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2 O 02MNRAS.331. .2 45D Mon. Not. R. Astron. Soc. 331 45D .2 Mon. Not. R. Astron. Soc. 331, 245-258 (2002) Mass segregation in young compact star clusters in the Large Magellanic 02MNRAS.331. O Cloud - II. Mass functions 2 R. de Grijs,1* G. F. Gilmore,1 R. A. Johnson1,2 and A. D. Mackey1 ^Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 OHA 2European Southern Observatory, Casilla 19001, Santiago 19, Chile Accepted 2001 November 19. Received 2001 November 16; in original form 2001 November 5 ABSTRACT We review the complications involved in the conversion of stellar luminosities into masses and apply a range of mass-to-luminosity relations to our Hubble Space Telescope observa- tions of the young Large Magellanic Cloud (LMC) star clusters NGC 1805 and 1818. Both the radial dependence of the mass function (MF) and the dependence of the cluster core radii on mass indicate clear mass segregation in both clusters at radii of r ^ 20-30 arcsec, for masses in excess of ~ 1.6-2.5 M0. This result does not depend on the mass range used to fit the slopes or the metallicity assumed. It is clear that the cluster MFs, at any radius, are not simple power laws. The global and the annular MFs near the core radii appear to be characterized by similar slopes in the mass range (—0.15 ^ logra/M© ^ 0.85), and the MFs beyond r ^ 30 arcsec have significantly steeper slopes. We estimate that while the NGC 1818 cluster core is between ~5 and —30 crossing times old, the core of NGC 1805 is likely to be ^3-4 crossing times old. However, since strong mass segregation is observed out to —6/?core and —3Æcore in NGC 1805 and 1818, respectively, it is most likely that significant primordial mass segregation was present in both clusters, particularly in NGC 1805. Key words: stars: luminosity function, mass function - Magellanic Clouds - galaxies: star clusters. Consequently, the high-mass stars will gradually sink towards 1 PRIMORDIAL VERSUS DYNAMICAL MASS the bottom of the cluster potential, i.e. the cluster centre (cf. Spitzer SEGREGATION & Hart 1971), with the highest-mass stars and those closest to the The effects of mass segregation in star clusters, with the more cluster centre sinking the fastest, although this process is not massive stars being more centrally concentrated than the lower- negligible even at the edge of the cluster (e.g. Chernoff & mass stars, clearly complicates the interpretation of an observed Weinberg 1990; Hunter et al. 1995). This leads to a more centrally luminosity function (LF) at a given position within a star cluster in concentrated high-mass component compared with the lower-mass terms of its initial mass function (IMF). Without reliable stellar population, and thus to dynamical mass segregation. corrections for the effects of mass segregation, and hence for the The time-scale for the onset of significant dynamical mass structure and dynamical evolution of the cluster, it is impossible to segregation is comparable to the dynamical relaxation time of the obtain a realistic global cluster LF. cluster (Spitzer & Shull 1975; Inagaki & Saslaw 1985; Bonnell & Davies 1998; Elson et al. 1998). The characteristic time-scale of a cluster may be taken to be its half-mass (or median) relaxation 1.1 Dynamical evolution in star cluster cores time, i.e. the relaxation time at the mean density for the inner half Dynamical evolution in dense stellar systems, such as Galactic of the cluster mass for cluster stars with stellar velocity dispersions globular clusters (GCs) and rich Large Magellanic Cloud (LMC) characteristic for the cluster as a whole (Spitzer & Hart 1971; star clusters, drives the systems towards energy equipartition, in Lightman & Shapiro 1978; Meylan 1987; Malumuth & Heap 1994; which the lower-mass stars will attain higher velocities and Brandi et al. 1996), and can be written as (Meylan 1987) therefore occupy larger orbits. 1 3 U ^ ir,h = (8.92 X 10 ) (1) ^E-mail: [email protected] {m) log(0.4Mtot/(m» ' © 2002 RAS © Royal Astronomical Society • Provided by the NASA Astrophysics Data System 45D .2 246 R. de Grijs et al. where Æh is the half-mass (median) radius (in pc), Mtot is the total on time-scales longer than its characteristic relaxation time, on cluster mass and {m) is the typical mass of a cluster star (both shorter time-scales the observed stellar density distribution is likely masses in M©). to be the result of dynamical relaxation and of the way that star Although the half-mass relaxation time characterizes the formation has taken place. The process is, in fact, more compli- 02MNRAS.331. O dynamical evolution of a cluster as a whole, significant differences cated, as the high-mass stars evolve on the same time-scale as the 2 are expected locally within the cluster. From equation (1) it follows lower-mass stars (cf. Aarseth 1999). In order to understand the immediately that the relaxation time-scale will be shorter for process of mass segregation in a cluster in detail, we have to get an higher-mass stars (greater (m)) than for their lower-mass idea of the amount of ‘primordial’ mass segregation in the cluster. companions; numerical simulations of realistic clusters confirm The nature and degree of primordial mass segregation is this picture (e.g. Aarseth & Heggie 1998, see also Hunter et al. presumably determined by the properties of interactions of proto- 1995; Kontizas et al. 1998). From this argument it follows that stellar material during the star-forming episode in a cluster. In the dynamical mass segregation will also be most rapid where the local classic picture of star formation (Shu, Adams & Lizano 1987), relaxation time is shortest, i.e. near the cluster centre (cf. Fischer interactions are unimportant and mass segregation does not occur. et al. 1998; Hillenbrand & Hartmann 1998). The relaxation time in However, Fischer et al. (1998) conclude that their observations of the core can be written as (Meylan 1987) NGC 2157 seem to indicate the picture in which encounters at the early stages in the evolution enhance mass accretion of the cluster vÆ t^0 = (1.55X10') yr, (2) caused by the merging of protostellar clumps until the mass of (m0)log(0.5Mtot/(m)) these clumps exceeds the initial mass of a star to be formed. More x where Rcore is the cluster core radius (in pc), vs (kms ) is the massive stars are subject to more mergers and hence accrete even velocity scale and (m0) is the mean mass (in M0) of all particles in more mass (cf. Larson 1991; Bonnell et al. 2001a,b and references thermal equilibrium in the central parts. therein), and therefore dissipate more kinetic energy. In addition, Thus, significant mass segregation among the most massive stars they tend to form near the cluster centre, in the highest-density in the cluster core occurs on the local, central relaxation time-scale region, where the encounter rate is highest (cf. Larson 1991; (comparable to just a few crossing times, cf. Bonnell & Davies Bonnell et al. 1997, 200la,b; Bonnell, Bate & Zinnecker 1998; 1998), whereas a time-scale octr h is required to affect a large Bonnell & Davies 1998). This will lead to an observed position- fraction of the cluster mass. dependent MF containing more low-mass stars at larger radii It should be borne in mind, however, that even the concept of compared with the MF in the cluster centre (although low-mass a ‘local relaxation time’ is only a general approximation, as stars are still present at small radii). This scenario is fully dynamical evolution is a continuing process. The time-scale for a consistent with the idea that more massive stars tend to form in cluster to lose all traces of its initial conditions also depends on the clumps and lower-mass stars form throughout the cluster (Hunter smoothness of its gravitational potential, i.e. the number of stars et al. 1995; Brandi et al. 1996, and references therein). (Bonnell & Davies 1998: larger clusters are inherently smoother, Although it has been claimed that the observed mass segregation and therefore mass segregation is slower than in smaller clusters in R136, the central cluster in the large star-forming complex 30 with a grainier mass distribution), the degree of equipartition Doradus in the EMC, is probably at least partially primordial (e.g. reached (e.g. Hunter et al. 1995: full global, or even local, Malumuth & Heap 1994; Brandi et al. 1996), its age of —3-4Myr equipartition is never reached in a realistic star cluster, not even is sufficiently long for at least some dynamical mass segregation, in among the most massive species), and the slope of the MF (e.g. particular of the high-mass stars in the core (r iS 0.5 pc), to have Lightman & Shapiro 1978; Inagaki & Saslaw 1985; Pryor, Smith & taken place (cf. Malumuth & Heap 1994; Hunter et al. 1995; McClure 1986; Sosin 1997: flatter mass spectra will speed up the Brandi et al. 1996). On the other hand, the presence of the high- dynamical evolution, whereas steep mass spectra will tend to a mass Trapezium stars in the centre of the very young Orion Nebula higher degree of equipartition), among others. Cluster (ONC; ^IMyr, equivalent to -3-5 crossing times; In addition, as the more massive stars move inwards towards the Bonnell & Davies 1998) is probably to be largely caused by mass cluster centre, their dynamical evolution will speed up, and hence the segregation at birth (Bonnell & Davies 1998, based on numerical dynamical relaxation time-scale for a specific massive species is simulations; Hillenbrand & Hartmann 1998, based on the appear- hard to define properly.
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