The Horizontal Branch of NGC 1851: Constraints on the Cluster Subpopulations
aa r X i v : . [ a s t r o - ph ] M a r The Horizontal Branch of NGC 1851: constraints on the clustersubpopulations
M. Salaris
Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House,Egerton Wharf, Birkenhead CH41 1LD, UK [email protected]
S. Cassisi and A. Pietrinferni
INAF - Osservatorio Astronomico di Collurania, Via M. Maggini, I-64100 Teramo, Italy cassisi,[email protected]
ABSTRACT
We investigate the distribution of stars along the Horizontal Branch of theGalactic globular cluster NGC 1851, to shed light on the progeny of the twodistinct Subgiant Branch populations harbored by this cluster. On the basisof detailed synthetic Horizontal Branch modelling, we conclude that the twosubpopulations are distributed in different regions of the observed HorizontalBranch: the evolved stars belonging to the bright Subgiant branch component areconfined in the red portion of the observed sequence, whereas the ones belongingto the faint Subgiant branch component are distributed from the blue to thered, populating also the RR Lyrae instability strip. Our simulations stronglysuggest that it is not possible to reproduce the observations assuming that thetwo subpopulations lose the same amount of mass along the Red Giant Branch.We warmly encourage empirical estimates of mass loss rates in Red Giant starsbelonging to this cluster.
Subject headings: globular clusters: individual (NGC 1851) — Hertzsprung-Russell diagram – stars: horizontal branch – stars: mass loss
1. Introduction
A recent
HST
ACS photometry of the Galactic globular cluster NGC1851 (Milone etal. 2008 – hereafter M08) has disclosed the existence of two distinct Subgiant branches (SGBs) 2 –in its Color-Magnitude-Diagram (CMD). With this discovery, NGC1851 joins NGC2808and ω Centauri in the group of globular clusters with a clear photometric signature ofmultiple stellar populations. M08 estimated an age difference of about 1 Gyr between thetwo subpopulations, in the assumption that they share the same initial [Fe/H] (spectroscopyof a few Red Giant Branch stars by Yong & Grundahl 2008, together with the narrow RGBsequence in the CMD confirm this assumption), He mass fraction Y and the same metalmixture. Cassisi et al. (2008 – hereafter Paper I) have explored the possibility that one ofthe two sub-populations was born with a different heavy element mixture (hereafter denotedas extreme) characterized by strong anticorrelations among the CNONa abundances, witha total CNO abundance increased by a factor of 2, compared to the normal α -enhancedmetal distribution of the other component (see Sect. 1 and 4 in Paper I for a brief discussionabout this choice). Both initial chemical compositions share the same [Fe/H] and Y values.If the faint SGB component (hereafter SGBf subpopulation) has formed with the extrememetal mixture, it results to be coeval with the bright SGB component (hereafter SGBbsubpopulation). If the reverse is true, the SGBb (extreme) subpopulation has to be about2 Gyr younger than the SGBf (normal) one. Following the considerations in Paper I and M08about the width of Main Sequence and Red Giant Branch (RGB), the slope of the HorizontalBranch (HB) in the cluster CMD, plus the [Fe/H] estimates by Yong and Grundahl (2008),one can also conclude that appreciable variations of the initial He abundance in the twosubpopulations are ruled out.In this paper we have gone a step further, focusing our attention on the HB. Based onthe similarity of the number ratio of the SGBb to the SGBf components, with the ratio ofstars at the red of the instability strip to stars at the blue side of the strip, M08 hypothesizedthat the progeny of the two SGBs occupy separate locations along the HB. Here we haveaddressed this issue in much more detail, analyzing the distribution of stars along the HB bymeans of synthetic HB models, to determine whether and for which choice of RGB mass loss,the progeny of the SGBb and SGBf subpopulations is able to reproduce the observed HBstellar distribution. We will also readdress the issue, from the point of view of HB modeling,of whether the extreme metal mixture of Paper I is compatible with the observed stellardistribution along the HB. Section 2 describes briefly the HB evolutionary tracks and theHB synthetic modeling, while Sect. 3 presents and discusses the results of our analysis.
2. Synthetic HB modeling
We employed three grids of 39 HB evolutionary tracks each (covering the range be-tween 0.47 and 0.80 M ⊙ ) all with [Fe/H]= − α -enhanced metal mixture, and from Paper I for theextreme mixture, respectively. For the latter models, two different He abundances have beenadopted, namely: Y =0.248 and Y =0.280. The models have been computed using initialHe-core masses derived from the evolution of a progenitor with an age of about 12-13 Gyrat the RGB tip. All tracks have been normalized to the same number (450 from the startto the end of central He-burning) of equivalent points ; this simplifies the interpolation toobtain tracks for masses not included in the grid.Figure 1 displays the Zero Age Horizontal Branch (ZAHB) and selected HB tracksfor the three chemical compositions considered. The ZAHB for the extreme mixture withenhanced He is much brighter than the case of the normal α -enhanced composition. Thismakes very difficult the coexistence of sub-populations with these two compositions alongthe observed HB. The extreme population with the same He abundance of the normal onehas a much closer ZAHB brightness, a consequence of similar He-core masses and surfaceHe abundances of their progenitors at the He-flash. Comparisons of HB tracks for selectedvalues of mass display some interesting features. As already shown in Paper I, models for theextreme compositions have a ZAHB location systematically redder than their counterpartwith the same mass and a normal composition, but the blue loops during the He-burningphase are more extended (for a given mass). The effect of these differences in terms of massdistribution along the observed HB can be thoroughly assessed only by means of syntheticHB modeling.Synthetic HBs have been calculated as pioneered by Rood (1973). The observed HB issimulated by a distribution of stars with different mass, that has to be specified as inputparameter, together with the time t since each star has first arrived on the HB (and thephotometric error, obtained from the photometry). It is assumed that stars are being fedonto the HB at a constant rate. Once the stellar mass and t are specified, a quadraticinterpolation in mass among the available tracks and a linear interpolation in time along thetrack determine the location of the object on the synthetic HB. The large number of pointsalong each of our HB tracks ensures that a linear interpolation in time is adequate. Themagnitudes of the synthetic star are then perturbed by a random value for the photometricerror in both F W and F W , according to a Gaussian distribution with dispersionprovided by the photometric analysis (the typical value in our case is ∼ M and dispersion σ as free parameters. This is equivalent to assume that the amount of See Pietrinferni et al. (2004) for a discussion on this issue B : V : R number ratio between starslocated at the blue side of the RR Lyrae instability strip, within the strip and at its redside, using a Gaussian mass distribution. Catelan et al. (1998) also conclude that the HBmorphology of the cluster can be reproduced with a unimodal (Gaussian) mass distribution,assuming a large 1 σ dispersion (0.055 M ⊙ ). On the other hand, Saviane et al. (1998) con-clude that a bimodal mass loss is needed to reproduce both the red and blue tails of theobserved HB.In our simulations, we consider two separate components coexisting on the HB, origi-nated from either the SGBb or the SGBf subpopulations. The pairs of values ( M , σ ) areleft free to vary between the two subpopulations. As a consequence – once the chemicalcomposition of the SGBf and SGBb subpopulations is fixed – one synthetic HB realizationis determined by the two pairs of ( M , σ ) values chosen for the two components. The ref-erence HB photometry is the HST /ACS ( F W, F W ) data by M08. Due to the smallnumber of exposures, M08 could not determine appropriate mean magnitudes for the RRLyrae population; therefore only stars detected at the blue (143 objects) and red (242 ob-jects) side of the instability strip are taken into account in our comparisons, plus the valuesof the B : V : R ratios taken from independent data. We assume as reference the values30 : 10 : 60, obtained from the number counts provided by Catelan et al. (1998), extractedfrom Walker (1992) photometry. They are consistent with analogous estimates by Lee etal. (1988), Walker (1998) and Saviane et al. (1998). Poisson statistics introduce uncertaintiesby, respectively, ± ±
3% and ±
8% in the B : V : R values. These ratios also agree withthe B : R ratio of (37 ±
9) : (63 ±
7) determined by M08 from their CMD.To be considered a match to the observations, a synthetic HB model is required tosatisfy the following constraints: (i) the empirical values of the ratios B : V : R ; (ii) the F W and F W magnitude distribution of the HB stars at the blue and red side of theinstability strip; (iii) the number ratio of the progeny of the SGBb to the progeny of theSGBf subpopulations has to satisfy the 55:45 ratio observed along the SGB. In case the twosubpopulations share the same age (extreme SGBf component and normal SGBb component)evolutionary times along SGB and RGB are such that the 55:45 ratio is conserved also atthe beginning of the HB phase. If the extreme component is 2 Gyr younger (belongs tothe SGBb) or both components share the normal composition, population ratios at thebeginning of the HB phase are altered by only a few percent, and this is taken into accountin our simulations. 5 –In practice, we have first corrected the observed magnitudes and colors of HB stars by thevalues of reddening ( E ( F W − F W )=0.04) and distance modulus (( m − M ) F W =15.52)determined in Paper I. The resulting magnitudes have then been used for the comparisonwith our synthetic models. After selecting the chemical compositions of the two subpopula-tions – for each SGB component we considered alternatively either a normal or an extrememetal mixture – we calibrated M and σ (adopting either a Gaussian or a uniform mass distri-bution) for their progenies by reproducing the observed B : V : R values, with the additionalconstraint posed by the ratio between the SGBb and SGBf components. All synthetic starsfalling in the gap between the red and blue HB stars selected by M08 are considered to beRR Lyrae variables. We wish to stress that we did not make any a priori choice of wherethe SGBb and SGBf progenies should be located along the observed HB.If the B : V : R constraint was satisfied, we finally compared the magnitude distributionsof the synthetic red and blue HB, with their observational counterparts, by means of aKolmogorov-Smirnov (hereafter KS) test, as applied by Salaris et al. (2007) to the analysisof the HB of 47 Tuc. The synthetic HB is considered to be consistent with observationsif the KS-test gives a probability below 95% that the observed and synthetic magnitudedistributions (in both F W and F W ) for both red and blue HB stars are different.The number of HB stars in the simulations is typically 20 times larger than the observedvalue in M08 photometry. In this way we minimize, in the synthetic HB model, the effect ofstatistical fluctuations in the number of objects at a given magnitude and color.
3. Results and discussion
We obtain only one solution for the case where both subpopulations have a normalmetal mixture (Model 1) as assumed by M08, and one solution for the case where one thetwo subpopulations is characterized by the extreme metal mixture (Model 2), i.e. the sce-nario proposed in Paper I. Figure 2 shows a qualitative comparison between the synthetic HBof Model 2 and the observed one, plus the synthetic star counts of the same simulation (nor-malized to the observed number of HB stars in M08 photometry) against the observationalcounterpart. A similar agreement is achieved also for Model 1. The relevant parameters ofthe two solutions are summarized in Table 1.Some important conclusions can be drawn from our synthetic HB analysis. First ofall, the progeny of the SGBb subpopulation must be restricted to the red part of the HB,whereas the progeny of the SGBf component has to be distributed from the blue to the red,including the whole instability strip, otherwise the KS-test and B : V : R ratios cannot besimultaneously satisfied. As a consequence, it is not possible to reproduce the observed HB 6 –by assuming that RGB stars belonging to the two subpopulations lose on average the sameamount of mass. In Model 1 the mass evolving at the RGB tip (in absence of mass loss) forthe SGBf component is 0.023 M ⊙ smaller than for the SGBb one (following the age estimatesin Paper I), whereas the HB modeling requires an upper mass limit smaller by more than0.035 M ⊙ for its progeny. In Model 2 the mass evolving at the RGB tip (in absence of massloss) for the SGBf sub-population is only 0.003 M ⊙ smaller than for the SGBb one, whereasthe HB modeling requires a maximum mass 0.054 M ⊙ smaller. The observed B : V : R ratios and the KS-analysis impose two further constraints on the model parameters. Themass spread for the red HB stars (the progeny of the SGBb sub-population) has to be small, σ < . M ⊙ . On the other hand, a uniform distribution spanning a large mass rangeis required to reproduce the stellar distributions along the blue part of the observed HB(due to the progeny of the SGBf subpopulation). Although B : V : R ratios can still bereproduced in Model 1 and Model 2 with a Gaussian distribution for the SGBf component( M = 0 . M ⊙ and σ = 0 . M ⊙ for an SGBf population with normal metal mixture, and M = 0 . M ⊙ and σ = 0 . M ⊙ for an extreme metal mixture), the resulting magnitudedistributions are at odds with observations.The results in Table 1 constrain also the relative ages of the SGBb and SGBf subpopu-lations for the scenario of Paper I. In Model 2 it is the SGBf population that is characterizedby the extreme composition; this corresponds to the case discussed in Paper I, where SGBband SGBf subpopulations share the same age. A SGBb subpopulation with the extrememixture cannot be accommodated on the HB while at the same time satisfying all empiricalconstraints described above.We also considered the case of a 50:50 ratio between the SGBb and SGBf subpopulations,that is still allowed – within the errors on the measured ratio – by M08 data. Synthetic modelswith the parameter choices of Model 1 and 2 still match the observations (the predicted B : V : R ratios are altered within the errors on the reference values). The mass lossnecessary to reproduce the HB must still differ between the two sub-populations. It is alsoobvious that in this 50:50 scenario an extreme subpopulation can be either the SGBf or theSGBb one (therefore being either coeval or 2 Gyr younger than the normal component) butits progeny has still to populate the extended region from the blue tail of the HB to the redside, otherwise the KS-test is not satisfied.We have also tested the possibility of having a subpopulation with a mild He-enhanced( Y =0.28) extreme mixture, but no match to the magnitude distribution along the observedHB in the CMD of M08 can ever be achieved.A different efficiency of mass loss in stars belonging to the same cluster seems difficult tojustify, especially if both subpopulations are assumed to share the same metal mixture, but 7 –given the lack of an established theory for the RGB mass loss, we can only use the constraintsposed by the HB modeling. If different populations in the same cluster lose different amountsof mass, the second parameter phenomenon in Galactic globulars may well be at least partlydue simply to different mass loss efficiencies in different clusters. These conclusions canin principle change if one hypothesizes a multimodal mass loss, or unimodal probabilitydistributions more complex than the standard Gaussian or uniform cases. But more freeparameters will have to be included and the predictive power of synthetic HB modelingwould be greatly weakened. Overall, our analysis points out that the RGB mass loss inNGC1851 is not simple. Either differential mass loss processes are efficient in stars in thesame cluster, or much more complicated probability distributions for the RGB mass lossmay have to be employed. Empirical determinations of mass loss rates in NGC1851 stars(see, e.g., the results by Origlia et al. 2007 for 47 Tuc) are badly needed. On this issue, wealso wish to note Caloi & D’Antona (2008) recent suggestion that a dispersion in the initialHelium content among the subpopulations within a single cluster can produce the observedHB morphologies, without invoking a large dispersion in the RGB mass loss, or a differentmass loss efficiency among the various components. In case of NGC 1851 this scenario seemsto be disfavored, raising the intriguing possibility that different processes affecting the earlychemical enrichment and RGB mass loss are at work in different clusters.Before closing we mention an additional test, involving the cluster pulsators. We didnot use the constraint posed by their period distribution in our main analysis, because weverified that recent theoretical pulsational models of RR Lyrae stars (Di Criscienzo, Marconi& Caputo 2004 – see also their discussion about uncertainties on the strip boundaries due tothe value of the mixing length parameter) predict an instability strip for NGC1851 too red by ∼ F W − F W ) compared to M08 data. We have made however thefollowing test, considering the periods determined by Walker (1998) for 29 cluster RR Lyraes(all first overtone pulsators have been fundamentalized by adding 0.13 to the logarithm oftheir periods in days). For all synthetic objects of Model 1 and 2 falling in the observed(not theoretical) RR Lyrae gap we determined the pulsation period from the fundamentalpulsation equation by Di Criscienzo et al. (2004 – their Equation 1). The period distributionof the synthetic RR Lyrae stars has been then compared to the observed one by means of aKS-test. Interestingly, we found that Model 1 gives a period distribution inconsistent withobservations with a probability larger than 95%, whereas in case of Model 2 this probabilityis well below the 95% threshold, and we consider this model to have periods statistically inagreement with observations.We warmly thank A. Sarajedini for allowing us the use - in this paper as well as inPaper I - of his photometric data, and G. Piotto for reading a preliminary draft of this paper 8 –and useful suggestions. REFERENCES
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