , R2 ¼ 0:21
0:01 R , TeA1 ¼ 3320
150 K, and TeA2 ¼ 2910
150 K. The small mass ratio and low secondary mass provide an unprecedented opportunity to test stellar models. Adopting an age of 150 Myr, consistent with the cluster turn-off, and testing a range of metallicities, covering plausible values for local open clusters, we find that none of the models are consistent with all the properties of both M dwarf stars in the eclipsing binary. Key words: binaries: eclipsing — open clusters and associations: individual (NGC 1647) — stars: fundamental parameters — stars: low-mass, brown dwarfs

1. INTRODUCTION

2003; Leung & Schneider 1978; Metcalfe et al. 1996; Maceroni & Montalba´n 2004; Creevey et al. 2005; Lopez-Morales & Ribas 2005), four of which are well studied. All these systems were discovered serendipitously and are in the field, with unknown ages and metallicities. These parameters affect the luminosity, and their large uncertainties limit our ability to use these systems to test stellar evolution models. In addition, the known systems have mass ratios close to unity, so that each binary tests the models over only a limited range of parameter space. All the current theoretical stellar evolution models for M dwarf stars fail to predict consistently correct values for the masses of main-sequence stars below 0.5 M (Hillenbrand & White 2004). The models underestimate the radii of M dwarf stars by 10%– 15% (Torres & Ribas 2002; Ribas 2003; Lopez-Morales & Ribas 2005) and are too luminous in the optical by 0.5 mag below 0.5 M (Delfosse et al. 2000). Furthermore, the optical data exhibit scatter in the mass-luminosity relation that is greater than the measurement errors (Delfosse et al. 2000). Precise and accurate measurements of intrinsic stellar parameters for a range of stars below 0.5 M and with known age and metallicity are necessary to provide further tests and calibration of stellar evolution models. Thus, we initiated a photometric monitoring survey targeting M dwarf stars in six open clusters with a range of metallicities (0.2 dex to solar) and ages (0.15–4 Gyr), searching for low-mass eclipsing binary systems. We observed each cluster over greater than 1 deg 2 while sampling the stars on timescales of hours to months, expecting a yield of several systems (Hebb et al. 2004). Our expectations have been realized, and the binary system we have discovered in NGC 1647 is the subject of this paper.

Determining the fundamental properties (mass, radius, luminosity, and effective temperature) of low-mass stars is particularly important, as they comprise 80% of the stars in the local universe (Gizis & Reid 1995). Their properties affect the measurement of the overall baryonic content of the universe, the determination of characteristic structure in the stellar initial mass function, and the calibration of star formation theories. Furthermore, it is easier to detect planets via transits around lowmass stars rather than solar analogs. The radius of the planet is closer in diameter to the stellar radius and has the ability to block more of the stellar disk, ultimately causing larger transit depths. However, the derived planet properties depend on precise knowledge of the mass and radius of the parent star. Detached eclipsing binary stars with late-type primaries provide the most accurate measurements of the intrinsic stellar parameters of low-mass stars. Orbital analyses of these systems place extremely stringent constraints on our understanding of stellar evolution, since they simultaneously provide measurements of the masses, radii, temperatures, and absolute luminosities for two stars that are (reasonably) assumed to have a single age and metallicity (Lastennet & Valls-Gabaud 2002). Other techniques used to derive the properties of low-mass stars are more limited. Visual binaries have been used to derive mass and luminosity measurements (Se´gransan et al. 2000) but not radius or temperature, and more recently G–M and F–M dwarf eclipsing systems have been used to derive the mass and radius but not luminosity or temperature (Pont et al. 2005; Bouchy et al. 2005). However, detached eclipsing binary systems with M dwarf primary stars are rare. There are currently six such systems known (Lacy 1977; Torres & Ribas 2002; Delfosse et al. 1999; Ribas

2. INITIAL IDENTIFICATION We observed a 1.08 deg 2 field built from several overlapping pointings and centered on the open cluster NGC 1647 with the Kitt Peak National Observatory (KPNO) 4 m telescope and Mosaic CCD imager over five nights from 2002 September 13 to 17. The processing, reduction, and initial analysis of these data are described in detail in Paper I (Hebb et al. 2004). Table 1 gives

1

Department of Physics and Astronomy, Johns Hopkins University, Baltimore, MD 21218; [email protected], [email protected]. 2 Institute of Astronomy, Cambridge University, Cambridge CB3 0HA, UK; [email protected]. 3 Astronomy Department, New Mexico State University, Las Cruces, NM 88003; [email protected].

555

556

HEBB ET AL.

Vol. 131

TABLE 1 The Open Cluster NGC 1647 Parameter

Value

Reference

(m  M )V ;0 ............................. Age ( Myr).............................. Radial velocity (km s1) .......
RV (km s1).......................... E(B  V )a...............................
E(BV ) a .................................. E(V  I )b ...............................
E(V I ) ....................................

8.67 150 2.0 4.4 0.40 0.09 0.48 0.11

Turner (1992) Dias et al. (2002) Rastorguev et al. (1999) Rastorguev et al. (1999) Turner (1992) Turner (1992) Turner (1992); Cardelli et al. (1989) Turner (1992); Cardelli et al. (1989)

a

Median and standard deviation of the reddening based on measurements from 73 bright stars covering an area of 20 0 ; 20 0 about the cluster center by Turner (1992). b Extinction law taken from Cardelli et al. (1989) with RV ¼ 3:1.

the cluster properties, including distance, age, systemic radial velocity, and reddening. There are no metallicity measurements of the cluster in the literature. The distribution of metallicities of intermediate-age, nearby, open clusters peaks at ½Fe/H  0 (Chen et al. 2003), so we adopt this value as a reasonable estimate for the metallicity of NGC 1647 and of the binary system. However, the metallicity of NGC 1647 could be different from solar by several tenths of a dex in either direction, and we are actively pursuing its determination through the analysis of brighter member stars. We captured the candidate M dwarf eclipsing binary system (2MASS 04463285+1901432, R:A: ¼ 04h 46m 32:s86, decl: ¼ þ19 01 0 43B2 [J2000.0]) on 66 deep I-band images and 19 deep V-band images of the cluster field. The object, whose location in the color-magnitude diagram (CMD) is consistent with cluster membership and whose position is only 80 from the cluster center, was flagged as a potential variable based on the large standard deviation of its initial light curve (
¼ 38 mmag) compared to the typical value for stars of similar brightness (
 7 mmag). Inspection of the light curves revealed nine significant dips in brightness and a first estimate of the period of k0.69 days. 2.1. Calibrated Photometry We obtained calibrated V- and I-band magnitudes of V ¼ 19:34 and I ¼ 16:75 from our survey data and IR magnitudes from the Two Micron All Sky Survey (J ¼ 15:246
0:043, H ¼ 14:361
0:037, and Ks ¼ 14:267
0:065). The spectral energy distribution over this wide wavelength range is consistent with the sum of an early-M star plus a late-M star. We show the position of the candidate eclipsing binary on the optical CMD (Fig. 1), which displays all objects classified as stars in our cluster field. The cluster main sequence is the overdense ridge of stars to the red edge of the CMD. We overplot the empirical colormagnitude data for young disk M dwarfs from Leggett (1992), shifted according to the distance and mean reddening of the cluster. All unresolved binaries within the cluster should lie on the CMD between the main sequence and the theoretical equalmass binary sequence (0.75 mag brighter), and this is indeed the location of our candidate system.

Fig. 1.—Calibrated V, V  I CMD for all objects identified as stars in the k1 deg 2 field we surveyed. The cluster main sequence is apparent close to the plus signs, which are empirical color-magnitude data for young disk M dwarfs from Leggett (1992), shifted in Vand V  I according to the dereddened V-band distance modulus [(M  M )V ;0 ¼ 8:67] and median reddening [E(B  V ) ¼ 0:40; Turner 1992] of the cluster. The candidate eclipsing system is marked by the large filled circle and has a location consistent with being an unresolved binary system within the cluster.

Point Observatory (APO) on 2004 September 22. We used the medium red grating (2.26 8 pixel1) combined with a 1B5 slit to give a 7.9 8 resolution. The spectrum was processed in IRAF4 using standard techniques. We subtracted a combined bias frame, applied the overscan correction, and flat-fielded the data with a normalized bright quartz lamp flat field. We cleaned the image of cosmic rays and then extracted a 10 pixel (4B2) wide region centered on the target star before using a 90 s argon arc-lamp spectrum to derive the dispersion solution. The resulting fluxcalibrated spectrum of our candidate system, shown in Figure 2, covers the wavelength range 5500–8500 8. This spectrum shows the characteristic features of a cool M star, including strong TiO bands and several CaH absorption features, plus H in emission. The overall shape and depth of the absorption features in the wavelength range 5500–7500 8 (restricted to minimize contribution by the cooler star) are well matched by an M3 V star, as is shown in Figure 2. The strengths of the absorption features provide more quantitative temperature

2.2. Spectral Classification We obtained a single 900 s medium-resolution spectrum of the object, plus a short exposure of the flux-standard Feige 110, using the DIS-III spectrograph and 3.5 m telescope at Apache

4 IRAF is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.

No. 1, 2006

PHOTOMETRIC MONITORING OF OPEN CLUSTERS. II.

Fig. 2.—Spectrum of the object obtained with the DIS-III spectrograph and the 3.5 m telescope at APO. The data were taken with the medium-resolution red grating (2.26 8 pixel1), resulting in R  1000. Note that we have removed regions of the spectrum that are contaminated by the strong telluric A and B bands at 7597 and 6868 8, respectively. The TiO5 index (Reid et al. 1995) measures the temperature of an early M star for the system, and the depths of the CaH k6975 and Ti i k7358 ( Kirkpatrick et al. 1991) lines indicate a dwarf star luminosity class. The dotted line is the empirical composite spectrum for an M3 V star from Pickles (1998) normalized to the data between 5550 and 5560 8. This provides an excellent fit to the bluer regions shortward of 7200 8, providing further evidence to support our identification of this system as a binary with an early M star primary. The shortfall redder than this wavelength indicates that the contribution from the cooler secondary star is nonnegligible.

and gravity estimates. We measure a value for the temperaturesensitive TiO5 index (Reid et al. 1995) of 0.54, consistent with the spectrum being dominated by an early M-type star, M2.5. The strengths of the gravity-sensitive CaH index at 6975 8 (1.14) and Ti i index at 7358 8 (Ti i/CaH index ratio of 0.79) imply a dwarf (Kirkpatrick et al. 1991). The presence of H in emission is also consistent with a 150 Myr old M2.5 Vobject (Gizis et al. 2002; Hawley et al. 1999). 3. HIGH TIME RESOLUTION LIGHT CURVE The eclipse period and phase derived from the initial survey data were sufficiently accurate to predict future eclipse events but not to derive orbital parameters. For this we obtained continuous monitoring, when the target was accessible at low air mass, with the New Mexico State University (NMSU) 1.0 m robotic telescope over nine nights during the period 2004 December 1 to 2005 January 6; this resulted in 797 exposures (180 s exposure time). The images were processed using standard techniques including bias and dark subtraction, flat-fielding, and defringing. We applied aperture photometry to the target object and three brighter nonvariable reference stars in the field of view using a 4 pixel (3B2) aperture radius (which produced the light curve with the smallest out-of-eclipse scatter). The mean magnitude of the three nonvariable stars was used as the reference object for the differential photometry of our target object. We then used a box-fitting algorithm (Kova´cs et al. 2002) to extract the eclipse period and phase from the complete differential photometry data set, both KPNO and NMSU. The routine tests a grid of periods, transit phases, and durations and fits a square step function to the phase-folded light curve for each set of trial input parameters. The results of our analysis give an ephemeris for the system of HJD ¼ ½2;452;530:2622(7)
0:0004þð0:618790
0:000005ÞE;

557

Fig. 3.—Top: Phase-folded I-band light curve created from all photometric data obtained with the KPNO 4 m and NMSU 1 m telescopes using the derived ephemeris of HJD ¼ ½2;452;530:2622(7)
0:0004 þ ð0:618790
0:000005ÞE. To find the ephemeris we applied a box-fitting algorithm (Kova´cs et al. 2002) that fits a square step function to the phase-folded light curve for a grid of test periods, phases, and eclipse durations and minimizes the residual fit. Bottom: Data obtained within a 3 week time in 2004 December with the NMSU 1 m telescope. The solid line is the best-fit simulated light curve obtained with an eclipsing binary light-curve modeling program (Orosz & Hauschildt 2000) and a genetic algorithm optimization routine. We include only a portion of the data obtained within a short timespan because we fitted a model with starspots that are likely to change over time.

which defines the heliocentric Julian Date, HJD, of the eclipse minima given the number of orbital cycles E since T0. We use the ephemeris to create the phase-folded light curve in Figure 3 (top). 4. RADIAL VELOCITY CURVE The rough estimates of period and spectral types derived from the initial survey photometric data suggested that we could expect radial velocity variations on the order of approximately
150 km s1. We obtained 33 radial velocity measurements of the target star with the KPNO 4 m telescope and Ritchey-Chre´tien spectrograph on two clear nights, 2004 December 15 and 18. We used the 860 line mm1 grating in second order (0.53 8 pixel1), with a central wavelength of 6900 8. We adopted a slit width of 1B5, which gave a resolution of R  3800. The unvignetted spectral range spanned 6400–7350 8 and included H and the strong TiO band head at 7053 8; these features were used in the subsequent radial velocity analysis. The exposure times were set by the dual requirements of sufficient signal-to-noise ratio and minimal orbital smearing. We monitored the target star throughout the first night (seeing 1B5) with 20 minute exposures, taking arc lamps before and after every two images for accurate wavelength calibration. The seeing degraded to 1B7 on the second night, so we increased the exposure time to 30 minutes. We processed all the spectra in IRAF with standard techniques that included two-dimensional bias and overscan subtraction, flat-fielding, bad pixel correction, and cosmic-ray removal. The wavelength calibration was derived from the 120 s HeNeAr arclamp exposures taken adjacent to each target star observation. After processing, the relevant regions of our spectra had a signalto-noise ratio of 7. We also observed a set of radial velocity standards from Nidever et al. (2002) with spectral types ranging from M0 V to M6 V to use as templates in the cross-correlation. The radial velocities of the template stars have been measured to 0.4 km s1 (Nidever et al. 2002) and are used in our analysis to provide absolute radial velocities for the binary system.

558

HEBB ET AL.

Vol. 131

Fig. 4.—Primary and secondary star absolute heliocentric radial velocity measurements for the target system obtained using the XCSAO cross-correlation routine in IRAF. Typical errors on the primary star velocity are 10 km s1. The solid line is the best fit from modeling the combined photometric and spectroscopic data. The rms for the residual between the observed data and the model is 10 km s1 for the primary and 29 km s1 for the secondary star radial velocity curves. These data indicate a mass ratio for the system of q ¼ 0:41
0:06 and a systemic radial velocity of  ¼ 0:2
0:8 km s1.

The radial velocity measurements were obtained by crosscorrelating the target star with the radial velocity templates using the XCSAO package in IRAF. We isolated regions of the spectrum that are free of telluric absorption lines and that contain narrow stellar features, namely, the regions between 7000 and 7200 8, which contain sharp strong TiO band heads, and between 6550 and 6590 8, which exhibit a narrow H line in emission. The preprocessing of both the target star and the template prior to cross-correlation includes rebinning into 2048 bins, continuum subtraction with a constant mean value, apodization of the endpoints (XCSAO:bell window ¼ 0:1), zero padding, and the removal of the low-frequency signal on scales larger than 30 8 (XCSAO:low bin ¼ 10, XCSAO:top low ¼ 20). The relative velocities of the two binary components are such that we can resolve peaks in the correlation function for both the primary and the secondary stars over a portion of the orbit using the wavelength region 7000–7200 8. We fit a Gaussian to the primary star correlation peak, subtract it off, and fit a Gaussian to the next highest peak. We measure a secondary star correlation peak in 13 of the 33 target star exposures. We tested each of the radial velocity templates independently, deriving absolute velocities for the primary and secondary stars. All the templates give consistent velocities to 10 km s1 or less, which is at the level of our errors. For our final results, we compared the target star to the M2.5 V–type radial velocity standard, GJ 411, which is matched in spectral type to the primary star. The absolute radial velocity measurements extracted from the spectra for both the primary and secondary stars are shown in Figure 4. The correlation peak from the region around the H line is well matched to a Gaussian with no indication of asymmetry at any orbital phase, and therefore, we only use this region to derive the velocities of the primary star. Only the M6 V template showed H in emission and could be used in this cross-correlation. The median absolute deviation between the primary star radial velocity measurements derived from the TiO region and those derived from the H is 11 km s1 (near the level of our errors). Thus, the radial velocities derived from the H and TiO are consistent within our errors. 5. ANALYSIS AND LIGHT-CURVE MODELING 5.1. Technique The orbital parameters are derived using the eclipsing lightcurve modeling routine from Orosz & Hauschildt (2000) applied to our combined photometric/light curve and spectroscopic/ radial velocity data. The overall shape of the light curve, in par-

ticular out-of-eclipse variations, suggests the presence of starspots (e.g., Torres & Ribas 2002; Lopez-Morales & Ribas 2005; Ribas 2003). Since starspots, and thus their effects on the light curve, are likely to change over time, we include in the modeling only I-band photometry obtained with the NMSU 1.0 m in 2004 December/2005 January. The program adopts orbital parameters, within ranges we define, according to a genetic optimization algorithm and then generates simulated radial velocity and light curves for the model system. The routine iteratively solves for the combination of binary system parameters that result in the lowest value of 2 when compared to the input data sets, taking account of observational errors. The code determines the surface gravity and effective temperature of each star based on the calculated gravitational potential, assuming full Roche geometry and the gravity brightening coefficients from Claret (2000). It includes theoretical NextGen model atmospheres (Hauschildt et al. 1999) to determine intensities over the stellar disks. We allowed the code to calculate reflection effects, adopting a bolometric albedo of 0.5, typical for a fully convective stellar envelope (Rucin´ski 1969), but this is an insignificant effect for the cool M dwarf pair. We determine starting input parameter ranges from initial estimates based on the following: We adopt a primary star mass of 0.45 M given the spectral classification (M2.5 V; see x 2.2) and using empirical data for young disk M dwarf stars compiled by Leggett (1992, their Table 6). Adopting a circular orbit, as may be expected from tidal effects given the short period, allows us to fit a sine wave to the radial velocity data and derive a mass ratio of 0.4. This implies a secondary star mass of 0.2 M. We use the absolute I-band magnitudes for young disk stars with these masses, again from Leggett (1992), to determine an initial estimate of the I-band luminosity ratio for the system of 15%. The temperature of the primary star is constrained by the spectral line strengths and V  I color of the composite system, assuming that the primary dominates the light at these wavelengths (and modulo the uncertainties due to reddening variations across the cluster). Available calibrations (e.g., Lejeune et al. 1998) suggest a range of 3300–3500 K. Assuming that the system is tidally locked, which again is reasonable given the short period, the resulting Roche lobe filling factors for the two stars are r1 /rL1  0:3 and r2 /rL1  0:12, indicating that the binary system is detached and the stars are essentially spherical. We consider scenarios with one or two starspots on the primary star but do not consider scenarios with spots on the secondary star. Due to the relative faintness of the secondary (predicted

No. 1, 2006

PHOTOMETRIC MONITORING OF OPEN CLUSTERS. II.

luminosity ratio 15%), we are not sensitive to starspots on this component. M dwarf eclipsing binary stars in the recent literature show spots with angular radii sp between 9 and 43 and temperature fractions Tspot /Tstar of 0.86–1.06 (Torres & Ribas 2002; Lopez-Morales & Ribas 2005; Ribas 2003). To test our ability to detect and characterize starspots on the secondary star, we adopt a spot with properties at the extremes of these ranges that would produce the largest effect on the light curve. Assuming that both the spot and the stellar photosphere emit thermally, a large, cool spot on the secondary star with sp ¼ 45 (covering 13% of the stellar surface) and Tspot /Tstar ¼ 0:85 would produce at most a 0.008 mag variation in the light curve. The same spot on the primary star would produce a peak variation of 0.06 mag if situated at the stellar equator. Given the photometric noise in the light curve (rms  0:03 mag), only the primary star starspot would be detectable in our data. Furthermore, smaller starspots with temperature fractions closer to unity are consistent with the literature values and would produce even smaller variations in the light curve. The remaining parameters are allowed to vary over a broad range consistent with M dwarf stars. We ran the optimization code with a population size of 100 for 300 generations. The population size determines how much of the parameter space is sampled in a single generation, or iteration. Large population sizes are computationally expensive, and small sizes do not sample enough of parameter space to allow the algorithm to converge on the best solution at the global minimum. We chose the largest population that allowed us to run the optimization routine in a reasonable time while allowing convergence. In general, convergence of the output binary parameters was achieved after around 200 generations. 5.2. Results The light-curve data overplotted with the best-fit model light curve are shown in Figure 3 (bottom). The fit has 2  957 with 627 degrees of freedom, resulting in a reduced 2  1:5. Table 2 gives the derived fundamental parameters of the individual stars and the orbital system. We estimate marginalized errors for a given parameter by examining how 2 changes from its absolute minimum when that parameter is constrained and the others roam freely over their allowed ranges. We define the 1
error as being when 2 changes by 1. The errors derived in this way for the stellar temperatures do not accurately reflect the errors in the atmospheric models. We adopt more realistic errors for these parameters based on the results of Leggett et al. (1996). The author compares the atmospheric models of low-mass stars with observed spectra and is able to determine effective temperatures with an accuracy of 150 K. This is the error we adopt for the temperature of both components. In the modeling, we derive a mean radial velocity for the binary system of  ¼ 0:2
0:8 km s1, which is perfectly consistent with open cluster membership. The cluster has a systemic radial velocity of 2.0 km s1 and an internal dispersion of 4.4 km s1 (see Table 1). This provides further evidence that the binary system is indeed a member of the cluster. The luminosities and absolute V-band magnitudes of the binary components given in Table 2 are not explicitly fitted for in the model. We derive the luminosity of both components from the derived radius and temperature according to 4 L 4R2
TeA ¼ : 2 4 L 4R
TeA;

We adopt TeA; ¼ 5778 K and Mbol; ¼ 4:72 M for the temperature and bolometric magnitude of the Sun. We use the bolo-

559

TABLE 2 Derived Binary Parameters Parameter

Value

P (days).............................................. T0 ........................................................ Eccentricity ........................................ Inclination (deg)................................. Separation (R) ..................................  ( km s1) ......................................... Mass 1 (M) ...................................... Mass 2 (M) ...................................... Radius 1 (R)..................................... Radius 2 (R)..................................... log g 1 (cgs) ....................................... log g 2 (cgs) ....................................... K 1 ( km s1)...................................... K 2 ( km s1)...................................... Teff 1 (K)............................................ Teff 2 (K)............................................ Lum 1 (L) ........................................ Lum 2 (L) ........................................ MV 1 ................................................... MV 2 ................................................... BCV 1 ................................................. BCV 2 .................................................

0.618790
0.000005a,b 2452530.2622(7)
0.0004a 0.0b 81.3
0.2 2.66
0.08 0.2
0.8 0.47
0.05 0.19
0.02 0.56
0.02 0.21
0.01 4.6
0.02 5.1
0.01 62.6
1.1 152.3
6.7 3320
150 2900
150 0.0341
0.003c 0.0028
0.0004c 9.75
0.26c 14.09
1.10c,d 1.36
0.16 2.99
1.07

a

Derived using the box-fitting alogrithm. Constrained in the light-curve modeling routine. c Adopting TeA; ¼ 5778 K and Mbol; ¼ 4:72 mag. d The large errors on this parameter are mainly due to the uncertain V-band bolometric correction. b

metric magnitudes for the primary and secondary stars, calculated from their luminosities, and the corresponding V-band bolometric corrections to determine the absolute V-band magnitude for both components. The empirical temperature–bolometric correction relation defined by Flower (1996) is poorly constrained in the temperature regime of our binary components (below TeA ¼ 3550 K), and therefore, we take an average bolometric correction from the stellar evolution models (Baraffe et al. 1998; Siess et al. 1997; Girardi et al. 2000; Yi et al. 2001). As a consistency check, we compare the absolute V-band magnitude for the binary system derived from the fitted parameters, MV ¼ 9:79
0:26, with the observed V-band magnitude of our object, MV ¼ 9:55, correcting for the distance modulus and reddening of the cluster. The two values are within the 1
V-band magnitude errors; however, there is a 0.25 mag discrepancy between them. This is most likely due to the errors in the primary star bolometric correction,
BC ¼ 0:16, and/or the differential reddening across the cluster field,
AV ¼ 0:28. As anticipated, models with starspots on the primary provided significantly superior fits than models with no spots. We test a range of properties for the spots on the primary star; however, there are degeneracies in these parameters. Different spot models are equally able to reproduce the light-curve shape. In general, the longitude positions of the spots are robust and set by the positions of the out-of-eclipse maxima in the light curve. The spot sizes can vary by
5 , but large spots (angular radius sp > 20 ) do not lead to good fits to the data. The latitudes of the spots can vary by
30 and still produce acceptable fits to the light curve, and acceptable temperature fractions can differ by 20%. The favored model includes two starspots on the primary; one spot is at longitude 1 (and is hence nearly aligned with the axis to the secondary star) and latitude 48 , with sp ¼ 14 and a temperature fraction Tspot /Tstar ¼ 0:88. The

560

HEBB ET AL.

Fig. 5.—Radius vs. mass (top), effective temperature vs. mass (middle), and log (bolometric luminosity) vs. mass (bottom). The circles mark the derived fundamental parameters for the primary and secondary stars in the binary system. The lines show the fundamental relations from theoretical stellar evolution models (solid lines, Baraffe et al. 1998; dashed lines, Yi et al. 2001; dot-dashed lines, Girardi et al. 2000; dotted lines, Siess et al. 1997).

second spot has a similar structure (sp ¼ 10 and Tspot /Tstar ¼ 0:77) but is on the opposite side of the star (longitude ¼ 168 , latitude ¼ 73 ). Figure 5 shows a comparison between the derived parameter values and the mass-radius, mass-Teff , and mass–bolometric luminosity relations predicted by four theoretical stellar evolution models (Baraffe et al. 1998; Siess et al. 1997; Girardi et al. 2000; Yi et al. 2001). We plot 150 Myr isochrones with three different metallicities for each set of stellar evolution models. The chosen metallicities span the range consistent with intermediate-age local open cluster metallicities, approximately solar
0.3 dex (Chen et al. 2003). For the Baraffe et al. (1998) models we plot the only available model tracks for solar metallicity and ½Fe/ H ¼ 0:5.

Vol. 131

Fig. 6.—Radius vs. mass (top) and absolute V magnitude vs. mass (bottom). The filled circles mark the derived fundamental parameters for the primary and secondary stars in the new M dwarf eclipsing binary, and the open circles show data for other M dwarf eclipsing binaries (compiled in Lopez-Morales & Ribas 2005). The squares mark the parameters of the secondary stars in the known F–M and G–M eclipsing binaries ( Pont et al. 2005; Bouchy et al. 2005), and the triangles give the properties of single M dwarfs with interferometrically measured radii (Se´gransan et al. 2000; Lane et al. 2001). The asterisks show data for the resolved, visual binary systems with measured masses ( Delfosse et al. 2000; Se´gransan et al. 2000). The lines are the fundamental theoretical relations from Baraffe et al. (1998) for two ages (solid lines, 150 Myr; dashed lines, 5 Gyr).

In Figure 6 we compare our new data to the existing empirical mass, radius, and absolute V-band magnitude data for M dwarf stars with measured masses. The empirical mass-radius data are taken from the six previously known M dwarf eclipsing binary systems, the interferometric radius measurements of single M dwarf stars (Se´gransan et al. 2003; Lane et al. 2001), and the F/G– M dwarf eclipsing binary systems discovered while searching for planetary transits (Pont et al. 2005; Bouchy et al. 2005). We plot the mass–absolute V magnitude data for the four well-studied M dwarf eclipsing binaries and the resolved, visual M dwarf binaries with known masses (Delfosse et al. 2000; Se´gransan et al. 2000). The individual components of the new M dwarf eclipsing binary we discuss here have observed properties that are within the range of other M dwarf stars with measured masses. However, in Figure 5, when comparing these new data against stellar evolution models with a range of metallicities, the results indicate that no models are consistent with all the properties of

No. 1, 2006

PHOTOMETRIC MONITORING OF OPEN CLUSTERS. II.

both stars in the new M dwarf eclipsing binary. The luminosity of the primary star is consistent with all the models within the range of tested metallicities, but the secondary star is underluminous. Many of the objects in Figure 6 with masses below M  0:35 also have absolute magnitudes that are fainter than predicted by the Baraffe et al. (1998) models. Furthermore, most of the models overestimate the temperature of the two new objects by several hundred degrees. Finally, while all the theoretical mass-radius relations are consistent, within our errors, with the secondary star parameters, the models underpredict the radius of the primary star. This result has been found in several recent analyses of M dwarf eclipsing binary systems (Torres & Ribas 2002; Ribas 2003; Lopez-Morales & Ribas 2005), and it has been suggested (Chabrier et al. 2006) that the larger observed radii of M dwarf eclipsing binaries could be a consequence of their magnetically active, starspot-covered surfaces impeding contraction as these stars evolve. Formation and evolution models specifically for binary systems would help resolve this discrepancy. Such models would likely be simulating the more common situation, as many stars exist and probably form in binary or multiple systems (60% for G dwarfs [Duquennoy & Mayor 1991]; 40% for M dwarfs [Fischer & Marcy 1992]). 6. CONCLUSIONS AND FUTURE WORK All observations indicate that the object we discovered is indeed an M dwarf eclipsing binary system in the open cluster NGC 1647, with component masses of 0.45 and 0.19 M. The binary system has the potential to place even more stringent constraints on theoretical stellar evolution models at the lowmass end because it is a member of an open cluster for which accurate age and metallicity determinations are possible from the brighter stars. The unequal masses of the components are

561

unusual and provide an additional opportunity to test the models simultaneously over a range of masses. We derive errors for the intrinsic parameters of the M dwarf stars of 10%. The errors here are too large to provide definitive tests of the models, and our lack of metallicity information on the cluster prevents us from fully exploiting the potential of this system. To address this, we have been awarded observing time with the Very Large Telescope UVES instrument to obtain high-resolution spectroscopic observations of the target star. A more precise radial velocity curve will significantly decrease the errors on the component masses to 1%. We are pursuing observations with the 3.5 m Apache Point Telescope to provide at least 1% differential photometry. Reducing the rms in the light curve will reduce the errors on the derived radii and better constrain the starspot configurations. Finally, we have obtained spectra of candidate G dwarf stars in the cluster that, when analyzed, will allow us to provide an improved metallicity estimate. With known metallicity, we will be able to compare the individual M dwarf stars to the appropriate stellar evolutionary tracks and place stringent constraints on the models.

We thank Kuenley Chiu for observing the APO spectrum of our target object and Jerry Orosz for providing us with his lightcurve modeling code and much advice on how to implement it. L. H. also thanks Imants Platais and Peter McCullough for many helpful chats. L. H. acknowledges the use of the National Optical Astronomy Observatory (NOAO) telescope facilities at KPNO, as well as financial support from NOAO for observing trips. L. H. also acknowledges support from the Gordon and Betty Moore Foundation.

REFERENCES Baraffe, I., Chabrier, G., Allard, F., & Hauschildt, P. H. 1998, A&A, 337, 403 Lane, B. F., Boden, A. F., & Kulkarni, S. R. 2001, ApJ, 551, L81 Bouchy, F., Pont, F., Melo, C. H. F., Santos, N. C., Mayor, M., Queloz, D., & Lastennet, E., & Valls-Gabaud, D. 2002, A&A, 396, 551 Udry, S. 2005, A&A, 431, 1105 Leggett, S. K. 1992, ApJS, 82, 351 Cardelli, J. A., Clayton, G. C., & Mathis, J. S. 1989, ApJ, 345, 245 Leggett, S. K., Allard, F., Berriman, G., Dahn, C. C., & Hauschildt, P. H. 1996, Chabrier, G., Baraffe, I., Allard, F., & Hauschildt, P. H. 2006, in ASP Conf. ApJS, 104, 117 Ser., Resolved Stellar Populations, ed. M. Chavez & D. Valls-Gabaud (San Lejeune, T., Cuisinier, F., & Buser, R. 1998, A&AS, 130, 65 Francisco: ASP), in press Leung, K. C., & Schneider, D. P. 1978, AJ, 83, 618 Chen, L., Hou, J. L., & Wang, J. J. 2003, AJ, 125, 1397 Lopez-Morales, M., & Ribas, I. 2005, ApJ, 631, 1120 Claret, A. 2000, A&A, 363, 1081 Maceroni, C., & Montalba´n, J. 2004, A&A, 426, 577 Creevey, O. L., et al. 2005, ApJ, 625, L127 Metcalfe, T. S., Mathieu, R. D., Latham, D. W., & Torres, G. 1996, ApJ, 456, Delfosse, X., Forveille, T., Se´gransan, D., Beuzit, J.-L., Udry, S., Perrier, C., & 356 Mayor, M. 2000, A&A, 364, 217 Nidever, D. L., Marcy, G. W., Butler, R. P., Fischer, D. A., & Vogt, S. S. 2002, Delfosse, X., Forveille, T., Udry, S., Beuzit, J.-L., Mayor, M., & Perrier, C. ApJS, 141, 503 1999, A&A, 350, L39 Orosz, J. A., & Hauschildt, P. H. 2000, A&A, 364, 265 Dias, W. S., Alessi, B. S., Moitinho, A., & Le´pine, J. R. D. 2002, A&A, 389, Pickles, A. J. 1998, PASP, 110, 863 871 Pont, F., Melo, C. H. F., Bouchy, F., Udry, S., Queloz, D., Mayor, M., & Santos, Duquennoy, A., & Mayor, M. 1991, A&A, 248, 485 N. C. 2005, A&A, 433, L21 Fischer, D. A., & Marcy, G. W. 1992, ApJ, 396, 178 Rastorguev, A. S., Glushkova, E. V., Dambis, A. K., & Zabolotskikh, M. V. Flower, P. J. 1996, ApJ, 469, 355 1999, Astron. Lett., 25, 595 Girardi, L., Bressan, A., Bertelli, G., & Chiosi, C. 2000, A&AS, 141, 371 Reid, I. N., Hawley, S. L., & Gizis, J. E. 1995, AJ, 110, 1838 Gizis, J., & Reid, I. N. 1995, AJ, 110, 1248 Ribas, I. 2003, A&A, 398, 239 Gizis, J. E., Reid, I. N., & Hawley, S. L. 2002, AJ, 123, 3356 Rucin´ski, S. M. 1969, Acta Astron., 19, 245 Hauschildt, P. H., Allard, F., & Baron, E. 1999, ApJ, 512, 377 Se´gransan, D., Delfosse, X., Forveille, T., Beuzit, J.-L., Udry, S., Perrier, C., & Hawley, S. L., Reid, I. N., Gizis, J. E., & Byrne, P. B. 1999, in ASP Conf. Mayor, M. 2000, A&A, 364, 665 Ser. 158, Solar and Stellar Activity: Similarities and Differences, ed. C. J. Se´gransan, D., Kervella, P., Forveille, T., & Queloz, D. 2003, A&A, 397, L5 Butler & J. G. Doyle (San Francisco: ASP), 63 Siess, L., Forestini, M., & Dougados, C. 1997, A&A, 324, 556 Hebb, L., Wyse, R. F. G., & Gilmore, G. 2004, AJ, 128, 2881 Torres, G., & Ribas, I. 2002, ApJ, 567, 1140 Hillenbrand, L. A., & White, R. J. 2004, ApJ, 604, 741 Turner, D. G. 1992, AJ, 104, 1865 Kirkpatrick, J. D., Henry, T. J., & McCarthy, D. W. 1991, ApJS, 77, 417 Yi, S., Demarque, P., Kim, Y., Lee, Y., Ree, C. H., Lejeune, T., & Barnes, S. Kova´cs, G., Zucker, S., & Mazeh, T. 2002, A&A, 391, 369 2001, ApJS, 136, 417 Lacy, C. H. 1977, ApJ, 218, 444