Age and mass segregation of multiple stellar populations in galactic nuclei and their observational signatures

0.48 MB·

by  Hagai B. Perets

Draftversion January10,2014
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
AGE AND MASS SEGREGATION OF MULTIPLE STELLAR POPULATIONS IN GALACTIC NUCLEI AND
THEIR OBSERVATIONAL SIGNATURES
Hagai B. Perets and Alessandra Mastrobuono-Battisti
Draft version January 10, 2014
Abstract
Nuclear stellar cluster (NSCs) are known to exist around massive black holes (MBHs) in galactic
4 nuclei. They are thought to have formed through in-situ star formation following gas inflow to the
1 nucleus of the galaxy and/or through the infall of multiple stellar clusters. Here we study the latter,
0 and explore the composite structure of the NSC, and its relation to the various stellar populations
2 originating from its progenitor infalling clusters. We use N-body simulations of clusters infall, and
show that this scenario may produce observational signatures in the form of age segregation: the
n
distribution of the stellar properties (e.g. stellar age and/or metallicity) in the NSCs reflect the
a
J infall history of the different clusters. The stellar populations of clusters infalling at different times
(dynamical ages), are differentially segregated in the NSC, and are not fully mixed even after few
8
Gyrs of evolution. Moreover,the radial properties of stellar populations in the progenitor cluster are

mappedtotheirradialdistributioninthefinalNSC,potentiallyleadingtoefficientmasssegregationin
]
A NSCs,eventhosewhererelaxationtimesarelongerthanaHubbletime. Finally,theoverallstructures
of the stellar populations present non-spherical configurations and show significant cluster to cluster
G
population differences.
.
h
p
- 1. INTRODUCTION gation in NSCs, and provides signatures of the cluster
o infallhistoryinthe radialdistributionofthe starsinthe
Nuclear stellar clusters (NSCs) hosting massive black
r NSC.Inadditionwesuggestthatthe formationofNSCs
t holes (MBHs) are thought to exist in a significant frac-
s from cluster infall can produce mass segregated NSCs,
tion of all galactic nuclei. The build-up of such dense
a even in cases where two-body relaxation processes are
[ clusters is likely linked to the growth of the MBH, and
the evolution of the galaxy and its nucleus, as sug- too slow. We suggest that such variations in the kine-
1 gested by statistical correlations between their prop- maticpropertiesofdifferentstellarpopulationsmightbe
v erties (e.g. Ferrarese & Merritt 2000; Tremaine et al. observable and serve as fossilized evidence for the evolu-
4 2002). Two scenarios were suggested for the origin tion and build-up of galactic nuclei.
2 In the following we begin by a brief description of our
of nuclear clusters: (1) The cluster infall scenario,
8 clusterinfallscenario(describedinmoredetailsinPaper
in which stellar clusters inspiral to the galactic nu-
1 I).Wethenpresentthedistributionofthestellarpopula-
cleus, disrupted, and thereby build up the nuclear
. tions of the different infalling cluster in the fully formed
1 cluster (bek+ Tremaine et al. 1975; Capuzzo-Dolcetta
NSC, and show the existence of the age-segregationand
0 1993; Bekki et al. 2004; Agarwal & Milosavljevi´c 2011;
masssegregationphenomena. Finally, wediscuss ourre-
4 Antonini et al. 2012; Antonini 2013; Gnedin et al. 2013
1 and references therein) the inspiraling clusters may also sults, discuss their implications and summarize.
: be the NSC of two galaxies in a merger scenario). (2)
v 2. SIMULATIONOFTHECLUSTERINFALLFORMATION
The nuclear star formation scenario,in which gas infalls
i OFANUCLEARCLUSTER
X into the nucleus and then transforms into stars through
r starformationprocesses(Loose et al.1982; possiblyina OurmodelingoftheclusterinfallformationofanNSC
a disk like configuration, e.g. observations of the Milky follows the same methods, and make use of the same
Way NSC; Levin & Beloborodov 2003; Lu et al. 2009; codeasusedinpaper I(Antonini et al.2012), wherede-
Bartko et al. 2009). Over time the in-situ star forma- taileddescriptionoftheinitialconditionsofGCsandthe
tion builds up the NSC. Naturally, both processes can galaxymodelofthebackgroundstellarpopulationcanbe
work in concert, and both could be important for the found. Inbrief,weuseddirectN-bodysimulations(using
formation and evolution of NSCs. the φGRAPE code Harfst et al.2007)ofthe consecutive
In this paper we explore the cluster infall scenario by infallandmergingofasetof12single-massglobularclus-
meansofN-bodysimulations,andneglectstarformation terseachstartingfromagalactocentricdistanceof20pc.
processesandtheireffects,whicharebeyondthe scopeof Onesimplificationthatwemakeistakingaconstanttime
this paper. Previous studies have dealt with the global intervalbetweenclusterinfalls,asdoneinpreviousworks
structure and build-up of NSCs from inspiral of globu- (e.g. Paper I). The total mass of these clusters sums to
lar clusters (GCs). Here we focus on the multiple stellar ∼ 1.5×107M⊙, which is roughly the observed mass of
populations in NSC and their mapping and relations to the Milky Way nuclear star cluster (Genzel et al. 2010).
their original host GCs. We study the evolution of the ThemassoftheGCsiscomparabletocurrentlyobserved
multipleGCpopulationsbothduringtheevolutionofthe MilkyWayGCs(seeGnedin & Ostriker1997, forMilky-
NSC and in its final form. In particular, we show that Way GC paramters),though a better comparisonwould
the cluster infall scenario introduces population segre- be to young superclusters (or their leftover nuclei) that
wouldhaveinspiarlledtothenucleus(e.g. Kroupa1998),
2
and are currently observed only in other galaxies (e.g. Gyrs after the last infall.
young super star-clusters such as R136 observed in the We find that stars in the NSC originating from early-
LMC). with a MBH of 4×106M⊙ . After the first clus- infall clusters are more segregated to the center of the
ter hadspiraledinto the center,we letthe systemreach NSC thantheir stellarcounterpartsfromlate-infallclus-
a nearly steady state (as evaluated via Lagrange radii), ters. This is true both afterthe lastinfallandevenlater
andthenaddedasecondcluster. Weiteratedthisproce- after a few Gyrs of evolution (See Fig. 1). In particular
dure until all clusters accumulated and merged to form the cluster inner population (central hundred particles),
an NSC around the central MBH. We note a few differ- show a clear segregation when comparing early and late
ences from the original simulations discussed in paper I: infalls, with relatively little additional mixing over the
(1) The scaling of the relaxation time used in paper I last two Gyrs of evolution (See the evolution of the La-
assumed a fully collisional simulation, where as in effect grangian radii of these populations in the NSC in Fig.
a softening radius of 0.01 pc is used; we now scale the 2). Note that the age segregation is reversed between
relaxation times correctly, accounting for the lower cut- the inner regions of the NSC and the outer regions, due
offofthe Coloumblogarithmdue to the softeningradius tothelater(earlier)strippingoftheearly(late)-infalling
used. The times usedin paperI were therefore2.9times clusters.
shorterthanthenowcorrectedestimates. (2)Wenowas- As can be seen in Fig. 2, the infall ofeachnew cluster
sumearandomdistributionoftheinitialinclinationsand affects the evolution of the stellar population of the pre-
phases of the inspiraling clusters, rather than a the con- viousinfalling cluster,effectively“compressing”itintoa
trived model in paper I; the initial conditions are shown more compact configuration around the MBH. The last
inTable 1. (3)The totalscaledtime ofthe simulationis infalling cluster did not experience such a later infall,
12 Gyrs, comparable to the age of the Galaxy; the time andthedistributionofitsstarsissignificantlylesssegre-
passed since the infall of the last cluster until the end gated. Observingsuchadistinctpopulationinagalactic
of the simulation is shorter than the relaxation time of nucleus could therefore provide an interesting clue on a
the NSC, but we have also followed the simulation up relatively recent infall. The more robust results apply
to the relaxation time of the NSC. We emphasize that for the earlier 11 clusters, in which the age segregation
thetimes usedhereareonlyanapproximation,basedon signatures can be observed even long after their infall.
scalingargumentsoftherelaxationtime, andshouldnot We also find that the 3D structure of the stellar pop-
be treated as an accurate time representation. ulations of each of the GCs could significantly differ. In
Wehavemadetworealizationsoftheinfallscenariofor Fig. 3weshowthetriaxialityparameter(seePaperI)for
the formationof the NSC. Bothrealizationsshowgener- eachof the GC populations asa function ofthe distance
allysimilar results,andwepresentresultsonly fromone fromtheMBH.Ascanbeseen,suchstructurecouldvary
of them (see Table 1 for the relevant initial conditions). significantly even between consecutive infalling clusters.
We briefly remark on some differences observedbetween We note that some bunching of the population of sev-
the two realizations. eral consecutive clusters can be observed (e.g. GCs 1-4,
then GCs 5-8, and then 9-11). This bunching relates to
3. RESULTS the specific initial conditions for each cluster (i.e. its
In this study we explore the mapping between the inclination and orbital phase; i and Ω), and different
properties of stellar populations in NSC, and their re- bunching is observed when different random initial con-
lation to the initial characteristics of the stellar popula- ditions are used (not shown). However, this interesting
tions in the progenitor clusters. We focus on two points phenomena do not affect the overall age and mass seg-
intimeduringtheNSCevolution;thefirstaftertheinfall regation processes discussed here, and are beyond the
and initial relaxationof the last cluster, and the second, scope of this paper.
aftermorerelaxationhasoccurredatanagecomparable
toa Hubble time. Ourfindings showthatthe dynamical 4. DISCUSSION
history of the cluster infall is still reflected in the radial 4.1. Age segregation
distribution of the stellar populations in the NSC, even
An additional aspect of NSC build-up from cluster in-
n Ω(deg) i(deg) Rt(pc) fall is the mapping of the infalling clusters structure to
1 82.4 60.7 1.29 the final configuration of the NSC. Typically stars at
2 327.7 178.7 1.29 a distance R (which contains M(< R ) of the cluster
c c
3 76.2 139.5 1.29 mass) from the center of their infalling host cluster are
4 290.6 171.3 1.34
stripped by the tidal forces due to the combinedmass of
5 335.4 24.6 1.48
the MBHandthe stellarmassofthe NSC, M atthe
6 300.6 18.2 1.54 NSC
stripping radius, R , defined as the tidal radius for stars
7 343.9 173.9 1.55 s
at that position:
8 47.9 128.9 1.6
9 272.0 2.3 1.78
10 41.3 139.0 1.80
11 300.9 153.5 1.85
1/3
12 318.2 120.2 1.86 MBH +MNSC(<Rs)
R = R . (1)
s c
(cid:18) M (<R ) (cid:19)
TABLE 1 c c
Initialorbitalparametersof the infallingclusters
(inclination iandlongitude ofascending node Ω),and At early stages, the NSC mass is dominated by the
their tidaldisruption radiusas foundfromthe MBH (M ≫ M(< R)) and the early falling clusters
simulations. BH
should have very similar tidal radii. At later stages the
3
103 Galaxy6000 2 GC 1
GC1 106 1.9 GC 2
GC 3
GC2 4000 1.8 GC 4
GC3 GC 5
GC4 1.7 GC 6
GC5 2000 c) GC 7
Particles102 GGGGCCCC6789 0 5Dis1t.0 (pc)15 20 105M)sun Radius (p111...456 GGGGGCCCCC 89111012
mber of GGGCCC111012 104Mass ( nigain 11..23 Tidal radii
Nu101 gra1.1
a
L
1
103
0.9
0.8
100 0.7
1100−−11 110000 0 1 2 3 4 5 6 7 8 9 10 11
DDiissttaannccee ((ppcc)) Time (Gyr)
Fig. 2.—Evolutionof the Lagrangian radiiforthe central hun-
103 GGaCl1axy6000 106 dpbrcoelsdfo),rsttaehareschoLfacegluarsacthnegroe.ftrOhandecicuelsutsthtreearncss.lTuitshitoeenrisniisftriodamilsLrubapegitrneagdngr(eesleraeatdisviteuasrtoissyt0mh.2e-
GC2 4000 location ofthe central density of the cluster to effectively become
GC3
thedistancefromtheMBH,hencetherisefrom0.2pc(noseen)to
GC4
GC5 2000 the tidal radius central density of each cluster. As can be clearly
es102 GC6 105 seen,thestellarpopulationoftheearlierfallingclustersisprogres-
Particl GGGCCC789 0 5Dis1t.0 (pc)15 20 M)sun sfaivlleilnygmcloursetecrse.ntrally concentrated than the populations of later
ber of GGGCCC111012 104Mass ( 1
m
u101
N 0.9
103 0.8
er0.7
et
m
100 a0.6
1100−−11 110000 ar
DDiissttaannccee ((ppcc)) y P0.5
Fig.1.—Radialdistributionoftheinfallingclustersstellarpopu- alit0.4
xi
lations. Top: theradialdistributionfollowingthelastclusterinfall a
(after the initial relaxation). Bottom: The same at 12 Gyrs. As Tri0.3
can be seen in both cases the clusters populations show clear dif-
ferences, with the earlier infalling clusters showing systematically 0.2
more compact configuration in the central region (< 2 pc), and
thenanoppositebehavioroutside. Insetsshowthelargescale(20 0.1
pc)distribution;notelinearscalesininsets.
0
1 1.5 2 2.5 3 3.5 4 4.5 5
NSC is slowly built up from the infalling clusters, un- Distance (pc)
til it reaches a mass comparable and even larger than
the MBH (M ∼ 2−3×M ). We therefore ex- Fig. 3.—TriaxialityoftheNSCstellarpopulations. Thetriaxi-
NSC BH
alityparameter of the different cluster populations (smoothed for
pect stars from later clusters to be stripped earlier, at
claritywitha1pcwindow)isshownasafunctionofdistancefrom
a stripping radius which is up to 21/3−31/3 (1.26-1.44) theMBH.Ascanbeseenthedifferentpopulationsshowdistinctly
larger than the corresponding stripping radius for stars different behavior, and significant triaxiality. In particular, some
from earlier GCs (i.e. initially at comparable distances oftheclustershowhighlyanisotropicproperties;somewhatresem-
blingthick-disk-likestructuresinsomecasesevenGyrsaftertheir
from the GC center in both clusters). This expecta-
infall.
tion is consistent with our results in table 1 and Fig.
2; indeed the first infalling clusters show the same tidal
radii, and the ratio between the tidal radii of the last lar age gradient. Alternatively, if earlier falling clusters
and the first infalling clusters is 1.86/1.29 ≃ 31/3. This differ in metallicity/color than their later counterparts
phenomenon produces a dynamical age gradient, where (e.g. later falling cluster arrive from larger distances
stars from earlier infalling clusters are stripped where colors differ; e.g. Balcells & Peletier 1994 ), such
at later stages, and dominate inner regions of gradientwouldbetranslatedintoacolor/metallicitygra-
the NSC. If earlier falling clusters are older (e.g. they dientintheNSC.Thedynamicalagesegregationprocess
formed earlier and therefore spiraled earlier to the nu- may therefore give rise to potentially observable stellar
cleus)thensuchgradientwouldbetranslatedintoastel- age/metallicity gradients.
4
We do note an important complication with this sim- much closer in to the NSC MBH, thereby producing an
plifiedpicture. In particular,morecompactandmassive even more compact configuration(see Mastrobuono and
GCswillbestrippedlater(seeEq. 1),andmaytherefore Perets, in prep. for such a scenario).
disposetheirstarsclosertotheMBH,comparedwiththe
stars of the earlier, more dispersed clusters. Note, how- 4.3. Relaxation time vs. mixing time
ever, that less compact clusters are less likely to inspiral Following the cluster infall formation of NSC, they
tothenucleusfromlargedistancesduringaHubbletime maycontinuetoevolvethroughtwo-bodyrelaxationpro-
(see Antonini et al. 2012), and therefore we expect only cesses. In theory, such later evolution may progressively
themostdensemassiveclusterstocontributetothestel- erase some or all of the signatures of the cluster infall
lar population in the NSC. Moreover, given the shorter scenario discussed above given sufficient time for evolu-
inspiraltime ofmoremassiveclusters,these arelikelyto tion. However, as shown above, we find that signatures
arriveearlier,onaverage,thantheirlightercounterparts, of the infall scenario are observed even at the age of
which would also contribute to their later stripping. the universe. Moreover, even at later times, comparable
4.2. Mass segregation to the relaxation time of the NSC after the last infall,
the NSC still shows clear signatures of the dynamical-
Irrespective of the age segregation process discussed mapping age and mass segregation. This may appear
above,themappingbetweenthestructureoftheinfalling counter intuitive, as one might expect any initial condi-
GC andthe structureofthe strippedpopulationofstars tions in the cluster to be erased after a relaxation time.
in the NSC suggestedby Eq. 1 could have an important Relaxation time is defined as the time it takes a star
role in building mass segregated NSCs. It is thought to change its kinetic energy by the order of itself (e.g.
that massive clusters are likely to be mass segregated Binney & Tremaine 1987). However, in order for a star
either primordially or from an early stage in their evo- in the outer region of an NSC to be transported to the
lution e.g. Baumgardt et al. 2008; Allison et al. 2009; innerregionoftheNSC,itneedsamuchmoresignificant
Portegies Zwart et al. 2010, and references therein; and change in energy, i.e. of the order of the energy of the
in even in the absence of such early mass segregation, star in the inner region, were the gravitationalpotential
GCsmayhavesufficienttimetosegregateduringtheirin- and velocities are much higher. As a first simplified ap-
fall. Suchmass segregationcouldpotentially be mapped proximation for the time it takes a stellar population at
into a mass segregationof galactic nuclei stellar popula- some distance r from MBH to mix with another stel-
out
tion. Indeed, the locations of stars initially outside the lar population at an inner region, r , one can replace
in
GC cores are strongly correlated with their positions in the velocity dispersion in relaxation time formula at the
the galaxy nucleus at the end of the simulation (linear position r with that in the position r while keeping
out in
correlationcoefficients, R, almost monotonically rise be- the number densities and the relative velocities between
tween the first infalling clusters, R = 0.48 to the last stars, the same i.e. the “mixing time” for the two popu-
infalling cluster, R=0.18). Note, however, that we find lations would be defined by
suchdirectmappingofcloserinstarsdonotholdforstars
initially inside the GC cores. These stars would still be t = σ(rin)2 t ≈ rout t ,
morecentrallyconcentratedaroundthe MBHatthe end mix(rout,rin) (cid:18)σ(r )2(cid:19) rout (cid:18) r (cid:19) rout
out in
ofthesimulationthanstarsinitiallyresidingintheouter
parts of the GCs (by a factor of 2-3), but among these where trout is the relaxation time at rout and the last
corestarsanydirectcorrelationbetweentheir initialpo- equality is obtained for regions where the MBH domi-
sition in the GC and their final position in the galaxy nates the gravitational potential of the NSC (i.e. up to
nucleus is lost. the MBH influence radius). A more accurate definition
TheinfallscenariowouldthereforesuggestthatNSCs wouldaccountforthechangingdiffusiontimeasthestel-
are likely to be mass segregated even when the larenvironmentchangesduringthediffusivetransportof
relaxation times in such NSCs are longer than astarfromoneenvironmenttoanother;afulldiscussion
a Hubble time (true for most NSCs hosting MBHs of the mixing time is beyond this scope and will be dis-
with M > few ×107). More generally, NSCs could cussed in details elsewhere. Irrespective of the accurate
BH
definition, it is clear that t > t ; stellar population
be more mass segregated than expected from typical re- mix r
segregation could therefore survive much longer than a
laxation processes (e.g. Bahcall & Wolf 1977; though
relaxationtime. Oneshouldnote,however,thateveryin-
strong mass segregation process may also contribute;
fallofanadditionalclusterdoesnotonlybringnewstars
Alexander & Hopman 2009). As a side note, it is in-
to the NSC, that would slowly change the two-body re-
teresting to point out that clues for an extreme mass
laxationtime,butcanproducesignificantchangesinthe
segregationare apparent in the stellar population of the
gravitationalpotentialondynamicaltimescales. Though
Galactic NSC (see Alexander 2007 for a discussion).
this may not significantly affect the inner regions deep
Such dynamical-mapping age segregation could have
in the potential of the MBH+NSC, such changes may
animportantroleinleadingtotheconcentrationofmas-
give rise to a more violent relaxation in the outer re-
sivestars,andinparticularstellarblackholesinthecen-
gionsthatcanmixthestellarpopulationsmuchmoreef-
tral regionof nuclear cusps aroundMBHs. The built-up
ficiently than two-body relaxationprocesses. One would
ofacentrallyconcentrateddarkcuspmadeofblackholes
therefore expect segregatedpopulations to be more pro-
is therefore an interesting potential outcome of the clus-
nounced in the inner regions of NSCs, and around more
terinfallscenarioforNSC formation(seeAntonini2014,
massive MBHs.
inprep. foradetaileddiscussionoftheseissues). Wealso
note that in cases an infalling GC harbors an intermedi-
4.4. Structure of the multiple stellar populations
ate mass black hole (103−104M⊙), it could bring stars
5
The particular final structure of the stellar population populationsfromearlierfallingclustersaremoreconcen-
of each GC is complex, as can be seen in Fig. 3, and trated in the central parts of the NSC compared to late
its detailed exploration is beyond the scope of this let- ones. This dynamical age segregation process can po-
ter. Here we only note that the significant differences tentially leave behind a signature in the form of an age
betweenthesestructurescouldprovideanadditionalsig- and/ormetallicityradialgradientintheNSCstellarpop-
natureforthe multi-clusterinfallscenario,similartothe ulation. The stellar population of each cluster forms a
radialsegregationdiscussedabove. Inparticularinfalling non-spherical complex structure, which behavior signifi-
clusters can produce thick flattened structures with var- cantly differs from one cluster population to another. In
ied orientations, possibly related to “disky” like struc- addition, any primordial/early mass segregation in the
tures are observed in galactic nuclei and clusters (see infalling GCs is mapped into a mass segregated popu-
Mastrobuono-Battisti& Perets2013fordiscussionofthe lations in the galactic nucleus; in particular even NSCs
evolution of such disks). whererelaxationtimeislongerthanaHubbletimecould
show a mass segregated stellar population, which could
5. SUMMARY not arise from two-body relaxation processes.
In this letter we explore the signatures and the impli-
cations of the cluster infall scenario on the structure of We would like to thank Fabio Antonini for for help-
nuclear stellar clusters and their multiple stellar popu- ful discussions and comments. We would also like to
lations. We use N-body simulations to study the infall thank the referee for helpful comments and suggestions
of 12 globular clusters into a galactic nucleus hosting a thatimprovedthismanuscript. Weacknowledgesupport
MBH of 4×106 M⊙, and we follow the evolution of the fromthe I-CORE Programof the Planning andBudget-
stellar populations from each cluster and their final dis- ing Committee and The IsraelScience Foundation grant
tribution in the NSC. We find that the infall history is 1829/12. HBP is a Deloro and BIKURAfellow. AMB is
reflected in the final structure of the NSC, where stellar partly supported by the Lady Davies Foundation.
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