The Radial Distribution of the Two Stellar Populations in NGC 1851
A. P. Milone, P. B. Stetson, G. Piotto, L. R. Bedin, J. Anderson, S. Cassisi, M. Salaris
aa r X i v : . [ a s t r o - ph . S R ] J un Astronomy&Astrophysicsmanuscript no. ms October 31, 2018(DOI: will be inserted by hand later)
The Radial Distribution of the Two Stellar Populations inNGC 1851 ⋆ A. P. Milone , P. B. Stetson , G. Piotto , L. R. Bedin , J. Anderson , S. Cassisi , and M. Salaris Dipartimento di Astronomia, Universit`a di Padova, Vicolo dell’Osservatorio 3, Padova, I-35122, Italy Dominion Astrophysical Observatory, Herzberg Institute of Astrophysics, National Research Council, 5071 West SaanichRoad, Victoria, BC V9E 2E7, Canada Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA INAF-Osservatorio Astronomico di Collurania, Via M. Maggini, Teramo I-64100, Italy Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Egerton Wharf, Birkenhead CH411LD, UKReceived Xxxxx xx, xxxx; accepted Xxxx xx, xxxx
Abstract.
We have analyzed ACS / WFC and WFPC2 images from
HST , as well as ground-based data to study the radialdistribution of the double sub-giant branch (SGB) recently discovered in the Galactic globular cluster NGC 1851. We foundthat the SGB split can be followed all the way from the cluster center out to at least 8 ′ from the center. Beyond this distance outto the tidal radius at ∼ .
1. Introduction
Precise Hubble Space Telescope (
HST ) photometry has pro-vided evidence that NGC 1851 hosts two distinct sub-populations of stars (Milone et al. 2008) as indicated by a clearbifurcation of the sub-giant branch (SGB) in its color magni-tude diagram (CMD). This discovery has sparked new interestin this object and, consequently, numerous e ff orts aimed at bet-ter understanding how this cluster formed and evolved.Milone et al. (2008) suggest that two star-formationepisodes delayed by about one Gyr could explain the observedsplit of the SGB. As an alternative scenario, Cassisi et al.(2008) suggest that the SGB split can be explained by the pres-ence of two stellar populations, one with normal α -element en-hancement, and the other characterized by a peculiar CNONachemical pattern with C + N + O abundance increased by a fac-tor of ∼
2. Two such populations could account for the observedbright and faint SGB (hereafter bSGB and fSGB), respectively,without requiring any significant age di ff erence.Interestingly, this latter scenario seems to be supported byearly spectroscopic measurements (Hesser et al. 1982) whichindicate the presence of two groups: CN-strong and CN-weakstars. In addition, the work of Calamida et al. (2007) showsthat in the Str¨omgren ( m , u − y ) CMD, the red giant branch Send o ff print requests to : A. P. Milone ⋆ Based on observations with the NASA / ESA
Hubble SpaceTelescope , obtained at the Space Telescope Science Institute, whichis operated by AURA, Inc., under NASA contract NAS 5-26555, un-der GO-11233. (RGB) of NGC 1851 splits into two sequences that, like theSGB split, can be explained by two populations with di ff erentCN abundances.A more recent spectroscopic investigation by Yong &Grundahl (2008) determined the chemical composition foreight bright giants in NGC 1851. Their analysis revealedlarge star-to-star light-element-abundance di ff erences of the el-ements Zr and La. These s -process elements are correlated withAl and anticorrelated with O. Furthermore, the Zr and La abun-dances appear to peak around two distinct values. Yong et al.(2009) show that the C + N + O abundance exhibits a large spread( ∼ + N + O, as expected in the scenario in which in-termediate mass AGB stars are responsible for globular-clusterlight-element abundance variation.Another important peculiarity of NGC 1851 is that it is oneof only a few examples of a bimodal horizontal branch (HB)cluster. On the basis of detailed numerical simulations, Salariset al. (2008) found that it is possible to account simultaneouslyfor the various empirical constraints such as the HB morphol-ogy, the star counts along the HB as well as the ratio betweenfaint SGB stars and bright SGB ones,if all the upper SGB starsand a small fraction of lower SGB stars evolves into the redHB, while most of the lower SGB stars populates the blue HB(including the RR Lyrae variables).Therefore it is tempting to associate the bSGB stars with theCN-normal, s -process-normal stars and with the red HB, while Milone et al.: NGC 1851 SGB’s gradient the fainter SGB should be populated by CN-strong, s -process-element-enhanced stars which should evolve mainly onto theblue HB. This scenario implies that fSGB stars correspond tothe second generation and that they formed from material pro-cessed through a first generation of stars.The study of the spatial distribution of the two stellar popu-lations associated with the double SGB occupies a pivotal rolein the current research on multiple stellar populations in GCs.Milone et al. (2008) studied a CMD containing stars with radialdistances smaller than ∼ r tidal = V , I images, of the South West quadrant of the clus-ter with the aim of following the extent of the double SGB from ∼ ∼
13 arcmin from the cluster center. Zoccali et al. (2009)claimed that the percentage of fSGB stars, which is ∼
45% inthe innermost region decreases at ∼ ∼ Table 1.
Description of the
HST data sets used in this paper.
INSTR DATE N × EXPTIME FILT PROGRAM (PI)ACS / WFC May 01 2006 20s + × / WFC May 01 2006 20s + × × × + ×
2. Observation and data reduction
In order to study the radial distribution of SGB and HB stars inNGC 1851, we considered three distinct data sets.To probe the most crowded regions of the cluster we tookadvantage of the high resolving power of
HST , using im-ages collected with the Wide Field Channel (WFC) of theAdvanced Camera for Survey (ACS) and with the Wide FieldPlanetary Camera 2 (WFPC2). NGC 1851 is not in a particu-larly dense region of the Galaxy ( l II = ◦ , b II = − ◦ ), andground-based observations can provide photometry outside thecrowded central region with precision comparable to that of themore central regions observed with the HST cameras.
Fig. 1.
For the innermost 8 arcmin, we show the footprints ofthe
HST -images used in this paper superposed on a DSS image.In cyan ACS / WFC (circles highlight the corners of the first chipof ACS), in red WFPC2. Large circles show the di ff erent radialbins described in Section 4. The di ff erent colors refer to di ff er-ent data-sets: cyan for ACS / WFC, red for WFPC2, and greenfor ground-based data-set.A brief description of the
HST images used in this work isgiven in Table 1, while Fig. 1 shows a finding-chart of theirfootprints.
The
HST
ACS / WFC images come from GO-10775 (PI:Sarajedini, see also Sarajedini et al. 2007) and were presentedin Milone et al. (2008); we have used the output of the reduc-tion described in Anderson et al. (2008). In brief, the proce-dure analyzes all the exposures of each cluster simultaneouslyto generate a single list of stars for each field. Stars are mea-sured independently in each image by using the best availablePSF models from Anderson & King (2006).This routine was designed to work well in both crowdedand uncrowded fields, and it is able to detect almost every starthat can be perceived by eye. It takes advantage of the many in-dependent dithered pointings of each scene and the knowledgeof the PSF to avoid including artifacts in the list. Calibration ofACS photometry into the Vega-mag system was performed fol-lowing recipes in Bedin et al. (2005) and using the zero pointsgiven in Sirianni et al. (2005).
The
HST
WFPC2 images come from GO-11233 (PI: Piotto),a proposal specifically dedicated to photometric detection ofmultiple populations. ilone et al.: NGC 1851 SGB’s gradient 3
The WFPC2 images have been reduced following themethod of Anderson & King (2000), which is based one ff ective-point-spread-function fitting. We corrected for the34 th row error in WFPC2 CCDs (see Anderson & King 1999for details) and used the best distortion solution available, asgiven by Anderson & King (2003). Photometric calibration hasbeen done according to the Holtzman et al. (1995) Vega-magflight system for WFPC2 camera. The ground-based data are taken from the image archive main-tained by one of us (Stetson 2000). The observations usedhere include 545 images from 14 observing runs with the MaxPlanck 2.2m telescope, the CTIO 4m, 1.5m, and 0.9m tele-scopes, and the Dutch 0.9m telescope on La Silla. Any givenstar may have as many as 69 independent measurements in the B filter, 78 in V , and 56 in I ; among these, 62, 70, and 56,respectively, were taken on occasions that were judged to beof photometric quality. These data were reduced following theprotocol outlined in some detail in Stetson (2005). We havecomplete photometric coverage of the cluster field out to a ra-dius of 14.5 arcmin, and partial coverage to 25.9 arcmin, but wewill restrict our discussion here to the area within 12.5 arcmin,which is slightly larger than the tidal radius of 11.7 arcmin.
3. The CMDs
Figure 2 shows the CMDs from
HST observations that coverthe densest regions of the cluster. The left panel shows theCMD already published by Milone et al. (2008), and the rightpanel shows the newly derived CMD from the WFPC2 datadescribed in Sect. 2.2.The CMDs from ground-based photometry are shown inFig. 3, where we have rejected all the stars within 2.5 arcminfrom the cluster center. The split of the SGB is clearly visibleboth in the ( V − I ) vs. V and the ( B − I ) vs. V CMD, and thesplit region is highlighted in the inset where we show a zoomof the SGB region. Note that the fact that we see the SGB splitbeyond ∼ ∼ V vs ( B − I ) CMD from ground based data for starswith radial distance from the cluster center larger than 2.5 ar-cmin. We marked in red the stars that more likely belong tothe fSGB. In the four right panels we plot the same CMD forstars in the four quadrants. The quoted numbers are the numberof selected fSGB stars with Poisson errors. Because of the un-certainties we conclude that there is not significant di ff erence inthe distribution in the CMD of fSGB stars in the four quadrants.We detected 23 probable fSGB stars in the S-W field coveredby Zoccali et al. (2009) most of them belonging to the lowerpart of the fSGB. Possibly, the di ff erence between our resultand the one obtained by Zoccali et al (2009) comes from thesmall number of fSGB stars with radial distance greater than ∼ V and I bands.Their larger photometric errors make di ffi cult the identificationof fSGB stars especially in the lower part of the SGB where thefaint and the bright SGB have a smaller color di ff erence.The CMD in the right panel of Fig. 3 suggests that the RGBof NGC 1851 has some spread in the B − I color. This spreadcould be related to the presence of the two RGB branchesobserved by Calamida et al. (2007) in the Str¨omgren ( m , u − y ) CMD which is possibly associated with the presenceof two groups of stars with di ff erent CN abundances (Yong& Grundahl 2008). To investigate how the upper and lowerSGB populations may vary with radius, we divided the clus-ter into seven concentric annuli. The inner three are covered bythe ACS data set out to 2.5 arcmin, and the outer four are cov-ered by the ground-based data set, going out to 12.5 arcmin.In Fig. 5 we show the CMD of the region around the SGB forstars in each annulus. Both the fainter and the brighter SGBsare clearly visible for radial distances smaller than ∼
4. Radial distribution of the population ratio
To determine the fraction of fSGB and bSGB stars, we adopteda procedure similar to that used by Milone at al. (2009). Fig. 6illustrates this four-step procedure for the ACS / WFC sample.We selected by hand two points on the fSGB ( P , f , P , f ) andtwo points on the bSGB ( P , b , P , b ) with the aim of delimitingthe SGB region where the split is most evident. These pointsdefine the two lines in panel (a), and only stars contained in theregion between these lines were used in the following analysis.In panel (b) we have transformed the CMD linearly (thetransformation equation is given in Appendix) into a referenceframe where: the origin corresponds to P , b ; P , f is mapped into(1,0), and the coordinates of P , b and P , f are (0,1) and (1,1)respectively. For convenience, in the following, we indicate as‘abscissa’ and ‘ordinate’ the abscissa and the ordinate of thisreference frame. The dashed green line is the fiducial of thebSGB. We drew it by marking several points on the bSGB, andinterpolating a line through them by means of a spline fit. Theblack lines of panel (a) correspond to the loci with ‘abscissa’of zero and one and to the loci with ‘ordinate’ of zero and one.In panel (c) we have calculated the di ff erence between the‘abscissa’ of each star and the ‘abscissa’ of the fiducial line ( ∆ ‘abscissa’).The histograms in panel (d) are the distributions in ∆ ‘ab-scissa’ for stars in four ∆ ‘ordinate’ intervals. These distribu-tions have been modeled as the sum of two partially overlap-ping Gaussian functions. To reduce the influence of outliers(such as stars with poor photometry, field stars and binaries)we did a preliminary fit of the Gaussian distribution using allavailable stars. Then we rejected all the stars more than two σ b Milone et al.: NGC 1851 SGB’s gradient
Fig. 2.
CMD of NGC 1851 from ACS ( le f t ) and WFPC2 ( right ) data. The inset show a zoom around the SGB region.
Fig. 3. V vs. V − I ( le f t ) and V vs. B − I ( right ) CMD of NGC 1851 from ground-based data. The inset show a zoom around theSGB region. Only stars with radial distance greater than 2.5 arcmin are plotted.to the left of the bSGB and more than two σ f to the right of thefSGB and repeated the fit (the σ ’s are those of the best fittingGaussian in each ∆ ‘ordinate’ bin fitted to the fSGB and bSGBrespectively). In panel (c) the continuous vertical lines indicatethe centers of the best-fitting Gaussians in each ∆ ‘ordinate’ in-terval. The red dashed line is located two σ b on the left side ofthe bSGB, and the blue dashed line runs two σ f on the rightside of the fSGB.We repeated the procedure for the ground-based sample, asillustrated in Figure 7. In this case we have reduced the num-ber of bins in ‘magnitude’ to just two intervals, because of thesmaller number of stars. The same procedure has also been ap- plied to the WFPC2 data. In this case, we use the entire dataset, without splitting it into bins, as illustrated in Fig. 8.It is important to notice that each of the points P , b , P , f , P , b , and P , f —which we have arbitrarily defined with the solepurpose of isolating a group of stars representative of each ofthe two SGBs—corresponds to a di ff erent mass ( M P b , M P f , M P b , and M P f ).To obtain a more accurate measure of the fraction of starsin each of the two populations (hereafter: f bSGB , f fSGB ) wehave to compensate for the fact that the two stellar groupsthat define the two SGBs cover two di ff erent mass intervals( M P f − M P f , M P b − M P b ), due to the di ff erent evolution- ilone et al.: NGC 1851 SGB’s gradient 5 Fig. 4. V vs. B − I CMD of NGC 1851 from ground-based data for stars with radial distances from the cluster center larger than2.5 arcmin ( le f t ) and CMDs the four quadrants right .ary lifetimes. Consequently, the correction we have to applywill be somewhat dependent on the choice of the mass func-tion.To this end, we can calculate the fraction of stars in eachbranch as: f bSGB = AbNb / Nf A f + AbNb / Nf f fSGB = A f A f + AbNb / Nf where A b and A f are the areas of the Gaussians that best fit thebSGB and the fSGB, and N f ( b ) = R P , F ( b ) P , f ( b ) φ ( M ) d M .As for the dependence on the adopted mass function, weran the following test. Because of the e ff ect of mass segrega-tion, we assumed a heavy-mass-dominated mass function forthe central regions ( α = − . α = .
35) massfunction for the external regions. Even with these extreme as-sumptions, we found that the mass function e ff ect can changethe relative fSGB / bSGB population ratio by a negligible 4%,in the small mass interval covered by our SGB stellar groups.Therefore, for simplicity, we adopted a Salpeter (1955) IMF for φ ( M ).Since the inferred population ratio depends on the as-sumed evolutionary lifetimes, our result is necessarily some-what model-dependent. In fact, the values could even be sce-nario dependent as well. Cassisi et al. (2008) propose that thetwo SGBs in NGC 1851 could in principle be explained by oneof the following scenarios: – A) the bSGB and the fSGB are both populated by two nor-mal α -enhanced stellar populations with ages of 10 and 11Gyrs, respectively; – B) the fSGB belongs to an 11 Gyr old, normal α -enhancedstellar population, while the bSGB belongs to a population2 Gyr younger with high C + N + O abundances; – C) the bSGB and the fSGB both correspond to a 10 Gyrold, normal α -enhanced stellar population, but the fSGBpopulation has C + N + O abundances a factor of two higherthan the bSGB population.Salaris et al. (2008) found that scenario C does the bestjob of reproducing both the spectroscopic and photometric ob-servations, while scenario B seems the least consistent withthe data. Regardless, these three possibilities illustrate that in-ferring the actual frequency ratio of the populations dependsupon the assumed astrophysical explanation of the di ff erencebetween them, through the di ff erent implications for the evolu-tionary lifetimes between our empirically chosen fiducial evo-lutionary states.To better characterize the radial distribution of SGB starswe divided both the ACS and ground-based data into concen-tric annuli as indicated in Fig. 1. The radial intervals have beenchosen so that the each of the four ACS bins have the samenumber of stars, and the three ground-based bins also have thesame number of stars among themselves. In each of these an-nuli, we calculated the fraction of bSGB and fSGB stars usingthe procedure described above. Table 2 summarizes the results.The first two columns list the radial interval and the averageradial distance for SGB stars within this radial interval ( R AVE ).The origin of the data and the number of SGB stars in each bin
Milone et al.: NGC 1851 SGB’s gradient
Fig. 5.
CMDs of the region around the SGB of NGC 1851 at di ff erent radial distances, from the center out to the tidal radius,and from the di ff erent data bases. The double SGB is visible out to where there are enough stars to see the SGB.are indicated in the third and forth columns, respectively, whilethe last three columns list the ratio of faint to bright SGB starsthat we obtain for each of the three scenarios of Cassisi et al.(2008).Since the values of the subpopulation ratios depend on themass interval corresponding to each SGB segment, the resultsdi ff er slightly depending on whether we assume that the SGBsplit corresponds to scenario A, B, or C, as we use stellarmasses from three di ff erent sets of isochrones. The main re-sult of the paper is summarized in Fig. 9. Although ScenariosA and B show a hint of a slight radial gradient, it is not statis- tically significant. Scenario C does not even show a hint of agradient. Even when we maximize our statistics by putting theACS data in one bin, the WFPC2 photometry in a second bin,and all the ground-based data in a third bin (see first three rowsin Table 2), there is no significant variation in the fSGB:bSGBratio with cluster radius.When comparing the three di ff erent scenarios, we note thatthe radial trends are slightly di ff erent. This has no reason to be,since di ff erent evolutionary times should not change the rela-tive trends of the ratios. The problem comes from the fact thatwe are using three di ff erent data-sets, and we can not avoid ilone et al.: NGC 1851 SGB’s gradient 7 Fig. 6.
This figure illustrates the procedure adopted to measure the fraction of stars belonging to the bSGB and fSGB inNGC 1851. Panel (a) shows a zoom of the ACS / WFC CMD. The two lines delimit the portion of the CMD where the splitis most evident. Only stars from this region are used to measure the population ratio. In Panel (b) we have transformed thereference frame of Panel (a). The green dashed line is the fiducial of the region around the bSGB. In Panel (c) we plotted starsbetween the two lines but after the subtraction of the fiducial line ‘abscissa’ The four right bottom panels show the ∆ ‘abscissa’distribution for stars in four ∆ ‘ordinate’ bins. The solid lines represent a bigaussian fit. For each bin, the dispersions of the bestfitting Gaussian are indicated.small transformation errors from theoretical to observationalplane. ACS, WFPC2, and ground-based data require slightlydi ff erent corrections because we are working with three di ff er-ent filter systems, and we have used the models to infer the rel-evant mass ranges. These uncertainties generate small system-atic errors in our estimate of the fSGB:bSGB ratio. However, these errors are well within our estimated error bars, and do notchange the main result of a flat trend.We want to emphasize that the fractions of faint to brightSGB stars calculated in this paper and listed in Table 2 accu-rately account for the mass interval covered by each SGB seg-ment. Therefore they di ff er from the numbers quoted in Milone Milone et al.: NGC 1851 SGB’s gradient
Fig. 7.
As in Fig. 6 for stars from the ground-based sample and with 2.5 < R < Table 2.
Percentage of fSGB and bSGB stars at several radial distances. R MIN - R MAX R AVE
INS TR N
SGB N fSGB / N bSGB (A) N fSGB / N bSGB (B) N fSGB / N bSGB (C)0.0-2.5 0.80 ACS 1746 0.60 ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ilone et al.: NGC 1851 SGB’s gradient 9 Fig. 8.
As in Fig. 6 for stars with 0.8 < R < m F606W − m F814W color interval.
As we mentioned above, NGC 1851 is a prototypical bimodalHB cluster. In Fig. 10 we show the HB region for several an-nular bins both from ACS / WFC (top panels) and ground-based(bottom panels) data. Red HB stars are marked with red sym-bols, while blue HB stars and RR Lyrae are indicated in blue. Table 3 lists the ratio between the blue HB stars plus RRLyrae and red HB stars in three di ff erent radial annuli. In calcu-lating these numbers we were careful to account for the fact thatthe lifetime of star in the blue HB is on average 11% greaterthan the lifetime in the red HB. This estimate has been obtainedby comparing the core He-burning lifetime for the mean stel-lar mass populating the red HB with that of the mean stellarmass populating the blue HB in the HB synthetic models madeby Salaris et al. (2008) for simulating the HB distribution inNGC1851.The small number of intervals into which we have dividedthe field of view is a consequence of our need for a statisti- Fig. 9.
Fraction of fainter over brighter SGB stars for the scenarios A , B , and C and fraction of blue HB over red HB. Circles,squares and triangles refer to the ACS / WFC, WFPC2 and WFI data sets. The dashed vertical lines mark the core and the half-massradius.cally significant number of stars in each subsample. The bot-tom right panel of Fig. 9 shows the trend of the (blue HB + RR Lyrae):(red HB) ratio as a function of the radial distancefrom the cluster center.Note that for these bright objects we can now safely includethe ground-based photometry within 2.5 arcmin from the clus-ter center, going as close as 0.8 arcmin, before crowding con-ditions become prohibitive even for these luminous stars. Theoverlap regions of the two data-sets, between 0.8 and 2.5 ar-cmin, provide us with an important cross-check on the solidityand consistency of the two independent sets of photometry.Fig. 9 shows that there is no statistically significant evi-dence of a radial gradient in either the fSGB:bSGB ratio or thebHB:rHB ratio. Moreover, the results shown in Fig. 9 providefurther support to the suggestion of Milone et al. (2008) andSalaris et al. (2008) that the blue HB stars are the progeny ofthe fSGB population, whilst the bulk of the red HB componentis related to the bSGB population. More accurate spectroscop-ical measurements are mandatory in order to fully assess thisscenario. R MIN - R MAX R AVE N INS TR ( HB b + RRLy ) / HB r ± ± ± ± Table 3.
Percentage of fSGB and bSGB stars at several radialdistances.
Fig. 10.
Zoom of the CMD region around the HB at severalradial distances from ACS (top) and WFI data (bottom). Weindicated in red the probable red HB stars and RR Lyrae and inblue the probable blue HB stars. ilone et al.: NGC 1851 SGB’s gradient 11
5. Discussion
D’Ercole et al. (2008) have shown that if a second generationof stars is formed by material coming from or polluted by afirst generation, then we would expect these stars to be bornin the core of a stellar cluster, where a cooling flow collectsthe gas ejected by the earlier population. As the cluster evolvesdynamically, the two populations mix and the ratio of secondover first generation tends to a constant value in the inner partof the cluster. Until mixing is complete, the radial profile of thisratio is flat in the inner part and decreases in the outer clusterregions. By studying the radial profiles of the di ff erent popula-tions, we might hope to see evidence of these initial gradientsbefore dynamical relaxation washes them out.Before this paper and the work by Zoccali et al. (2009), ω Centauri was the only cluster where the radial distributionof di ff erent stellar sub-populations had been analyzed. In ω Centauri the stellar population associated with the blue, moremetal rich MS is more centrally concentrated than the red, moremetal poor one, with the relative ratio of blue over red MS starcounts being quite constant within the cluster core beyond ∼
12 arcmin and increasing by a factor of two from 8 arcmin(Sollima et al. 2007) to about 5 arcmin from the center. Thenthe blue MS to red MS ratio remains constant in the cluster core(Bellini et al. 2009).In this paper, we have investigated the radial distribution ofthe two stellar populations associated with the double SGB ofNGC 1851. By coupling
HST and ground-based data we fol-lowed the distribution of the two populations from the centerout to the tidal radius, both on the SGB and the HB. Salariset al. (2008) claimed that the ratio of the two SGBs is con-sistent with the idea that the the progeny of the fSGB si dis-tributed from the blue to the red HB, including the whole insta-bility strip, while the bright one should be confined to the red.According to the scenario of Salaris et al. (2008), the fractionof fSGB that evolves into the red HB corresponds only to the5% of the total number of stars.At variance with Zoccali et al. (2009), we have clearly de-tected both the brighter and the fainter SGB at all radial dis-tances, out to ∼ ω Centauri, found that—within theerror bars—the two stellar populations have the same radialdistribution. This conclusion does not depend on which of thethree scenarios proposed by Cassisi et al. (2008) we assume toexplain the observed SGB dichotomy. The ratio of the blue HBstars to the red HB stars also shows no significant trend withcluster radius.Whatever the origin and formation process of the two stel-lar generations in NGC 1851, now the two groups seem to bewell mixed within the cluster. Because of the short relaxationtime of NGC 1851 (log t rh ∼ ω Centauri has a very long relax-ation time (log t rh ∼ ff erent initial radial distri-butions for the various populations. Acknowledgements.
The authors wish to thank Francesca D’Antonafor useful discussion. We also thanks the anonymous referee forher / his comments and suggestions which helped to strenghen the re-sults presented in this paper. APM and GP acknowledge support byPRIN2007 and ASI under the program ASI-INAF I / / /
0. J.A. ac-knowledges support from STScI Grants GO-10775 and GO-11233.
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Appendix
Upon request from the referee, we give here thetransformation equations used to pass from panel (a) to panel(b) in Figs. 6, 7, and 8. For simplicity we indicate the color andthe magnitude as C and M respectively, and the ‘abscissa’ andthe ‘ordinate’ as abs and ord . abs = ( CR − c / c ord = yr / c where: CR = ( C − C P , b ) cos θ + ( M − M P , b ) sin θ (3) MR = − ( C − C P , b ) sin θ + ( M − M P , b ) cos θ (4) θ = atan MR P , b − MR P , b CR P , b − CR P , b (5) c = MR P , b − MR P , f CR P , b − CR P , f CR + CR P , b MR P , f − CR P , f MR P , b CR P , b − CR P , f (6) c = CR P , b − CR P , b ord P , b − ord P , b ord + ord P , b CR P , b − ord P , b CR P , b ord P , b − ord P , b (7) c = CR P , f − CR P , f − c P , f + c P , f ord P , f − ord P , f ord + ord P , f ( CR P , f − c P , f ) − ord P , f ( CR P , f − c P , f ) ord P , f − ord P , ff