New insights on the formation of nuclear star clusters
MMNRAS , 1–11 (2016) Preprint 9 October 2018 Compiled using MNRAS L A TEX style file v3.0
New insights on the formation of nuclear star clusters
Nicolas Guillard , (cid:63) , Eric Emsellem , & Florent Renaud Excellence Cluster Universe, Boltzmannstr. 2, D-85748 Garching, Germany European Southern Observatory, Karl-Schwarzschild-str. 2, D-85748 Garching, Germany Universit´e de Lyon 1, CRAL, Observatoire de Lyon, 9 av. Charles Andr´e, F-69230 Saint-Genis Laval; CNRS, UMR 5574; ENS de Lyon, France Department of Physics, University of Surrey, Guildford, GU2 7XH, UK
Accepted 2016 June 27. Received 2016 June 17; in original form 2016 May 24
ABSTRACT
Nuclear Clusters (NCs) are common stellar systems in the centres of galaxies. Yet,the physical mechanisms involved in their formation are still debated. Using a parsec-resolution hydrodynamical simulation of a dwarf galaxy, we propose an updated for-mation scenario for NCs. In this “wet migration scenario”, a massive star cluster formsin the gas-rich disc, keeping a gas reservoir, and growing further while it migrates tothe centre via a combination of interactions with other substructures and dynamicalfriction. A wet merger with another dense cluster and its own gas reservoir can occur,although this is not a pre-requisite for the actual formation of the NC. The mergingprocess does significantly alter the properties of the NC (mass, morphology, star for-mation history), also quenching the on-going local star formation activity, thus leadingto interesting observational diagnostics for the physical origin of NCs. A population oflower mass clusters co-exist during the simulation, but these are either destroyed viatidal forces, or have high angular momentum preventing them to interact with the NCand contribute to its growth. The proposed updated scenario emphasises the role ofgas reservoirs associated with the densest star clusters formed in a gas-rich low-massgalaxy.
Key words:
Galaxy: nucleus – Galaxy: evolution – methods: numerical
Nuclear Star Clusters (NCs) are present in a wide variety ofgalaxies, from early (e.g. Carollo et al. 1998; Turner et al.2012; den Brok et al. 2014) to late-type galaxies (e.g. B¨okeret al. 2002; Georgiev & B¨oker 2014; Carson et al. 2015). Ob-servational studies with the Hubble Space Telescope showthat about 75% of spiral and dwarf elliptical galaxies havea prominent NC (Cˆot´e et al. 2006; Seth et al. 2006, 2008;Neumayer & Walcher 2012). NCs have typical sizes of a fewto a few tens of parsecs and a mass from 10 M (cid:12) to 10 M (cid:12) (e.g. Georgiev & B¨oker 2014), which rank them among thedensest stellar objects in the Universe. The mass of NCsroughly scales with the galactic host properties such as thegalactic mass, the velocity dispersion of the spheroidal com-ponent or and the total galactic luminosity (e.g. Ferrareseet al. 2006; Rossa et al. 2006; Graham 2012; Scott & Gra-ham 2013; Georgiev et al. 2016). Understanding the physicalorigins of the properties of NC could thus shed new lightson the galaxy evolution.To date, two main formation scenarios have been pro-posed (see top and middle rows of Fig. 1): (cid:63) E-mail: [email protected] • in-situ (Milosavljevi´c 2004): gas falls onto the galacticcentre which subsequently triggers star formation in the cen-tral few parsecs and forms the NC. • migration (Tremaine et al. 1975): a massive clusterforms, then migrates towards the centre by dynamical fric-tion. This process is potentially followed by dry mergers (i.e.,gas free) with other clusters (Andersen et al. 2008; Antonini2013).These formation scenarios imprint specific signatures onthe properties of NCs. Probing the galaxy properties or ex-amining the above-mentioned scaling relations should thushelp us to disentangle between the various formation scenar-ios. The power-law relation between the mass of the NC andthe velocity dispersion of the galaxy host observed by Fer-rarese et al. (2006) is not reproduced by the in-situ scenario(see analytical model Antonini 2013), while predictions fromthe migration model, including a dry-merger step, seem tobe more successful (Antonini 2013; Arca-Sedda & Capuzzo-Dolcetta 2014). Dynamical simulations from Hartmann et al.(2011) also show that the mergers of star clusters in mod-els tuned for NGC 4244 and M33 retrieve the propertiesexpected from the scaling relations.More recent studies emphasise the fact that these two © a r X i v : . [ a s t r o - ph . GA ] J un Guillard, Emsellem, Renaud
1) gas inflow2) nuclear cloud3) in-situ cluster formation
In-situ scenario
1) ex-situ star cluster formation2) cluster migration to centre3) possible dry merger with other clusters
Migration scenario
1) ex-situ star cluster formation2) cluster and gas migration to centre3) possible migration of another cluster and wet
Wet migration scenario
Figure 1.
Schematics representation of NC scenarios from the literature and the one proposed in this work. scenarios are not exclusive and likely contribute together tobuild the properties of the NC (e.g. den Brok et al. 2014;Cole et al. 2016). Hartmann et al. (2011) points out thatdespite the fact that properties induced by cluster mergersare in agreement with observations, in-situ star formationwould still contribute for ∼
50% of the mass of the NC. Semi-analytic models by Antonini et al. (2015) lead to similarconclusions showing that stars formed in-situ contribute toa large fraction (up to 80%) of the total NC mass.To further investigate the diverse origins of stellar pop-ulation in NCs, we present a self-consistent hydrodynami-cal model of NCs formation in its galactic context. Using aparsec-resolution hydrodynamical simulations of a gas-richdwarf galaxy, we propose a new scenario for the formationof NC (see bottom panel of Fig. 1) based on ex-situ forma-tion of massive clusters, their continuous growth, migrationto the galactic centre, potentially followed by a wet mergerwith other clusters bringing their own gas reservoirs.In Section 2, we describe the numerical methods. Theformation scenario of the NC is described in Section 3. Weshow the interaction between the NC and the galactic clusterpopulation in Section 4 and finally discuss the implicationsof this new scenario in Section 5.
We run hydrodynamical simulations of an isolated dwarfgalaxy using the Adaptive Mesh Refinement (AMR) code
RAMSES (Teyssier 2002). We define 3 types of particles: thedark matter (DM), the stars included in the initial condi-tions (hereafter referred to as primitive stars), and stars weformed during the course of the simulations (hereafter re-ferred to as new stars). The code solves the equations ofmotion with a particle-mesh scheme. The code uses a soft-ening of the gravitational acceleration for the DM and prim- itive stars of 7 pc, while the softening for the new stars is thelocal resolution of the AMR grid, which is specific to eachsimulation (see Table 1 in Sect. 2.1). For the gas, the codesolves the Euler equations on the AMR grid, allowing thedensest regions to be refined while keeping a low resolutionon more diffuse media. To avoid the artificial fragmentationof the densest regions, we add a pressure floor that ensuresthat a thermal Jeans length is always resolved by at leastfour cells. The physical ingredients we use in this simulationare similar to the ones used in Renaud et al. (2015).The size of the simulated volume is of 30 × ×
30 kpc ,with the least resolved cells spanning 120pc. We run a setof 3 simulations in which we vary the maximal resolutionfrom 15 pc to 3.5 pc (see Table 1). The galaxy is modeledin isolation, thus neglecting the cosmological context. Thesimulations have been run on the C2PAP facilities (Excel-lence Cluster, Garching) for about 1 million CPU-hours on512 cores.The gas is heated by ultraviolet radiation and cooleddown by atomic cooling tabulated at solar metallicity(Courty & Alimi 2004). The minimal temperature reachedis of 200K.Star formation follows the Schmidt law: ρ SFR = (cid:15)ρ/ t ff ∝ (cid:15)ρ / where ρ is the gas density, (cid:15) is the dimensionlessefficiency of the star formation and t ff = (cid:112) π/ (32 Gρ ) is thefree-fall time. This only concerns densities higher than agiven threshold. We set an efficiency of 2% and a densitythreshold of 100 cm − , so that the star formation rate (SFR)of the dwarf is about 0 . (cid:12) . This corresponds to the ratesobserved for galaxies of ∼ M (cid:12) at redshift z=2-3 whichis the type of galaxies we model in this work (e.g., Behrooziet al. 2013). The stellar particles have a mass of 130 M (cid:12) .The stellar feedback recipes we used are described inRenaud et al. (2013). Photo-ionization is modeled by cre-ating a Str¨omgren sphere around massive stars (20% of thestars mass explode as SNe) younger than 10 Myr. The ra- MNRAS , 1–11 (2016) ormation of Nuclear Cluster dius of the sphere depends on the ambient gas density andthe time-varying stellar luminosity. The interstellar medium(ISM) in the sphere is heated up to 4 × K. In the bub-ble, the code injects momentum-driven feedback in the formof radial velocity kicks to model radiative pressure. Type IIsupernova (SN) feedback is implemented as a Sedov blastwave (see Dubois & Teyssier 2008 for details). SN injects10 erg in a kinetic form. Feedback from a potential activegalactic nucleus is not included in these simulations. Galaxies with stellar mass of ∼ − M (cid:12) have the high-est fraction of nucleated galaxies (Pfeffer et al. 2014), andwe therefore set the total baryonic mass of our galaxy modelin this range, namely to 3 . M (cid:12) . Taking conditions rep-resentative of redshift z ∼ − and 2 . M (cid:12) , respectively. The DM halo has a massof 10 M (cid:12) , following the scaling relation between DM haloand stellar disc from Ferrero et al. (2012). We model the DMhalo with a Navarro-Frenk-White (NFW) profile (Navarroet al. 1996) that has a concentration of 16 and a virial ra-dius of 120 kpc. We truncate the halo at a radius of 15 kpcsince we focus on the central regions of the galaxy.At t = 0, our simulation volume is composed of bothgaseous and stellar exponential discs embedded in a darkmatter halo. We use the code PyGME (Python Multiple Gaus-sian Expansion) to generate the stellar component, the DMand gas. This code makes use of the Multi-Gaussian Ex-pansion method (Monnet et al. 1992; Emsellem et al. 1994),and spatially decomposes the mass of the galaxy in a setof Gaussian functions. We used a total of 26 Gaussians togenerate the galaxy components: 8 for the DM Halo, 9 forthe stellar disc and 9 for the gas disc. The velocities of theparticles are derived via the Jeans equations considering allcomponents (gas, stars, dark matter) for the gravitationalpotential. The gas particles are then replaced by AMR cells.The initial properties of the galaxy are summarized in Ta-ble 1, and Fig. 2 displays the initial rotation profiles of thegalaxy and of its components.Star formation and feedback are not active at the be-ginning of the simulations. We progressively increase the re-finement level of the grid. After a relaxation phase of 80 Myrwe activate the SF and the feedback. After another 15 Myrof evolution, the simulation reaches the maximum spatialresolution with all physical processes activated. We then letthe system evolve for ∼ . . × M (cid:12) and 3 . × M (cid:12) respectivelyand a nuclear cluster has formed with a surface density of2 × M (cid:12) pc − (see right panel of Fig. 3).We detect three smaller clusters orbiting around thenucleus with a period of a few hundreds Myr and orbitaleccentricity between 0.3 and 0.6. The radial profile of thegalactic surface density can be decomposed in three parts:the central region ( R <
200 pc) which is dominated by newstars, a transition range for 0 . < R [kpc] < . Table 1.
Initial conditionsBox length ( kpc) 30AMR coarse level 8AMR finest level 11 12 13Highest resolution (pc) 14.6 7.3 3.7
DM Halo
Virial mass ( × M (cid:12) ) 100Virial radius ( kpc) 120Cut radius ( kpc) 15Concentration 16Profile Navarro-Frenk-WhiteNumber of particles (x 10 ) 37.5 Primitive stars
Mass ( × M (cid:12) ) 1Profile ExponentialScale radius ( kpc) 1Cut radius ( kpc) 7.5Scale height ( pc) 250Cut height ( pc) 750Number of particles (x 10 ) 15 Gas
Mass ( × M (cid:12) ) 2.3Profile ExponentialScale radius ( kpc) 1.65Cut radius ( kpc) 7.5Scale height ( pc) 165Cut height ( pc) 750Average number of cells ( × ) 2.4 kpc V c i r c [ k m / s ] TotalStarsGasHalo
Figure 2.
Rotation curves of the galactic components at t = 0Myr. When increasing the resolution, we have access to denserregimes of gas, which thus potentially increases the SFR.This increase is however regulated by feedback. We testedthe efficiency in providing numerical convergence by runningtwo additional otherwise identical simulations with maxi-mum resolutions of 15 pc and 7 . MNRAS000
Rotation curves of the galactic components at t = 0Myr. When increasing the resolution, we have access to denserregimes of gas, which thus potentially increases the SFR.This increase is however regulated by feedback. We testedthe efficiency in providing numerical convergence by runningtwo additional otherwise identical simulations with maxi-mum resolutions of 15 pc and 7 . MNRAS000 , 1–11 (2016)
Guillard, Emsellem, Renaud − − − l o g ( Σ [ M ⊙ . p c − ] ) -2 -1 radius (kpc)10 -2 -1 S u r f a c e d e n s i t y ( M ⊙ . p c − ) Figure 3.
Top: Face-on and edge-on surface density maps of allstars at the beginning (left) and at the end (right) of the simula-tion. Bottom: Radial profile of the surface density of the galaxyat the beginning (dashed) and the end (solid) of the simulation.The new stars (red) dominate the central hundred parsecs. global properties do converge. Figure 4 thus shows that theSFR is quantitatively different between the 15 and 7.5 pcresolution simulations. The former has an almost constantSFR, while the latter shows a rapid increase within the first500 Mr and a steady decrease hereafter. In that context, the3.5 pc resolution simulation shows a very similar behaviour,even though the higher resolution allows to capture highergas densities. This is confirmed by the fact that for the cu-mulative mass of new stars, convergence in the final stellarmass seems to occur between 7 . . . . . × M (cid:12) ) by the end of thesimulation. In the rest of the paper, we thus focus on thesimulation at the highest resolution, i.e. 3 . To detect star clusters, we use the friend-of-friend algorithmHOP (Eisenstein & Hut 1998). With this method, clustersare defined as over-densities regions above a given thresh-old. Namely, a cluster is detected when the peak of the localstellar density exceeds 1.5 M (cid:12) pc − . Two clusters are thenmerged if the saddle density between them is higher than1 M (cid:12) pc − . The clusters properties can be significantly af-fected by the choice of parameters in this algorithm. Lower-ing the densities would obviously result into a contaminationfrom the background stars, while increasing it would lead to Time (Gyr) -3 -2 -1 S F R ( M ⊙ . y r − ) C u m u l a t i v e M a ss ( M ⊙ ) Figure 4.
Cumulative Mass of new stars (dashed) and SFR(filled) for simulations at resolutions of 15 pc (blue), 7 . . ∼ . more compact (detected) clusters. We test that changingthe detection parameters by a factor of two slightly affectsthe derived properties of the clusters, but does not alter theconclusions of the paper. Based on the simulation, we propose a new scenario for theformation of nuclear clusters. This wet migration ˝ scenarioconsists of two main phases: the formation, growth and mi-gration of a massive cluster toward the centre of the galaxyduring which the cluster retains part of its gas, followed bya potential merger with another cluster. The cluster seed of our NC (named Cluster1) forms 1 . t = 562 Myr. At this stage,gas is still the major baryonic component of the galaxy disc,which has a rather irregular structure (see Fig. 5). A varietyof clusters also form at the same epoch, with masses rangingfrom 10 M (cid:12) to 10 M (cid:12) . Cluster1 collapses out of a clump of ∼ × M (cid:12) ( ∼ × M (cid:12) ,and converging flows supply the cluster with gas (see thegas velocity field in Fig. 6). The gravitational potential ofCluster1 is deep enough to retain this reservoir, keeping arelatively constant mass of gas (2 − × M (cid:12) ) in its vicinitydespite its stellar feedback. Sustained star formation makesCluster1 steadily grow in mass (see the solid lines in Fig. 7).Cluster1 also grows in size from ∼
12 pc to 30 −
40 pc.We can split the growth of Cluster1 into two phases:1) a rapid growth during the first 100 Myr. The gas dom-inates the mass budget within 200 pc.2) a slower growth in the following 800 Myr during whichthe mass of Cluster1 dominates the environment over thegas reservoir.
MNRAS , 1–11 (2016) ormation of Nuclear Cluster −4−2024 y ( k p c ) −4 −2 0 2 4 x (kpc) −3−2−10123 z ( k p c ) −0.50.00.51.01.52.02.53.03.5 l o g ( Σ [ M ⊙ . p c − ] ) Figure 5.
Surface density of stars that have been formed during the simulation. Cluster1 is the NC’s seed. Cluster2 is the second mostmassive cluster in the simulation. It merges with Cluster1 at t=1.7 Gyr.
During the first phase, the amount of gas ( > M (cid:12) ) re-mains higher or of the same order of magnitude than themass of Cluster1 (see Fig. 7). Variations of the gas reser-voir mass have a strong impact on the mass growth rate ofCluster1: a decrease of the reservoir mass stops the growth(e.g. at t (cid:48) = 60 Myr where t (cid:48) is the relative time afterthe cluster formation) and its refilling accelerates it (e.g.at t (cid:48) = 100 Myr). The refilling occurs both by local infalland during interactions with another dense cluster bringingits own gas. The decrease is mostly due to star formationand to SN blasts from the cluster itself or its neighbours.Fig. 8 shows that, since its formation, Cluster1 is one of themain contributors to the global SFR.Fig. 9 shows that Cluster1 migrates toward the centre relatively slowly. Indeed, it takes 350 Myr to Cluster1 tocover a radial distance of 1 . t <
900 Myr. Multipleinteractions between Cluster1 and the surrounding struc-tures slightly affects its orbits, and disturbs its migrationtowards the galactic centre.SNe also have an impact on the orbital evolution of thecluster. For example, at t = 730 Myr ( t (cid:48) = 170 Myr in rel-ative time), Cluster1 experiences a burst of star formation(see Fig 8). The newly formed stars slowly drift away fromthe remaining gas clump (due to asymmetric drift e.g. Re-naud et al. 2013). 10 Myr later, SNe feedback inject energyinto the ISM, forming a bubble which is therefore off-centredwith respect to the gas clump (see Fig. 10). Since the gas rep-resents a significant fraction of the local mass budget (52% MNRAS000
900 Myr. Multipleinteractions between Cluster1 and the surrounding struc-tures slightly affects its orbits, and disturbs its migrationtowards the galactic centre.SNe also have an impact on the orbital evolution of thecluster. For example, at t = 730 Myr ( t (cid:48) = 170 Myr in rel-ative time), Cluster1 experiences a burst of star formation(see Fig 8). The newly formed stars slowly drift away fromthe remaining gas clump (due to asymmetric drift e.g. Re-naud et al. 2013). 10 Myr later, SNe feedback inject energyinto the ISM, forming a bubble which is therefore off-centredwith respect to the gas clump (see Fig. 10). Since the gas rep-resents a significant fraction of the local mass budget (52% MNRAS000 , 1–11 (2016)
Guillard, Emsellem, Renaud = 30 km/s −1.4 −1.3 −1.2 −1.1 −1.0−0.7−0.6−0.5−0.4−0.3 = 30 km/s −3.8 −3.7 −3.6 −3.5 −3.4 −3.3x (kpc)−1.1−1.0−0.9−0.8−0.7 y ( k p c ) l o g [ ρ ( c m − )] Figure 6.
Maps of gas density at the earliest detection of thetwo most massive clusters in the galaxy. Cluster1 (top) formsthe nuclear cluster by migration, while Cluster2 (bottom) mergeslater with the NC. The velocity field in the (x,y) disc plane isshown with red arrows. M a ss ( M ⊙ ) StarsGas
Cluster1Cluster2
Figure 7.
In blue: stellar mass of Cluster1 (solid) and of thesecond most massive cluster Cluster2 (dashed) starting at theirrespective first detection. In red: gas mass within 200 pc aroundthe clusters. t (cid:48) = 0 corresponds to the respective earliest detectionepoch of the clusters. At t (cid:48) = 100 Myr, Cluster1 merges withanother cluster which rapidly increases its mass. at that time for Cluster1, see Fig. 7), the local gravitationalpotential is significantly altered when the gas is expelled.As a result, Cluster1 gets a velocity kick which increasesits orbital eccentricity, and sends it away from the galacticcentre (see Fig. 9). About 50 Myr later, the cluster reachesits apocentre and moves back towards the centre, reachingthis time a smaller galactocentric distance ( d = 180 pc at t = 900 Myr). At that stage, the cluster represents 67% of -2 -1 S F R ( M ⊙ . y r − ) Cluster1Cluster2NC
Figure 8.
Contribution of Cluster1 (solid), Cluster2 (dashed)and their merger (NC, red) in the total SFR (black). The latteris dominated by Cluster1 and Cluster2 and by the NC in the end.Cluster1 and Cluster2 cannot be distinguished from each otherafter t = 1 . G a l a c t o c e n t r i c d i s t . ( k p c ) Cluster1Cluster2
Figure 9.
Galactocentric distance of Cluster1 (solid) and Clus-ter2 (dashed). The galactic centre is defined as the centre of massof particles (stars + DM). the galactic central (r < Another massive (4 × M (cid:12) ) cluster (Cluster2) evolvesalongside Cluster1. It forms in a different environment (seebottom panel of Fig. 6) in the external region of the galaxy( d = 3 . t = 360 Myr) where the stellar and gas den-sities are much lower. The ISM around Cluster2 is slightlyless turbulent than around Cluster1 (Mach number of 0.33and 0.66, respectively, on a scale of ∼
240 pc). The earlymass evolution of Cluster2 is similar to that of Cluster1 (seeFig. 7). Figure 8 shows that Cluster2 is another importantcontributor to the overall SFR in the galaxy. We also notethat the stellar mass dominates Cluster2 300 Myr after itsformation, like Cluster1. Cluster1 and Cluster2 are thus ini-tially in the same mass regime and share similar properties,while formed in rather different environments.
MNRAS , 1–11 (2016) ormation of Nuclear Cluster y ( k p c ) -1.0-0.50.00.51.01.52.02.53.0 l o g ( ρ [ c m − ] ) -0.50.00.51.01.52.02.53.03.54.0 l o g ( Σ [ M ⊙ . p c − ] ) Figure 10.
Maps of the gas (top) and new stars (bottom) den-sities. The shell from the supernova which explodes 5 Myr beforeis visible on the gas density map. The asymmetric extension ofCluster1 (on the right) is the combined result of its orbit and ofthe supernova blast.
Figure 9 shows that after interactions with the sub-structures in the galactic disc ( t <
950 Myr), Cluster2 losesangular momentum and progressively migrates towards thecentre. We estimate that the dynamical friction time is ∼ t = 1 . ∼
35 pc anda mass of 1 . × M (cid:12) (see bottom-right row of Fig. 5).Because of the transfer of orbital momentum from Cluster2to the stars of the merger, the resulting NC is flattened inthe orbital plane of the interaction (which coincides with theplane of the galactic disc), with an axis ratio of 0.4 .After the merger, the SFR drops by almost two ordersof magnitude (see Fig. 8). Fig. 11 shows the evolution of thegas density Probability Distribution Function (PDF) withinthe central kpc, during the merger phase. Before the merger,the PDF yields a classical log-normal shape correspondingto supersonic ISM (Vazquez-Semadeni 1994), and a power-law tail for ρ (cid:38) − indicating self-gravitating gas(Elmegreen 2011; Renaud et al. 2013). The collision between We estimate the height and radius using iso-surface densitycontours of 10 M (cid:12) pc − in its edge-on projection. -3 -2 -1 Density ( cm − ) M a ss ( M ⊙ ) Pre-merger (1.58Gyr)Merger (1.70Gyr)Post-merger (2.01Gyr)
Figure 11.
PDFs inside a 1 kpc × × −2.5 −2.0 −1.5 −1.0 −0.5 0.0Look-back time (Gyr)0.000.050.100.150.200.25 S F R ( M ¯ : y r ¡ ) Merger
With mergerWithout merger
Figure 12.
Star formation history 700 Myr after the formationof the final NC (t=0). Only the stars within a radius of 100pccentered on the NC are considered. When the NC experiences amerger (arrow at t = − . t = − . t = − . t = − . the gas clouds around the NC and Cluster2 generates anexcess of dense gas ( > cm − ), leading to a starburstlocalized in the central 25 pc. In the mean time, the tidalinteraction strips gas from the outskirts of the clouds, thusdepleting gas at intermediate density ( ∼
100 cm − ). The de-pendence of star formation on ρ / implies that the deple-tion at intermediate densities approximately balances thecentral excess at high densities. Thus, despite the centralmini starburst, the net SFR remains almost constant over100 pc. After the merger, the central star formation hasconsumed a large fraction of the dense gas, and the associ-ated feedback disperses most of the gas left in this volume.This lack of dense gas reduces significantly the SFR to a few10 − M (cid:12) yr − , thus almost quenching star formation in theNC. MNRAS000
100 cm − ). The de-pendence of star formation on ρ / implies that the deple-tion at intermediate densities approximately balances thecentral excess at high densities. Thus, despite the centralmini starburst, the net SFR remains almost constant over100 pc. After the merger, the central star formation hasconsumed a large fraction of the dense gas, and the associ-ated feedback disperses most of the gas left in this volume.This lack of dense gas reduces significantly the SFR to a few10 − M (cid:12) yr − , thus almost quenching star formation in theNC. MNRAS000 , 1–11 (2016)
Guillard, Emsellem, Renaud −2 −1 0 1 2 x (kpc) y ( k p c ) -1.0-0.20.51.22.0 l o g [ § ( M ¯ : p c ¡ )] Figure 13.
Disruption of a cluster through time. The galactic stellar background is shown in grey scale (Cluster1 is the closest to centreof the maps). The colour scale represents the surface density of the stars initially detected in the cluster (first panel). Interactions betweenclusters in the galaxy (mainly Cluster1 and Cluster2) generate tidal tails and eventually lead to the dissolution of the low density cluster.
To test the importance of the merging step in the formationscenario of the NC, we artificially remove the stars associ-ated with Cluster2 from the simulation, before it interactswith cluster1 ( t = 500 Myr, i.e. when Cluster2 has formedabout half of its final mass). This procedure is sufficient toprevent the further formation of a massive cluster, and doesnot alter the large scale dynamics of the rest of the galaxy.In this alternative simulation, a cluster similar to Clus-ter1 still forms at t = 800 Myr and reaches the centre inabout the same amount of time, namely 300 Myr. The NCforms as described in Section 3.1. We then let the NC evolvefor 700 Myr ( t = 1 . • the depletion of the dense gas reservoir does not oc-cur and the NC continuously forms stars. This affects thestar formation history of the NC as shown in Fig. 12. In themerger scenario, both NC cluster progenitors form stars dur-ing their entire lifetimes, until star formation gets quenchedat the time of the collision. This leads to the mixing of stel-lar populations with different ages, and the lack of a youngpopulation. • the angular momentum re-distribution noted during themerger does not happen and the NC maintains an almostspherical morphology (axis ratio of 0.8), as opposed to theflattened shape visible in Fig. 5. • Without merger, there is no increase of the angular mo-mentum and the resulting NC exhibits a lower amplituderotation than in the case of a merged system: the differencein angular momentum is approximately of a factor of 10. • the resulting NC is less massive but has a similar size(5 × M (cid:12) and 40 pc in our cases) without the mergerstep.Note that the first three points could be used as observa-tional diagnostics to establish the formation scenario of realNCs.This demonstrates that the merger step is not manda-tory for the formation of the NC, but can significantly alterthe properties of the NC when it takes place. In our fiducial simulation, Cluster1 and cluster2 represents15% of the new stars of the disc, and set the dynamics oftheir surroundings. The rest of the star cluster populationthus experiences several interactions with Cluster1, Clus-ter2 and the NC, and some get disrupted by tidal forces.Signatures of tidal disruptions are visible throughout thesimulation (see e.g., bottom-left panel of Fig. 5).One example of this disruption process is shown inFig. 13, where we monitor the stars of one cluster duringabout 300 Myr, until its complete destruction by tidal forces.At t = 853 Myr (first panel of Fig. 13), a bound cluster isdetected 1 kpc away from Cluster1. The tidal interactionbetween Cluster1 and this ∼ M (cid:12) cluster induces tidaltails (second panel of Fig. 13). Subsequent interactions, in-cluding one with the approaching Cluster2, accelerate thedisruption, finally leading to complete dissolution. The tidalfeatures can still be detected as elongated over-densities foranother 250 Myr after the dissolution, until the surface den-sity contrast with the background becomes too low. Thissituation is similar for other less dense clusters. This showsthe key role of massive clusters such as Cluster1 and Clus-ter2 in the evolution of the cluster population as a whole,accelerating the disruption of the most fragile objects. As illustrated in Fig. 5, some clusters survive the disruptivepresence of the NC. We detect three of these clusters (namedA, B and C) keeping a constant mass for most of the simu-lation ( ∼ M (cid:12) , see Fig. 14 and Fig. 15). However, theirmass evolutions strongly differ from that of Cluster1 andCluster2. Their growth phase only lasts about 10-40 Myr.This star formation activity leads to a rapid injection of su-pernova energy into the ISM, but their lower density is notenough to retain the feedback winds, which thus depletingthe gas reservoir mass by one to three orders of magnitude(in mass). Figure 16 illustrates this by showing the evolutionof the gas density PDFs in the regions of the clusters.For clusters A, B and C, stellar feedback happens totruncate the PDFs close to the density threshold associatedwith star formation, thus preventing further star formation. MNRAS , 1–11 (2016) ormation of Nuclear Cluster M a ss ( M ⊙ ) Figure 14.
Evolution of the stellar (solid) and gas (dashed) massof the clusters surviving the presence of the NC, compared to thatof Cluster1 (blue). We measure the gas mass in a cube of 50 pccentred on the cluster. Each color corresponds to one cluster (A inred, B in green and C in yellow). As in Fig. 7, the time is relative,with t (cid:48) = 0 marking the earliest detection of each cluster. Mass ( M ⊙ )10 H a l f - m a ss r a d i u s ( p c ) x x Cluster1Cluster2
Figure 15.
Evolution of size and mass of all clusters detected atthe end of the simulation. Colours are as in Fig. 14. The dashedlines follow constant surface density values in M (cid:12) pc − . The rapid gas removal by stellar feedback in clusters A, Band C has a significant impact on the local gravitationalpotential. The least bound stars are then ejected from theclusters (Hills 1980; Boily & Kroupa 2003). This lowers theclusters masses by a factor 2 to 7 and their surface densitiesby one order of magnitude (see Fig. 15), which then remainroughly constant until the end of the simulation. The massof the gas reservoirs shows fluctuations over time. A sharpincrease of the gas mass can lead to an increase of the clus-ters mass for a short period. This is for example the case forcluster B at t (cid:48) = 250 Myr in Fig. 14. The stellar mass of thecluster then decreases as the least bound stars are ejectedfrom the cluster.The main difference between NC progenitors and therest of the cluster population is then their ability to retaina significant fraction of their stellar mass. In Cluster1 andCluster2, the injected feedback energy is not high enoughto significantly alter the existing gas reservoir. By keeping adense gas reservoir, they can further form stars and becomeeven more massive and resistant to subsequent tidal dis- Cluster1Cluster2 Density ( cm − ) G a s m a ss ( M ⊙ ) Before After
Figure 16.
Gas density PDFs in regions of 50 pc centred on theclusters 5 Myr before (left column) and after (right column) theremoval of gas by SN-blasts. The blue curve shows the evolutionfor Cluster1 and Cluster2 for reference. The vertical lines showthe density threshold above which gas can be converted into stars. ruptions induced along their orbits. Altogether, these pointsindicate that the low density clusters have a much lowerprobability to survive and become seeds for a NC, in con-trast with e.g., Cluster1 (see Section 3.1).The dynamical friction time of clusters A, B and C ismuch longer, of the order of tenths of Gyr, since the dy-namical friction time is inversely proportional to the clustermass. Therefore they cannot contribute to the building ofthe NC through mergers within several Gyr, unlike Cluster2(see Section 3.2).
Using hydrodynamical simulations of an isolated gas-richdwarf galaxy, we propose a wet migration ˝ scenario for theformation of nuclear clusters. The main steps are (see alsoFig. 1): • A population of star clusters forms across the galacticdisc. • Clusters dense enough to retain a gas reservoir aroundthem maintain a star formation activity for a few 100 Myr,which steadily increases their masses. • These clusters loose orbital energy through dynamicalfriction and interactions with the rest of the disc and mi-grates to the centre to form a nuclear cluster. • The NC eventually experiences (wet) mergers withother dense clusters, increasing its mass and quenching itsstar formation activity.The last step is not mandatory for the formation of the NCbut strongly affect its properties (mass, shape, star forma-tion history), as discussed in Section 3.3.The other star clusters in the galaxy have lower initialdensities, which affects their early evolution and tells themapart from the NC progenitors. They are either tidally dis-rupted by the central structures (including the NC itself) orhave high orbital angular momentum which prevents themto interact with the NC and participate to its build-up.
MNRAS000
MNRAS000 , 1–11 (2016) Guillard, Emsellem, Renaud M a ss o f t h e h o s t ( M ⊙ ) This work - with mergerThis work - without mergerGeorgiev et al. 2016 - late typeGeorgiev et al. 2016 - early type Mass ( M ⊙ )10 H a l f - m a ss r a d i u s ( p c ) Figure 17.
Position of the nuclear clusters formed in our simu-lation on the galaxy mass - observed cluster mass scaling relation(top) and in a size-mass diagram (bottom).
By comparing the properties of the NC modeled withthat of the observed population, Fig. 17 shows that our sim-ulation is in line with the observed scaling relations (e.g.Georgiev et al. 2016). Our NC lies in the high mass andsize regime (40 pc and 5 × M (cid:12) without merger, and35 pc and 1 . × M (cid:12) with merger). Although well withinthe dispersion of observational data, NCs in this mass rangewould be preferentially detected in slightly more massivegalaxies. However, galaxies with different masses are likelyto play different roles on the formation process of their NCs,as underlined by previous works. Observations by den Broket al. (2014) favour the migration scenario in the low-massregime ( (cid:46) − M (cid:12) , see also the theoretical confirma-tion by Arca-Sedda & Capuzzo-Dolcetta 2014). The relativeimportant of in-situ star formation increases with galacticmass, as showed by Antonini et al. (2015), suggesting thatmassive galaxies are more prone to drive gas flows towardthe NC and fuel in-situ star formation than their low-masscounterparts.Such gas flows are related to kpc-scale dynamics of thegalactic disc, in particular the presence of substructures. Forinstance, torques from bars are well-know to drive gas infalltowards the galactic centre (Roberts et al. 1979; Athanas-soula 1992; Garc´ıa-Burillo et al. 2014; Emsellem et al. 2015). This process would then supply the nuclear cluster with gasand maintain its star formation activity over long timescales.Ongoing star formation would then occur preferentially inthe plane of the galactic disc (Seth et al. 2006; B¨oker 2010;Feldmeier-Krause et al. 2015), thus leading to a flattenedNC. A similar morphology is predicted by our model in thecase of a cluster merger. However in our case, the mergerquenches star formation. Therefore, the absence of youngstars in a flattened NC favours our merger scenario, while ayoung population denotes in-situ formation.We also note that spiral arms would lead to star clusterformation providing more candidates for dry or wet mergerswith the NC. It is however not clear whether these potentialNC progenitors would survive the radial migration throughspirals and bars (Fujii & Baba 2012). Probing these pro-cesses would require to model galaxies of different massesand disc stabilities over several rotation periods to allow forthe formation and evolution of substructures.Accounting for the cosmological context would also bekey for replenishing the gas reservoir with low metallicitygas (through cold gas accretion), and/or triggering the for-mation and destruction of spirals and bars (see e.g. Kraljicet al. 2012). Over such long timescales, and particularly inthe redshift range considered here ( z ∼ − ∼ yr, although the massiveends of the population, including our case yield much longertimescales ∼ yr, see also Seth et al. 2006). Followingthe co-evolution of the NC and its host over such long pe-riods would then require to consider collisional processes toproperly treat the internal physics. Among other internalmechanisms, a full treatment of stellar evolution would pro-vide insights on the formation of stellar mass black holesin the NC and its progenitor clusters. Then, the possiblemerger step in our scenario would represent an importantchannel in the formation of intermediate and possibly su-permassive black holes in galactic centres (Seth et al. 2006;Antonini et al. 2015), potentially followed by an active phaseof the galactic nucleus. MNRAS , 1–11 (2016) ormation of Nuclear Cluster ACKNOWLEDGEMENTS
REFERENCES
Andersen D. R., Walcher C. J., B¨oker T., Ho L. C., van der MarelR. P., Rix H.-W., Shields J. C., 2008, ApJ, 688, 990Antonini F., 2013, ApJ, 763, 62Antonini F., Barausse E., Silk J., 2015, ApJ, 812, 72Arca-Sedda M., Capuzzo-Dolcetta R., 2014, MNRAS, 444, 3738Athanassoula E., 1992, MNRAS, 259, 345Behroozi P. S., Wechsler R. H., Conroy C., 2013, ApJ, 770, 57Boily C. M., Kroupa P., 2003, MNRAS, 338, 665B¨oker T., 2010, in de Grijs R., L´epine J. R. D., eds, IAU Sympo-sium Vol. 266, Star Clusters: Basic Galactic Building BlocksThroughout Time and Space. pp 58–63 ( arXiv:0910.4863 ),doi:10.1017/S1743921309990871B¨oker T., Laine S., van der Marel R. P., Sarzi M., Rix H.-W., HoL. C., Shields J. C., 2002, AJ, 123, 1389Carollo C. M., Stiavelli M., Mack J., 1998, AJ, 116, 68Carson D. J., Barth A. J., Seth A. C., den Brok M., CappellariM., Greene J. E., Ho L. C., Neumayer N., 2015, AJ, 149, 170Chandrasekhar S., 1943, ApJ, 97, 255Cole D. R., Debattista V. P., Varri A. L., Hartmann M., SethA. C., 2016, preprint, ( arXiv:1605.02881 )Cˆot´e P., et al., 2006, ApJS, 165, 57Courty S., Alimi J. M., 2004, A&A, 416, 875Daddi E., et al., 2010, ApJ, 713, 686Dubois Y., Teyssier R., 2008, A&A, 477, 79Eisenstein D. J., Hut P., 1998, ApJ, 498, 137Elmegreen B. G., 2011, ApJ, 731, 61Emsellem E., Monnet G., Bacon R., 1994, A&A, 285, 723Emsellem E., Renaud F., Bournaud F., Elmegreen B., CombesF., Gabor J. M., 2015, MNRAS, 446, 2468Feldmeier-Krause A., et al., 2015, A&A, 584, A2Ferrarese L., et al., 2006, ApJ, 644, L21Ferrero I., Abadi M. G., Navarro J. F., Sales L. V., Gurovich S.,2012, MNRAS, 425, 2817Fujii M. S., Baba J., 2012, MNRAS, 427, L16Garc´ıa-Burillo S., et al., 2014, A&A, 567, A125Georgiev I. Y., B¨oker T., 2014, MNRAS, 441, 3570Georgiev I. Y., B¨oker T., Leigh N., L¨utzgendorf N., Neumayer N.,2016, MNRAS, 457, 2122Graham A. W., 2012, MNRAS, 422, 1586Hartmann M., Debattista V. P., Seth A., Cappellari M., QuinnT. R., 2011, MNRAS, 418, 2697Hills J. G., 1980, ApJ, 235, 986Kraljic K., Bournaud F., Martig M., 2012, ApJ, 757, 60Milosavljevi´c M., 2004, ApJ, 605, L13Mo H., van den Bosch F. C., White S., 2010, Galaxy Formationand Evolution (Cambridge University Press)Monnet G., Bacon R., Emsellem E., 1992, A&A, 253, 366Navarro J. F., Frenk C. S., White S. D. M., 1996, ApJ, 462, 563Neumayer N., Walcher C. J., 2012, Advances in Astronomy, 2012,15 Norris M. A., Escudero C. G., Faifer F. R., Kannappan S. J., ForteJ. C., van den Bosch R. C. E., 2015, MNRAS, 451, 3615Pfeffer J., Baumgardt H., 2013, MNRAS, 433, 1997Pfeffer J., Griffen B. F., Baumgardt H., Hilker M., 2014, MNRAS,444, 3670Renaud F., et al., 2013, MNRAS, 436, 1836Renaud F., Bournaud F., Duc P.-A., 2015, MNRAS, 446, 2038Roberts Jr. W. W., Huntley J. M., van Albada G. D., 1979, ApJ,233, 67Rossa J., van der Marel R. P., B¨oker T., Gerssen J., Ho L. C.,Rix H.-W., Shields J. C., Walcher C.-J., 2006, AJ, 132, 1074Scott N., Graham A. W., 2013, ApJ, 763, 76Seth A. C., Dalcanton J. J., Hodge P. W., Debattista V. P., 2006,AJ, 132, 2539Seth A., Ag¨ueros M., Lee D., Basu-Zych A., 2008, ApJ, 678, 116Teyssier R., 2002, A&A, 385, 337Tremaine S. D., Ostriker J. P., Spitzer Jr. L., 1975, ApJ, 196, 407Turner M. L., Cˆot´e P., Ferrarese L., Jord´an A., Blakeslee J. P.,Mei S., Peng E. W., West M. J., 2012, ApJS, 203, 5Vazquez-Semadeni E., 1994, ApJ, 423, 681den Brok M., et al., 2014, MNRAS, 445, 2385This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS000