The "dynamical clock": dating the internal dynamical evolution of star clusters with Blue Straggler Stars
aa r X i v : . [ a s t r o - ph . GA ] J a n Rendiconti Lincei. Scienze Fisiche e Naturali. LINCEI PRIZEWINNERS manuscript No. (will be inserted by the editor)
The “dynamical clock”: dating the internal dynamicalevolution of star clusters with Blue Straggler Stars
Francesco R. Ferraro · Barbara Lanzoni · Emanuele Dalessandro
Received: November 12, 2019 / Accepted: January 12, 2020
Abstract
We discuss the observational properties ofa special class of objects (the so-called “Blue StragglerStars”, BSSs) in the framework of using this stellar pop-ulation as probe of the dynamical processes occurringin high-density stellar systems. Indeed, the shape of theBSS radial distribution and their level of central concen-tration are powerful tracers of the stage of dynamicalevolution reached by the host cluster since formation.Hence, they can be used as empirical chronometers ableto measure the dynamical age of stellar systems. In ad-dition, the presence of a double BSS sequence in thecolor-magnitude diagram is likely the signature of themost extreme dynamical process occurring in globularcluster life: the core collapse event. Such a feature cantherefore be used to reveal the occurrence of this pro-cess and, for the first time, even date it.
Keywords
Faint blue stars (blue stragglers) · Hertzsprung-Russell, color-magnitude, and color-colordiagrams · Globular clusters in the Milky Way · Stellardynamics and kinematics
The author F. R. Ferraro received the international prize“L. Tartufari” for Astronomy in 2018, attributed by the Ac-cademia Nazionale dei Lincei, Rome.Francesco R. FerraroDipartimento di Fisica e Astronomia, Universit`a degli Studidi Bologna, Via Gobetti 93/2, I–40129 Bologna, ItalyTel.: +39-051-2095774E-mail: [email protected] LanzoniDipartimento di Fisica e Astronomia, Universit`a degli Studidi Bologna, Via Gobetti 93/2, I–40129 Bologna, ItalyEmanuele DalessandroINAF-Osservatorio di Astrofisica & Scienza dello Spazio, viaGobetti 93/3, I–40129 Bologna, Italy
PACS
PACS 97.20.Rp · · · Globular Clusters (GCs) are compact aggregates of upto a million stars held together by their mutual gravi-tational attraction in a nearly spherical configuration.They are sub-galactic structures, with typical massesof 10 − M ⊙ , ages as old as the Hubble time ( ∼ Francesco R. Ferraro et al. M3 Fig. 1
Left: indicative illustration of the location of BSSs (large blue circles) in a Temperature - Luminosity diagram.Luminosities are expressed in Solar units, temperatures in Kelvin. Right: artistic illustration of the two main BSS formationchannels, namely stellar collisions (upper panel), and vampirism phenomena between two companion stars in a binary system(lower panel). tral density followed by stages during which the clus-ter rebounds toward a structure with lower density andmore extended core. The recurrent gravitational inter-actions among stars thus modify the structure of thesystem over the time (the so-called ”dynamical evo-lution”), with a time-scale (the relaxation time) thatdepends in a very complex way on the initial and thelocal conditions, thus differing from cluster to clusterand, within the same system, from high- to low-densityregions (e.g., Meylan & Heggie 1997).As a consequence of the internal dynamical evolu-tion, clusters born with a given size progressively de-velop more and more compact cores, the timescale ofthese changes being hard to determine. Indeed, esti-mating the formation epoch of a cluster (correspondingto the chronological age of its stars) is relatively sim-ple from the measure of the luminosity of the MainSequence Turn-Off (MS-TO) level, while measuring its“dynamical age” (corresponding to the level of dynam-ical evolution it reached since formation) is much morechallenging. Following an analogy to human experience,as people with the same biological age can be in verydifferent physical shapes, so stellar aggregates with thesame chronological age can have reached quite differ-ent levels of internal dynamical evolution. While theage of people is easily readable in the identity card, de-termining their physical shape is not straightforward(and it depends on the capacity of correctly reading afew characteristics impressed on their body). The same holds for star clusters. Thus, a proper characterizationof any GC requires the knowledge, not only of its inter-nal structure and kinematics, but also of its dynamicalage.1.1 Blue Stragglers as gravitational test particles ofGC dynamicsThe internal dynamical activity of GCs is thought toalso generate a variety of stellar exotica, as blue strag-gler stars (BSSs) and interacting binaries containingheavily degenerate objects, like black holes and neutronstars (see Bailyn, 1995; Ransom et al., 2005; Cool et al.,1998; Strader et al., 2012; Cadelano et al., 2017, 2018;Dalessandro et al., 2014; Pallanca et al., 2013, 2017; Ferraro et al.,2015). Among these, BSSs are certainly the most abun-dant and they are the easiest to distinguish from nor-mal stars in a color-magnitude diagram (CMD), sincethey define a sort of sequence extending brighter andbluer than the cluster MS-TO point, mimicking a sub-population of young stars (see Fig. 1; Sandage, 1953;Ferraro et al., 1992, 1993, 1997a, 2003; Leigh et al., 2007;Moretti et al., 2008; Simunovic & Puzia, 2016; Parada et al.,2016).Their history dates back to 1953, when the Ameri-can astronomer Allan Sandage first discovered this puz-zling population of stars that seemed to go against therules of the stellar evolution theory, in the GalacticGC Messier 3 (M3). He dubbed them “stragglers” be- he stellar dynamical clock 3
Fig. 2
Ultraviolet CMDs of two massive globular clusters (namely, M3 and NGC 2808). In both cases, BSSs are plotted aslarge blue circles. In the right panel, the position of the main evolutionary sequences are also marked. cause they are located outside the main evolutionarysequences in the CMD and they seem to be trailing inthe evolution with respect to the vast majority of starsin the cluster. The presence of these (apparently) youngstars in a GC was completely unexpected, since star for-mation essentially stopped 13 billion years ago in thesesystems. Indeed, BSSs are not thought to be a youngstellar population, and it is widely accepted that theyare hydrogen-burning stars more massive than the MS-TO objects (Shara et al., 1997; Gilliland et al., 1998).However, the details of their formation mechanism arenot completely understood yet, and two main mech-anisms are commonly advocated to explain their ori-gin (see Fig. 1): (1) direct collisions (COLL), in whichthe stars might actually merge, mix their nuclear fueland “re-stoke” the fires of nuclear fusion (Hills & Day,1976), and (2) mass-transfer (MT) in tight binary sys-tems, where the less massive object acts as a “vam-pire”, siphoning fresh hydrogen from its more massivecompanion, possibly up to the complete coalescenceof the two stars (McCrea, 1964). Both processes aresuggested to add fresh fuel (hydrogen) into the stel-lar core, thus prolonging the star lifetime and makingit look more youthful (blueness and brightness beingthe attributes of stellar youth). Both these processeshave an efficiency that depends on the local environ-ment (Fusi Pecci et al., 1992; Ferraro et al., 1995, 1999,2006a; Piotto et al., 2004; Davies et al., 2004; Dalessandro et al.,2008a; Sollima et al., 2008; Knigge et al., 2009; Chen & Han,2009; Beccari et al., 2013; Chatterjee et al., 2013), andthey can act simultaneously within the same cluster(e.g., Ferraro et al., 2006b, 2009; Dalessandro et al., 2013a; Leigh et al., 2013; Xin et al., 2015; Beccari et al., 2019;Portegies Zwart , 2019).Irrespective of their formation mechanism, BSSs rep-resent a population of heavy objects ( M BSS = 1 . − . M ⊙ ; e.g., Fiorentino et al., 2014; Raso et al., 2019;see also Ferraro et al., 2016) orbiting in an “ocean” oflighter stars (the average stellar mass in an old GC is h M i = 0 . M ⊙ ; e.g., Djorgovski, 1993). For this reason,BSSs can be used as powerful gravitational probes toinvestigate key physical processes (such as mass segre-gation and dynamical friction) characterizing the dy-namical evolution of star clusters (e.g., Ferraro et al.,2009, 2012; Dalessandro et al., 2013a; Simunovic et al.,2014). But, how difficult is to collect complete samplesof BSSs in GCs? T eff ∼ UV route to BSS studyin GCs (see Ferraro et al., 1997a,b, 1999, 2001, 2003).This approach consists first in identifying the stellarsources in images acquired at UV wavelengths, then, inusing the positions of those stars to enable the sourcedetection in images acquired in the other filters. Such atechnique naturally optimizes the detection of relativelyhot stars and allows the collection of complete sampleof BSSs even in the central region of high-density clus-ters. Indeed UV CMDs are the ideal diagrams where to
Francesco R. Ferraro et al.
Fig. 3
Normalized radial distribution of BSSs (colored symbols) compared to that of normal cluster stars taken as reference(grey strips) in the three main families defined by Ferraro et al. (2012):
Family I = dynamically young clusters (left panel),
Family II = dynamically intermediate-age clusters (central panel),
Family III = dynamically old clusters (right panel). study BSSs, since these stars appear to be clearly dis-tinguished from the other evolutionary sequences andcan be safely selected (see Fig. 2). In particular, (1) to-gether with the hottest horizontal branch (HB) stars,BSSs are the brightest objects in UV CMDs, while mostof the RGB stars are significantly fainter (at odds withwhat happens in the optical diagrams), and (2) BSSsdraw a narrow and well-defined sequence spanning ap-proximately 3 magnitudes.By following this approach, we derived completesamples of BSSs in the central cores of several Galac-tic GCs, including systems of very high central density(see Lanzoni et al. 2007a,b,c; Dalessandro et al. 2008b,2009; Sanna et al. 2012, 2014; Contreras Ramos et al.2012; Dalessandro et al. 2013a,b). The dataset recentlyacquired within the HST UV Legacy Survey of GalacticGlobular Clusters (Piotto et al., 2015) allows the exten-sion of this approach to a significant number of addi-tional clusters (see Section 2.2). By using this dataset,Raso et al. (2017) quantitatively demonstrated the clearadvantages of the
UV-guided search for BSSs, with re-spect to the optical-guided approach. In fact, the de-tailed comparison between the catalogs obtained throughthe two different methodologies in four GCs (namely,NGC 2808, NGC 6388, NGC 6541 and NGC 7078) hasshown that a large sample of stars in the innermost re-gion of these systems are missed in the optical-guided case. The number of missed stars depends on the clusterstructure, varying from a few hundreds up to thousandsin high density clusters. The vast majority ( > According to their formation mechanisms, BSSs are sig-nificantly heavier than the average cluster population.Hence, as the dynamical evolution of the parent clusteradvances, these objects progressively tend to migrateto the innermost regions. Of course, this modifies theradial distribution of BSSs, by producing a progres-sive depletion of these stars in the outer regions andan increase of their density toward the cluster center.Hence, the dynamical age of a star cluster is mirroredby the shape of the radial distribution and by the levelof central sedimentation of its BSS population, exactlyas the physical shape of people is imprinted on theirbody through many observable features. Because theprogressive flow of BSSs toward the center measuresthe dynamical age of the parent cluster in a similarway as the progressive sedimentation of sand grains inan hourglass measures the flow of time, we named thismethod the “dynamical clock”.2.1 Reading the signature of dynamical evolution fromthe BSS radial distributionFerraro et al. (2012) analyzed the BSS distribution overthe entire radial extension in a sample of 21 GalacticGCs (Ferraro et al., 1997a, 2004, 2006a; Sabbi et al.,2004; Lanzoni et al., 2007a,b,c; Dalessandro et al., 2008a,b,2009; Beccari et al., 2006a,b, 2011; Contreras Ramos et al.,2012; Sanna et al., 2012) and first demonstrated thatits shape can be used to measure the level of dynamicalevolution reached by the host system.To this aim, Ferraro et al. (2012) used the “BSS nor-malized radial distribution” (hereafter BSS-nRD), de-fined as the ratio ( R BSS ) between the fraction of BSSs he stellar dynamical clock 5
Fig. 4
The sample of BSSs (black dots) identified in the n-CMD for a representative sample of 9 clusters discussed inFerraro et al. (2018). The BSS selection box is drawn in the first panel, the one adopted for the MS-TO population is markedfor all clusters. sampled in a radial bin and the fraction of cluster lightsampled in the same bin (Ferraro et al., 1993). Sincethe number of stars scales as the sampled luminosity,this ratio is equal to one for any population not affectedby dynamical evolution. Hence, this parameter is par-ticularly powerful in quantifying any excess or deficit ofstars with respect to the “normal” radial distribution,as indeed observed for exotic populations, like BSSs.Thus, by analyzing the shape of the BSS-nRD, the sur-veyed sample of chronologically old and coeval GCs hasbeen partitioned in three main families (see Fig. Fig. 3): – Family I, where the BSS-nRD is flat (i.e., the ra-dial distribution of BSSs within the cluster is fullycompatible with that of the sampled light and in-distinguishable from that of “normal” stars); – Family II, where the BSS-nRD is bimodal, with ahigh peak in the cluster center, a dip at an inter-mediate radius ( r min ), and a rising branch in theexternal regions (this behavior indicates an excessof BSSs in the center and a depletion at intermedi-ate radii, with respect to normal cluster stars); – Family III, where the BSS-nRD shows only a cen-tral peak, followed by a monotonically decreasingtrend (this indicates a huge excess of BSSs in thecenter and a severe lack of them anywhere else inthe cluster).This variety of shapes (also detected in extra-GalacticGCs; see Li et al., 2013) has been interpreted as themanifestation of the effect of dynamical friction, whichdrives the objects more massive than the average to-ward the cluster centre (e.g. Mapelli et al., 2004, 2006;
Francesco R. Ferraro et al.
Fig. 5
Cumulative radial distributions of BSSs (blue line) and REF stars (red line) in the nine GCs shown in Figure 4. Thehorizontal axis provides the logarithm of the cluster-centric distance, in units of the half-mass radius r h . The size of the areabetween the two curves (shaded in grey) corresponds to the labelled value of A + . Clusters are ranked in terms of increasingvalue of A + . Miocchi et al., 2015), with an efficiency that mainly de-pends on the local star density (i.e., it decreases at in-creasing radial distance; see Alessandrini et al., 2014).Hence, a flat BSS-nRD indicates that dynamical fric-tion has not affected the BSS population yet (not evenin the innermost regions), and therefore Family I globu-lar clusters are “dynamically young” (left panels in Fig.3). In more evolved GCs (Family II), dynamical frictionhas progressively removed BSSs at increasingly largerdistances from the center, thus generating a minimumin the BSS-nRD at increasingly larger values of r min (from top to bottom, in the central panels of Fig. 3). InFamily III systems, dynamical friction already affectedalso the most remote BSSs, accumulating all of thesestars toward the cluster center and thus producing amonotonic BSS-nRD with a central prominent peak; these are “dynamically old” GCs (right panel in Fig.3).2.2 Reading the signature of the dynamical evolutionfrom the BSS segregation levelIn Alessandrini et al. (2016) we proposed a new pa-rameter ( A + ) to measure the level of BSS central sedi-mentation. A + is defined as the area enclosed betweenthe cumulative radial distribution of BSSs and thatof a reference (REF), lighter, population (as the HB,RGB, or MS-TO stars), measured within a given dis-tance from the cluster center (the half-mass radius).N-body simulations demonstrate that this parametersystematically increases as a function of time, follow- he stellar dynamical clock 7 ing the dynamical evolution of the cluster and, morespecifically, tracking the process of BSS segregation (seeFigure 5 in Alessandrini et al., 2016). At initial times,when all stars are spatially mixed regardless of theirmass, BSSs and the REF population share the samecumulative radial distributions and A + = 0. As theaction of dynamical friction proceeds, BSSs migrate to-ward the centre of the system and the two curves startto separate, thus providing a progressively increasingvalue of A + . Lanzoni et al. (2016) measured the newparameter within one half-mass radius ( A + rh ) for thesame set of GCs discussed in Ferraro et al. (2012), find-ing a tight correlation with r min (see their Figure 2).This demonstrates that both parameters measure theeffect of dynamical friction: as clusters get dynamicallyolder, dynamical friction progressively removes BSSs atincreasingly larger distances from the center (thus gen-erating a minimum at increasingly larger values of r min )and accumulates them toward the cluster center (thusincreasing A + ). In addition, Lanzoni et al. (2016) founda strong correlation between A + and the central relax-ation time of the cluster ( t rc ) (similar to that foundby Ferraro et al., 2012 using the parameter r min ), thusfully confirming that A + can be efficiently used to mea-sure the level of dynamical evolution reached by starclusters (see also the simulations by Sollima, & Ferraro,2019).This approach was recently extended (Ferraro et al.,2018) to 27 additional systems observed within the HSTUV Legacy Survey of Galactic Globular Clusters (Piotto et al.,2015, see also Raso et al., 2017). Combined with theclusters studied in Lanzoni et al. (2016), this providedus with a total sample of 48 GCs, corresponding to al-most 33% of the entire Milky Way population. To per-form a fully homogeneous selection of BSSs in clusterswith different values of distance, reddening and metal-licity, Ferraro et al. (2018) made use of “normalized”CMDs (see also Raso et al., 2017), where the magni-tudes and colors of all the measured stars in a givencluster are arbitrarily shifted to locate the cluster MS-TO at (0,0) coordinates (see, e.g., Fig. 4, where the“normalized” magnitudes and colors are indicated with m ∗ F275W and ( m F275W − m F336W ) ∗ , respectively). Theadvantage of using n-CMDs is that, independently ofthe cluster properties, BSSs are expected to populatethe same region of the diagram. Hence, the same se-lection box can be used in all GCs for a homogeneousselection of the BSS population. For the sake of illus-tration, Fig. 4 shows a sample of nine n-CMDs ana-lyzed in Ferraro et al. (2018), with the BSS selectionbox marked in the top-left panel.To compute the A + parameter, the radial distribu-tion of BSSs must be compared with that of a REF Fig. 6
The strong correlation between A + and log( N relax )for the sample of 48 GCs discussed in Ferraro et al. (2018).The parameter N relax quantifies the number of current cen-tral relaxation times occurred since cluster formation. Thetight relation between these two parameters demonstratesthat the segregation level of BSSs measured by A + can beused to evaluate the level of dynamical evolution experiencedby the parent cluster. The best fit relation (eq. 1) is alsoshown as a solid line. The arrow indicates increasing dynam-ical ages. population of normal cluster stars tracing the over-all density profile of the system. As REF population,Ferraro et al. (2018) adopted MS stars in the MS-TOregion, since this portion of the CMD includes severalhundred objects and therefore is negligibly affected bystatistical fluctuations. Fig. 5 illustrates the cumulativeradial distributions obtained for the sub-sample of nineclusters shown in Fig. 4, covering the entire range ofvalues measured for A + in the full sample of 48 GCs(NGC 5986 the lowest value, and NGC 6397 having thelargest one).To investigate the connection between the BSS seg-regation level and the dynamical status of the parentcluster, we studied the relation between the measuredvalues of A + and the number of current central relax-ation times ( t rc ) that have occurred since the epoch ofcluster formation ( t GC ): N relax = t GC /t rc . Because allGalactic GCs have approximately the same age, for allthe program clusters we assumed t GC = 12 Gyr (seethe compilation of Forbes & Bridges, 2010). A strongcorrelation was found (Fig. 6):log N relax = 5 . × A + + 0 . , (1)clearly demonstrating that A + is a powerful indicator ofGC internal dynamical evolution. This is indeed a key Francesco R. Ferraro et al.
Fig. 7
Relation between A + and three physical parametersthat are expected to change with the long-term dynamicalevolution of GCs: the core radius r c ( top panel , the concen-tration parameter c ( middle panel ), and the central luminos-ity density ρ ( bottom panel ). The values of r c , c and ρ aretaken from Harris (1996). The arrows indicate increasing dy-namical ages. relation: it allows the empirical determination of thedynamical age of a star cluster from just the measureof the central sedimentation level of its BSS popula-tion. By using this relation it is possible to learn howmuch dynamically-old is a GC, and if it is more or lessevolved than other systems with comparable or differ-ent structural/dynamical properties.Measuring the A + parameter offers the opportunityto empirically describe the effect of the dynamical ag-ing of star clusters on their structural parameters. Fig.7 shows the behavior of the core radius ( r c ), the concen-tration parameter c (defined as the logarithm of the ra-tio between the tidal and the core radii), and the centralluminosity density ( ρ ; all are taken from Harris 1996,2010 edition), as a function of A + . Quite well-defined Fig. 8
Cumulative radial distributions of BSSs (blue line)and REF stars (red line) for the five GCs in the LMC dis-cussed by Ferraro et al. (2019). The size of the area betweenthe two curves (shaded in grey) corresponds to the labelledvalue of A + . Clusters are ranked in terms of increasing valueof A + . trends are apparent in the figure, with r c decreasing,and c and ρ increasing with A + (i.e., with increasingdynamical age), confirming that star clusters tend todevelop small and dense cores as a consequence of theirlong-term internal dynamical evolution, in nice agree-ment with what expected from the theoretical frame-work. The next obvious step in this line of investigation wasto apply the same method to star clusters in othergalaxies, and the Large Magellanic Cloud (LMC) isindeed the closest, and hence the most natural, tar-get. Moreover the LMC is also the most intriguing one.In fact, there is a 30 year old dilemma related to theLMC clusters: the so-called “core size-age conundrum”(Mackey, & Gilmore, 2003). It can be summarized injust one question: why all the young star clusters in theLMC are compact, while the old ones show both smalland large core radii? . One of the most commonly ac-cepted solution to this dilemma was that all clustersin the LMC formed compact, then they suffered moreor less significant expansions of their core driven bypopulations of binary black holes (Mackey et al., 2008).However, studies of GC dynamical ageing in the MilkyWay show that compact cores tend to be developed astime passes (top panel in Fig. 7), which is just the op-posite of what suggested to occur in the LMC. Hence,deeper investigations appeared to be necessary to solve he stellar dynamical clock 9
Fig. 9
The application of the “dynamical clock” to extra-Galactic clusters: N relax − A + relation for the five LMC clus-ters discussed in Ferraro et al. (2019) (large red squares). Forthe sake of comparison, the sample of 48 Galactic GCs pre-viously investigated (Ferraro et al., 2018) is shown with greycircles. The LMC GCs ranked for increasing value of the dy-namical age ( A + ) are NGC 1841, Hodge 11, NGC 2257, NGC1466, and NGC 2210. The arrow indicates increasing dynam-ical age. the r c -age dilemma in this external galaxy. Li et al.(2019) applied the “dynamical clock” to measure thedynamical evolutionary stage of 7 intermediate-age (be-tween 700 Myr and 7 Gyr) clusters in the LMC, find-ing a low-level of dynamical evolution. On the otherhand, the dynamical ageing effects are expected to bemost evident in old star clusters, with chronologicalages comparable to those of the Milky Way systems(12-13 Gyr). Hence, Ferraro et al. (2019) selected five13 Gyr-old GCs in the LMC, showing different core sizes(ranging from 1 to 7 parsec), and measured their stageof internal dynamical evolution via the BSS sedimenta-tion level.The application of the dynamical clock in the LMCclusters is much more tricky than in our galaxy, be-cause field stars (not belonging to the clusters) inter-vening along the line of sight can strongly contaminatethe region of the CMD where BSSs are selected. Thesituation appeared particularly critical for two clusters(Hodge 11 and NGC 2210). However the use of appro-priate parallel HST observations in the cluster neigh-borhoods, allowed us to statistically decontaminate theBSS samples. Indeed, the LMC field stars turned outto be slightly brighter and redder than the bulk of gen-uine BSSs, thus affecting only the reddest portion of the Fig. 10
Top panel: the r c − A + relation for the five LMCclusters discussed in Ferraro et al. (2019) (large red squares),compared to that obtained for Galactic GCs (grey circles).The arrow indicates increasing dynamical age. Bottom panel: the relation between A + and the ratio between the core ra-dius and the effective radius ( r e ) for the five investigatedLMC clusters (red squares), compared to that obtained for 19GCs in the Milky Way (grey circles; r e is from Miocchi et al.,2013). population. Hence, the statistical decontamination wasquite effective and the results were surprisingly stable:over 5000 repeated random subtractions, the values of A + showed a very peaked distribution with a small dis-persion, thus certifying the reliability of the measure.The estimate of the BSS sedimentation level in allfive selected clusters confirms that these systems areat different stages of internal dynamical evolution (seeFig. 8). Indeed, A + shows a nice correlation with thenumber of relaxation times they suffered since forma-tion, and the impressive match with the trend definedby the Galactic population (grey circles) demonstratesthat the “dynamical clock” can be efficiently used inany stellar environment and is weakly affected by thetidal field of the host galaxy.The five surveyed LMC GCs also follow the tightcorrelation between dynamical age and core radius foundby Ferraro et al. (2018) for the Galactic systems (toppanel of Fig. 10), confirming that the long-term dynam-ical evolution tends to generate compact objects. Thisresult has been recently confirmed by Lanzoni et al.(2019) who re-computed all relevant structural param-eters of these five LMC clusters from newly determinedstar density profiles. In particular, they re-determinedthe core radius and the effective radius ( r e ), which is Fig. 11
The double BSS sequence in M30 (fromFerraro et al., 2009). The thick grey line is the 2 Gyr colli-sional isochrone from Sills et al. (2009). The black line is the12 Gyr-old isochrone, best reproducing the cluster MS-TO(from Cariulo et al., 2004). defined as the radius of the circle that, in projection,includes half the total counted stars. The ratio between r c and r e has been found to correlate with the dynam-ical age in a sample of 19 Galactic GCs, with systemscharacterized by large values of r c /r e being dynami-cally younger than those showing small values of thisratio (see Miocchi et al., 2013), as expected from dy-namical evolution driven by two-body relaxation. Thebottom panel of Figure 10 shows that the 5 LMC GCsnicely fit the trend defined by the Galactic population,and reveal that no dynamically-old system with largevalue of r c /r e exists. In turn, this indicates that theobserved properties of these systems are just consis-tent with their natural dynamical ageing, with no needof anomalous energy sources responsible for significantcore expansion (as, e.g., a population of binary blackholes; Mackey et al., 2008).These results confirm that the internal dynamicalevolution tends to produce clusters with more and morecompact cores, and demonstrate that the spread in coresize observed for the old LMC GCs is the natural con-sequence of these processes. On the other hand, theanalysis discussed in Ferraro et al. (2019) also demon-strates that only low-mass systems have been recently(in the last ∼ r c -age distribution of LMC GCs, which doesnot require the action of a population of black holes (assuggested by Mackey et al., 2008), and is just the nat-ural manifestation of the long-term internal dynamicalevolution (Ferraro et al., 2019). Thus, from one side,this deepens our understanding of the processes thatgovern the internal dynamical evolution of dense stel-lar systems in different environments, allowing a directconnection between the old GCs in the LMC and thosein our Galaxy. From the other side, these findings of-fer an alternative (and less exotic) reading of the long-standing LMC conundrum, with a strong impact on ourunderstanding of star cluster formation and their evo-lution over cosmic time. Moreover, as it often happensin science, while answering an old dilemma, this discov-ery poses a new, probably deeper, question that needsto be addressed: why did only relative low-mass clustersform in the last 3 Gyr in the LMC? The BSS observational features might also provide cru-cial information about the most spectacular dynamicalevent in cluster lifetime: core collapse (CC). This wasfirst realized by Ferraro et al. (2009) with the discoveryof two well-separated and almost parallel sequences ofBSSs in the post-core collapse (PCC) cluster M30 (Fig.11). This was the very first time that such a featurewas detected in any stellar system, opening the possibil-ity to disentangle between the two BSS formation pro-cesses. In fact, the comparison with evolutionary mod-els of BSSs formed by direct collisions of two MS stars(Sills et al., 2009) showed that the blue-BSS sequenceis well reproduced by a collisional isochrone with an ageof ∼ he stellar dynamical clock 11 Fig. 12
Left Panel:
The double BSS sequence in M15 (from Beccari et al., 2019). Two branches are apparent along the bluesequence: they are reproduced by a 2 Gyr-old and a 5.5 Gyr-old collisional isochrone, respectively.
Right Panel:
The evolutionin time of the 1% Lagrangian radius (top panel) and of the collisional parameter (bottom panel) in dynamical simulations.The epochs of core collapse and the main post-core collapse re-bounces are indicated with arrows. few Gyrs that are shorter for brighter (more massive)stars. Hence, the extension in magnitude of the bluesequence and the existence of a clear-cut gap betweenthe two chains suggest that these BSSs are nearly co-eval and have been generated by a recent and short-lived event. This latter characteristic is typical of CC(Djorgovski & King, 1986), during which the stellar col-lision rate is also known to significantly increase. On thebasis of these considerations, Ferraro et al. (2009) con-cluded that most BSSs along the blue sequence formedsimultaneously during the CC event, approximately 2Gyr ago.
This scenario has been fully confirmed byPortegies Zwart (2019), who presented detailed stellarmerger simulations for M30, concluding that the BSSdistribution along the blue sequence is well consistentwith a burst of formation started ∼ . ∼ . M15: another surprise –
By applying an advancedphotometric de-blending technique to a set of high-resolution images, Beccari et al. (2019) discovered aneven more peculiar double BSS sequence in the inner-most regions of the PCC cluster M15 (see Fig. 12). Alsoin this case the red BSS sequence cannot be reproducedby collisional isochrones of any age, but this time theblue BSS sequence showed a quite complex structure.In fact two distinct branches are visible: the first branchappears to be extremely narrow and it extends up to 2.5mag brighter than the cluster MS-TO point, while thesecond branch extends up to 1.5 mag from the MS-TO.The comparison with formation models of collisionalBSSs (Sills et al., 2009) indicates that both these pop-ulations formed through this channel, at two differentepochs: approximately 5.5 and 2 Gyr ago, respectively.The two branches could therefore be the observationalsignatures of two major collisional episodes suffered byM15, likely connected to the most advanced stages ofdynamical evolution of its core: the first one (possiblytracing the beginning of CC) occurred approximately5.5 Gyr ago, while the most recent one (possibly as-sociated with a core oscillation in the PCC evolution)dates back to 2 Gyr ago. This scenario is consistentwith the results of Monte Carlo simulations (Fig. 12),showing that the deep initial CC (clearly distinguish-able at t/t CC = 1) leads to the largest increase of thecollision rate (Γ), and it is followed by several distinctre-collapse episodes leading to secondary peaks of theΓ parameter. These results further provide strong evidence in sup-port to the tight connection between the BSS propertiesand the internal dynamical evolution of collisional stel-lar systems, also opening new perspectives in the studyof the most extreme phenomena, as the CC event andpost-CC evolution.
Acknowledgements
Funding
The research is funded by the project Dark-on-Lightgranted by MIUR through PRIN2017 contract (PI: Fer-raro).
Compliance with ethical standards
The manuscript complies to the Ethical Rules applica-ble for this journal.
Conflict of interest
The authors declare that they have no conflict of inter-est.
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