RUPRECHT 147: THE OLDEST NEARBY OPEN CLUSTER AS A NEW BENCHMARK FOR STELLAR ASTROPHYSICS

Despite its promising scientific potential due to the unique combination of its age and distance, and despite having a similar distance and size to Praesepe, R147 was completely overlooked by stellar astronomers until the works by Dias et al. and Kharchenko et al. This is likely because its proximity makes R147 a very sparse cluster on the sky: there are only ∼50 members with V < 11 and only ∼10 with V < 9 spread over 5 deg². Its presence is also obscured by its location in the Galactic plane (−14° < b < −12°, in Sagittarius), and the fact that due to its age, it lacks the many bright A stars that made similarly nearby clusters so obvious, even to the astronomers of antiquity.

In fact, a complete pre-2000 bibliography of R147 consists almost exclusively of entries in various catalogs. R147 was originally discovered in 1830 by John Herschel, who described it as "a very large straggling space full of loose stars" (Herschel 1833, p. 463), and labeled it GC 4481 (Herschel 1863). Since then it has appeared with numerous designations including NGC 6774, OCL 65, and Lund 883 (Dreyer 1888; Alter et al. 1958; Lynga & Palous 1987; Mermilliod 1995). Some star charts have even designated R147 as an asterism, and not a true cluster (e.g., "Burnham's Celestial Handbook: An Observer's Guide to the Universe Beyond the Solar System" lists NGC 6774 as "possibly not a true cluster"; Burnham 1966, p. 1558). The name we use here originates from Ruprecht (1966), who classified R147 as a III-2-m cluster in the Trumpler system (Trumpler 1930, p. 160). According to Archinal & Hynes (2003), Brian Skiff realized that NGC 6774 and R147 are likely the same star cluster. Archinal & Hynes (2003, p. 185) describe R147 as a "45' sized V-shaped group of bright stars" that is "a sparse possible open cluster," and estimate the cluster center as the location of HD 180228 (while this star's photometry apparently places it on the R147 red giant branch, the Tycho-2 proper motions, −1.6 and −6.3 mas yr⁻¹ in right ascension and declination, are inconsistent with cluster membership, see Figure 3). Figure 2 highlights our high-confidence members on an optical image. Herschel's cluster identification is truly amazing, given the lack of a well defined cluster core. But those arguing for the asterism status were not entirely wrong either: of the 51 stars with V < 9 within ≈2° of the cluster center, we confirm only 11 as members.

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Only in the last decade has R147 received any individual attention in studies of open clusters. Dias et al. (2001) first identified R147's membership based on the stellar population's common proper motion: selecting stars in the Tycho-2 Catalogue (Høg et al. 2000) that were spatially coincident with BDA clusters (The Open Cluster DataBase; Mermilliod 1995), they determined cluster membership with the Tycho-2 proper motions using the statistical method of Sanders (1971) and found 33 stars with mean proper motion of μ_α = −0.8 ± 2.3 and μ_δ = −28.5 ± 2.3 mas yr⁻¹. Dias et al. (2001) also provided the first distance estimate based on only two Hipparcos parallax measurements⁹ (HIP1; Perryman & ESA 1997): π = 3.57 ± 1.01 mas (280 ± 79 pc) for HIP 94635 (CWW 1),¹⁰ and 3.75 ± 1.04 mas (267 ± 74 pc) for HIP 94803 (CWW 2), which they average to 3.7 ± 0.2 mas, estimating the distance to R147 to be 250 pc.¹¹ Since then, van Leeuwen (2007, HIP2) has performed a new data reduction and issued an updated catalog with parallaxes of 5.48 ± 0.65 mas (182 ± 22 pc) for HIP 94635, and 4.92 ± 0.79 mas (203 ± 33 pc) for HIP 94803.¹²

Dias et al. (2002) compiled all available data for 2095 galactic clusters (The New Catalogue of Optically Visible Open Clusters and Candidates, or DAML02) and published an updated membership list and cluster properties for R147: 25 members, proper motion μ_α = −0.9 ± 0.3 and μ_δ = −29.3 ± 0.3 mas yr⁻¹, RV = 41 km s⁻¹ (from the single published measurement in Wilson 1953, see Section 3.2), distance = 200 pc, color excess E(B − V) = 0.2 mag, and an age of 3.2 Myr (presumably from misidentifying blue stragglers as main-sequence turnoff (MSTO) stars). Dias et al. re-classified R147 as IV-2-p (Trumpler system).

Following their 2002 work, Dias et al. (2006) selected all clusters in their DAML02 catalog with known distances and queried the UCAC-2 catalog (Zacharias et al. 2004b) for all stars within the measured cluster radii, plus 2', of their tabulated cluster centers. Employing similar methods as Dias et al. (2001), they derived a mean proper motion for R147 of μ_α = −4.6  ±  0.4 and μ_δ = −5.6 ± 0.4, and identified 200 cluster members. Figure 3 shows the proper motions for stars in the R147 field, color-shaded by membership probability as derived by Dias et al. (2006). The black circle highlights the proper motion of R147 according to Kharchenko et al. (2005) and confirmed in this work, and shows that the Dias algorithm missed the cluster, locating the field stars instead. The Dias et al. (2006) membership list and cluster parameters are thus unreliable. Dias et al. (2006) attribute their algorithm's failure to the large angular size of R147.

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A similar automated effort has been undertaken by Kharchenko (2001), who assembled the All-Sky Compiled Catalogue of 2.5 Million Stars (ASCC-2.5), including proper motions from the Tycho-2 catalog (Høg et al. 2000), Johnson BV photometry, and radial velocities (RVs) and spectral types when they are available.

Kharchenko et al. (2005) searched this catalog and identified 520 Galactic open clusters, including R147. Their algorithm determined the core and cluster angular radii, and the distances, mean space motions (proper motion and RV), and ages of the clusters. Three important differences exist between the Dias et al. (2006) membership and properties and those of Kharchenko et al. (2005): (1) Kharchenko et al. correctly identify the cluster, cataloging 41 1σ members; (2) they provide the first reliable age estimate of 2.45 Gyr from their isochrone fitting; and (3) they claim a new distance of only 175 pc, 75 pc closer than that inferred from the original Hipparcos parallaxes, but similar to the distances derived in HIP2. While we determine a similar age of ∼2.5 Gyr, we derive a distance d ≈ 300 pc (Sections 4.3 and 4.4) by fitting isochrones to a spectroscopically derived T_eff–log g diagram, and Two Micron All Sky Survey (2MASS, J − K_S) and CFHT/MegaCam (g' − i') color–magnitude diagrams (CMDs). Figure 4 plots the CMD used by Kharchenko et al. (2005) to derive age and distance. The Tycho-2 BV photometry is magnitude limited at V ∼ 11, near the R147 MSTO. ASCC-2.5 is supplemented with various ground-based photometry for fainter magnitudes, which Figure 4 demonstrates is insufficient for main-sequence fitting. While the MSTO provides a strong constraint on the age, the discrepancy between our derived distance and that of Kharchenko et al. can be explained by the ill-defined (B − V) main sequence. Their analysis was also hindered by a lack of a spectroscopically determined composition, and they assumed Solar metallicity. Without an accurate metallicity, and with a main sequence dominated by photometric error, it is difficult to disentangle visual extinction, age, composition, and distance. Instead, Kharchenko et al. (2005) assumed A_V = 0.465 from the Schlegel et al. (1998) dust map at their location for the cluster center, even though according to this dust map A_V varies from 0.3 to 0.6 mag across the cluster (see Section 4.1). Although Dias et al. (2001) were the first to determine the distance, Schilbach et al. (2006) were the first to discuss Ruprecht 147 specifically as an old nearby cluster in a peer-reviewed publication.

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Despite these issues, the works of Dias et al. and Kharchenko et al. are significant because they essentially re-discovered Ruprecht 147 and provided the first good evidence that R147 is in fact the oldest nearby star cluster.

Most recently, Pakhomov et al. (2009) observed three cluster red giants and spectroscopically measured RVs and stellar properties (discussed in Sections 3.2 and 4.2). They determined the cluster metallicity to be super-Solar, thereby decreasing the estimated age, from a fit to an enriched Padova isochrone (Girardi et al. 2000; Marigo et al. 2008)¹³ to ∼1.25 Gyr, and derived a distance of 280 ± 100 pc, along with a color excess of E(B − V) = 0.11 (or A_V = 0.34, assuming R_V = 3.1).

Ruprecht 147 has also appeared in the open cluster luminosity function study of Elsanhoury et al. (2011) and a paper on Galactic kinematics and structure as defined by open clusters by Zhu (2009), but these works undoubtedly suffer from a poorly determined membership and uncertain cluster properties.

We have begun an observational campaign to characterize R147, catalog its members, and prove its benchmark status. Here we present our initial efforts, detailing in particular our R147 membership search that more than doubles the number of known cluster members (Section 3), and our derivation of the cluster's age, distance, and metallicity (Section 4). We begin with an overview of our photometric and spectroscopic data sets.

Our initial list of candidate members was drawn from the NOMAD and UCAC-3 catalogs. The Naval Observatory Merged Astrometric Data set (NOMAD; Zacharias et al. 2004a) combines data (positions, proper motions, and BVR/JHK photometry) for over 1 billion stars from the Hipparcos (Perryman & ESA 1997), Tycho-2 (Høg et al. 2000), UCAC-2 (Zacharias et al. 2004b), USNO-B1.0 (Monet et al. 2003), and 2MASS (Skrutskie et al. 2006) catalogs. The Third USNO CCD Astrograph Catalog (UCAC-3; Zacharias et al. 2009) expands on NOMAD by improving UCAC-2 in many ways, including complete sky coverage, reduced systematic errors for CCD observations, deeper photometry (R ≈ 8–16) for ∼80 million stars, and improved astrometry (resolved double stars, inclusion of several new catalogs, and re-reduction of early epoch photographic plates to derive proper motions).

In this paper, we use proper motions from the PPMXL catalog (Roeser et al. 2010). PPMXL utilizes astrometry from the USNO-B1.0 and 2MASS catalogs to calculate proper motions in the ICRS system for approximately 900 million objects, including ∼410 million with 2MASS photometry. The catalog covers the entire sky down to V ≈ 20. PPMXL was released in 2010, after we had derived our initial membership catalog. Some stars have NOMAD and/or UCAC-3 proper motions consistent with cluster membership, but are discrepant according to the PPMXL values (and vice versa). We include these stars in our membership list despite this, and we evaluate their probability of membership based on all available kinematic and photometric data (Section 3).

We performed initial RV confirmation of suspected members to verify the existence of the cluster with the Hamilton echelle spectrometer on the 120 inch Shane telescope at Lick Observatory (R ∼ 50, 000; Vogt 1987). Our objectives were to obtain RVs of known and suspected members, to identify new members, and to obtain high-resolution spectra of the brightest members at high signal-to-noise ratios (S/Ns) for more detailed analysis of abundances and chromospheric activity.

We observed candidate cluster members on UT 2007 July 31–August 1 and August 22–23, including the members identified by Kharchenko et al. (2005). To locate additional candidate members, we selected stars from the NOMAD catalog that were within 125 of the published cluster center and that had UCAC-2 and Tycho-2 proper motions within 5 mas yr⁻¹ of the Kharchenko et al. value. Although there are over 750,000 NOMAD stars in the field due to its large size and location in the Galactic plane, the cluster is separated enough from the field in proper motion space that this yielded a list of 1348 stars, illustrated in Figure 5.

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To further vet this list, we used NOMAD (B − V) and 2MASS (J − K_S) CMDs to identify stars consistent with an assumed distance of 230 pc, a compromise between the HIP1 distance to the cluster (270 pc) and the value of Kharchenko et al. (175 pc). We combined the CMDs and proper motion information to estimate crude membership probabilities based on the Hipparcos main sequence with no reddening corrections, calculated generously to account for uncertainties in the cluster parameters and for the poor quality of some of the NOMAD proper motion entries, and we favored brighter targets to improve the efficiency of vetting candidate members at the telescope.

We drew from this list, sorted by membership probability, to choose targets for spectroscopic study at Lick Observatory. We used these spectra to measure RVs for the stars and determine the space motion of the cluster.

2.2.1. Data Acquisition and Raw Reduction

2.2.2. Palomar Spectra

2.2.3. Radial Velocity Determination

Spectra of four cluster members were obtained on 2008 September 12 and 18 and for two members on 2011 October 17 with the High Resolution Echelle Spectrometer (HIRES; Vogt et al. 1994) on the 10 m telescope at Keck Observatory. The stars were kindly observed by the California Planet Survey team (CPS¹⁴) without an iodine cell, and with the B5 decker (slit of 35 length and 0861 width), giving a typical resolution R ∼ 50, 000 in the 3360–8100 Å bandpass. Exposure times were monitored with a photomultiplier tube exposure meter to ensure high S/N (∼50–100). These observations are summarized in Table 1, and were reduced by the standard CPS pipeline. Chubak et al. (2012) measured absolute RVs (results discussed in Section 3.2) and we derive stellar properties in Section 4.2.

We obtained high-resolution spectra with MMT/Hectochelle in the vicinity of the Ca ii H & K lines for 48 members (as determined from Lick/Palomar RVs), 10 candidate members (from astrometry and photometry alone), and 23 potential astrometric reference stars. These data provide RVs, chromospheric activity indicators (e.g., Wright et al. 2004), and gravity diagnostics (via the Wilson–Bappu effect; Wilson & Vainu Bappu 1957) useful for identifying background giants as astrometric references. The remaining fibers not allocated for sky subtraction were assigned to proper motion candidates with inconsistent photometry to assess how R147 members are kinematically distinct from the field.

MMT is a 6.5 m telescope located at the Fred Lawrence Whipple Observatory on Mt. Hopkins, AZ (Fabricant et al. 2004). Hectochelle is a high-resolution (R ∼ 32,000–40,000) fiber-fed spectrograph, which provides simultaneous observations for 240 targets in a 1 deg² field (Szentgyorgyi et al. 1998; Fürész et al. 2008). We observed the central square degree with the "Ca41" Ca ii H & K filter with 1 × 1 on-chip binning. Eight total hours were obtained to ensure sufficient S/N for a future chromospheric activity study. All observed targets have g' = 9–15.5.

Twelve 40 minute exposures were obtained over the nights of UT 2010 July 4–5. These data were reduced with an IRAF¹⁵-based automated pipeline developed at the Harvard-Smithsonian Center for Astrophysics, provided and run by Gabor Fürész and Andrew Szentgyorgyi, which flat-fielded, cosmic-ray removed, and wavelength calibrated our targets and sky flats. The wavelength solution was determined from ThAr lamp comparison spectra, with an rms precision of 0.2–0.5 km s⁻¹ (for reduction details, see Mink et al. 2007).

RVs were measured by cross-correlating the target spectrum with solar spectra obtained from the sky flat exposures, then corrected for Earth's heliocentric motion. We checked the fiber-to-fiber and day-to-day stability of the spectrograph by measuring velocity shifts determined by cross-correlating matched ThAr, solar, and target spectra. The fiber-to-fiber velocity shift on the first night was 12 ± 35 m s⁻¹ (for the ThAr spectra) and 200 ± 200 m s⁻¹ (for the solar spectra). We also measure a night-to-night variation between each fiber of 31 ± 41 m s⁻¹ (ThAr) and 200 ± 180 m s⁻¹ (solar). The RVs measured each day for R147 stars show a mean absolute difference of 0.23 km s⁻¹. In summary, fiber-to-fiber and day-to-day offsets and errors are well under or comparable to the precision set by the wavelength solution. The RV distribution for 49 member stars is shown in Figure 8, and is discussed in Section 3.2.

We imaged a 4 deg² field in the optical g'r'i'z' bands in 2008 April and May with CFHT/MegaCam (Hora et al. 1994).¹⁶ With MegaCam's 1 deg² field of view, four fields were required to cover the majority of the known cluster. The fields are outlined over a 2MASS J band mosaic image in Figure 6. Six additional surrounding fields were imaged solely in i' band, for the purpose of first-epoch astrometry for the entire cluster, including any extended halo. We obtained both a series of short (1 s) and long (few minutes) exposures in queued service observing mode. Typically, five dithered exposures were obtained for each field and exposure time.

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These observations were pre-processed at Canada–France–Hawaii Telescope (CFHT) with the Elixir pipeline (Magnier & Cuillandre 2002).¹⁷ Elixir creates master bias, dark and flat images, which are used to detrend the observation frames. SExtractor identifies sources and determines their pixel coordinates and raw flux. The astrometric calibration is performed by comparison to the USNO-B1.0 catalog.

Photometric magnitudes are calibrated from the instrumental magnitude with the application of a zero point, an airmass term, and a color term. The coefficients are derived from observations of standard stars. Every night, one Landolt (1992) field was observed (SA-101, SA-107, and SA-113), along with two spectrophotometric standards (i.e., an O star or white dwarf: Feige 110, GD 153, HZ 43, BD+28 4211) and at least one CFHTLS Deep field. The zero points for each frame were determined from 13 to 26 standards observed in four to nine separate images during a run. Standards were not necessarily observed in all the filters utilized on a given night, but the zero point scatter across an observing run for each filter ranged from 0.0073 to 0.0180, and is therefore quite stable. Frames obtained on photometric nights provide the means to calibrate observations taken under less transparent conditions (the image scaling is done by TERAPIX, see below). The zero points were determined after the application of the superflat, and therefore are valid for all 36 CCDs. The photometric and astrometric calibration data are stored in the FITS image headers, and the data transferred to the Canadian Astronomy Data Centre (CADC) in Victoria.¹⁸

TERAPIX performed the final photometric and astrometric reduction of our MegaCam imagery.¹⁹ The TERAPIX pipeline (Bertin et al. 2002) takes the detrended images and the preliminary calibration from Elixir, and completes a final photometric and astrometric calibration and provides source merged catalogs. First the images are re-scaled: the photometry is analyzed in each overlapping frame, and the frames are re-scaled to the photometry in the image with highest flux per source, which is considered to be the least extinguished. The overlapping images are stacked and the sources are re-extracted. The TERAPIX pipeline co-addition and astrometric calibration modules are now maintained at AstrOmatic.net, and documentation for each can be found at the SWarp²⁰ and SCAMP (Software for Calibrating AstroMetry and Photometry; Bertin 2006)²¹ Web sites.

TERAPIX handles the CFHT Legacy Survey reduction. The CFHTLS²² and TERAPIX CFHTLS reduction²³ Web sites provide additional details relevant to the final photometric and astrometric calibrations.

TERAPIX kindly provided us merged g'r'i'z' source catalogs for each field and exposure duration. The short exposures saturate at g' ≈ 9.5 and the long exposures saturate at g' ∼ 16. Sources with g' ∼ 17–18 have consistent photometric magnitudes in each catalog, and sources are detected down to g' ∼ 24 in the long exposure catalog. We therefore have photometry covering 10 ≲ g' ≲ 24.

Our faintest red giant branch member is g' = 10.53 and i' = 9.73. Given the saturation limit in each band at approximately 9.5, the majority of the red giant branch stars are saturated in g' and i'. We will include the optical red giant branch (RGB) in our figures in this work, but with stars plotted with open circles to distinguish these data from the more reliable optical photometry for the rest of the membership.

We estimate the photometric error by making use of the overlapping regions between the four imaged fields (see Figure 6). We matched all stars in the overlap regions in our bright source catalog (short exposures), and find a total of 1575 unique sources with g' < 18. Figure 7 plots the mean versus standard deviation of g' for the two to four independent measurements, depending on the number of overlapping regions containing the source. We find a typical value of $\Delta _{g^{\prime }} = 0.035$ mag, but this is probably larger than what should be assumed for the photometric precision across the field, because one of the sources usually lies very close to the edge of one of the fields, where the mosaic dithering is incomplete and the photometry less reliable.

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We have identified a ≈0.15 mag zero point error in the z' band, and the persistence of a low-frequency mode that was not removed by the flat fielding. Given these issues with z'-band, we cautiously analyze the (g' − i') CMD. We will first analyze our spectroscopic results and 2MASS photometry, before fitting isochrones to our optical data. We will show in Section 4.4 that essentially identical cluster properties are determined from these three data sets. This consistency suggests the g' and i' zero points are likely accurate.

The Elixir and TERAPIX pipelines were developed and have been successfully used to reduce similar MegaCam imaging for the CFHT Legacy Survey.²⁴ Despite these quality assurances, we consider this photometry to be preliminary, and we are currently working to further validate the accuracy of the Elixir and TERAPIX calibration.²⁵

We now primarily use PPMXL proper motions to assess membership, although our original membership list was derived from NOMAD and UCAC-3. The typical PPMXL errors range from 1 to 5 mas yr⁻¹ in proper motion, and so we designate stars with proper motion within this 5 mas yr⁻¹ of the cluster mean, as "Y" members. Only stars within ∼8 mas yr⁻¹ were considered in our initial candidate list and we found that the majority of bright candidates had velocities consistent with cluster membership. There are six stars that we had originally classified as "Y" or "P" according to their NOMAD proper motions, but which have PPMXL proper motions more than 8 mas yr⁻¹ different than the cluster's mean motion. Despite this large discrepancy from the PPMXL data, we classify these stars with conflicting proper motion data as "P," and will consider their velocities and photometry when assigning their final probability.

The General Catalogue of Stellar Radial Velocities (Wilson 1953) contains a single entry for a cluster member: HD 180015 (HIP 94635, classified as K0III, CWW 1). Wilson reported RV = 41 km s⁻¹, with quality designation "C," corresponding to a typical uncertainty = 2.5 km s⁻¹ and maximum uncertainty = 5 km s⁻¹. This was the first and only available RV until Pakhomov et al. (2009) observed three other cluster red giants: HD 179691 (CWW 9) at 46.7 km s⁻¹, HD 180112 (CWW 10) at 40.1 km s⁻¹, and HD 180795 (CWW 7) at 40.8 km s⁻¹, with S/N >100, and precision estimated at 0.5–0.8 km s⁻¹. The RV for HD 179691 is 6 km s⁻¹ larger than the other two stars, too large to be explained by the cluster velocity dispersion, which implies this star is either a SB1 binary or a non-member. We observed these stars at Lick/Palomar and measure RV_LP = 42.1, 41.4, 42.4 km s⁻¹, respectively. While our measurements for the second two stars are in basic agreement with Pakhomov et al. (2009), the velocity for HD 179691 now appears consistent with the cluster mean, supporting its membership and corroborating its SB1 status.

Chubak et al. (2012) have also measured RVs with rms errors ∼50 m s⁻¹ for our five single-lined Keck/HIRES spectra (Table 5). We list these here in km s⁻¹, with our Lick/Palomar velocities in parenthesis for comparison: CWW 44: 41.41 (42.2), CWW 91: 41.50 (42.8), CWW 21: 40.35 (41.9), CWW 78: 41.02 (40.8), and CWW 22: 46.63 (51.9). We followed up CWW 22 with Hectochelle and measure RV = 38 km s⁻¹ on both nights, and classify it a SB1.

Selecting the six stars above showing no evidence of binarity, we find a typical cluster RV of 40.86 ± 0.56 km s⁻¹(if we take only the four Keck stars analyzed by Chubak et al., then we find the cluster RV is 41.07 ± 0.52 km s⁻¹). We take stars with RVs consistent with this value as high-probability cluster members. Figure 8 plots 98 stars with Lick/Palomar velocities (shown in gray hash) with RV_LP = 43.8 ± 3.2 km s⁻¹. Also shown are 45 stars with Hectochelle velocities (black line) with RV_H = 41.6 ± 1.5 km s⁻¹. The blue tick mark at the top shows the typical cluster velocity from above at 40.57 km s⁻¹. The width of each distribution is consistent with the RV precision of each survey, and should not be interpreted as a resolved cluster velocity dispersion.²⁶

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We have RVs from Lick/Palomar (RV_LP) for nearly all stars listed in Table 3, except the six putative blue stragglers and four double-lined spectroscopic binaries (SB2s); and RVs from Hectochelle (RV_H) for 50 stars in the central square degree. The Hectochelle velocities are more precise (Figure 8), so whenever available, RV_H is used to determine the confidence in membership. Some stars have RV_LP within the highest confidence interval, and RV_H in a lower level. In these cases, if the star has "Y" confidence level proper motions, RV_LP, and photometry, we set the overall confidence to "P," and consider the star a candidate SB1 (e.g., CWW 92 has RV_LP = 45 km s⁻¹ and RV_H = 25 km s⁻¹).

Before assigning membership confidence designations, we check that the stars are confined to the region of color–magnitude space expected for a coeval stellar population with the properties that we determine best describe R147.

We mapped out this locus by simulating a rich cluster with the properties we find for R147 from isochrone fitting (Section 4.4). Figure 9 shows CMDs for such simulated clusters. In this case, we simulated a cluster with 10⁶ stars, with masses uniformly distributed between 0.6 and 1.6 M_☉. We set the binary fraction to 50%, with companion masses uniformly distributed between zero and the primary mass. Differential extinction is introduced according to a Gaussian with μ = 0.25 and σ = 0.05 mag, and photometric precision is set at 0.02 mag for g'r'i'z' and 0.025 mag for JHK_S. The simulated photometry is drawn from a Padova isochrone with log t = 9.4 (2.5 Gyr), [M/H] = +0.065, and m − M = 7.35 mag. We bin, log-scale, and smooth the synthetic photometry to highlight the R147 locus in color–magnitude space.

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Stars overlying the shaded region (basically, the region bound by the single star and equal mass binary sequences) are given the highest confidence designation. The simulation demonstrates that atypical differential reddening along a particular line of sight or relatively high photometric error can place stars outside the locus. Stars in these regions are assigned "P." These could also be triple systems or exotic products of stellar mergers. CWW 67 is the only star existing beyond the equal mass triple sequence, and we assign it the lowest designation, "N."

Confidence assignment is an iterative process, since we identify high-confidence members using isochrone fits, and these fits require a list of high-confidence members so that unlikely or non-members do not throw off the fit.

3.3.1. Stellar Populations

3.4.1. Apparent Non-members

3.4.2. Notes on 2MASS Photometry

Our g'r'i'z' imaging shows CWW 51 is an optical double, with a star 165 away with a similar g'r'i'z' spectral energy distribution (SED; the magnitude difference in each band is 0.02–0.05 mag between the two stars). The components are separated by 165, which translates into a minimum physical separation of 495 AU, assuming a cluster distance of 300 pc. This suggests that the pair actually form a wide binary, although their angular proximity could also be explained by a chance alignment. This double was not resolved in the 2MASS Point Source Catalog. Adding 0.75 mag to the J band magnitude (halving the brightness, to reflect just the one star) moves CWW 51 next to the stars it neighbors in the (g' − i') CMD. Table 3 quotes, and the figures in this work plot, the 2MASS photometry for CWW 51 despite this realization, although we do include a footnote referencing this in the table.

The 2MASS Point Source Catalog provides point spread function (PSF) photometry by default in most cases. Figure 10 shows 23 outlier stars on either side of the (J − K_S) main sequence, out of the 80 stars "Y/P" stars with aperture photometry that are not blue stragglers. If aperture photometry is used instead, each of these stars moves toward the cluster locus. No star already in the locus shifts appreciably outside when aperture photometry is used instead. One star slides from blueward from the main sequence by 0.037 mag, or approximately equal to the J and K_S errors added in quadrature. The fact that the majority of outliers' photometry systematically moves toward the cluster locus suggests to us that for many stars in these fields and at these magnitudes, the aperture photometry is superior. We do not assign lower confidence levels to PSF photometry outliers, if their aperture photometry is consistent with membership. We include the aperture photometry for 18 stars in Table 3 and all other figures (CWW 22, 24, 27, 28, 30, 37, 38, 43, 48, 49, 57, 59, 67, 68, 90, 91, 94, and 100).

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3.4.3. SB2 Systems

CWW 64, 65, 66, 68, and 72 showed double-peaked CCFs in one of the RV epochs, indicating these systems to be nearly equal mass binaries (the case of CWW 72 is discussed above). Figure 11 plots the (g' − i') and (J − K_S) CMDs, with the five SB2s highlighted red. The single star and equal mass binary sequences from our best isochrone fit (Padova model) are plotted in green. All five SB2s are clustered around the equal mass binary sequence, corroborating their equal mass status and the validity of our isochrone fit.²⁷

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3.4.4. SB1 Binary Candidates from Discrepant RVs

The large apparent size of R147 on the sky introduces the possibility of differential extinction across the cluster. Figure 12 plots A_V from the dust map of Schlegel et al. (1998), assuming R_V = 3.1.²⁸ Many cloud structures are apparent in the field, showing A_V to vary from 0.3 to 0.5 mag.

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Considering the cluster's proximity, some of this dust undoubtedly lies beyond the cluster. Drimmel & Spergel (2001) determine the Sun to lie 14.6 ± 2.3 pc above the Galactic midplane, and measure a dust scale height of h_d = 188 pc at the Solar Circle. The Galactic latitude of R147 ranges from −12° to −14°. At a distance of 250–300 pc, this latitude places R147 50–70 pc below the Sun, and 35–55 pc below the midplane (less, if a larger Z_☉ is assumed), or about 20%–30% of the dust scale height. The local bubble has very little dust in it out to ∼150 pc (Lallement et al. 2003), suggesting it is possible that most of the dust is behind the cluster.

Section 3.3 described star cluster simulations used to assess photometric membership probabilities, by introducing photometric scattering sources to explain the observed width of the R147 main sequence, including photometric error, binarity, and differential extinction. Figure 9 plots simulated cluster CMDs including each of these photometric scattering sources separately, and all combined. The binarity simulation demonstrates that the single star and equal mass binary sequences pinch together near the MSTO. Differential reddening smears the CMD along a negative-sloped diagonal (extinction plus reddening). If there is non-negligible differential reddening, the "binary pinch" should be smeared out.

Unfortunately, we have only identified six members at this pinch. Figure 13 shows four are confined within the pinch. CWW 50 sits 0.08 mag blueward, and CWW 53 sits 0.06 mag redward. These values are two to three times larger than the expected photometric error. CWW 53 has RVs from two epochs at 5 km s⁻¹ greater than the cluster mean, and photometry placing it near the equal mass triple sequence. The uncertainty in membership and multiplicity means we cannot use CWW 53 to test for differential reddening. CWW 50 must be reddened by δA_V = 0.13 mag in order to place it on the single star sequence. In Section 4.3, we find an optimal A_V = 0.23 mag, so a particular line of sight of A_V = 0.10 mag is not impossible. Ideally, we would like to check if the nearest R147 neighbors to CWW 50 also appear less extinguished than expected. Unfortunately, the nearest neighbor is ∼10' away. It is also noteworthy that the Schlegel et al. (1998) dust map extinction along this line of sight is A_V = 0.296 mag, the lowest value in the entire field, and 0.13 mag lower than the median A_V for the region of radius r =12 encompassing all R147 members.

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The R147 main sequence is thicker than 1 mag at various points. Unfortunately in many cases, our RVs do not have sufficient precision to firmly establish these stars as cluster members (we still designate them "Y" members because the RVs are consistent with the R147 bulk motion, within the precision of our Lick/Palomar RV survey). We also only have one RV epoch for the majority of stars, and so stellar multiplicity is impossible to diagnose at this point. More precise velocities are required before we attribute these photometric outliers to differential extinction.

There is also a strip of seven main sequence dwarf stars blueward of our best isochrone fit in the (g' − i') CMD. Adding δA_V = 0.05 mag to these stars shifts them onto the isochrone, This translates into a 0.03 mag shift in color, which is within the photometric precision, and so differential extinction is not required to explain these stars' apparent blueward offset in the optical CMD. No net offset is seen in the NIR CMD.

We will postpone further investigation into differential extinction to a future study, and in this work will fit single A_V models, with values constrained by the dust map at A_V < 0.5.

We analyzed five Keck/HIRES spectra with Spectroscopy Made Easy (SME; Valenti & Piskunov 1996), using the procedure described in Valenti & Fischer (2005). SME uses the Levenberg–Marquardt algorithm to fit observed echelle spectra with synthetic spectra generated assuming LTE and plane-parallel geometry, yielding effective temperature, surface gravity, metallicity, projected rotational velocity, and abundances of the elements Na, Si, Ti, Fe, and Ni.²⁹

Upon obtaining an initial fit to a spectrum, T_eff was perturbed ±100 K and run again. The three solutions were then averaged, with the standard deviation set as the parameter uncertainty, except in cases where this uncertainty is less than the statistical uncertainties measured in Valenti & Fischer (2005): 44 K in effective temperature, 0.03 dex in metallicity, 0.06 dex in the logarithm of gravity, and 0.5 km s⁻¹ in projected rotational velocity. Additional corrections are applied to the final values based on the analysis in Valenti & Fischer (2005) of Vesta and abundance trends in binary pairs with T_eff (see Figure 14 for the CWW 44 Keck/HIRES spectrum and SME synthetic spectrum fit in the order encompassing Mg b).

Our results for the five stars are presented in Table 5 and indicate that the cluster has a slightly super-Solar metallicity of [M/H] = +0.07 ± 0.03, from CWW 91, 44, and 21.³⁰ We neglected the results from CWW 22 because it is hottest (complicating the fit to gravity, described in the next subsection) and has the poorest $\chi _\nu ^2$ fit. Valenti & Fischer (2005) suggest using [Si/H] as a proxy for the α-process abundance. We find [α/Fe] = [Si/H] − [Fe/H] ≈ 0.0 ([Si/Fe] = −0.03 and 0.0 for CWW 44 and 91).

We find a much lower metallicity for CWW 78, [M/H] = −0.11 ± 0.03 and [Fe/H] = 0.0 ± 0.02. This outlier has otherwise satisfied every criterion for membership, with proper motions, photometry, and a precise RV all consistent with the cluster. For this work, we will assume that this peculiar metallicity can be explained by a complication in the SME analysis, and will look into this in a future study.

Pakhomov et al. (2009) analyzed high-resolution, high S/N spectra of three red giant members of R147, and their results are compiled in Table 5. The first star, HD 179691, has a RV inconsistent with the cluster, indicating it is either an SB1 or not a member. The other two red giants show super-Solar iron abundance, consistent with our SME results.

In the future, we will more rigorously determine the cluster metallicity combining photometry, spectroscopy, and cluster properties.

Figure 15 shows the T_eff–log g diagram resulting from our SME analysis, along with a (g' − i') CMD for the five stars, along with their CWW IDs. The CMD shows that our SME results place the stars on the T_eff–log g diagram with the correct relative positions. We have selected Padova isochrone models with [α/Fe] = 0 and [M/H] = +0.1, and attempt a "chi-by-eye" fit by overlaying models with ages at ∼2, 2.5, and 3 Gyr (log t = 9.3, 9.4, 9.5). Fitting the T_eff–log g diagram is powerful because it is independent of m − M, A_V, and color–temperature transformations.

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The MSTO star CWW 44 in theory provides a tight constraint on age and metallicity, but we are cautious of the accuracy of log g, because the broad wings of the Mg b lines provide the gravity constraint, and their sensitivity decreases at higher temperature and lower gravity. Jeff Valenti has suggested that the Mg b wings provide useful constraints on gravity for dwarfs cooler than ∼6200 K,³¹ which is approximately the temperature for four of five stars we analyze. Fuhrmann et al. (1997) is able to derive an accurate log g for Procyon (F5V) from Mg b, so perhaps our concern is unwarranted. Assuming we have derived accurate stellar properties, we find that models fit best with log t = 9.4 ± 0.05 (2.25–2.8 Gyr), which encompass the error bars of CWW 44.

The models barely pass through the error bars for the early G dwarf, CWW 91, even though this should be the one star of the five that we know has broad enough Mg b wings to provide adequate constraint on log g, since it is most similar to the Sun. If we fix log g according to the Padova isochrone (log t = 9.4 (2.5 Gyr) and [M/H] = +0.064), we find log g = 4.45 instead of 4.35, at mass M = 1.03 M_☉.

We queried the g'r'i' and JHK_S photometry for a 1.03 M_☉ star from this isochrone and perform a brute force least-squares fit for distance modulus and visual extinction for CWW 91 in the range m − M = 7–8 and A_V = 0–0.5, with 0.01 mag step sizes, JHK_S errors according to 2MASS (σ = 0.023, 0.026, 0.021 mag), and g'r'i' errors set to σ = 0.03 mag. We find a minimum χ² at m − M = 7.42 ± 0.02, A_V = 0.22 ± 0.03 (see Figures 15 and 16). We perturbed [M/H] ±0.02 dex (our error bar from the SME analysis) and log t ± 0.5 (our error bar from fitting isochrones to the T_eff–log g diagram), then re-fit and find uncertainties of 0.04 and 0.01 mag for m − M and A_V. We then perturbed T_eff by ±50 K (the SME statistical error bar) and re-fit, and find uncertainties of 0.06 and 0.04 mag for each parameter.

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Adopting these conservative errors, we find m − M = 7.42 ± 0.06 and A_V = 0.22 ± 0.04. We repeated this analysis with solely the optical g'r'i' photometry, and then with just the 2MASS NIR JHK_S photometry, and find m − M = 7.45 and 7.43, respectively, and A_V = 0.19 for both cases. This give us confidence in the g' > 10 CFHT photometry.

We introduced reddening to the synthetic SED using the relationships provided by the Padova CMD Web site³²: $A_{g^{\prime }}/A_V = 1.167$, $A_{r^{\prime }}/A_V = 0.860$, $A_{i^{\prime }}/A_V = 0.656$, A_J/A_V = 0.290, A_H/A_V = 0.183, $A_{K_S}/A_V = 0.118$.

Up to this point, we have fit isochrones to a T_eff–log g diagram with values derived with SME for five stars with Keck/HIRES spectra. Now we perform a more traditional fit to the broadband optical and NIR photometry of all cluster members, and find results consistent with our spectroscopic solution. We initially worked with Padova models (Girardi et al. 2000; Marigo et al. 2008)³³ because they were the only group, to our knowledge, that provided isochrones in the CFHT/MegaCam g'r'i'z' filter set. Aaron Dotter has since released Dartmouth models in this set, and we will briefly compare results between these two models in Section 4.6.

Given the high degree of degeneracy between age, distance, and visual extinction (we fix metallicity according to our SME result, [M/H] = +0.064, [Fe/H] = +0.1), we developed an automated isochrone fitting technique that can efficiently cover a large parameter space. Inspired by the τ² method of Naylor & Jeffries (2006), described and utilized in Section 4.5, our method simulates a star cluster with a particular age and composition, and computes 2D cross-correlations between the resulting synthetic and actual CMD density distributions in order to find the distance and visual extinction that best aligns the model to the data. The age and composition control the morphology of the stellar locus on a CMD, while changes in distance modulus and extinction simply translate the locus across the CMD plane.

Using our cluster simulator (Section 3.3), we map the stellar locus with 10⁴ stars, the binary fraction set at 70%, and no differential extinction, for ages ranging from 1 to 4 Gyr. The simulated cluster CMD is binned by 0.005 mag in each dimension, as is the actual R147 CMD. Photometric error is not introduced to the synthetic photometry. Instead, the position for each star on the real CMD is broadened by a 2D Gaussian according to the assumed photometric error for each band: we use 0.02 mag for g' and i', and the errors provided by the 2MASS Point Source Catalog for J and K_S.

For the NIR (J − K_S) fit, all "Y" members were binned except for the blue stragglers, and the giants that appear to be undergoing core helium fusion according to their optical and NIR photometry offset from the main red giant branch. Dotter et al. (2008) note that the Padova isochrones are hotter in the lower main sequence, starting at ≈0.8 M_☉, than other commonly used models including the DSEP (Dartmouth Stellar Evolution Program) and Yale–Yonsei (Y²). The left and central panels of Figure 20 illustrates this difference in T_eff–log g and (g' − i'), but the right panel shows that the discrepancy does not significantly affect the NIR isochrone. We remove the K dwarfs from our optical isochrone fits. We also discard the optical red giant branch because of the saturated i' band photometry.

We compute the 2D cross-correlation between the real and synthetic CMD distributions with the IDL function CONVOLVE. Locations on the resulting image corresponding to negative extinction are set to zero. The point of peak signal provides the shift required to best align the isochrone model to the data.

Although this is not a statistically rigorous method for isochrone fitting, this cross-correlation method is conceptually straightforward, simple to code, can efficiently test hundreds of models in an automated fashion to more quickly cover the age–composition parameter space (a few minutes), and provides a diagnostic for model selection: the model with the maximum cross-correlation signal. In the next section, we will demonstrate that this method provides solutions essentially identical to the τ² maximum likelihood method. Three panels in Figure 17 plot age, distance, and extinction versus the cross-correlation signal, normalized to the maximum value, with metallicity fixed at [M/H] = +0.064. The results from fitting Dartmouth models are also plotted, and offset by +0.06 for clarity (see Section 4.6). Although broad, there are clear peaks in each diagram at log t = 9.4 (2.51 Gyr), m − M = 7.32 (291 pc), and A_V = 0.23 or E(B − V) = 0.075 assuming R_V = 3.1.

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The fourth panel of Figure 17 plots the isochrones (gray) of each solution for log t = 9.1 to 9.56, in steps of 0.01. The R147 members used in the fit are plotted in black. The best model quoted above is overlaid in yellow, and two additional models are also included at younger and older ages, providing points of reference for how the fits appear to rotate across the CMD counter clockwise with increasing age. This rotation is primarily caused by the overabundance of cluster members at the MSTO, which serves to anchor each fit to the MSTO location. Those models that also pass through the handful of K dwarfs and red giant branch are rewarded with a higher cross-correlation signal, creating the broad peaks in the other panels of Figure 17. Perhaps if the K dwarfs and red giants were weighted more heavily than the turnoff stars we would see more strongly peaked results.

We ran the optical fit with [M/H] = +0.08 and find the best model is log t = 9.39, m − M = 7.35, A_V = 0.26. The optical results are presented in Figure 18. The consistency between the optical and NIR CMD fits and the parameters obtained with the T_eff–log g diagram further justifies our use of these preliminary optical data.

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Naylor & Jeffries (2006) have developed a maximum-likelihood method called τ² for fitting model isochrones to CMDs (see also Naylor 2009).³⁴ This method simulates a cluster CMD from an isochrone, with a user-defined binary fraction. The user supplies a star catalog including the color, magnitude, and photometric errors, which the τ² code assumes are normally distributed. This method is powerful because it naturally accommodates errors in both color and magnitude, and accounts for the binary sequence. The code performs a grid search across a specified range of distances and ages, for isochrones of a given metallicity and reddening, and identifies best values, confidence intervals, and returns two diagnostics for assessing how well the model describes the data: a reduced-τ² (analogous to $\chi ^2_\nu$) and a probability value, Pr.

While the τ² code includes an isochrone library, we make use of the user-supplied isochrone feature and pass it the Padova grids, with [M/H] = +0.064. The τ² code does not currently solve for A_V, so we de-redden our catalog before running τ², and iterate for a range of reddening values. We selected the 56 R147 members of highest confidence ("Y"), excluding the later K dwarfs and red giants. We ran τ² for A_V = 0.0 to 0.5, and allowed τ² to search distances ranging from 200 to 400 pc (range suggested by the HIP1 (∼270 pc) and HIP2 (∼200 pc) parallaxes, plus a little extra on the far side), and ages 1 to 4 Gyr (step size is 0.01 in log t, encompassing the 2.5 Gyr value suggested by our fit to the T_eff–log g diagram in Figure 15).

We find high probabilities for a large suite of models demonstrating the flatness of the τ² space and high degree of degeneracy between age, metallicity, distance, and extinction. The degeneracy is accentuated in this particular case because we had to remove the saturated red giant branch from the fit. Figure 19 plots the best distance and age values for the range of extinctions. If we apply the age constraint from the T_eff–log g diagram fit (2.25 to 2.7 Gyr, illustrated by the black error bar on the right side of Figure 19), then this restricts distance and extinction to m − M = 7.25–7.4 and A_V = 0.2–0.3. At 2.63 Gyr, the τ² maximum-likelihood method derives values m − M = 7.29 and A_V = 0.23, equivalent to those we determined with our 2D cross-correlation method.

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Many groups are developing stellar evolution models. While there is remarkable agreement between these models, there are noticeable departures especially around the turnoff and red giant branch due to choice of input physics and solar composition (Dotter et al. 2008). In fact, the model choice is the greatest source of uncertainty when determining the fundamental properties of star clusters via isochrone fitting.

When we began our analysis, the Padova group provided the only models with synthetic MegaCam photometry. Since then, Dartmouth models have become available. Most recently, Padova has issued updated isochrones, which are now referred to as PARSEC models (Bressan et al. 2012)³⁵: they have revised the major input physics, lowered the solar metallicity from Z = 0.019 to Z≊0.0152, and now include the pre-main sequence (irrelevant for this work).

The Padova (now PARSEC) web tool parameterizes composition with Z, where [M/H] =log (Z/Z☉). We used Z = 0.022 and 0.017 to query Padova and PARSEC models at [M/H] ≈ +0.065. The Dartmouth Web tool³⁶ uses [Fe/H] instead of Z, and we set [Fe/H] = +0.1, according to the SME result for CWW 91. The left panel of Figure 20 shows that isochrones from Padova at 2.51 Gyr, PARSEC at 3.25 Gyr, and Dartmouth at 3 Gyr map out the same sequence on the T_eff–log g diagram, except for the low mass departure at ∼0.8 M_☉ already noted. The middle and right panels plot the optical and NIR isochrones, with A_V = 0.25 and m − M = 7.35. The differences between models introduce an additional age uncertainty of at least 750 Myr. Assuming PARSEC more accurately models stellar evolution than their Padova predecessor, the difference between PARSEC and Dartmouth reduces the age uncertainty to only ∼250 Myr. Figure 17 displays the results from fitting the 2MASS (J − K_S) CMD with Dartmouth [Fe/H = +0.1 models, illustrated with the square symbols, and offset vertically from the Padova results by +0.06 for clarity. The peak is shifted to older ages relative to Padova, while the distance and extinction remain basically consistent—a consequence of the similarity between the 2.5 Gyr Padova model and 3 Gyr Dartmouth model in T_eff–log g space, and each group's color–temperature transformations.

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We will explore additional models (e.g., BaSTI: Bag of Stellar Tracks and Isochrones) in a more detailed analysis in a future work, where we intend to perform a simultaneous seven-band isochrone fit using our optical g'r'i'z'  2MASS JHK_S, and our UKIRT JK photometry.

Dias et al. (2001) identified HIP 94635 (CWW 1) and HIP 94803 (CWW 2) as kinematic members of Ruprecht 147, and used their HIP1 parallaxes to derive a distance of 270 pc to the cluster. HIP1 lists π = 3.57 ± 1.01 and 3.75 ± 1.04 mas for these stars, respectively, while HIP2 provides larger values of 5.48 ± 0.65 and 4.92 ± 0.79. Disregarding the advice of van Leeuwen (2007) against deriving distances and distance moduli from parallaxes when the relative error is greater than 10%, one would determine a distance from HIP1 of 270 pc, and 193 pc from HIP2.

We also identify HIP 94435 (CWW 13) as a member of R147. Although HIP1 lists a discrepant parallax π = 2.42 ± 1.25 (413 pc), HIP2 gives 4.64 ± 1.19 (216 pc) consistent with the other two HIP stars. While the HIP2 results are self-consistent, Figure 21 demonstrates there is simply no way an isochrone can be drawn through either the optical (g' − i') or NIR (J − K_S) CMDs at the HIP2 distance moduli. The HIP2 parallax distances are all too close by ≈100 pc, compared with the photometric distances. This is reminiscent of the Pleiades problem, where the HIP1 parallax placed the cluster 0.23 mag closer than distances inferred from main sequence fitting and other methods. Soderblom et al. (2005) utilized the HST Fine Guidance Sensor to measure a new parallax distance consistent with the other non-HIP results.

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The R147 single star main sequence is not well defined, but blends smoothly into what is apparently the binary population. Evidently, R147 has a large binary fraction. The stellar population has encountered approximately 3 Gyr of Galactic gravitational tidal forces. Evaporation of the lightest-mass members should proceed first, both because low mass stars are preferentially ejected in three-body encounters, and mass segregation gives them a larger effective radius and more susceptibility to Galactic tides. This process also preferentially ejects single stars from the cluster, as multiple star systems of similar spectral type have a greater bound mass. The ongoing dynamical evolution of an open cluster thus tends to increase the binary fraction, and we may be seeing this effect in the R147 main sequence.

Our membership list is top heavy, dominated by F stars (dwarfs, MSTO and subgiants) and red giants, with fewer numbers of G dwarfs, and only a handful of early K dwarfs. This dynamical evolution and evaporation could also explain the paucity of low mass members, and perhaps if any are left, they exist predominantly in multiples. But this can also be explained by observational bias: the NOMAD and UCAC-3 proper motion errors increase for the fainter members. These stars also begin to blend into the Galactic background in the CMDs, further complicating candidate identification. We are currently conducting a RV survey for lower mass members, but this question will only finally be settled by deriving precise proper motions for the faint stars in the R147 field, which we intend to do by re-imaging the cluster with MegaCam in the near future.

If we are able to identify single M dwarfs, these will be the only old (>1 Gyr), single cool dwarfs with known ages and compositions bright enough to admit close spectroscopic study. Once the white dwarf population is identified, it will provide an independent age estimate for the cluster and inform studies of white dwarf cooling curves. At 300 pc, chromospheric activity diagnostics are measurable, as is L_X, and R147 should prove useful for studying the evolution of angular momentum and magnetic activity at intermediate ages.

For these reasons and more, we will continue our efforts to characterize Ruprecht 147 and establish it as a new and important benchmark for stellar astrophysics.