Formation of intracluster globular clusters

Mon. Not. R. Astron. Soc. 364, L86–L90 (2005) doi:10.1111/j.1745-3933.2005.00111.x

Formation of intracluster globular clusters

Hideki Yahagi1� and Kenji Bekki2�1Department of Astronomy, University of Tokyo, 7-3-1 Hongo, Bunkyo ward, Tokyo 113-0033, Japan2School of Physics, University of New South Wales, Sydney 2052, NSW, Australia

Accepted 2005 September 23. Received 2005 September 21; in original form 2005 August 30

ABSTRACTWe first present the results of numerical simulations on formation processes and physicalproperties of old globular clusters (GCs) located within clusters of galaxies (‘intracluster GCs’)and in between clusters of galaxies (‘intercluster GCs’). Our high-resolution cosmologicalsimulations with models of GC formation at high redshifts (z > 6) show that about 30 percent of all GCs in a rich cluster can be regarded as intracluster GCs that can freely drift, beingtrapped by gravitational potential of the cluster rather than by the cluster member galaxies. Theradial surface density profiles of the simulated intracluster GCs are highly likely to be flatterthan those of GCs within cluster member galaxies. We also find that about 1 per cent of allGCs formed before z > 6 are not located within any virialized haloes and can be regarded as‘intercluster’ (or ‘intergalactic’) GCs. We discuss the dependencies of the physical propertiesof intracluster and intercluster GCs on the initial density profiles of GCs within low-mass darkmatter haloes at high redshifts (z > 6).

Key words: globular clusters: general – galaxies: evolution – galaxies: star clusters – galaxies:stellar content.

1 I N T RO D U C T I O N

Recent observational studies of globular clusters (GCs) in clustersof galaxies have suggested that there can be a population of GCs thatare bounded by cluster gravitational potentials rather than those ofcluster member galaxies (e.g. West et al. 1995; Bassino, Cellone &Forte 2002; Bassino et al. 2003; Jordan et al. 2003), though the ex-istence of these intracluster GCs (ICGCs) in the Coma cluster is ob-servationally suggested to be highly unlikely (e.g. Marın-Franch &Aparicio 2003). Structural and kinematical studies of a population ofvery bright star clusters – known as ‘ultracompact dwarfs (UCDs)’ –have also suggested that these clusters can be also freely floating in-tracluster objects (Mieske, Hilker & Infante 2004; Drinkwater et al.2005; Jones et al. 2005). Physical properties of intracluster stellarobjects such as ICGCs and planetary nebulae (PNe) are consideredto be sensitive to dark matter properties and cluster-related physi-cal processes (e.g. tidal stripping of GCs and hierarchical growthof clusters) and thus provide some fossil information on formationof galaxies and clusters of galaxies (see e.g. Arnaboldi 2004, for arecent review).

Although there have been developments on the observationalfront, there has been little theoretical and numerical work carried outas to how ICGCs are formed in clusters environments (e.g. Forte,Martinez & Muzzio 1982; Muzzio 1987; Bekki et al. 2003). These

�E-mail: [email protected] (HY); [email protected] (KB)

previous models showed that tidal stripping of GCs from clustermember galaxies though galaxy–galaxy and galaxy–cluster inter-action is a mechanism for ICGC formation. These previous works,however, used fixed gravitational potentials of already virializedclusters and accordingly could not discuss how ICGCs in a clusterare formed as the cluster grows through hierarchical merging ofsmaller groups and clusters. Thus it remains unclear (i) how ICGCare formed under the currently favoured cold dark matter (CDM)theory of galaxy formation and (ii) what physical properties ICGCscan have if their formation is closely associated with hierarchicalformation of clusters.

The purpose of this Letter is thus to demonstrate, for the first time,how ICGCs are formed during hierarchical formation of clusters ofgalaxies, based on high-resolution cosmological simulations thatcan follow both hierarchical growth of clusters through merging ofsmaller subhaloes and dynamical evolution of old GCs. We also dis-cuss physical properties of GCs that were formed within subhaloesat z > 6 yet are not within any virialized haloes at z = 0: these GCscan be regarded as ‘intergalactic’ (van den Bergh 1958) or ‘inter-cluster’ GCs. For convenience and clarity, GCs within any virializedhaloes with the masses larger than 3 × 109 M� are referred to ashalo globular clusters (HGCs) and the meanings of these acronymsare given in Table 1.

2 T H E M O D E L

We simulate the large-scale structure of GCs in a �CDM universewith � = 0.3, � = 0.7, H 0 = 70 km s−1 Mpc−1 and σ 8 = 0.9 by

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Intracluster globular clusters L87

Table 1. Meaning of acronyms.

INGC Intergalactic GCsICGC Intracluster GCsGGC Galactic GCsHGC Halo GCs

using the Adaptive Mesh Refinement N-body code developed byYahagi (2005) and Yahagi, Nagashima & Yoshii (2004), whichis a vectorized and parallelized version of the code described inYahagi & Yoshii (2001). We use 5123 collisionless dark matter (DM)particles in a simulation with the box size of 70 h−1 Mpc and thetotal mass of 4.08 × 1016 M�. We start simulations at z = 41 andfollow it until z = 0 in order to investigate physical properties of oldGCs outside and inside virialized dark matter haloes at z = 0. Weused the COSMICS (Cosmological Initial Conditions and MicrowaveAnisotropy Codes), which is a package of FORTRAN programs forgenerating Gaussian random initial conditions for non-linear struc-ture formation simulations (Bertschinger 1995; 2001).

The way of investigating GC properties is described as follows.First we select virialized dark matter subhaloes at z = z form by us-ing the friends-of-friends (FoF) algorithm (Davis et al. 1985) witha fixed linking length of 0.2 times the mean DM particle separa-tion. The minimum particle number N min for haloes is set to be10. For each individual virialized subhalo with the half-mass radiusof Rh, some fraction ( f gc) of particles within Rh/3 are labelled as‘GC’ particles. This procedure for defining GC particles is based onthe assumption that energy dissipation via radiative cooling allowsbaryons to fall into the deepest potential well of dark-matter haloesand finally to be converted into GCs. The value of the truncationradius (R tr,gc = Rh/3) is chosen, because the size of the very oldGCs in the Galactic GC system (i.e. the radius within which mostGalactic old GCs are located) is similar to Rh/3 of the dark matterhalo in the dynamical model of the Galaxy (Bekki et al. 2005). Weassume that old, metal-poor globular cluster formation is truncatedafter z = z form, because previous theoretical studies demonstratedthat such truncation of GC formation by some physical mechanisms(e.g. reionization) is necessary for explaining the colour bimodalityof GCs, very high specific frequency (SN) in cluster Es, and struc-tural properties of the Galactic old stars and GCs (e.g. Beasley et al.2002; Santos 2003; Bekki 2005; Bekki & Chiba 2005).

Secondly, we follow the dynamical evolution of GC particlesformed from before z = z form until z = 0 and thereby derive lo-cations (x , y, z) and velocities (vx, vy, v z) of GCs at z = 0. Wethen identify virialized haloes at z = 0 with the FoF algorithm andinvestigate whether each of GCs is within the haloes. If a GC isfound to be within a halo, the mass of the host halo (M h) and thedistance of the GC from the centre of the halo (Rgc) are investigated.If a GC is not in any haloes, it is regarded as an intergalactic GC(INGC) and the distance (Rnei) between the INGC and the nearestneighbour halo and the mass of the halo (M h,nei) are investigated. Ifa GC is found to be within a cluster-size halo (M h > 1014 M�), weinvestigate which galaxy-scale halo in the cluster-scale halo con-tains the GC. We examine local mass densities around particles in acluster and thereby select galaxy-scale haloes that have high enoughdensities to be identified as galaxy-scale haloes (Bekki & Yahagi, inpreparation – hereafter BY). If we find the GC within the tidal radius(R t) of one of the galaxy-scale haloes in the cluster-scale halo, itis regarded as a galactic GC (GGC): Otherwise it is regarded as anICGC. R t is assumed to be the radius where the slope α in the GCS

density profile of ρ(r ) ∝ rα in a galaxy-scale halo becomes smallerthan −5 (i.e. much steeper than the outer profile of the dark matterhalo).

Thus, the present simulations enable us to investigate physicalproperties only for old GCS owing to the adopted assumptionsof collisionless simulations: physical properties of metal-rich GCslately formed during secondary dissipative galaxy merger events atlower redshifts (e.g. Ashman & Zepf 1992) cannot be predicted bythis study. We present the results of the model with z form = 6, andthe dependencies of the results on z form will be given in BY. If z form

is closely associated with the completion of cosmic reionization,z form may well range from 6 (Fan et al. 2003) to 20 (Kogut et al.2003). Physical properties of hypothetical GC particles for ICGCsin a rich cluster with M h = 6.5 × 1014 M� are described for themodel with f gc = 0.2 in which the number ratio of GC particlesto all particles is 1.5 × 10−3 at z = 0. We adopt f gc = 0.2 so thattypical subhaloes at z = 6 can contain at least one GC particle. Thepresent results does not depend on f gc at all as long as f gc � 0.1.Physical properties of ICGCs in groups and clusters with differentmasses will be given in our forthcoming papers (BY).

We assume that the initial radial (r) profiles of GCSs [ρ(r )] insubhaloes at z = 6 are the same as those of the simulated darkmatter haloes that can have the universal ‘NFW’ profiles (Navarro,Frenk & White 1996) with ρ(r ) ∝ r−3 in their outer parts. The meanmass of subhaloes at z = 6 in the present simulations is roughly1.8 × 1010 M�, which is similar to the total mass of bright dwarfgalaxies. Minniti, Meylan & Kissler-Patig (1996) found that theprojected (R) density profiles of GCSs in dwarfs is approximatedas ρ(R) ∝ R−2, which is translated roughly as ρ(r ) ∝ r−3 by usinga canonical conversion formula from ρ(R) into ρ(r ) (Binney &Tremaine 1987). Therefore, the above assumption on ρ(r ) can beregarded as reasonable. Thus we mainly show the fiducial modelwith ρ(r ) similar to the NFW profiles and R tr,gc = Rh/3.

Although we base our GC models on observational results ofGCSs at z = 0, we can not confirm whether the above ρ(r ) andR tr,gc of the fiducial model are really the most probable (and thebest) for GCSs for low-mass subhaloes at z = 6 owing to the lackof observational studies of GCSs at high redshifts. Therefore we in-vestigate how the numerical results depend on initial ρ(r ) and R tr,gc

of subhaloes at z = 6. As the dependencies on ρ(r ) and R tr,gc aregiven in details by BY, we briefly describe the dependence on R tr,gc,which is the most important dependence for physical properties ofGCSs at z = 0 (BY).

3 R E S U LT

3.1 ICGCs

Fig. 1 shows the large-scale (∼100 Mpc) structure of INGCs andHGCs and the distributions of GCs in a halo with the total mass(M h) of 6.5 × 1014 M�, corresponding to a rich cluster of galaxiesat z = 0. It is clear from Fig. 1 that there exists ICGCs that are notbounded in any cluster member galaxy-scale haloes, though mostGCs are within the galaxy-scale haloes. About 29 per cent of all GCsin this cluster can be classified as ICGCs with the number fractionof ICGCs ranging from 0.28 at R cl < 1 Mpc (where R cl is thedistance between a GC and the center of the cluster) to 0.35 at 1 �R cl < 2 Mpc. Although the number fraction of ICGCs in the central200 kpc of the cluster is only 0.02, the presence of such centralICGCs may well support the scenario by West et al. (1995) thatvery high SN of ICGCs in the central giant Es in some clusters canbe due to ICGCs.

C© 2005 The Authors. Journal compilation C© 2005 RAS, MNRAS 364, L86–L90

L88 H. Yahagi and K. Bekki

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Figure 1. Left: the large-scale distributions of INGCs (big magenta dots) and HGCs (cyan dots) projected on to the x–y plane at z = 0 in the fiducial model.Here INGCs represent GCs that are not within any virialized haloes at z = 0 and thus include intergalactic and intercluster GCs. HGCs are GCs that are withinvirialized haloes at z = 0. Right: distributions of GCs projected on to the x–y plane at z = 0 for a cluster-scale halo with the total mass of 6.5 × 1014 M�. GCswithin circles represent those within tidal radii of galaxy-scale haloes and the radii of the circles represent the tidal radii. GCs that are not within any circlesare regarded as ICGCs.

Fig. 2 shows that the projected number density distributions(�GC) within the central few hundred kpc are quite different be-tween ICGCs and GCs within any galaxy-scale haloes in the cluster(GGCs) in the sense that �GC is significantly flatter in ICGCs than inGGCs. This is because most GCs in the central few hundred kpc ofthe cluster can be identified as GCs within galaxy-scale haloes (i.e.smaller number of ICGCs). If GCs that are freely drifting under theinfluence of the cluster potential are located close to the central gi-ant halo(es) of the cluster (e.g. at their pericentre passages of orbitalevolution), they can be identified as GGCs using the present selec-tion method of ICGCs. Therefore we suggest that �GC of ICGCs inthe central region of the cluster can be somewhat underestimated inFig. 2.

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Figure 2. Projected radial density profiles (�GC(R)) of ICGCs (thick) andGGCs (thin). Here GGCs represent GCs within any galaxy-scale haloes ina cluster-scale halo. Accordingly GGCs are not GCs of the Milky Way: wehere use this term in order to distinguish these GC populations (i.e. GGCs)from ICGCs. For clarity, �GC(R) normalized to the maximum value in eachGC population is shown. For comparison, the power-law density profileswith �GC(R) ∝ Rα for α = −1.0, −1.5, −2.0 and −2.5 are shown by dottedlines.

The number fraction of ICGCs ranges from ∼0.2 to ∼0.4 for thesimulated clusters with 1.0 × 1014 � M h � 6.5 × 1014 M�. Thepower-law slopes of �GC range from ≈ −1.5 to ≈ −2.5 forthe clusters with the above mass range. About 10–20 per cent ofall GCs are located in the central 50 kpc of the simulated rich clus-ters, which implies that these inner GCs formed at high redshifts(z > 6) can be responsible for high SN of the central cD galaxies.The more details on the parameter dependences of ICGC propertieswill be discussed in our forthcoming paper (BY).

3.2 INGCs

INGCs in the fiducial model comprises about 1 per cent of all GCsformed in subhaloes before z = 6 (See Fig. 1). Although theseINGCs are formed as a result of tidal stripping of GCs from sub-haloes during hierarchical structure formation through interactionand merging of subhaloes between z = 0 and z = 6, there appearsto be no remarkable differences in the large scale distributions be-tween INGCs and HGCs at z = 0 (see Fig. 1). Fig. 3, however,indicates clear differences in Rnei and M h,nei distributions betweenINGCs and HGCs. For example, the number fraction of INGCswith Rnei > 1 Mpc is 0.46, whereas that of HGCs with Rnei >

1 Mpc is 0.09. The derived higher fraction in INGCs stronglysuggests that INGCs are truly ‘free-floating’ GCs in intergalac-tic/group/cluster regions. The M h,nei distribution of INGCs showstwo peaks around M h,nei ≈ 1011 M� and ≈ 1013 M�, and the num-ber fraction of M h,nei > 1013 M� is 0.27 for INGCs, which is signifi-cantly smaller than that (0.61) for HGCs. These results imply that thefraction of intercluster GCs among all INGCs can be observed to besmall.

Fig. 4 describes (i) where progenitor GCs of INGCs were locatedwith respect to the centres of their host subhaloes at z = 6 and(ii) what the mass ranges of their host subhaloes were at z = 6. The


Intracluster globular clusters L89

Figure 3. Distributions of Rnei (left) and M h,nei (right) for INGCs (solid)and for HGCs (dotted). Here Rnei represents the distance between a GC andthe center of a halo that is nearest to the GC, and M h,nei is the mass of thenearest neighbour halo. Therefore, Rnei and M h,nei for HGCs are those oftheir host haloes.

Figure 4. Distributions of R/Rh,gc (left) and M h (right) for INGCs (solid)and HGCs (dotted) at z = 6. Here R, Rnei, and M h represent the distance ofa GC from the centre of its host halo at z = 6, the half-number radius of theGC system in the host halo, and the mass of the host halo, respectively.

number fraction of GCs in the outer parts (R/Rh,gc > 2) of their hostsubhaloes at z = 6 is 0.17 for INGCs and 0.06 for HGCs in Fig. 4.This result suggests that GCs in the outer parts of subhaloes, whereGCs are more strongly influenced by external tidal force, are morelikely to become INGCs, and it thus confirms that tidal stripping ofGCs during interaction and merging of subhaloes between z = 0 andz = 6 is a major mechanism for INGC formation. The mean massesof host subhaloes of INGCs and HGCs at z = 6 are 2.5 × 1010 and1.8 × 1011 M�, respectively, in Fig. 4. This is also consistent withthe above formation process of INGCs, because less massive sub-haloes are more strongly influenced by tidal stripping. If there arenegative metallicity gradients of GC systems and positive relationsbetween halo masses and GC mean metallicities in subhaloes at z =6, as observed for nearby GC systems (e.g. Ostrov, Geisler & Forte1993; Cote, Marzke & West 1998), the results shown in Fig. 4 implythat INGCs can be significantly more metal-poor than HGCs.

Fig. 5 describes how the number fraction of INGCs among allGCs ( f INGC) depends on initial density profiles of GCSs at z = 6. Itis clear from this figure that (i) f INGC is higher for larger R tr,gc and(ii) this R tr,gc dependence can be seen both in the NFW profile andthe power-law one with the slope of −3.5 (i.e. the observed profileof the Galactic GCS). Fig. 5 also shows that only ∼0.5 per cent ofGCs that were initially in the nuclear regions of subhaloes at z = 6can finally become INGCs. These results imply that f INGC can rangefrom ∼0.005 to ∼0.02 for a reasonable set of model parameters oninitial density profiles of GCSs.

f INGC also depends on the methods to identify haloes and GCs.f INGC is 0.0121, 0.0075, 0.0043 and 0.0024 for N min = 10, 20,50 and 100, respectively. The number fraction of INGCs that werenuclei at z = 6 ( f INGC,N) are 0.0046, 0.0014, 0.0003 and 0.0001for N min = 10, 20, 50, and 100, respectively. This f INGC,N mightwell depend on the resolution of simulations. f INGC is 0.0067 in themodel with the FoF linking length of 0.025. About 80 per cent ofGCs that are identified as INGCs are not bounded gravitationally by

0 0.2 0.4 0.6 0.8 10

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Figure 5. Dependencies of the number fraction of INGCs ( f INGC) on thetruncation radii of GCSs at z = 6 (R tr,gc) for the models with initial GCprofiles similar to density profiles of dark matter haloes (filled squares) andpower-law ones with the slope of −3.5 (open squares). For comparison, themodel in which only the very central particle in each subhalo is regarded asa GC (represented by ‘nuclei’) is shown by a filled circle.

any of the closest haloes. These dependencies imply that f INGC canrange from an order of 0.1 to 1 per cent, given some uncertainties inthe best possible parameter values of the methods (e.g. FoF linkinglength).

4 D I S C U S S I O N S A N D C O N C L U S I O N S

Although van den Bergh (1958) already suggested the existenceof INGCs in the local universe, the present study first showed that(i) INGCs can be formed during hierarchical formation processesof galaxies and clusters, (ii) these INGCs are about 1 per cent ofall GCs formed before z = 6, and (iii) they can be typically moremetal-poor than those within virialized galaxy-scale haloes at z =0. These INGCs are highly unlikely to suffer destruction processesby strong galactic tidal fields, which are suggested as importantfor understanding the origin of the observed mass function of GCs(e.g. Fall & Zhang 2001). Therefore, we suggest that (i) the massfunction of INGCs can be significantly different from that of GCsin galaxies and (ii) INGCs possibly retain fossil information on GCmass function at the epoch of GC formation.

Then how many INGCs are expected to be observed in the in-tergalactic regions close to the Galaxy? We can provide an answerfor this question by using the present result on the number fractionof INGCs and the initial GC number of the Galactic GCS beforeGC destruction. McLaughlin (1999) showed that the total numberof initial GCs in a galaxy can decrease by a factor of 25 within theHubble time, owing to GC destruction by the combination effect ofgalactic tidal fields and internal GC evolution (e.g. mass loss frommassive and evolved stars). This means that the initial GC numberis about 4000 for the Galaxy with the observed GC number of 160at z = 0 (van den Bergh 2000). By using the present result that∼1 per cent of all GCs can become INGCs, the expected number ofICGCs in the intergalactic regions close to the Galaxy can be ∼40.We thus suggest that some bright objects of these ∼40 intergalacticGCs can be found in currently ongoing ‘all-objects’ spectroscopicsurveys for targeted areas (e.g. 6dF).

Since White (1987) pointed out that clusters of galaxies mightcontain ICGCs, several authors have suggested some observationalevidences for or against the existence of ICGCs (e.g. West et al.1995; Blakeslee 1997; Harris, Harris & McLaughlin 1998). Ourfuture, more extensive, numerical studies of ICGC formation will


L90 H. Yahagi and K. Bekki

provide observable predictions on some correlations between thenumber of ICGCs and the global properties (e.g. mass and X-raytemperature of hot gas) in their host clusters and thus help observersto confirm the existence of ICGCs. Furthermore, if physical prop-erties of ICGCs strongly depend on z form after which GC formationwas severely suppressed by some physical processes (e.g. cosmicreionization), they can provide some observational constraints onz form.

AC K N OW L E D G M E N T S

We are grateful to the anonymous referee for valuable comments,which contributed to the improvement of the present paper. The nu-merical simulations reported here were carried out on Fujitsu-madevector parallel processors VPP5000 kindly made available by theAstronomical Data Analysis Center (ADAC) at National Astronom-ical Observatory of Japan (NAOJ) for our research project why36b.H. Y. acknowledges the support of the research fellowships of theJapan Society for the Promotion of Science for Young Scientists(17-10511). KB acknowledges the financial support of theAustralian Research Council throughout the course of this work.

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Formation of intracluster globular clusters