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Home All issues Volume 575 (March 2015) A&A, 575 (2015) A120 Full HTML
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Issue
A&A
Volume 575, March 2015
Article Number A120
Number of page(s) 6
Section Stellar structure and evolution
DOI https://doi.org/10.1051/0004-6361/201425505
Published online 09 March 2015

© ESO, 2015

1. Introduction

Different galactic environments, it is assumed, produce distinct populations during the star formation episodes. From very loose and young associations such as Taurus-Auriga, doomed to be dispersed very soon in the galactic gravitational well, to the very old halo population in massive globular clusters, there is a large gamut in ages, compactness, metallicity, internal dynamics, total mass, spatial distribution and distribution of the individual masses, perhaps indicating differences in the initial mass functions (IMF). It is clear that a significant improvement in the completeness of the census of different associations provides key information to understanding star formation and evolution.

Table 1

Overview of previous studies of M 35.

Table 2

Instruments used in this study.

In this context, the open cluster Messier 35 (NGC 2168, hereafter M 35) is very interesting in several aspects. First, it is a quasi-twin of the Pleiades cluster, with a similar age (Vidal 1973) but a different metallicity. Second, the Kepler K2 mission (Howell et al. 2014) has just provided exquisite photometric time series, so that a detailed distribution of the rotational periods for different masses will soon become available (e.g. Meibom et al. 2009). Moreover, M 35 is not so crowded that confusion is a major problem and its size (about 1 sq. deg) is very suitable for follow-up multiobject spectroscopy (Barrado et al. 2001a).

Several studies have provided estimates of other key cluster parameters, such as its age, census, and metallicity. Table 1 gives an overview of the cluster’s properties found in the literature in the past 15 years. However, there is no a clear consensus for most of them. Sung & Bessell (1999) derived a distance modulus of (m − M)0 = 9.60 ± 0.10 corresponding to 832 pc, a reddening of E(B − V) = 0.255 ± 0.024 mag and an age of 200 Myr. Kalirai et al. (2003) pushed the cluster a little bit further, to pc and derived an isochrone fitting age of 180 Myr. More recently, McNamara et al. (2011) obtained a distance of 732 ± 145 pc from the internal proper motions. This dynamical distance and the radial velocity dispersion obtained by Geller et al. (2010) imply an age of 133 Myr, according to the same authors. Meibom et al. (2009) performed an age determination based on a completely different technique, gyrochronology, yielding a value between 134 Myr and 161 Myr. Reimers & Koester (1988), by using the white dwarf cooling age, derived an age in the range 70–100 Myr, whereas Barrado (2001), with the same technique, estimated 180 Myr. The rotation pattern suggests an age slightly older than the Pleiades (175 Myr compared to 125 Myr). The same conclusion is reached when the lithium abundances are compared. This is because the lithium dispersion, which is itself related to rotation for a given stellar mass, is no longer obvious for M 35 (Barrado et al. 2001a) while it is very significant in the case of the Pleiades (see, for instance Soderblom et al. 1993).

Regarding chemical composition, Steinhauer & Deliyannis (2004) quoted an unpublished work with a metallicity [Fe/H] = −0.143 ± 0.014, very similar to the value obtained by our group ([Fe/H] = −0.21 ± 0.10) using high spectral resolution data and spectral synthesis, (Barrado et al. 2001a).

The cluster is also relatively massive: Leonard & Merritt (1989) derived a central total mass in the range 1600–3200 M⊙ using dynamical models. Our own estimate, for the central of 27.5 × 27.5 square arcmin, is ~1600 M⊙, which allows for an exquisite determination of a complete stellar mass function (Barrado et al. 2001b, so far the deepest for M 35) which is totally compatible with the IMF of much younger and unevolved clusters, such as such as Collinder 69 (Barrado et al. 2005; Bayo et al. 2011), and suggests that M 35 includes several tens of potential substellar members.

The goal of this paper is to complete the census reaching well inside the substellar domain and including the cluster outskirts up to a radius of 1°, providing multi-epoch, multiband photometry from public archives and from our recent observations.

2. Data sets

We searched the Canada France Hawaii Telescope (CFHT), National Optical Astronomical Observatory (NOAO), Subaru, Kiso, Sloan Digital Sky Survey (SDSS DR9, Ahn et al. 2012) and Isaac Newton Group (ING) public archives for wide field images of the cluster. Table 2 gives an overview of the data set found in these archives and in our own private archives.

In each case, we downloaded the raw data and associated calibration frames. We processed the individual raw images using an updated version of Alambic (Vandame 2002), a software suite developed and optimized for processing large multi-CCD imagers, which we adapted for the instruments used here. Alambic includes standard processing procedures, such as overscan, bias, and dark subtraction for the individual readout ports of each CCD, flat-field correction, bad pixel masking, CCD-to-CCD gain harmonization in the case of multichip instruments, fringing correction (when needed for the reddest filters), de-stripping, background subtraction, and nonlinearity correction in the case of near-infrared detectors.

Aperture, point spread function (PSF), and model photometry were extracted from the individual images using SExtractor (Bertin & Arnouts 1996) and PSFEx (Bertin 2011). The individual catalogs were then registered and aligned on the same photometric scale using Scamp (Bertin 2006).

We derived the photometric zero-points using standard fields obtained for the same night whenever available or all-sky catalogues such as 2MASS (Skrutskie et al. 2006) in J,H and Ks, SDSS in g,r,i,z and IPHAS (Drew et al. 2005) in Hα. The zeropoint rms were typically in the range between 0.02 mag and 0.12 mag, and were added quadratically to the measurement uncertainty. We did not attempt to calibrate the nonstandard VR filters used with the Mosaic and SuprimeCam cameras and the He I narrow-band filter obtained with the WFC.

Proper motions for all the sources were computed using the method described in Bouy et al. (2013). The final residuals on the astrometric solution show a dispersion on the order of 11 ~ 12 mas. Figure 1 shows the estimated error on the proper motion as a function of i-band apparent magnitude. We note that the proper motion measurements are not tied to an absolute reference system such as the International Celestial Reference System (ICRS). They are nevertheless expected to be close to the ICRS since extragalactic sources and background stars largely dominate the sample and display very little motion with respect to the ICRS.

thumbnail Fig. 1

Estimated error on the proper motion as a function of i-band magnitude. The color scale represents the maximum time difference used for each measurement. The prediction for Gaia is over-plotted for comparison.

thumbnail Fig. 2

Spatial distribution of sources used as training set (green squares, from Barrado y Navascués et al. 2001) and of the 4349 sources of the final sample with membership probability greater than 0.5. Background image: 2MASS J-band.

A final master catalog of all sources (338 892 in total) was then produced including the measured photometry in the grizJHKs filters. We detected a total of 194 452 sources (approximately half) at more than two epochs, and the proper motions of these sources are also included. Since the main goal of the survey focuses on the study of M 35, only objects with | μαcosδ | ≤ 100 mas yr-1 and | μδ | ≤ 100 mas yr-1 were considered for the membership analysis.

thumbnail Fig. 3

Color magnitude and proper motion diagrams of the 194 452 sources of the sample detected at more than two epochs. Left: r vs. r − i. Middle: i vs. i − Ks. Right: proper motion diagram. Sources with a membership probability greater or equal to 0.5 are represented in the top panels with a color scale proportional to their probability. The remaining sources are represented in the bottom panels.

3. Membership

We use the method described in Sarro et al. (2014) to derive membership probabilities of all the sources. Briefly, the method uses a training set – in this case the sample of candidate members from Barrado y Navascués et al. (2001) – to identify the features that most efficiently separate the cluster’s population from the field and background population among all combinations of proper motion, luminosities and colors available. In the case of M 35, the best set was found to include the proper motions, the z, H, Ks luminosities and the (r − z), (r − i) and (J − H) colors. Once the best set of colors, luminosities and proper motion is selected, a model of the cluster’s locus defined by the training set is fitted in the corresponding multidimensional space. A mixture of Gaussians is used for the proper motion diagram and principal curves for the cluster’s sequence in all color–magnitude and color–color diagrams. Membership probabilities are then computed using this first model. The highest probability members are selected as the new training set, and the models and the membership probabilities are recomputed until they converge.

This method was originally developed and optimized for clusters like the Pleiades, i.e. clusters with a relatively large proper motion and photometric sequence clearly separated from the field and background sequences in many color–magnitude diagrams. Unfortunately M 35 is a worst-case scenario for the method. Its proper motion is relatively small and its sequence largely overlaps with the field and background sequence in almost all color–magnitude and color–color diagrams. To limit the contamination and enhance the contrast between cluster members and field and background sources, we chose to restrict the analysis to a radius of 1°  around the cluster’s center located at α = 06h08m54.0s, and δ = + 24°20′00′′ (J2000). Figure 2 shows their spatial distribution. It shows that the northwestern part of the survey was shallower than the rest of the survey, as fewer members were selected. It also shows that a number of high probability members have (r − i) or (i − Ks) color apparently inconsistent with the cluster’s sequence. Their high probability is due to their proximity to the isochrone in all other color–magnitude and color–color diagrams as well as to the cluster’s locus in the proper motion diagram. These sources, probably suffering from inaccurate photometry in one of these bands, illustrate the robustness of the selection method based on a high dimensional space.

Table 3 gives the astrometry, photometry and membership probability for the 338 892 unique sources detected in the corresponding area. Only the sources with a proper motion measurement have a membership probability (194 452 in total), as the availability of a proper motion measurement was a necessary condition in our membership analysis. Using sources with membership probability greater or equal to 0.9, we derive a median proper motion for the cluster of (μαcosδ,μδ) = (1.99, − 0.23) ± (0.82,0.71) mas yr-1, where the uncertainties correspond to the scaled median absolute deviation.

Figure 4 shows the membership distribution and cumulative distribution (computed from large to small values) for all the sources in the catalog. The vast majority of the sources has a membership probability of ≈0.0. A monotonously decreasing distribution fills the probability range between 0 and 1.0, as the result of the loose constraints on the photometric and astrometric properties of the cluster.

NGC 2158 is an intermediate age (1 ~ 2 Gyr) cluster at a distance of ≈3600 pc (Carraro et al. 2002) located at a projected distance of only 25′  from M 35. It is therefore included in the area covered by the present study and possibly contaminates the membership analysis. To estimate the level of contamination due to NGC 2158 members, we select all the sources located within 3′ of its center. Given the distance and projected density profile of NGC 2158, the vast majority of these sources are expected to be members of NGC 2158. Figure 5 shows the sequence formed by these sources in various color–magnitude diagrams made of colors and luminosities used for the membership analysis presented here, and compares it to the sequence formed by objects with a probability of membership to M 35 greater than 0.5 according to our analysis. The two sequences overlap mostly at the bright end, and contamination must occur mostly above i ≲ 17 mag. We find that only 27 sources with a probability of membership to M 35 greater than 0.5 are located within 3′  of NGC 2158, and 53 within 5′. Given the projected size of NGC 2158 core, little contamination is expected beyond 5′, and the contamination by NGC 2158 members must not reach more than 1 ~ 2% at most.

thumbnail Fig. 4

Distribution (blue, left scale) and cumulative distribution (red, computed from large to small values, right scale) of membership probabilities for the 194 452 sources of the sample.

thumbnail Fig. 5

Color–magnitude diagrams of the M 35 high probability members (≥0.5. red dots) and of all the sources within 3′  of NGC 2158 center (blue dots).

4. Conclusions

We have processed and analyzed a total of 4867 wide-field optical and near-infrared images of M 35 obtained from various public astronomical archives. The images cover 18 years of time baseline and typically reach a depth of 21 ≈ 22 mag in the optical and ≈19 mag in the near-infrared, while saturation arises around 12 ~ 13 mag at the bright end. This data set allows us to derive multiwavelength photometry from the optical to the near-infrared for 338 892 sources, and proper motions for 194 452 of them. We use these measurements to derive the membership probability of all the sources with a proper motion measurement. We obtain:

  • 4349 candidate members with probability greater than 50%.

  • 1726 candidate members with probability greater than 75%.

  • 305 candidate members with probability greater than 95%.

These numbers are consistent with the census presented in Barrado y Navascués et al. (2001) over a smaller area. Contamination is expected to be significant as the locus of the cluster in the proper motion, color–magnitude and color–color diagrams overlaps largely with the field and background locus. This new study nevertheless provides a coherent and quantitative membership analysis of M 35 based on a large fraction of the best ground-based data sets obtained over the past 18 years.

Acknowledgments

H. Bouy is funded by the Ramón y Cajal fellowship program number RYC-2009-04497. This research has been funded by Spanish grants AYA2012-38897-C02-01. E. Moraux ackowledges funding from the Agence Nationale pour la Recherche program ANR 2010 JCJC 0501 1 “DESC (Dynamical Evolution of Stellar Clusters)”. A. Ribas is funded by ESAC Science Operations Division research funds with code SC 1300016149. Based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. Based on observations obtained with WIRCam, a joint project of CFHT, Taiwan, Korea, Canada, France, at the Canada-France-Hawaii Telescope (CFHT). This paper makes use of data obtained from the Isaac Newton Group Archive which is maintained as part of the CASU Astronomical Data Centre at the Institute of Astronomy, Cambridge. The data was made publically available through the Isaac Newton Group’s Wide Field Camera Survey Programme. The Isaac Newton Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. This research draws upon data distributed by the NOAO Science Archive. NOAO is operated by the Association of Universities for Research in Astronomy (AURA) under cooperative agreement with the National Science Foundation. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. This work is based in part on data obtained as part of the UKIRT Infrared Deep Sky Survey. This research has made use of the VizieR and Aladin images and catalog access tools and of the SIMBAD database, operated at CDS, Strasbourg, France. This research made use of data from the SDSS survey. Funding for the creation and distribution of the SDSS Archive has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the US Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Based on data collected at Subaru Telescope and Kiso observatory (University of Tokyo) and obtained from the SMOKA, which is operated by the Astronomy Data Center, National Astronomical Observatory of Japan.

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All Tables

Table 1

Overview of previous studies of M 35.

In the text
Table 2

Instruments used in this study.

In the text

All Figures

thumbnail Fig. 1

Estimated error on the proper motion as a function of i-band magnitude. The color scale represents the maximum time difference used for each measurement. The prediction for Gaia is over-plotted for comparison.
In the text
thumbnail Fig. 2

Spatial distribution of sources used as training set (green squares, from Barrado y Navascués et al. 2001) and of the 4349 sources of the final sample with membership probability greater than 0.5. Background image: 2MASS J-band.
In the text
thumbnail Fig. 3

Color magnitude and proper motion diagrams of the 194 452 sources of the sample detected at more than two epochs. Left: r vs. r − i. Middle: i vs. i − Ks. Right: proper motion diagram. Sources with a membership probability greater or equal to 0.5 are represented in the top panels with a color scale proportional to their probability. The remaining sources are represented in the bottom panels.
In the text
thumbnail Fig. 4

Distribution (blue, left scale) and cumulative distribution (red, computed from large to small values, right scale) of membership probabilities for the 194 452 sources of the sample.
In the text
thumbnail Fig. 5

Color–magnitude diagrams of the M 35 high probability members (≥0.5. red dots) and of all the sources within 3′  of NGC 2158 center (blue dots).
In the text

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