A NEW LOOK AT THE OLD STAR CLUSTER NGC 6791

NGC 6791 is an extreme Galactic star cluster with an old age of ∼8 Gyr (Grundahl et al. 2008), a high metallicity [Fe/H] = +0.30 (Boesgaard et al. 2009), and an unusual orbit that periodically brings it close to the bulge of the Milky Way (Bedin et al. 2006). Kinman (1965) was the first to provide an estimate for the total mass of NGC 6791: ∼3700 M_☉ down to V= 20, confirmed by Kaluzny & Udalski (1992). It is widely acknowledged that NGC 6791 is one of the most massive old open clusters in our Galaxy.

As indicated by the discovery of several extremely blue subdwarfs (Kaluzny & Udalski 1992) and the presence of a prominent red clump, morphology of the color–magnitude diagram (CMD) for NGC 6791 is complex. The proposed enhanced mass loss along the red giant branch (RGB) appears to explain the presence of hot subdwarfs and the abnormally young 2.4 Gyr white dwarf cooling age (Kalirai et al. 2007). Recently, Twarog et al. (2011) reported that the CMD in the inner part of NGC 6791 (R < 2' is somewhat different from that in its outer part (2' < R < 5'). Specifically, there is a dichotomy near the main-sequence turnoff, which the authors interpret as a result of protracted star formation.

This cluster is critically important to understanding a number of issues, such as stellar evolution and population synthesis at high metallicity in the Milky Way and other galaxies, specifically, in ellipticals and in spirals with bulges. Due to its relative proximity and its abundance of members, NGC 6791 provides perhaps the best opportunity for detailed studies of old and metal-rich populations. Despite a rich array of extant photometric and spectroscopic studies, however, the basic knowledge of cluster membership by kinematic means has been limited until now to radial velocities of a few dozen bright stars (e.g., Scott et al. 1995; Carraro et al. 2006) and preliminary proper motions for a few thousand stars (Cudworth & Anthony-Twarog 1993; Bedin et al. 2006). NGC 6791 is located in the field of view (FOV) of NASA's Kepler mission (Borucki et al. 2010) and is one of the targets of the Kepler Open Cluster Study (Meibom & Kepler Team 2010). It is also one of the clusters in the WIYN Open Cluster Study⁷ (Mathieu 2000)—again, largely owing to its extreme properties.

This Letter presents the highlights of a new and comprehensive proper-motion study of NGC 6791, based upon the selection of exquisite deep photographic plates in combination with a decade of CCD imaging. The resulting proper motions provide nearly definite cluster membership for stars brighter than g'∼ 22 and, thus, unveil most of the cluster's population with unprecedented clarity.

NGC 6791 is a rich but faint star cluster with a main-sequence turnoff at V∼ 17.5 (Stetson et al. 2003, hereafter SBG), thus requiring relatively long exposures even with 3–4 m class telescopes. Fortunately, there are deep photographic plates dating back to 1961. We selected the best 33 plates (assessed by the depth and sharpness of images) taken with the Lick 3 m and the Kitt Peak National Observatory (KPNO) 4 m telescopes. These plates were digitized using the Space Telescope Science Institute's GAMMA II multi-channel scanning microdensitometer. The second epoch includes 66 frames obtained with the NOAO CCD Mosaic Imager at the KPNO 4 m telescope in 1999–2007. The finest 24 CCD mosaic frames in g'r' filters (1, 30, and 300 s exposures) were obtained in 2009 November with MegaCam at the 3.6 m Canada–France–Hawaii Telescope. These frames served for construction of a master catalog consisting of 128,771 objects down to g'∼ 25 and over an FOV of 1 deg². We put positions on the system of the UCAC3 catalog (Zacharias et al. 2010) and calculated proper motions on this system using the iterative central-plate-overlap algorithm (e.g., Jones & Walker 1988). The final catalog contains a total of 58,901 objects down to g'∼ 23.8 over a smaller area of ∼0.8 deg², defined by a circular FOV (with radius 30') of the KPNO photographic plates. The highest precision of our proper motions is 0.08 mas yr⁻¹. Cluster membership probabilities are calculated using the frequency functions for cluster and field stars, obtained in selected magnitude and spatial ranges. Discrimination between cluster members and field stars is excellent down to g'∼ 22. Details of the astrometric reductions and the description of the catalog itself will appear elsewhere (I. Platais et al. 2011, in preparation).

For photometry, we used only the MegaCam images in g'r' filters. The central part of NGC 6791 is fairly crowded, often resulting in blended images. We note that all MegaCam images are preprocessed with Elixir which, besides the standard steps, also normalizes the instrumental photometric zeropoint between the chips (see Magnier & Cuillandre 2004; Clem et al. 2008). The short, 1 s exposures obtained in subarcsecond seeing were instrumental in constructing an initial catalog of positions and aperture photometry (MAG_AUTO magnitudes from SExtractor). Magnitudes from longer exposures were added only if they matched specified tolerances on position and magnitude. In this way it was possible to minimize the deleterious effects of image blending. Nevertheless, image blending and CCD chip edge effects may occasionally yield stellar colors that are significantly off. Our instrumental photometry was put into the standard g'r' system by employing the extant secondary photometric sequence in NGC 6791 (Clem et al. 2008). The rms error of the calibrating fits is 0.02 mag. On average, a calibrated g' magnitude near the main-sequence turnoff of NGC 6791 is ∼0.41 mag fainter than that in V.

One of the most comprehensive photometric surveys of NGC 6791 is that by SBG, who also provide extensive lists of bright stars, red giants, and faint blue stars in this cluster—all possible or likely members. Now, we are in a position to provide nearly definite star-by-star kinematic membership, with a caveat that stars with blended images may not appear in our proper-motion catalog or, if they do, may be biased. An example of such a case is the eclipsing binary V20—a definite cluster member (Grundahl et al. 2008) but incorrectly classed as a field star in our catalog. Its measured proper motion is apparently corrupted by the adjacent star (Δ_pos = 2'') in the amount of ∼6σ_μ. The CMD in Figure 1 shows the cleanest and the most complete census of NGC 6791 to date. It contains all stars with cluster membership probability P_μ⩾ 19%, as well as stars with 19%>P_μ > 1% but located on the main sequence, all within a radius R ⩽ 15' from the cluster center—very close to that adopted by Twarog et al. (2011). The cluster membership probabilities for peripheral members of NGC 6791 (R > 15') are less reliable because of the overwhelming number of field stars and numerical instabilities in finding the cluster population. Hence, in this region the selection of cluster members is limited to stars that are on the main sequence and have P_μ > 2%. From the combined CMD we deleted all stars below the main sequence and with g'>19, except for a few very blue stars with P_μ ≳ 50%. Likewise, all stars with g'>16 and located well above the main sequence and to the right of the RGB were eliminated. This leaves us with a total of 5699 probable cluster members.

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3.1. Horizontal Branch

3.2. Sub-subgiants

The depth and spatial extent of our survey allow the derivation of a reliable luminosity function (LF) for the entire cluster down to g' ∼ 24. The only omissions are secondaries in binary stars and severe blends. We have counted all stars from the cropped CMD (Figure 1) in 0.5 mag bins, in two ways: star-by-star and by weighting each star with its membership probability (Figure 2). To translate g' into $M_{g^\prime }$, an apparent distance modulus of 13.56 was applied. The peak at $M_{g^\prime } \sim +4.5$ and the smooth downward trend toward fainter magnitudes is unmistakable. It is consistent with the appearance of the LF in King et al. (2005), although we cannot replicate the flattening of their LF at g'>22—even less so, the flat luminosity functions provided in Kaluzny & Udalski (1992) and Kaluzny & Rucinski (1995). A total of ∼1000 cluster members per 1 mag bin around the main-sequence turnoff ($M_{g^\prime }\sim +4.5$) in our present sample is a record high among the known old Galactic open clusters.

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We constructed a (number) surface-density profile for NGC 6791 using the 4830 stars in Figure 1 brighter than g' = 22 (where the proper-motion discrimination between cluster members and field stars is best). This is shown in Figure 3. The filled circles in this plot show the number of stars per unit area, as a function of projected cluster-centric radius, defined by adding up stars weighted by their membership probabilities in a series of concentric circular annuli. The open circles result from adding up the total numbers of the same stars directly, without weighting by P_μ.

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We fitted a single-mass, isotropic King (1966) model to the P_μ-weighted density profile in Figure 3, using only the data inside R < 15' to constrain the fit. This implies a rather low central concentration for the cluster, c ≡ log (r_t/r₀) = 0.74 ± 0.05, corresponding to a dimensionless central King potential, W₀ = 3.4 ± 0.3. The best-fitting King scale radius is r₀ = 422 ± 030, which, given the low fitted concentration, implies a projected core (half-power) radius of R_c = 328 ± 012. The associated tidal radius is r_t = 231 ± 10, and the effective (projected "half-mass") radius is R_h = 442 ± 002 (it is normally the case that estimates of R_h are more robust than those of other characteristic radii). For a distance of 4.0 kpc to NGC 6791 (Grundahl et al. 2008), 1' = 1.16 pc; thus, we have that the projected core radius of the cluster is R_c ≃ 3.8 pc, the effective radius is R_h ≃ 5.1 pc, and the fitted tidal radius is r_t ≃ 27 pc.

Fitting to various other number density profiles defined by both brighter and fainter magnitude cuts and both weighted and not weighted by P_μ, yields results for R_c, R_h, and r_t that are generally compatible with the range of values suggested by the numbers just given for the g' < 22 case. The same is true for fits to luminosity surface-density profiles defined by adding up the luminosities of all the stars in our series of annuli. In exploring these various definitions of the density profile, we saw a clear tendency for the inferred tidal radius (and thus the concentration, log (r_t/r₀)) to increase systematically—along with R_h, to a lesser extent—as stars with fainter and fainter magnitudes were included to define the observed density profile. This is primarily because stars with g' ≳ 19–20 in our sample are somewhat depleted, relative to the brighter stars, in the innermost ∼2'–3' of NGC 6791. However, it is not clear whether this is a physical effect (e.g., due to mass segregation) or an artifact of crowding and image blending in the core of the cluster.

The total luminosity of all stars with g' < 22 in our catalog is L_tot ≈ 5500–$6500 \,L_{\odot,g^{\prime }}$ (assuming D = 4.0 kpc, corrected for $A_{\rm g^{\prime }}=0.55$ mag of extinction, and depending on whether or not the luminosities are weighted by P_μ). Adopting a theoretical g' stellar mass–luminosity relation from the Padova isochrones (Marigo et al. 2008) implies a total mass of M_tot ≈ 5000 M_☉ for the observed stars. This is a lower limit to the cluster mass because we have not attempted corrections for stellar binarity or incompleteness. We note that, if a King (1966) model with c = 0.74 and R_h = 5 pc accurately describes the internal mass profile of NGC 6791, then the projected, one-dimensional velocity dispersion averaged within the effective radius should be 〈σ〉_h ≃ 0.36(GM_tot/R_h)^1/2 ≈ 0.75 km s⁻¹. This corresponds to an intrinsic proper-motion dispersion of σ_μ ≈ 0.04(D/4 kpc)⁻¹ mas yr⁻¹, which is much smaller than the formal uncertainties in our proper motions. It is also significantly lower than the radial-velocity dispersion of ≈2 km s⁻¹ reported for about a dozen red giants by Carraro et al. (2006), suggesting either that the Carraro et al. dispersion may be spuriously high, or that NGC 6791 may not be in virial equilibrium. Perhaps related to the second option, we note that a 5000 M_☉ cluster in a Galactic orbit with a pericenter of ≃3 kpc and an apocenter of ≃10 kpc (Bedin et al. 2006) is expected to have a tidal radius of r_t ≈ 13 pc ≃ 11' at pericenter, and r_t ≈ 28 pc ≃ 24' at apocenter—as against a value of r_t ≳ 23' suggested by our King-model fitting of NGC 6791. Deciding the true dynamical state of this cluster will require much more comprehensive and higher-precision proper-motion and radial-velocity surveys, to obtain the tightest possible constraints on its orbit and to delineate accurately its internal kinematics.

Even a casual inspection of the cluster's CMD reveals an unusually broad RGB—on the order of Δ(g' − r')∼ 0.1 mag, while the formal uncertainties in the colors of these stars do not exceed ∼0.02 mag. There are a variety of potential sources of increased scatter in the CMD, such as instrumental effects including the limitations of aperture photometry in crowded fields, presence of field stars, differential reddening, binarity of stars, metallicity variations, and possible effects on color/luminosity of RGB stars by variable mass loss suggested by Kalirai et al. (2007).

Our proper-motion-vetted CMD offers a better look at the morphology of the RGB, which is more sensitive to differential reddening than the main sequence (apart from its turnoff region). In addition, our sample covers the largest area ever considered, thus enhancing the chances of finding the signs of differential reddening.

Unfortunately, we cannot take advantage of significantly reduced reddening effects in the near infrared. There is a poorly understood scatter in the J − K color of our RGB stars from either 2MASS or Carney et al. (2005), which prevents us from using this color as a nearly reddening-free reference. Instead, we examined the morphology of the RGB branch in g'r' CMD using approximately equal numbers of inner and outer probable cluster members by dividing the cluster at R= 5'. Then, we draw a ridge line for the inner sample, encompassing subgiants and RGB stars; see Figure 4. The majority of RGB stars at R < 5' are bluer than this ridge line but, surprisingly, nearly all RGB stars at R > 5' are redder than the ridge line of the inner sample. The shift in RGB color between the inner and outer samples is ∼0.05 mag, whereas the age difference of 1 Gyr suggested by Twarog et al. (2011) would produce only a ∼0.01 mag color shift in g' − r' across the RGB region (Girardi et al. 2004). We conjecture that this color shift, at least in part, is due to differential reddening. Among the effects listed above, it is the only physical effect known to have an undeniable spatial dependency.

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Our data provide evidence that differential reddening may not be ignored across the face of NGC 6791. Further advancements in our understanding of such a small effect require accurate near-infrared photometry and reliable identification of binaries in the upper part of the CMD.

This study provides a comprehensive and clean list of cluster members in one of the astrophysically most important Galactic star clusters. We hope that our findings in NGC 6791 and excellent cluster membership will stimulate in-depth future studies of individual cluster members.

We thank D. Crawford, J. Cummings, E. Hubbard, T. Kinman, B. Lynds, S. Majewski, R. Michie (deceased), K. Mighell, A. Sarajedini, and M. Sosey, whose time and effort at the telescope made this project possible. We thank the referee Barbara Anthony-Twarog for pointing out the limitations of our data. This work has been supported in part by NSF grant AST 09-08114 to JHU (I.P.) and by NASA grant NNX09AH18A (The Kepler Open Cluster Study). Astrophysics at Keele University is supported by an STFC Rolling Grant. This study is based on observations obtained with MegaPrime/MegaCam, a joint project of Canada–France–Hawaii Telescope (CFHT) and CEA/DAPNIA, at the CFHT which is operated by the NRC of Canada, the Institute National des Sciences de l'Universe of the CNRS, and the University of Hawaii.