AAOmega Observations of 47 Tucanae: Evidence for a Past Merger?
Richard R. Lane, Brendon J. Brewer, László L. Kiss, Geraint F. Lewis, Rodrigo A. Ibata, Arnaud Siebert, Timothy R. Bedding, Péter Székely, Gyula M. Szabó
aa r X i v : . [ a s t r o - ph . GA ] F e b AAOmega Observations of 47 Tucanae:Evidence for a Past Merger?
Richard R. Lane , Brendon J. Brewer , L´aszl´o L. Kiss , , Geraint F. Lewis , Rodrigo A.Ibata , Arnaud Siebert , Timothy R. Bedding , P´eter Sz´ekely and Gyula M. Szab´o ABSTRACT
The globular cluster 47 Tucanae is well studied but it has many characteristicsthat are unexplained, including a significant rise in the velocity dispersion profileat large radii, indicating the exciting possibility of two distinct kinematic pop-ulations. In this Letter we employ a Bayesian approach to the analysis of thelargest available spectral dataset of 47 Tucanae to determine whether this appar-ently two-component population is real. Assuming the two models were equallylikely before taking the data into account, we find that the evidence favours thetwo-component population model by a factor of ∼ × . Several possible expla-nations for this result are explored, namely the evaporation of low-mass stars, ahierarchical merger, extant remnants of two initially segregated populations, andmultiple star formation epochs. We find the most compelling explanation for thetwo-component velocity distribution is that 47 Tuc formed as two separate pop-ulations arising from the same proto-cluster cloud which merged . . ± . Subject headings: globular clusters: individual (47 Tucanae)
1. Introduction
As one of the closest and most massive Galactic globular clusters (GCs), 47 Tucanae (47Tuc) is a test-bed for Galaxy formation models (Salaris et al. 2007, and references therein), Sydney Institute for Astronomy, School of Physics, A28, The University of Sydney, NSW, Australia 2006 Department of Physics, University of California, Santa Barbara, CA, 93106-9530, USA Konkoly Observatory of the Hungarian Academy of Sciences, PO Box 67, H-1525, Budapest, Hungary Observatoire Astronomique, Universite de Strasbourg, CNRS, 67000 Strasbourg, France Department of Experimental Physics, University of Szeged, Szeged 6720, Hungary ω Centauri, e.g. Merritt et al. 1997;Anderson & King 2003; Lane et al. 2009b) and an apparently unique rise in its velocity dis-persion profile at large radii (Lane et al. 2009b).Furthermore, the mass-to-light ratio (M/L V ) of 47 Tuc is very low for its mass (Lane et al.2010), that is, it does not obey the mass-M/L V relation described by Rejkuba et al. (2007).Note that this mass-M/L V relation is not due to the presence of dark matter but becauseof dynamical effects (Kruijssen 2008). Explanations for these unusual properties may beintimately linked to its evolutionary history. In this Letter we describe and analyse variousexplanations for the rise in velocity dispersion in the outer regions of 47 Tuc initially reportedby Lane et al. (2009b).Lane et al. (2009b) provided a complete description of the data acquisition and reduc-tion, radial velocity uncertainty estimates, the membership selection process, and statisticalanalysis of cluster membership for all data presented in this Letter.
2. Plummer Model Fits
The Plummer (1911) model (see also Dejonghe 1987) predicts that the isotropic, pro-jected velocity dispersion σ falls off with radius r as: σ ( r ; { σ , r } ) = σ (cid:16) (cid:16) rr (cid:17)(cid:17) / , (1)where σ is the central velocity dispersion and r is the scale radius of the cluster. We nowdescribe how we fitted Plummer profiles to the 47 Tuc radial velocity data to infer the valuesof the parameters σ and r , and also to evaluate the overall appropriateness of the Plummerhypothesis ( H ) by comparing it to a more complex double Plummer model ( H ).The mechanism for carrying out this comparison is Bayesian model selection (Sivia & Skilling2006). Suppose we have two (or more) competing hypotheses, H and H , with each possibly 3 –containing different parameters θ and θ . We wish to judge the plausibility of these twohypotheses in the light of some data D , and some prior information. Bayes’ rule providesthe means to update our plausibilities of these two models, to take into account the data D : P ( H | D ) P ( H | D ) = P ( H ) P ( H ) P ( D | H ) P ( D | H )= P ( H ) P ( H ) × R θ p ( θ | H ) p ( D | θ , H ) dθ R θ p ( θ | H ) p ( D | θ , H ) dθ . (2)Thus, the ratio of the posterior probabilities for the two models depends on the ratio ofthe prior probabilities and the ratio of the evidence values. The latter measure how wellthe models predict the observed data, not just at the best-fit values of the parameters, butaveraged over all plausible values of the parameters. It should be noted that we rely solelyon the velocity information for our Plummer model fits. Taking the stellar density as afunction of radius into account would be useful in further constraining the models. However,the Plummer model fits by Lane et al. (in prep.) based exclusively on velocity informationare also good fits to the surface brightness profiles of the four GCs analysed in that study. The data are a vector of radial velocity measurements v = { v , v , ..., v N } of N stars,along with the corresponding distances from the cluster centre r = { r , r , ..., r N } and ob-servational uncertainties on the velocities σ obs = { σ obs , , ..., σ obs ,N } . We will consider v tobe the data, whereas r and σ obs are considered part of the prior information. In this casethe probability distribution for the data given the parameters is the product of independentGaussians, whose standard deviations vary with radius: p ( v | µ, σ ,r ) = N Y i =1 p πσ i exp − (cid:18) v i − µσ i (cid:19) !! , (3)where µ is the systemic velocity of the cluster. The standard deviation σ i for each data pointis given by a combination of the standard deviation predicted by the Plummer model, andthe observational uncertainty: σ i = q σ ( r i ; { σ , r } ) + σ ,i (4)To carry out Bayesian Inference, prior distributions for the parameters must also be defined.We assigned a uniform prior for µ (between −
30 and 30 km s − ). For σ , we assigned 4 –Jeffreys’ scale-invariant prior p ( σ ) ∝ /σ for σ in the range 0 . −
100 km s − . Finally, r was assigned the Jeffreys’ prior p ( r ) ∝ /r for r in the range 0 . −
220 pc. These threeprior distributions were all chosen to be independent and to cover the approximate range ofvalues that we expect the parameters to take.
The double Plummer model is a simple extension of the Plummer model. The stars arehypothesised to come from two distinct populations, each having its own Plummer profileparameters (but with a common systemic velocity µ ). Thus, at any radius r from the clustercentre, we model the velocity distribution as a mixture (weighted sum) of two Gaussians.From previous work (Lane et al. 2009b) we also expect the inner regions of the cluster tobe well fitted by a single Plummer profile, so the weight of the second population of starsshould become more significant at larger radii.Thus, instead of having a single σ parameter and a single r parameter, there are nowtwo of each. The probability distribution for the data given the parameters is then theweighted sum of two Gaussians: p ( v | µ, { σ } , { r } , w ( r )) = N Y i =1 w ( r i ) q πσ i, exp − (cid:18) v i − µσ i, (cid:19) ! + 1 − w ( r i ) q πσ i, exp − (cid:18) v i − µσ i, (cid:19) ! . (5)Here, w ( r ) is a weight function that determines the relative strength of one Plummer profilewith respect to the other, as a function of radius. We expect one component to dominateat smaller radii, and to eventually fade away as the second component becomes dominant.Hence, we parameterise the function w ( r ) as: w ( r ) = exp ( u ( r ))1 + exp ( u ( r )) (6)where u ( r ) = u α + r − r min r max − r min ( u β − u α ) . (7)That is, the log of the relative weight between one Plummer component and the otherincreases linearly over the range of radii spanned by the data, starting at u α and ending at a 5 –value u β . Parameterising w via u makes it easier to enforce the condition that w ( r ) must bein the range 0 − r . The prior distributions for u α and u β were chosen to be Gaussianwith mean zero and standard deviation 3. This implies that w ( r ) will probably lie between0.05 and 0.95, with a small but not negligible chance of extending lower than 0.001 or above0.999.The standard deviations of the two Gaussians at each data point are given by a combi-nation of that predicted by the Plummer model and the observational uncertainty: σ i, = q σ ( r i ; { σ , r } ) + σ ,i (8) σ i, = q σ ( r i ; { σ , r } ) + σ ,i (9)The priors for all the parameters µ , { σ , r } were chosen to be the same as in the singlePlummer case.
3. Results
An obvious rise in the velocity dispersion of 47 Tuc was described by Lane et al. (2009b,their Figure 11) at approximately half the tidal radius ( ∼
28 pc). The tidal radius is ∼
56 pc(Harris 1996). To confirm the reality of this rise, several tests were performed, includingresizing the bins and shifting the bin centres, as described by Lane et al. (2009b). Nodifference in the overall shape of the dispersion profile was found during any tests.We used a variant (Brewer et al. 2009) of Nested Sampling (Skilling 2006) to samplethe posterior distributions for the parameters, and to calculate the evidence values for thesingle and double Plummer models. The results are listed in Table 1. The double Plummermodel is favoured by a factor ∼ × , and consists of a dominant Plummer profile thatfits the inner parts of the radial velocity data (Figure 1), and a second, wider profile thatmodels the stars at large radius.As a test of the veracity of our model we altered the model so that w ( r ) was linear (withendpoints in the range 0 − u ( r ) being linear. Thishad the effect of reducing the log evidence to ≈ − ∼ . This best-fit model has a more subtle increase in widthat large radii, when compared with Figure 1. Presumably this is because w ( r ) being linearprevents more rapid fade-outs. Correspondingly, the Plummer profile represented by thethin curve in Figure 2 was shifted slightly lower. Note that the model in Figure 1 is narrowerthan the spread of the data, because the spread also arises partly from observational errors.The most extreme points at large radii are likely to be those for which the intrinsic velocity 6 –dispersion is large and the observational errors have pushed the points further away fromthe mean. In Figure 2, the Plummer profiles of the two population components are shown.The inner component is a good fit to the binned velocity dispersions by Lane et al. (2009b).We now discuss possible explanations for this two-component population, and calculate anupper limit on when the second component was introduced. Drukier et al. (2007) carried out N -body simulations of GCs through core-collapse andinto post-core-collapse. They showed that the evaporation of low-mass stars due to two-bodyinteractions during these phases alters the velocity dispersion profiles in predictable ways.At approximately half the tidal radius ( r t /
2) the velocity dispersion reaches a minimum of ∼
40% of the central dispersion, then rises to ∼
60% of the central level at r t . These criteriaare certainly met within 47 Tuc (again, see Figure 11 of Lane et al. 2009b). Furthermore,Lane et al. (2009b) conclude that the rise in velocity dispersion could be explained by evap-oration due to the core collapsing, and the Fokker-Planck models by Behler et al. (2003)show that 47 Tuc is nearing core-collapse.This appears to be reasonable evidence that 47 Tuc is evaporating. However, basedon the conclusions drawn by Drukier et al. (2007) and Lane et al. (2010), it is unclear howmuch Galactic tidal fields affect the outer regions of Galactic globular clusters, and whateffect this has on the external velocity dispersion profile. While our best-fit double Plummermodel matches the overall form of the trend shown by Drukier et al. (2007) reasonably well(see Figure 1), this scenario does not explain its multiple stellar populations (although thesemight be explained by chemical anomalies, e.g. Piotto et al. 2007, and references therein),nor its low M/L V in comparison with its mass (see Figure 6 of Lane et al. 2010), or itsextreme rotation. In addition, the extra-tidal stars are spread uniformly across all regionsof the colour magnitude diagram (see Figure 3 of Lane et al. 2009b), which is inconsistentwith the the two-component population being a consequence of evaporating low-mass stars.We cannot, however, completely discount evaporation without detailed chemical abundanceinformation. Another scenario, which appears to explain most of the unusual properties of 47 Tuc,is that it has undergone a merger in its past (note that this is not the first evidence for 7 –Table 1: Inferred parameter values for the single Plummer and the double Plummer fitsto the 47 Tuc data. The values quoted are the posterior mean ± the posterior standarddeviation, when the marginal posterior distributions were sufficiently symmetric for this tobe a reasonable summary. For the few parameters with asymmetric posterior distributions,we instead give the symmetric 68% credible interval. The evidence values imply that ifthe two models were equally likely before taking into account the data, the data makes thedouble Plummer model more likely by a factor of e . ≈ × . For the double Plummermodel, the first value listed is for the component that dominates at r = 0.Parameter Value Single Plummer Profile µ -16.87 ± − σ ± − r ± Double Plummer Profile µ -16.94 ± − σ ± − [5.70, 13.51] ± km s − r ± u α ± u β -2.30 ± -50-40-30-20-10010 0 10 20 30 40 50 60 70 80 R ad i a l V e l o c i t y ( k m / s ) Distance from Cluster Centre (pc)
Fig. 1.— The radial velocities of stars in 47 Tuc together with the best fit double Plummermodel for the velocity distribution as a function of radius. The inner part of the cluster iswell modelled by the dominant Plummer profile, while at larger radii, the second plummerprofile dominates. The radius at which the two profiles have equal weight is 55 pc. V e l o c i t y D i s pe r s i on ( k m / s ) Distance from Cluster Centre (pc)
Fig. 2.— Binned velocity dispersion as a function of radius (from Lane et al. 2009b), withthe radial velocity profiles of the two stellar populations from the best fit double Plummermodel. The Plummer profile that dominates at small radii is shown as the thick black curve,while the thin curve shows the Plummer profile for the stellar population that dominates atlarge radii. 9 –such a merger within Galactic GCs, see Ferraro et al. 2002). Several observed quantitiescan be explained by this hypothesis: (1) the bimodality of the carbon and nitrogen linestrengths, (2) the mixed stellar populations, (3) the large rotational velocity, (4) the lowM/L V compared with total mass and (5) the increase in velocity dispersion in the outskirtsof the cluster.In addition to our evidence for two kinematically distinct stellar populations, Anderson et al.(2009) showed that 47 Tuc also has two distinct sub-giant branches, one of which is muchbroader than the other, as well as a broad main sequence. The authors determined thatthis broadening may be due to a combination of metallicities and ages, and it is knownfrom previous studies (e.g. Harbeck et al. 2003) that 47 Tuc has a bimodality in its carbonand nitrogen line strengths. While this bimodality is not unique, a merger could explainits origin. Therefore, another possible scenario, which explains many of the properties of 47Tuc, is a past merger event.While it might seem unlikely that this is the remnant of a merger, extant kinematic sig-natures of subgalactic scale hierarchical merging do exist (e.g. within ω Centauri; Ferraro et al.2002), and there have been hints that the distinct photometric populations in 47 Tuc mightbe remnants of a past merger (e.g. Anderson et al. 2009). A possible explanation for thismerger hypothesis is given in Section 3.3.
The two components may have formed at the same epoch, and the distinct kinematicpopulations are, therefore, extant remnants from the formation of the cluster itself. If GCsform from a single cloud (see Kalirai & Richer 2009, for a discussion of GCs as simple stellarpopulations), it is possible for the proto-cluster cloud to initially contain two overdensitiesundergoing star formation independently at almost the same time. In this case, the twoproto-clusters, which would inevitably be in mutual orbit due to the initially bound natureof the proto-cluster cloud, eventually coalesced through the loss of angular momentum dueto dynamical friction.Note that this scenario is similar to the capture of a satellite described by Ferraro et al.(2002) to explain the merger hypothesis for ω Centauri, and explains the two kinematicand photometric populations, and the high rotation rate assuming the proto-cluster cloudinitially had a large angular momentum. It might also explain the low M / L V of this cluster.Interestingly, Vesperini et al. (2009) show that clusters with initially segregated massesevolve more slowly than non-segregated clusters, having looser cores and reaching core- 10 –collapse much later. Because the core of 47 Tuc is highly concentrated and near core-collapse(e.g. Behler et al. 2003) it must be very old if it was initially mass-segregated. 47 Tuc isthought to be 11–14 Gyr old (e.g. Gratton et al. 2003; Kaluzny et al. 2007), hence initial masssegregation is plausible. However, even if 47 Tuc is ∼
11 Gyr old the original populationswould be kinematically indistinguishable at the present epoch (Section 3.5) indicating thatsome other process was the cause of the two extant populations described in this Letter.Furthermore, Milky Way GC formation ended about 10.8 Gyr ago (e.g. Gratton et al. 2003),long before the upper limit for the initial mixing of the two populations derived in Section3.5.
Two star formation epochs in GCs result in the radial separation of the two popula-tions, with the second generation initially concentrated in the core (e.g. D’Ercole et al. 2008,and references therein). Furthermore, the kinematics of the second generation are virtu-ally independent of that of the first generation and the second generation contain chemicalanomalies which are consistent with having arisen in the envelopes of the first generation(e.g. Decressin et al. 2007; D’Ercole et al. 2008).This scenario might explain the two kinematic populations and chemical anomalies of47 Tuc, however, it is unclear how this would cause the extreme rotation, or the anomalousM / L V . The scenarios described in Sections 3.2, 3.3, and 3.4 require a second population be-ginning to mix with an initial population at a particular epoch. Decressin et al. (2008)performed detailed N -body simulations of globular clusters containing two distinct popu-lations of stars to determine their dynamical mixing time via two-body relaxation. Theyconcluded that ∼ t rh ) of a GC decreases by ∼ . t rh for each consecutive relaxation time, i.e. t rh ( i ) ∼ . t rh ( i + 1). Because the two 11 –populations are kinematically distinct at the present epoch, and the current relaxation timeof 47 Tuc is t rh ≈ .
02 Gyr (Harris 1996), an upper limit on when the two populations beganto mix is 7 . ± . ∼
4. Conclusions
With a Bayesian analysis of the velocity distribution of 47 Tuc, we conclude that thescenario which best explains the observed properties of 47 Tuc is that we are seeing thefirst kinematic evidence of a merger in 47 Tuc, which occurred . . ± . . . ± . V compared with its mass.All the other explanations for this two-component population are less plausible than themerger hypothesis. Evaporation of low mass stars is unlikely due to the various stellar typesthat are found beyond the tidal radius, and this also cannot explain its low M/L V . Thepossibility of multiple star formation epochs does not explain the large rotational velocity,nor the low M/L V .Detailed chemical abundances and high resolution N -body simulations of merging glob-ular clusters are now required to further analyse the merger scenario. Several observedquantities need to be addressed, namely how much angular momentum can be impartedthrough a 9:1 merger, what consequence it has on the velocity dispersion in the outer re-gions of the cluster over dynamical timescales, and what effect it would have on the globalM/L V .Of course, alternative explanations exist for the observed rise in dispersion. For example,if GCs form in a similar fashion to Ultra Compact Dwarf galaxies, there may be a largequantity of DM in the outskirts of the cluster as discussed by Baumgardt & Mieske (2008).However, no evidence exists supporting GCs forming in this manner and GCs do not appearto have significant dark matter components (e.g. Lane et al. 2009a,b, 2010). 12 –This project has been supported by the University of Sydney, the Anglo-AustralianObservatory, the Australian Research Council, the Hungarian OTKA grant K76816 and theLend¨ulet Young Researchers Program of the Hungarian Academy of Sciences. GyMSz ac-knowledges the Bolyai Fellowship of the HAS. RRL thanks Martine L. Wilson for everything. REFERENCES
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