arXiv:0904.0523v1 [astro-ph.GA] 3 Apr 2009 hnodr( pic- older this than ( eventu- support 2008), stars young Observations because 2006; stars. of al. ture Bastian field et & into majority Bastian Goodwin turning lead- 2007; the ally dynam- 1980; Kroupa where and (Hills & of expansion Baumgardt them that stel- unbound out cluster exposing via a become clusters stars to cluster eventually the stars. O ing stars brings the equilibrium, early-type massive of thousand expulsion from ical supernovae gas gas a contain and This ionisation of of also winds, expulsion wave- lar consist they the infrared clusters drive more, at the observable or em- If only 2003; clusters Lada lengths. often dense & un- (Lada in poorly 2002) clouds Pudritz still form molecular giant is stars within formation most bedded star because of phase derstood early very The Introduction 1. in(il 90 rua20;Gown&Bsin2006; expected. Bastian then & is Goodwin 2008) disper- 2005; Bastian velocity Kroupa & dissolution super-virial Gieles 1980; rapid their (Hills a of density expulsion, because sion entire gas cluster this the the over of of result formed wide assump- a also The general As are the range. determined. clusters to poorly lead that has are tion containing densities stars clusters cluster dozen of of variety density few and a size only the since included, rmteltrtr ore r loepand.Hr only Here M 1000 explained). than also radii massive are and more sources masses clusters 2008), ma- the literature al. online of the et the Borissova methods from in 2007, determination al. 1 the et Table where Wolff in 2008, given Figer is terial: properties cluster of esta .1t eea 10 several to 0.01 than less special planetary of when time-span period a the developing. is precisely are It is systems here. it address first because the we interest over that clusters exposed Myr of been 20 evolution far this so is has itself It expansion lacking. cluster the of picture titative srnm Astrophysics & Astronomy coe 6 2018 16, October h bevddniiso on trcutr ag from range clusters star young of densities observed The .Pyiaice nttt nvriyo oon,Z¨ulpi Cologne, of University Institut, Physikalisches I. e words. Key i This plane. age. density-radius the its in tracks pre-defined along ilo tr ihselrdniisrnigfo .1t se to 0.01 from ranging densities stellar with stars million ocutrsz n density. Conclusions. and size cluster to ihn2 y.Tegnrlasmto sta lsesaebo are clusters that Results. is assumption general Methods. The Myr. 20 within Aims. otsasd o omi slto u spr facutrcom cluster a of part as but isolation in form not do stars Most ∼ tdmntae ht nfc,cutrdsa omto wor formation star clustered fact, in that, demonstrates It 0Mr lses u ytmtcadquan- and systematic a but clusters, Myr) 20 e nlsso lse bevtosi presented. is observations cluster of analysis new A clusters h bevdmliueo lse este ipyresults simply densities cluster of multitude observed The ∼ y)cutr r sal smaller usually are clusters Myr) 1 nvraiyo on lse sequences cluster young of Universality 5 M aucitn.ms6 no. manuscript ⊙ pc − ⊙ 3 msiecutr)are clusters) (massive sFg hw alist (a shows 1 Fig. as .Pfalzner S. ABSTRACT hrSr 7 03 oon,Germany Cologne, 50937 77, Str. cher pista h lse iecnatal eue odetermin to used be actually can size cluster the that mplies ea 10 veral es(h emnlg ilb xlie ae)ec start each later) clus- explained leaky of be and classes will starburst two terminology the called 2, following (the Fig. the ters in in seen - evolu- be clusters density- cluster can as bi-modal the Moreover, a in tion. suggesting tracks strongly that well-defined plane, is two radius shows unambiguously along plot evolve existing this these clusters what from groups, Apart remark- two the Fig.2. in to in leads structure material) simple online ably the in given are points ieetwyb ltigisedtedniya function a a in as 1 radius density Fig. cluster the in the instead as of plotting clusters by same way the different at closely looking When Results 2. a for well as material bars. online error in the refer- 1 of and Table discussion (2008) See al. therein. et Borissova ences and (2007), Wolff (2008), asv hn10 than massive 1. Fig. -3 nmr rls vrti niedniyrange. density entire this over less or more rn Cluster density [Msun pc ] 10000 1e+06 1e+05 1000 0.01 100 0.1 sudrsrrsnl ih osrit ihrespect with constraints tight surprisingly under ks 10 5 1 lse est safnto faefrcutr more clusters for age of function a as density Cluster M rsn nweebtenafwdznt several to dozen few a between anywhere prising rmsasoso w eune vligi time in evolving sequences two of snapshots from ⊙ 2 1 pc Trumpler 14 − r bNGC7380 Ori Ib NGC 3603 3 h aoiyo hs lsesdissolve clusters these of majority The . Arches 3 NGC 2244 Westerlund 2 M ⊙ R Cyg OB2 IC 1805 h auswr ae rmFiger from taken were values The . Cluster age[Myr] dfiiin o h niiuldata individual the for (definitions DBS2003 NGC 6611 Ori Ic NGC 6823 U Sco Westerlund 1 5 CI 1806-20 Quintuplet Lower Cen_Crux chi Per 101010 h Per RSGC1

c Ori Ia U Cen-Lup S 2018 ESO RSGC2 15 I Lac 20 e 2 S. Pfalzner: Universality of young cluster sequences from unique points in the mass-radius plane and develop at approximately the same speed along these two tracks. All clusters shown originate from one of these birth points 1e+06 -3 4 15000 M pc /R in mass and radius. Arches STAR BURST CLUSTERS sun -3 3 5000 M pc /R This is not so surprising for starburst clusters since their NGC 3606 sun ] Trumpler Westerlund 1 > 10 Myr -3 relatively similar mass has already led to speculations that 10000 Westerlund 2 RSGC1 4Myr < age < 10Myr pc < 4Myr they might have a common origin. For leaky clusters, how- DBS2003 sun Quintuplet Galactic center cluster ever, the prevailing view is that young clusters form more or RSGC2 h Per chi Per less at arbitrary density and somehow dissolve afterwards 100 Cyg OB2 on timescales of 20 Myrs. However, the new representa- NGC 6611 NGC 2244 IC 1805 tion of already known cluster parameters in Fig. 2 shows NGC 7380 Ori Ib the common history of these clusters for the first time. The 1 LEAKY CLUSTERS Ori Ic single track and sequential nature of the data points means Cluster density [M U Sco Ori Ia Lower Cen Crux that, contrary to the usual viewpoint, these clusters also Upper Cen Lup start out with the same mass density and radial extent I Lac 0.01 (and therefore mass) and all expand in the same way. 1 10 Here a word about determinating of radii and densities Cluster radius [pc] in the different sources is nessesary. All starburst cluster data, apart from that for DBS 2003, were taken from Figer Fig. 2. Cluster density as a function of cluster size for clus- (2008). The data for DBS 2003 were taken from Borissova 3 ters more massive than 10 M⊙. The values were taken from et al. (2008). In Figer (2008) the radius gives the average Figer (2008), Wolff et al. (2007) and Borissova et al. (2008) projected separation from the centroid position. The total and references therein. See although Table 1 in online ma- cluster mass is given by extrapolating down to a lower mass terial. cut-off of 1 solar mass, assuming a Salpeter initial mass function and an upper mass cut-off of 120 solar masses (ex- ceptions from this method are given in Figer 2008). The to- It is thought that clusters and associations are formed tal mass of the cluster was determined by assuming that the with mass functions that are powerlaws with index -2. stars in the mass range 6-12 M⊙ constitute 5.5% of the total However, the results described here imply that the leaky mass of the complete population of stars spanning the range clusters form in a narrow mass range (3.6 < log Mc < 4.4) 0.1-100 M⊙. They compared their values with other mass- and develop quickly within 20 Myrs to lower masses (3.3 determining methods by Slesnick et al. (2002) and Weidner < log Mc < 3.6). The small sample size currently does not & Kroupa (2006) and found good agreement. In Borissova allow further constriction of the primordial mass function et al. the radius was defined by distance where the density for loss clusters. profile exceeds twice the standard deviation of the surface The situation is simpler for the starburst clusters. They density in the surrounding field. All values for the leaky all appear to be born with a cluster density of at least 105 −3 clusters were taken from Wolff et al. (2007). There the ra- M⊙pc (red data points in the top left corner of Fig. 2) dius was determined as the median distance in degrees of and then simply diffuse without further mass loss, i.e. a the B stars in the sample from the centre of the cluster, so R−3dependence. In fact the expansion proceeds more or that, although not all cluster sizes were determined exactly less linearly in time, i.e. as R ∼ tc (see Fig. 3). Having in the same way, for each subset - the starburst clusters established a common history, one can easily deduce an ex- and the leaky clusters - the cluster radii were determined pansion velocity of 0.1-0.2 pc/Myr. From this expansion fairly consistently. The density was in all cases defined as velocity, it should be possible to determine the star forma- 3 ρ = 3Mc/4πR , so it is extremely unlikely that the result tion efficiency through numerical simulations in the future. is an artefact of the applied method. A possible reason for the expansion velocity in star-burst Quantitative analysis of Fig.2 shows that, as the leaky clusters to be lower than in leaky clusters is that the poten- clusters expand, they do not simply diffuse (which would tial well is too deep for the ionised gas to leave the cluster give an R−3-dependence), but the cluster density decreases quickly (Kroupa 2008). This means a much higher star for- as R−4. This means that the cluster loses mass via various mation efficiency for starburst clusters than for the massive processes such as outgassing, stellar mass loss, tidal evapo- clusters. ration, and escapers created through three-body encounters Fig. 2 shows an additional feature, namely the location close to its centre. The relative importance of these mass- of the Galactic center clustre. Since the Galactic centre har- loss processes will need clarification in the future. As a di- bours a massive black hole, one would expect its dynamics rect consequence of the common history of these clusters, to differ considerably from starburst clusters. However, it one can now determine the cluster size as a function of clus- lies directly on the starburst cluster track close to the data 0.6−0.7 ter age and finds a tc -dependence. As demonstrated point of Arches. Given that the Galactic centre cluster is in Fig. 3, the expansion velocity is ∼ 2pc/Myr in the early older than the Arches cluster, it follows that it must have phases and drops to ∼1pc/Myr at cluster ages ∼20 Myr. started out at a higher initial mass and/or expanded more In Fig.3 it is shown that comparing simulations of clusters slowly. expanding due to gas expulsion showing similar expansion If the above systematics is true, then no clusters should velocity (Olczak 2008) indicates that ∼ 75% of the gas is exist with R> 2 pc ages ages < 4Myr that possess masses 4 expelled, though more detailed studies are required to con- higher than several 10 M⊙. An interesting consequence of firm this. However, this would already suggest that all leaky the sequential nature of cluster development is that the ra- clusters shown in Fig.2 formed with the approximately the dius of the cluster can actually be used to determine its same star formation efficiency of ∼ 25%. age. Cluster age determination is notoriously problematic, S. Pfalzner: Universality of young cluster sequences 3

striction that at least 200 cluster stars were detected. The embedded clusters are not located on the main evolution- ary sequence but form their own side-arm off the leaky clus- ter sequence below its extension to younger ages. It joins up when the embedded clusters become exposed after hav- 10 ing reached a size of ∼ 2-4 pc at an age of > 1 Myr. A further argument for the sequential nature of the cluster development is that the ONC is likely to be expanding (Kroupa et al. 2001), hence evolving along a time-density track. In other words, a relatively sparse cluster like Upper 1 Cen Lup must once have been in a state similar to the Cluster size [pc] starburst clusters Orion Nebular Cluster now the densest nearby cluster (see leaky clusters 0.7 Fig. 4). Note as well that Ori Ib, Ori Ic, and Ori Ia form a 3.6*t c temporal sequence of once leaky clusters with initial densi- 0.16*tc simulation result ties as high as the ONC. The initial stellar mass content of 1 10 leaky clusters at the end of the embedded phase is at least cluster age [Myr] 3500 M⊙. with a radius exceeding ∼ 4pc, One would expect a similar side-arm for the starburst Fig. 3. Cluster size as a function of cluster age for the same clusters, but so far no such embedded starburst clusters clusters in Fig. 2. The squares correspond to the leaky clus- have been observed. However, this is not surprising since ters and the circles to the starburst clusters. The dotted line they would be very small (R < 0.1 pc) and located either indicates simulation results by Olczak (2009) for an ONC- close to the Galactic centre (at a distance of ∼ 8kpc) or like cluster with 75% gas expulsion. The drawn and the inside spiral arms within the Galactic plane. In addition, dashed lines are not fits but just there to guide the eye. starburst clusters are intrinsically rare, and the embedded phase very short, so not many are expected to be found.

1e+06 3. Discussion and conclusions ] -3 10000 The above results imply that star formation occurs only

pc under an extremely limited set of conditions, and may

sun NGC 2024 02232+6138 therefore require a fundamental revision of its theories in IC348 Gem4 our Galaxy, possibly including our own solar system. The 100 02575+6017 MonR2 “leaky clusters” could also be known as “mass-loss clus- ONC embedded clusters ters”, as this is what distinguishes them from starburst > 10 Myr 4Myr < age < 10Myr clusters.”. For this leaky cluster density regime, recent sim- 1 < 4Myr

Cluster density [M -3 4 ulations (K¨upper et al. 2008) have found that the dynamics 15000 Msun pc /R -3 3 of embedded clusters show a strong correlation between the 5000 Msun pc /R Galactic center cluster kinetic energy of the cluster stars and that of stars leaving 0.01 1 10 the cluster, leading to a common sequence. This prediction Cluster radius [pc] might well be linked to the results described herein. The embedded cluster side-arm implies that many of Fig. 4. Same as Fig. 2 but here the cluster density of em- the older clusters (like Ori Ia-c, Upper Sco, I Lac, etc.) bedded clusters with more than observed 200 members are must have gone through a phase like the ONC is in to- also shown. The values were taken from Lada & Lada 2003. day. Thus the ONC can serve as model cluster for both the earlier phase of older leaky clusters and the future of the younger embedded clusters. Results for the ONC there- especially for very young clusters, where the uncertainty of fore serve as a template for a multitude of other clusters. the tracks of pre-main sequence star development can lead For example, observations and theory indicate that the cen- to very different age estimates. The density-radius relation tral density in the ONC is so high that encounters between defined here might be an easier and potentially more accu- young disc-surrounded stars might affect the protoplane- rate method for cluster age determination. Clusters with a tary discs (Herbig & Terndrup 1986; Pfalzner et al. 2006) radius between 2-4 pc pose a special problem. Only the dis- and changes in the disc properties are likely to have direct tinction between very young leaky clusters (< 4Myr) and consequences on the ongoing planet formation process. old starburst clusters (> 10 Myr) will require additional Finally the proposed reordering immediately raises the information due to their similar radii. However, as one can question of the origin of these two distinct cluster group- expect that in older starburst clusters some red supergiants ings. The critical parameter is possibly the higher density, are present, telling them apart is probably not too difficult. but could equally be the density-temperature ratio or dif- How do embedded clusters fit into this picture? Fig. 4 ferent types of turbulence, etc. The obvious task for the again shows the cluster density as a function of size but also near future is to understand why these specific conditions includes embedded clusters. The embedded clusters were are favoured in our Galaxy and whether the same applies selected from the data by Lada & Lada (2003) with the re- in other spiral galaxies, too. 4 S. Pfalzner: Universality of young cluster sequences

References Baumgardt & Kroupa 2007, MNRAS, 380, 1589. Bastian et al. 2008, MNRAS, 389, 223. Borissova, J., Ivanov, V.D., Hanson, M.M., Georgiev, L., Minniti, D., Kurtev, R., Geisler, D. 2008, A&A, 488, 151. de Grijs, R., Lee, J.T., Mora Herrera, M. C., Fritze-v. Alvensleben, U., Anders, P., 2003, New Astronomy, 8, 155. Figer, D.F., 2008, ”Massive Stars as Cosmic Engines”, Proc. of Intern. Astron. Union, IAU Symposium, 250, 247. Gieles, M., Bastian, N., 2008, A&A 482, 165. Goodwin, S. P., Bastian, N., 2006, MNRAS 373, 752. Herbig, G. H., Terndrup, D. M., 1986, ApJ, 307, 609. Hills, J.G., 1980, ApJ 235, 987 Kroupa, P., 2005, Proc. of ”The Three-Dimensional Universe with Gaia” (ESA SP-576)., Paris-Meudon, ed.: C. Turon, K.S. O’Flaherty, M.A.C. Perryman, p.629 Kroupa, P., Aarseth, S., Hurley, 2001, MNRAS, 321, 699. Kroupa, P., 2008, in Proc. of “Mass Loss from Stars and the Evoltution of Stellar Clusters”, ASP Conf. Ser. 388, p. 271, eds. A. de Koter, L. Smith, R. Waters, Astron. Soc. Pac., San Francisco. K¨upper, A.H., Kroupa, P., Baumgardt, H., 2008, MNRAS 389, 889. Lada, C.J., Lada, E.A., Annu.Rev. Astron. Astrophysics, 2003, 41, 57. Olczak, C., private communication Pfalzner, S., Olczak, C., Eckart, A., 2006, A&A, 454, 811. Pudritz, R.E., 2002, Science, 295, 68 Slesnick et al. 2002, ApJ, 576, 880 Wolff, S. C., Strom, S. E., Dror, D., Lanz, L., Venn, K., 2007, Astron. J., 132, 749. Weidner & Kroupa, 2006, MNRAS, 365, 1333 S. Pfalzner: Universality of young cluster sequences 5

Identification distance age log(Mc) size log(ρc) −3 [pc] [Myr] [M⊙] [pc] [M⊙pc ] 1 +1 +0.03 +1 Arches 8 −1 2-2.5 4.3 0.19 −0.03 5.6 −1 1 +1 +0.04 +0.1 NGC 3603 7.6−1 2-2.5 4.1 0.3 −0.04 5.0 −0.1 1 +0.6 +0.1 +0.05 Trumpler 14 2.8−0.2 ¡2 4.0 0.5 −0.04 4.3 −0.3 1 +0.17 +0.05 +0.06 Westerlund 1 3.55−0.01 4-6 4.7 1.0 4.1 −0.03 Westerlund 21 2.8 1.5-2.5 4.0 0.8 3.7 1 +1.9 +0.04 +0.1 RSGC 1 5.83−0.78 10-14 4.5 1.3 −0.04 3.5 −0.3 1 +1 +0.13 +0.7 Quintuplet 8−1 4-6 4.3 1.0 3.7 −0.2 2 +1.2 +0.18 +0.5 DBS2003 7.9−1 2-5 3.8 1.2 −0.5 3.05 −0.3 1 +1.91 +0.77 +0.05 RSGC 2 5.83−0.78 14-21 4.6 2.7 −0.77 2.7 −0.03 3 +0.1 +0.1 +0.5 χ Per 2.34−0.5 12.8 4.1 2.5 −0.7 2.61 −0.05 3 +0.1 +0.1 +0.5 h Per 2.34−0.5 12.8 4.2 2.1 −0.7 2.25 −0.05 3 +0.2 +0.06 +0.02 CYg OB2 1.74−0.5 1-4 4.4 5.2 −2.5 1.61 0.4 3 +0.01 +0.1 +0.22 NGC 6611 1.995−0.25 1-5 4.4 5.9 −0.8 1.45 0.11 3 +0.33 NGC 2244 1.88−0.4 1-3 3.9 5.6 −1.2 1.03 3 +0.1 +0.3 +0.03 IC 1805 2.34−0.1 1-3 4.2 7.1 −0.3 0.98 3 +0.2 +0.3 +0.11 Ori Ib 0.363−0.2 1.7 3.6 6.3 −0.3 0.55 −0.02 NGC 73803 3.73 2 3.8 6.5 0.72 3 +0.2 +0.6 +0.12 Ori Ic 0.398−0.2 4.6 3.8 12.5 −0.6 -0.15 −0.01 3 +0.2 +0.9 +0.05 Ori Ia 0.380−0.2 11.4 3.7 16.6 −0.9 -0.54 −0.09 3 +0.003 +0.2 +0.06 U Sco 0.144−0.003 5-6 3.5 14.2 −0.2 -0.59 −0.01 3 +0.002 +0.3 +0.05 Lower Cen-Crux 0.116−0.002 11-12 3.3 15.0 −0.3 -0.85 −0.01 3 +0.002 +0.4 +0.01 Upper Cen-Lup2 0.142−0.002 14-15 3.6 22.1 −0.4 -1.05 −0.01 3 +0.06 +3 +0.2 I Lac 2 0.368 12-16 3.4 20.7 −3 -1.15 −0.17 3 1 Table 1. Properties of clusters and associations more massive than 10 M⊙ in the Galaxy (Figer 2008, and references therein), 2 (Borissova et al. 2008), 3(Wolff et al. 2007, and references therein). The errors in age result from (a) their deduction from theoretical pre-main-sequence star tracks for young stars, which show large discrepancies; (b) the age of the cluster is found by averaging over the so deduced ages of the single stars; and (c) the age determination depends on the knowledge of the distance to the cluster - a parameter that is often poorly constrained. In cases where there is no error bar this does not mean that the age is accurately known, but rather that the authors did not give any error value. Usually there are no error values quoted for the mass or the density of the cluster, nor is the cluster size consistently defined for the different clusters. An error of a factor of 2 is probably realistic and can be expected to be even larger for the more distant clusters, so for this and the following figures one should always keep in mind that the errors of these observed values are rather large.

Identification distances Mc size log(ρc) −3 [pc] [M⊙] [pc] [M⊙pc ] 02232 + 61381 2.4 130 0.91 2.23 02575 + 60171 2.4 150 1 2.17 IC 3481 0.32 160 1 2.20 ONC 1 0.45 1100 3.8 1.30 NGC 2024 1 0.4 180 0.88 2.42 MonR2 1 0.8 340 1.85 1.72 Table 2. Properties of embedded clusters containing more than 200 observed stars. 1 (Lada & Lada 2003, and references therein)

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