The dynamical fingerprint of gas-expulsion: Insights into the assembly of the Milky Ways' old GC system
aa r X i v : . [ a s t r o - ph . GA ] O c t The dynamical fingerprint of gas-expulsion: Insights into the assembly ofthe Milky Ways’ old GC system
Marks, Michael , , a and Kroupa, Pavel Argelander-Institut f¨ur Astronomie, Universit¨at Bonn, Auf dem H¨ugel 71, D-53121 Bonn, Germany Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, D-53121 Bonn, Germany
Abstract.
Since the oldest globular clusters (GCs) are early residuals from the formation of the Milky Way(MW), GCs were exposed to the likely evolving potential of our Galaxy. The expulsion of the residual-gas fromthe GC’s embedded progenitors is sensitive to the conditions in the pre-MW gas cloud. By means of N-bodycomputations it is shown that gas throw-out from initially mass-segregated GCs a ff ect the shape of the low-massstellar mass function (MF) and that its imprint might still be visible in the present-day MF (PDMF). The strengthof the tidal-field at birth influences the degree of gas-expulsion driven low-mass-star depletion and therefore thePDMF probes the MW potential at the time of GC formation. It is argued that among the old GC population inthe MW, younger GCs show stronger low-mass-star loss than older GCs. This is shown to be consistent with acontracting and self-gravitating cloud in which fluctuations in the pre-MW potential grow with time. An initiallyrelatively smooth tidal field evolved into a grainy potential within a dynamical time-scale of the collapsing cloud(based on [1]). GCs of the MW may be categorized into old and younghalo GCs (Fig. 1). The latter group follows an age-metallicityrelation and is thought to have an accretion origin [2]. Theold group of GCs is roughly coeval, spanning a metallic-ity range from [M / H] = − − .
5. The age dispersion ofonly ≈
600 Myr, comparable to the free-fall time of a ho-mogeneous sphere with the mass and size of the MWs darkmatter halo (1 . × M ⊙ ,
170 kpc, [3]), is “not in con-tradiction with the formation from a single proto-system”[4], which formed the proto-MW probably along the linesoriginally suggested by Eggen et al. [5]. Therefore the MWGC halo consists of an in-situ (old GCs) and an accretiondominated, or more probably a tidally generated [6], halo(younger GCs) with a radial transition between the two atabout ≈
10 kpc (see also [7]). The old and coeval GCs thuswitnessed the formation of the proto-MW.In order to access the ambient conditions prevalent atGC birth we use the early violent residual-gas expulsionprocess which we show to leave an imprint in the PDMF.This dynamical fingerprint depends on the strength of thetidal-field imposed on the GCs by the proto-MW which al-lows us, in combination with information about the metal-licity (age) of the GCs, to trace back the very early eventsthat contributed to the formation of the MW. a Member of the International Max Planck Research School(IMPRS) for Astronomy and Astrophysics at the Universities ofBonn and Cologne, e-mail: [email protected]
Classically, computations of star clusters start with an in-variant IMF and the evolution of their stellar mass-function(MF) is determined by the evaporation of low-mass starsover the tidal-boundary through two-body relaxation [8,9].However, since clusters are observed to be segregated bystellar mass already at very young ages, frequently inter-preted as evidence for primordial mass-segregation, it maybe questioned whether this is the whole story. Upon gas-expulsion and the subsequent expansion of the cluster, starsin the cluster outskirts are stripped o ff the cluster throughthe external tidal-field. If low-mass stars form at the clusterperiphery, the low-mass star population will be preferen-tially depleted, leading to a flattening of the mass-functionbefore classical evolution starts.Marks et al. [10] showed this to be the case by makinguse of the grid of residual-gas expulsion models of Baum-gardt & Kroupa [11]. If clusters expell their gas on a shorttime-scale, the stars in the cluster, assumed to be close tovirial equilibrium before gas throw-out starts, cannot ad-just quickly enough to the changing potential, hence lead-ing to strong cluster expansion and e ff ective loss of starsfrom the cluster outskirts. The e ff ect of mass-loss over thetidal-boundary is enhanced if the star formation e ffi ciencyis low, i.e. a significant fraction of the total mass remainsin the form of gas which is to be expelled, and if the tidal-field is strong.Marks et al. [10] show that if the cluster is mass-segregated,low-mass stars will be removed at first, hence flattening thelow-mass stellar MF. If the expansion and tidal-field (and,thus, mass-loss) are strong, the concentration of the clus-PJ Web of Conferences Fig. 1.
Distribution of GC relative ages as a function of metallicity (taken from [4]). Open and filled circles denote GCs with Galactocen-tric distance smaller and larger than 10 kpc, respectively. Clusters group into coeval old GCs (relative age of 1 corresponds to ≈ . ≈ . -2-1.5-1-0.5 0 0.5 1 1.5 2 0.5 1 1.5 2 2.5 3 P D g l oba l l o w - m a ss M F s l ope α concentration c=log (r t /r c ) modelsobservationseye-ball fitlimits to observations -1-0.5 0 0.5 1 1.5 2-2.4 -2.2 -2 -1.8 -1.6 -1.4 -1.2 -1 -0.8 -0.6 -0.4 P D g l oba l l o w - m a ss M F s l ope α metallicity [Fe/H] Fig. 2.
Left:
Concentration parameter, c = log ( r t / r c ), vs. low-mass stellar PDMF slope, α , ( dN / dm ∝ m − α ) in the mass-range 0 . − . M ⊙ . Weakly concentrated clusters are strongly depleted in low-mass stars and no cluster with a high concentration and a depletedMF is found (filled dots). This trend (black solid line) can’t be understood in terms of purely secular dynamical evolution. However, N -body integrations of mass-segregated clusters at the time of the emergence from their birth molecular cloud (squares with error bars)reasonably reproduce the observed trend within the observational limits (dashed lines). Right:
Global cluster metallicity, [Fe / H], vs.low-mass MF slope, α . Data points are labelled with the respective NGC or Pal catalogue number of the GC. Clusters having a largermetallicity ([Fe / H] & − .
5) are depleted in low-mass stars ( α .
1) giving support to the metallicity-dependent gas expulsion scenario(Sec. 2). ter decreases in parallel with the depletion of the low-massstar population in a mass-segregated cluster. But if expan-sion and the tidal-field (and mass-loss) are weak, the con-centration remains close to the initial value and the MF isonly weakly depleted of low-mass stars.This has indeed been observed by de Marchi et al. ([12],Fig. 2). That gas-expulsion is indeed at work in initiatingthis trend is strengthened by Marks & Kroupa [1], whoshow higher-metallicity GCs to have flatter present-day mass-functions (PDMFs). Although the observed trend had beenrecognized earlier [13,14] it lacked an explanation until re-cently. In particular, this trend is di ffi cult to reconcile withstandard dynamical evolution scenarios with a universalIMF as it is unclear how dynamics could possibly knowabout the metal content of a cluster. Marks & Kroupa [1]interpret the PDMF trend with metallicity as evidence for metal-dependent cluster winds in initially mass-segregatedclusters: As radiation couples better to metal-rich gas, theexpulsion of the left-over gas from star formation is quickerand perhaps more e ffi cient, leading to strong expansion ofthe cluster as a whole and thereby loosing preferentiallylow-mass stars over the tidal boundary.The de Marchi trend [12] was also unexpected from aclassical point of view but is a natural outcome of gas ex-pulsion. Although it has been shown that the depletion oflow-mass stars occurs quicker if clusters start mass-segregatedinitially [15], such classical scenarios without gas lack anunderstanding of the metallicity trend.ssembling the puzzle of the Milky Way Fig. 4.
Contraction scenario as described in Sec. 2.1.
Left-hand picture:
In a collapsing cloud the first clusters (the stars in the pic-ture) form all over the cloud in a smooth potential. The conditions are similar for all of them leading to comparable MF slopes andconcentrations after gas expulsion. These clusters enrich their immediate environment with metals.
Right-hand picture:
As the collapseproceeds more clusters form and the potential becomes grainy enhancing the mean tidal-field strength. Star clusters, e.g. the right filledcluster, forming near other clusters or dense clouds experience extreme conditions. They are more strongly enriched in metals from thesurrounding objects than other clusters, e.g. the left filled cluster which is located in a more isolated place of the grainy potential, andthey experience stronger tidal-fields than the first-forming clusters. This leads to strong di ff erences between the formation sites and, inturn, to variations in the PDMF slope. From the models it is found that as the concentration de-creases, the tidal-field strength increases, i.e. present-daylow-concentration clusters have formed in stronger tidal-fields (Fig. 3). Furthermore the GCs of the old halo appearto be co-eval to a good approximation (Sec. 1). Despitetheir formation at the same time the clusters show a largespread in metallicity ( − . < [ Fe / H ] < − . α GCs (Fig. 2) suggests that these clusters formed from anICM enriched in metals and they should thus be somewhatyounger than the relatively more metal-poor clusters. Theage di ff erence can then be at most a few hundred Myr only,corresponding to the free-fall time-scale (Sec. 1).These ideas lead us to a picture of the formation of theold inner and co-eval Galactic GC system, which mighthave formed during the contraction of the pre-MW gascloud out of which finally, after an additional long periodof ongoing accretion and merging of formerly extragalac-tic systems [2], the MW has emerged (possibly along thelines originally proposed by Eggen et al. [5]). These ideasare summarised in Fig. 4.In this frame, clusters which are depleted of low-massstars, i.e. those that reside in stronger tidal-fields were bornat a later stage of galaxy formation. The environment in which the clusters formed must then have changed dras-tically within a short time. The initial conditions can beunderstood if the overall potential was rather smooth inthe beginning. The first GCs formed all over the cloudexperiencing similar smooth tidal-fields more or less in-dependent of Galactocentric distance and explaining thecomparable strengths of the tidal-fields. These first clus-ters enriched the ICM of their local environment with met-als, from which the somewhat younger clusters of the oldpopulation were born.The pre-galaxy gas cloud contracted due to self-gravitationduring this process. The cloud may have become clumpyand substructures emerged. Fragmentation of the cloud intomassive star cluster forming regions made the potentialgrainy, thereby explaining the di ff erent and on average strongertidal-field strengths among the younger clusters. Clustersforming next to other massive, dense objects are forced toexpel their gas under more extreme conditions (a strongertidal-field) than expected from their present-day Galacto-centric distance.Gas expulsion from early forming clusters may trig-ger the formation of new clusters (via gas compression)in their immediate surrounding perhaps leading to clus-ter complexes, i.e. clusters of star clusters. It is imaginablethat similar processes were at work in the GC forming gascloud, increasing the average local tidal-field strengths.These e ff ects lead to depleted MFs and lower concen-trations after gas expulsion in the younger of the old haloGCs. In this sense the history of events that lead to the in-ner GC system may involve local rapid (on time-scales ofhundreds of Myr) re-arrangements of the interstellar mat-PJ Web of Conferences -2-1.5-1-0.5 0 0.5 1 1.5 2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 P D g l oba l l o w - m a ss M F s l ope α modified concentration c mod =log (r t /r h,proj ) r h,cl /r t,cl Fig. 3.
As in Fig. 2 (left) but with a modified concentration pa-rameter (see [1]) on the abscissa. The theoretical data are codedfor the initial tidal-field strength, in the simulations of [11] withdi ff erent symbols. Open symbols and crosses depict the N -bodyresults, the filled circles labelled with their respective cataloguenumber are the data from the de Marchi GC sample. Quadranglesand triangles show areas with similar tidal-field strengths. All ini-tial models started from the dashed line, which is the slope of thecanonical IMF [16] in the mass-range 0 . − . M ⊙ ( α ≈ . ter superposed on the overall contraction or collapse to thefinal population II spheroid. Acknowledgements
MM was supported for this research through a stipend fromthe International Max Planck Research School (IMPRS)for Astronomy and Astrophysics at the Universities of Bonnand Cologne.
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