Death of a cluster: the destruction of M67 as seen by the SDSS
aa r X i v : . [ a s t r o - ph . GA ] J a n Death of a Cluster: the Destruction of M67 as seen by the SDSS
James R. A. Davenport , , Eric L. Sandquist Received ; accepted Corresponding author: [email protected] Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195 Department of Astronomy, San Diego State University, 5500 Campanile Drive, SanDiego, CA, 92182-1221 2 –
ABSTRACT
We probe the spatial and dynamical structure of the old open cluster M67using photometric data from the Sloan Digital Sky Survey’s sixth data release.Making use of an optimal contrast, or matched filter, algorithm, we map thedistribution of high probability members of M67. We find an extended andelongated halo of likely members to a radius of nearly 60 ′ . Our measured coreradius of R core = 8 . ′ ± . ′
60 is somewhat larger than that of previous estimates.We attribute the larger core radius measurement to the SDSS probing lower massmain sequence stars than has been done before for similar studies of M67, and theexclusion of post main sequence M67 members in the SDSS sample. We estimatethe number of M67 members in our SDSS sample to be 1385 ±
67 stars. A lowerlimit on the binary fraction in M67 is measured to be 45%. A higher fraction ofbinary stars is measured in the core as compared to the halo, and the luminosityfunction of the core is found to be more depleted of low-mass stars. Thus thehalo is consistent with mass segregation within the cluster. The galactic orbit ofM67 is calculated from recent proper motion and radial velocity determinations.The elongated halo is roughly aligned to the proper motion of the cluster. Thisappears to be a result of mass segregation due to the galactic tidal field. Ouralgorithm is run on 2MASS photometry to directly compare to previous studiesof M67. Decreasing core radii are found for stars with greater masses. We test theaccuracy of our algorithm using 1000 artificial cluster Monte Carlo simulations.It is found that the matched filter technique is suitable for recovering low-densityspatial structures, as well as measuring the binary fraction of the cluster.
Subject headings: open clusters and associations: individual (M67) – galaxy:kinematics and dynamics
1. Introduction
For over 40 years the spatial structure of stellar clusters has been characterizedby the widely accepted King model (King 1962). This density model matches a widerange of observed clusters well (e.g. McLaughlin & van der Marel 2005). As King (1966)notes, however, the model does not describe the specific dynamical evolution or stateof a particular cluster. As clusters age their constituent stars inevitably undergo closegravitational encounters with other members of the cluster. Through energy equipartition,lower mass stars are given higher velocities, and thus larger orbits in the cluster. Many willbe given velocities greater than the escape speed for the cluster’s gravitational well. Weobserve this dynamical equipartition in the segregation of masses radially across a cluster,with lower mass stars being found preferentially further from the center than higher massstars. Binary stars are also more centrally concentrated than their single-body counterparts.The King model does not deal with the unique history a cluster may have within its parentgalaxy, or the state and location of stars previously associated with it.Escaped stars may be projected across large areas on the sky. Within disruptingclusters (such as most open clusters for example) the ejected stars may be a significantfraction of the cluster’s initial mass. It is also likely that the ejected stars are notdistributed in a spherical manner, due to tidal disruptions from the galactic potential orclose encounters with giant molecular clouds. By understanding the total amount and rateof mass lost in a cluster, we may begin to paint a picture of the cluster initial mass function,and the history of its disruption in the galaxy. Since open clusters are plentiful and foundwith a wide variety of ages, we may hope to study this process at many stages.M67 (NGC 2682) is an old ( ∼ ∼ ∼ year timescales(Binney & Tremaine 1987), the existence of old open clusters is somewhat of an anomaly.While M67 is a classic example of a highly evolved open cluster (e.g. van den Bergh 1957),older examples do exist. NGC 6791 has an age of at least 8Gyr (Carraro et al. 2006),roughly twice that of M67. This open cluster is believed to be one of the most massivein our galaxy, and its high stellar density is surely a prerequisite for its survival to suchexceptional age. Clearly this is an abnormal open cluster, and its origins under the typicalopen cluster formation scenarios have been questioned (Carraro et al. 2006). Despite itsuncertain origins, NGC 6791 like other older clusters displays a dynamically evolved massfunction, indicative of mass segregation (Kaluzny & Rucinski 1995).Due to the paucity of old open clusters such at M67 and NGC 6791, and the largenumber of younger clusters, it is reasonable to assume that a great many open clustersexisted in the past and have since been destroyed. These lower mass clusters, like the youngclusters found today, likely had a wide range of masses and numbers of members. Indeed itis believed that most stars which are now part of the galactic disk originated in clusters ofvarious sizes. These clusters must have had densities that were sufficiently low as to allowthem to be completely dissociated within about 600 Myr (Bergond et al. 2001).Ongoing work to fully model the evolution of M67 over its entire lifespan has beenpromising. Hurley et al. (2005) have created an N-body simulation of M67 whose result 5 –over 4 Gyr of evolution shows reasonably good agreement with observations of the spatialdistribution and stellar composition of the cluster. These types of simulations allowobservers to study the cluster’s initial conditions and their effect on the present state. M67is found in this model to have lost at least 75% of its stellar mass to dynamical and stellarevolution, and it is suggested that the cluster will continue to dissipate.Mass segregation has previously been suggested as the cause for the observed structuralproperties of M67. Bonatto & Bica (2003, hereafter BB03) find a notable difference betweenthe luminosity functions of the core and halo of M67, with the halo having significantlymore faint star contributions. This is found as well in several other studies, such asMontgomery et al. (1993) and Fan et al. (1996)BB03 make use of the Two Micron All Sky Survey (Skrutskie et al. 2006, hereafter2MASS) to probe M67 over a large and continuous area. M67 has a large enough spatialprojection on the sky that it could not be imaged by most large telescopes in a singleexposure. Unlike dedicated “pencil-beam” surveys which could be carried out overindividual portions of the cluster, large scale surveys such as 2MASS and the Sloan DigitalSky Survey (York et al. 2000, hereafter SDSS) can uniformly image regions much largerthan a single cluster. This makes them ideal resources for studies of cluster structure.In this paper we use SDSS data to probe the spatial and stellar structure of M67 asit is seen today. Our selection of SDSS photometry is described in §
2. The matched filtertechnique which separates M67 from the surrounding field population is outlined in §
3, andour results are presented in §
4. In §
2. SDSS Photometry
The SDSS is a major survey consisting of both five-band ( ugriz ) photometric andoptical spectroscopic data. The photometric data are collected in adjoining stripes overa quarter of the sky, covering the north galactic cap. It has been used to study objectsranging from nearby asteroid families (Parker et al. 2008) to incredibly distant quasars(Inada et al. 2009). The SDSS provides nearly simultaneous imaging in five photometricbands ( ugriz ), down to r ∼
23 (Adelman-McCarthy et al. 2008). These data are carefullycalibrated (Tucker et al. 2006; Davenport et al. 2007), achieving excellent photometricerrors averaging 1% in u,g,r,i and 2% in z . The large spatial coverage combined withaccurate photometry has been useful for studying low-density structures such as tidalstreams in the galactic halo and globular cluster disruptions (e.g. Grillmair & Dionatos2006b). The SDSS thus provides an ideal source of information about several nearby openclusters, which are often distributed over large portions of the sky.Our data came from the sixth SDSS data release (Adelman-McCarthy et al.2008, hereafter DR6) which is publicly available online via a SQL database . Thereader is referred to DR6 and references therein for a highly detailed description ofthe survey. Our query returned sources from the STARS view of the PhotoObjAlltable, which includes all objects which the SDSS pipeline (Lupton et al. 2001) detectsas point sources (as opposed to extended sources or cosmic rays for example) andare not quasars. To ensure a clean sample of only stars in our analysis we set thefollowing photometric flags: SATURATED = 0, BRIGHT = 0, OK SCANLINE > >
0, EDGE = 0, LOCAL EDGE = 0, PRIMARY >
0, PSF FLUX INTERP= 0, INTERP CENTER = 0, BAD COUNTS ERROR = 0, PEAKCENTER = 0,NOTCHECKED = 0. Some of these flags are redundant to those automatically applied http://casjobs.sdss.org . We have chosen to use thePSF magnitudes as they are considered the most unbiased measurement for point sourcesby the SDSS. We queried a 20 ◦ × ◦ box centered around M67 ( α =132.825, δ =+11.8, J2000) whichreturned 2,111,236 point sources with 15 < g <
23 and 14 < r < .
5. These magnitudecuts were made to remove major photometric scatter which grows rapidly near the faintlimit, and to avoid bright stars which may have spurious photometry. The entire sample isshown in Figure 1, which shows the density of point sources found by SDSS as filled contours(where darker is increasing density). Estimated photometric reddening is computed by theSDSS from the Schlegel et al. (1998) dust maps. We carried out the analysis in the followingsections both with raw magnitudes and reddening corrected magnitudes. These reddeningadjustments are critical for extragalactic or distant cluster science as they correct for theextinction of light from the interstellar medium. Because M67 is quite close, extinction isnot suspected to be a major contribution to the observed photometry. Indeed, no significantdifferences arose in our results when using de-reddened magnitudes. The final analysis wascompleted with the de-reddened data.
3. The Matched Filter
The matched filter technique, also known as optimal contrast filtering, has been usedin galactic astronomy for some time. Rockosi et al. (2002, hereafter R02) used a matchedfilter on early SDSS photometry around the globular cluster Palomar 5. They were able todetect large symmetric tails of stars leading and trailing the cluster in its orbit. Follow-upmatched filter work by Odenkirchen et al. (2003) and Grillmair & Dionatos (2006a) showedthese tails to extend at least 22 ◦ , a limit imposed by the edge of the SDSS footprint. Weused the DR6 data around Palomar 5 as a benchmark for our algorithm, and were able torecover the ∼ ◦ tails. A similar algorithm has been employed to detect low-density streamsof stars with no detectable nucleus (e.g. Grillmair & Johnson 2006; Grillmair & Dionatos2006b). R02 provide a good description of the matched filter process, and the reader isencouraged to seek further discussion therein. We will however briefly describe our methodand its application to the open cluster M67 as well as our artificial clusters below. Traditionally in the absence of more detailed information, such as proper motions,radial velocities, or spectra, cluster membership can be crudely estimated based on thepositions of stars in a color vs magnitude diagram (CMD). To maximize the contrast of thecluster against the surrounding field stars we must characterize the probability functionsfrom both the field and cluster in color-magnitude space. These two CMD probabilityfunctions are then used to determine the probability of membership for every star.The M67 CMD was determined by selecting the stars within 0 . ◦ of the cluster center.Figure 2 shows the M67 CMDs for g − i vs g and r − z vs r in our SDSS data. The mainsequence is clearly visible in both panels, and a faint equal-mass binary sequence can be 9 –seen above it. We chose to use the colors g − i and r − z because they better separatethe M67 main sequence from the significant field contamination. The galactic field starswere crudely filtered out by rejecting any stars not within a few photometric σ of a splinehand-fit to the main sequence and equal mass binary sequence. A 2-D gaussian smoothingalgorithm was then applied to these rough cluster CMDs, creating a continuous CMDdistribution for M67.The number of cluster stars in a given solid angle is described by the equation n cl = αf cl , where α is the number of stars in a region, and f cl ( color, mag ) is a normalizedprobability function for the cluster in the color-magnitude plane. By normalizing thecontinuous CMD distributions described above, we created the f cl functions for M67. Thiswas done for both ( g − i, g ) and ( r − z, r ) independently, and are shown in Figure 3. Thenon-uniform distribution shown in Figure 3 is a result of sampling f cl from the stars in thecore of M67 which are not evenly distributed along the main sequence. R02 investigatedwhether the mass function of the cluster core would detract from the matched filter’s abilityto detect tidal debris that would generally have a different mass function. Their conclusionis that the method is robust against such biases, but we do bear this in mind in our analysislater on.The same task must be carried out for the field to describe the background filter.It is clear from Figure 1 that the field does not have a uniform density of sources in oursample. Instead we see the density of stars rise at lower galactic latitudes, near the galacticplane. To investigate the effect the changes in the field star population would have on ouranalysis, we sampled the background population in several regions. Figure 4 shows thebackground ( g − i, g ) CMD in four quadrants of the field. Other than the number of starsin each quadrant, the differences between these four CMD samples is minor, and we believethe changes in the CMD will not greatly affect our analysis, as was also concluded in R02. 10 –Thus we make the assumption that the background has a uniform CMD structure acrossthe field studied, and that the stellar density may be described by a low-order surface fit,as described in Grillmair & Johnson (2006).The background filter is referred to as n bg ( color, mag ), which, given any area on thesky provides the number of background stars in each color vs. magnitude bin within thatsolid angle. It is valid to use n bg and not f bg here because the background is a continuousand relatively smooth population, and the number of stars in any area can be estimated.By using all of the stars around M67 with a radius between 1 . ◦ and 8 ◦ (1,011,776) ourbackground population is very well sampled. This annulus was chosen to avoid both thecluster and any potential tidal features, and the large hole in the data set in the south-eastcorner. Applying a boxcar smoothing algorithm and dividing by the area used, we createthe two n bg filters shown in Figure 5.Because the field population does not have a uniform distance or age, the familiarfeatures of an ideal CMD (e.g. main sequence, turn off, red giant branch, etc) becomeseverely blurred. The resulting color vs. apparent magnitude diagram is known as a Hessdiagram (e.g. see Alcock et al. 2000). In the Hess diagrams in Figures 4 and 5, severaldistinct features are visible in the CMD contours. The peak at ( g − i, g ) = (0 . ,
17) is fromthe galactic disk (the thick disk according to R02). This feature is strongest in Figure 4d,which has the lowest galactic latitude and thus should contain the most disk stars. Thesmooth feature at g − i ∼ . g − i ∼ . f cl and n bg distributions have steep declines near the limiting magnitudes. 11 –To produce the optimal contrast, the normalized cluster filter is divided by the scaledbackground. This yields h = f cl n bg , which is shown in Figure 6. This produces a CMDmatched filter that describes the stars which stand out from the background the strongest.For any given star, its color and magnitude will yield a value of h related to its probabilityof membership in M67. Naturally this probability function will promote regions of theCMD where there are many M67 members but few field stars, and conversely punish starswith CMD positions having large field populations.The spatial distribution of the cluster is then mapped by summing the values of h inside small (0 . ◦ , . ◦ ) spatial bins. We complete this entire process independently for boththe ( g − i, g ) and ( r − z, r ) CMDs, and co-add the results, as per Grillmair & Dionatos(2006a). While the probability distribution h produces the maximum likelihood indicatorfor the stars, corrections for the field response to the h filter must be done. To solve for theactual number of cluster stars found in each spatial bin, α , the following formula from R02is used: α = (cid:26)X (cid:20) f cl n bg (cid:21) − Z f cl d ( color, mag ) (cid:27) / (cid:26)Z f cl n bg d ( color, mag ) (cid:27) , (1)where f cl n bg = h is summed for all stars in a spatial bin as mentioned above, the integral of f cl accounts for the background response in a solid angle d Ω, and the integral of f cl n bg is thesignal-to-noise response of the filtering. This equation is the basis for our analysis withboth the SDSS and 2MASS data sets, as well as the Monte Carlo simulations described inthe following section. In order to test the robustness of the matched filter method, we ran our algorithmusing artificial clusters of known stellar composition and structure. By characterizing theefficiency and reliability of the algorithm we were able to examine issues of biases and 12 –errors for our results in §
4. To accurately measure the efficiency and determine the greatestsources of error, we inserted artificial clusters at random locations within our field. Thesetests were run 1000 times on our SDSS data set in order to determine the reliability andsignificance of low-contrast features seen in § ≤ N ST ARS ≤ . ′ ≤ R core ≤ ′ . This wide range was used to fully explore thedensities and spatial compositions which open clusters might have.The spatial composition of each cluster was created by randomly generating radialpositions for every member, each being drawn from a gaussian profile with a standarddeviation radius of R core . The angular positions were then chosen randomly between 0 ◦ and 360 ◦ , creating a roughly uniform circular distribution of stars. No tidal elongationwas explicitly included, however the gaussian distribution of stars did at times produceasymmetric halos at large radii consisting of up to a few dozen stars.The griz magnitudes were formed using the handmade splines fit to M67 in § g band was used which had the form g = ( g . ∗ ) × g ∗ is an array of N ST ARS elements filled with random values between 0 and 1. This functionwas chosen to provide an increasing number of stars with decreasing luminosity, but tohave a deficiency as compared to the field star population of low-mass stars, as observed inold open clusters. We also found that it approximately reproduces the observed luminosityfunction of M67. An equal mass binary sequence was created by increasing the magnitudesof a subset of stars by 0.75 mag in every band. The fraction of equal mass binaries waschosen at random between 10% and 60%.Appropriate photometric scatter was created by sampling errors for the actual SDSSdata. The mean error and the standard deviation of the errors were calculated for griz
13 –bands in bins of 0.1 magnitudes. These errors were then mapped to the artificial starsby their corresponding griz magnitudes, choosing for each star a random number withinthe gaussian error envelope. Adding these errors to the artificial photometry created avery realistic scatter about the M67 splines which increased with increasing photometricmagnitude.For every model run, the simulated data was placed randomly in the field aroundM67, but was required to be greater than 1 . ◦ radially away from M67 to avoid cross-contamination, and less than 8 ◦ away to stay well within the bounds of the SDSS datasample. The full matched filter analysis code was then run, sampling f cl from a 0 . ◦ radiusaround the model cluster and smoothed as before with the M67 f cl . The background n bg wasdetermined from an annulus around this with a radius between 1 . ◦ and 6 ◦ , encompassing ∼ . ′
60 for R c . The number of stars detected by our algorithm was larger than theinput models by, on average, 17%, and we computed a standard deviation on the numberof stars recovered to be 67 stars. We also determined that the input binary fraction was1.27 times more than our recovered binary fraction, and found a standard deviation of 6%for the resulting binary fraction. None of the recorded statistics changed as functions ofthe background density, suggesting that our matched filter algorithm consistently was ableto remove the field contamination. We are attempting to improve these biases for futureimplementation of our algorithm.Since each model run was required to be at least 1.5 ◦ away from M67, in some casesthe artificial cluster can be close enough to M67 for it to be present on the radial profileplot at it’s furthest extent. This can be seen in Figure 8a for instance. These examplesprovide a useful benchmark for the robustness of the matched filter. Despite low-orderchanges in the local background population surrounding each run, and the variations in themodel f cl compositions and model core densities, M67 is always nearly perfectly recovered.The elongated features of M67 seen in these examples match those found in the analysis ofthe following sections.Visual inspection of a subset of the models, as demonstrated in Figure 8, showed noexamples of spurious extra-tidal features which deviated from the gaussian distributioncaused by fluctuations in the background population. Any elongated features appeared tobe caused by the input model. Further, our algorithm itself, while slightly overestimatingthe number of stars in the clusers’ core, does not produce random cluster halo signatures. 15 –We therefore conclude that the matched filter method is effective in characterizing andremoving the field star population and providing an accurate representation of the clusterwithin the range of our sample. Any extra-tidal structures or elongations found in thevicinity of M67 are therefore considered to be real and intrinsic to the cluster.
4. Results4.1. M67 Properties
By analyzing SDSS data for M67 using the technique outlined in § . ◦ ) boxcar smoothing kernelhas been applied to the summed α data, and a low-order surface fit to the background wassubtracted to remove any residual large-scale variation of the field density. The core ofM67 is strongly detected, and shows a circular distribution. The over-plotted circle, 25 ′ inradius, denotes the furthest radius which BB03 detected the cluster against the surroundingfield population using 2MASS data. There is however a significant low density asymmetrichalo of stars well outside the core. The contours from light to dark are increasing levels ofdensity. They are defined by the equation level j = M ED ( α ) + ( σ α × j ) where M ED ( α )is the median value of α over all spatial bins, σ α is the standard deviation of α , and j ≡ { , , , , , } . To ensure that α was well characterized, we created a histogram of α from every 0 . ◦ × . ◦ spatial bin in our SDSS sample. This is shown in Figure 11,and appears gaussian in shape and is centered around α = 0. Since our contours beginat two standard deviations above the peak shown in Figure 11, and noting the reliabilitydetermined in § § α values in that bin, divided by the area that thebin encompasses. This is directly analogous to the spatial map in Figure 10, and the unitsof ( α arcmin − ) are equivalent to ( stars arcmin − ). The extended halo seen in Figure 10is visible from a radius of ∼ ′ to ∼ ′ where it falls to background levels.We fit this surface density profile using a King-like profile (King 1962) to our data,which has the form n ( r ) = n bkgd + n r/R c ) , where R c is the core radius, n bkgd thebackground surface density (not to be confused with the background filter n bg ), and n thecentral peak surface density. This surface density profile equation was used perviously byBB03 to model M67. This fit is shown in Figure 12 as the solid lines. Our King model fitprovides R c = 8 . ′
24 after correcting for biases from § R c = 4 . ′
86 by BB03. From our testing with the modelcluster, we estimate the error to be 0 . ′
60. We believe the difference between our radialprofile and that of BB03 is due primarily to the lower limiting mass our study probes. Wedo give a direct comparison to BB03 by using the matched filter algorithm on the M672MASS data and provide more discussion in § R t . Using the equation n ( r ) = n bkgd + n { [1 + ( r/R c ) ] − / − [1 + ( R t /R c ) ] − / } from King (1962) and the valueswe determined for the first-order fit above, we found the estimated tidal radius for M67 tobe R t = 64 ′ ± ′ . Errors here are determined from standard deviation of the RMS scatteron our fit. This corresponds to a radius of 16.8 pc at the distance of M67, much larger thanthe determination using bright stars in M67 by Piskunov et al. (2007). By summing thenumber of stars in each radial bin in Figure 12 we estimate the total number of visible M67members to be 1385 ±
67, where our error is again adopted from our models in § Having found evidence for a large halo around M67, we investigated the differencesbetween the halo and core populations. Variations in the types of stars in the inner andouter regions of the clusters might suggest an origin for the elongated halo. In dynamicallyun-evolved systems, the initial stellar luminosity function rises towards lower masses. BB03use this property to investigate the evidence for mass segregation in M67. They createda set of 2MASS J-band luminosity functions in three regions (core, inner-halo, and outerhalo). A higher fraction of low-mass and faint J-band stars were seen in the outer halo, andthus mass-segregation is implicated.Binary star systems are composed of two stars which are often too close to be visuallyresolved. This single point source is observed to be brighter than a single-star of the sameapparent color. These systems also have higher mass than single-star systems by definition.The effects of mass segregation discussed above are therefore applicable to binary starswhich act as more massive single stars. Previous cluster studies have observed a strongerconcentration of binary stars in the cores than in the outer envelopes of older clusters (e.g.Fan et al. 1996).The binary fraction and luminosity function for each region of our data can be probedin much the same way as the spatial structure. Rather than summing α , the number ofpotential member stars, in each spatial bin, we summed α in three concentric regions forevery magnitude bin (for the luminosity function) or across the main sequence (for thebinary fraction). These three regions were the core, halo, and a large background annuluscentered around M67.Calculating the binary fraction across the entire magnitude range requires properlycollapsing the CMD into the color plane. We employed a technique used by Clark et al.(2004) to collapse the main sequence of the globular cluster Palomar 13. Since a spline 18 –has already been fit by hand along the M67 main sequence in §
3, we subtracted themain sequence spline color from every star’s color, thus centering the main sequence on∆
Color = 0. Because the equal-mass binary sequence is 0.75 mag brighter than the mainsequence, it’s ∆
Color bin position was easily tracked. We then divided ∆
Color by the∆
Color bin of the binary sequence, creating a reduced color R ≡ ∆ Color/ ∆ Color bin . Thisplaced the main sequence at R = 0 and the equal mass binary main sequence at R = 1. Tocalculate the binary fraction we summed all of the α values in each reduced color bin, witha range of − ≤ R ≤
2. The luminosity function is found by summing all of the α values inevery magnitude bin, again cutting out stars outside the reduced color range − ≤ R ≤ α sums in each CMD bin. The right panel shows the sum of α values alongthe magnitude axis, while the bottom shows the same along the reduced color axis. Sincethe equal-mass binary main-sequence was created by translating the main-sequence spline0.75 magnitudes brighter, a discontinuity in the calculation of ∆ Color bin arises at the endpoints. Thus we have reduced our magnitude range by 0.75 on both the bright and faintend to avoid these biases.The core population in Figure 13 (radius < . ◦ ) shows a clear double gaussian peakalong the reduced color R axis, and a deficiency of faint (low-mass) members along themagnitude axis. The halo in Figure 14 (0.8 < radius < . ◦ ) contains a more flattenedluminosity function, and a diminished secondary peak in the binary fraction. These twofigures do not however properly account for the contribution the field population wouldhave, especially in the halo which samples a larger area and has a lower expected densityof cluster members. Thus in Figure 15 we made the same measurements for a much largersample of stars (1 . < radius < ◦ ) to estimate the field contamination in our binary fraction 19 –and luminosity function. This shows the response to the h filter that the background has.The background contribution was normalized and then scaled by the area in thecore and halo regions respectively. This bias contribution was then subtracted from theM67 core and halo samples. Figure 16 shows the background subtracted binary fractionestimations for the core and halo of M67. A gaussian profile was fit to the primary peak for R < .
25. The residual in the core was nicely fit by a second gaussian profile, centered at R ≈
1. Integrating the two gaussian profiles, we measure a fraction of binary point sourcesto be 21% in the core of M67. This is comparable to the Fan et al. (1996) determination of16% and 22% from Montgomery et al. (1993). Correcting for the artificial cluster tests in § α = 0 for R <
R >
1. The luminosity function is given the same treatment, and the backgroundcorrected functions are presented in Fig. 17. The halo shows a more flattened low-masscontribution. The core however contains a significant lack of low-mass members, even afteraccounting for the background field contribution.The dichotomy between the core and halo populations is consistent with qualitativeideas about mass segregation. As discussed in §
1, an old cluster such as M67 is expectedto be losing low-mass members to the outer regions of the cluster, while the core becomesincreasingly more concentrated with higher mass stellar systems. This simplification ofcourse assumes a single static population of stars and also ignores the effects of classicalstellar evolution, whereby higher mass stars die before lower mass, and skew the observedpresent day mass function. Assuming an age for M67 of ∼ To provide a complete comparison of our matched filtering method with previousresults for M67, we ran our algorithm on
J, H, and K s band photometry from 2MASS. Usingthe 2MASS interface available on the internet entitled Gator , we retrieved a 10 ◦ × ◦ box surrounding M67. This produced 264,354 point sources. The cluster CMD probabilitydistributions f cl ( J − H, J ) and f cl ( J − K s , J ) were drawn from all stars within a radius of0 . ◦ around M67, and the background CMD from everything with a radius greater than1 . ◦ . Our IDL code for the SDSS data set was modified to use the 2MASS J HK s data,and the analysis was carried out to measure the spatial distribution of M67. We did notmeasure the binary fractions or luminosity functions for the halo and core populations withthe 2MASS data.M67 as seen by 2MASS contains a different range in spectral types than is observed bythe SDSS, reaching significantly higher masses. This is shown Figure 2 of BB03, with the http://irsa.ipac.caltech.edu 21 –M67 CMD reaching a spectral type K0 at the faint limit, which we adopted to be J = 17.In addition to the upper main sequence, the 2MASS CMD also contains the turn-off and redgiant branch. The average stellar density in our 2MASS sample was 0.73 stars arcmin − ,whereas the average in our SDSS sample was 1.4 stars arcmin − over the same spatial area.Figures 18 and 19 summarize our 2MASS results for M67. These are analogous toFigures 10 and 12 respectively. An asymmetric distributions of stars are seen in Figure18 which extend beyond the detection of the BB03 study. The elongation seen in Figure10 is not well reproduced by the 2MASS data, however the mass ranges are considerablydifferent.Two significant differences between the SDSS and 2MASS results are apparent inFigure 19: the 2MASS data yields a significantly higher surface density in the core, and thecore radius fit with a King profile is much smaller ( R c = 4 . ′ § J = 12 . . ′ . ′
67 respectively, indicating that mass segregation among the high mass sample isclearly evident, as found in § ◦ each. Their optical data was also limited to a photometric depth of V = 21and 0.3 magnitude errors making comparison to our SDSS data tenuous. Qualitatively thecore radius and tidal features of Fan et al. (1996) match our 2MASS analysis of M67. Ourmatched filtering has been able to reproduce known structure for M67 using 2MASS, andrevealed a slightly increased radius of detection for the halo compared to BB03 due to ourmore complete subtraction of the contaminating field population.
5. Discussion and Summary
We have used a matched filter algorithm on SDSS photometry for identifying probablemembers of the open cluster M67. This study has revealed a core radius R core = 8 . ′ ± . ′ ′ from the cluster center. The total number of starsmeasured within our SDSS data for M67 is 1385 ± ± ± Z = 0), and that the current position of M67 is near the vertical apex of itsorbit ( Z = 0 . × years into the past and future. This is in excellent agreement with Carraro & Chiosi(1994) and earlier estimations.Typically long streams of tidal debris, such as those trailing/leading Pal 5, are assumedto lie along the orbital path of the cluster(Montuori et al. 2007). However this assumptionhas recently come under scrutiny for Pal 5 (Odenkirchen et al. 2009). Bergond et al.(2001) also show examples of tidal debris around open clusters which is not grouped intodynamically cold streams. In order to determine the projected direction tidal debris tailswould be expected to lie along for M67, we computed star paths in a reference frame movingwith the average orbital velocity of the cluster. Simply put, stars that are leading or laggingthe main body of the cluster in its orbit around the galaxy do not diffuse to completely 25 –ring the galaxy because they mostly share the orbital motion of the cluster. Rather theywill occupy a more modest range of azimuthal angles in the galaxy, with smaller rangescorresponding to smaller orbital eccentricity. M67 moves both in the radial and verticaldirections (as shown in Fig. 20). For an open cluster orbiting with vertical excursions fromthe disk, the orbit will not be closed, and the cluster (and dynamically cold stars that haveescaped the cluster) will eventually sample different parts of a boxy volume moving withthe average orbital velocity of the cluster. To visualize this three-dimensional dynamicalstructure, we subtracted the average angular velocity of the cluster multiplied by the timesince the present day from the azimuth angle. The projection of this motion onto our line ofsight towards M67 looks nearly straight, as shown in Fig. 10. Any kinks or sharp changesin the projected co-moving deviation are well outside our SDSS field.Since the most elongated feature of M67’s halo seen in Fig. 10 is not aligned withthe projected co-moving deviation, or the projected orbital path of M67, we believe theasymmetric tidal feature’s origins seen with SDSS cannot be singularly attributed to thegalactic tidal field. However a separate smoking gun, such as a nearby molecular cloud orcluster, is not readily apparent to us. It is more probable that with such small numbers ofstars found outside the core, tidal shocking from passing through the galactic disk producesthese types of weakly elongated features in open clusters, rather than the dramatic tails asseen in Pal 5. This can only be verified, however, using a detailed survey of the kinematicsof the cluster members on a large spatial scale to compare the core and halo dynamics,along with future N-body modeling of cluster disruption.The optimal contrast filtering we have employed here will be of great use inthe next generation of wide field surveys. Programs such as LSST (Ivezic et al.2008) and PanSTARRS (Kaiser et al. 2002) will map the sky with never before seenlevels of photometric precision and depth, with a spatial coverage far exceeding even 26 –SDSS. The most recent SDSS public release (Abazajian & Sloan Digital Sky Survey2008, DR7) includes the Sloan Extension for Galactic Understanding and Exploration(Newberg & Sloan Digital Sky Survey Collaboration 2003) data, which includes photometryin and around the galactic plane. This new data set includes well over a hundred openclusters, with a great range in ages, masses, and surely dynamical states. We anticipate thematched filtering technique will help detect many new open and globular cluster features,as well as continue to find other faint substructure in the galactic halo.The authors gratefully acknowledge the support of this work by the National ScienceFoundation grant AST 0507785, awarded to ELS & M. Bolte. JRAD would like to thankDr. Suzanne L. Hawley for her illuminating discussions on stellar populations and clustermodeling. JRAD and ELS thank Dr. Kathryn Johnston for her help with galactic orbitcalculations. 27 – REFERENCES