Reconstructing the Arches cluster – I. Constraining the initial conditions

S. Harfst 1 2 S. Portegies Zwart 2 A. Stolte 0 0 1. Physikalisches Institut, University Cologne , Zu lpicher Str. 77, 50937 Ko ln , Germany 1 Department of Astronomy & Astrophysics, Technical University of Berlin , 10623 Berlin , Germany 2 Leiden Observatory, Leiden University , PO Box 9513, 2300 RA Leiden , the Netherlands A B S T R A C T We have performed a series of N-body simulations to model the Arches cluster. Our aim is to find the best-fitting model for the Arches cluster by comparing our simulations with observational data and to constrain the parameters for the initial conditions of the cluster. By neglecting the Galactic potential and stellar evolution, we are able to efficiently search through a large parameter space to determine, for example, the initial mass function (IMF), size and mass of the cluster. We find that the cluster's observed present-day mass function can be well explained with an initial Salpeter IMF. The lower mass limit of the IMF cannot be constrained well from our models. In our best models, the initial total mass down to a mass limit of 0.5 M is (4.9 0.8) 104 M . The initial virial radius of the cluster is 0.77 0.12 pc. A concentration parameter of the initial King model W0 = 3 gives the best results. 1 I N T R O D U C T I O N The Arches cluster is one of only a few young and massive starburst clusters in the Milky Way. Its location at a projected distance of less than 30 pc from the Galactic Centre and an age of only 2.5 Myr (Figer et al. 2002; Najarro et al. 2004) make this cluster a unique object for studying star formation and dynamical processes in the centre of galaxies (Portegies Zwart, McMillan & Gieles 2010). The observed present-day mass of the Arches cluster within R = 0.4 pc has been estimated with (12) 104 M (Figer et al. 1999b; Espinoza, Selman & Melnick 2009). With this mass, a cluster will not survive long in the Galactic Centre environment and evaporate on a time-scale maybe as fast as 10 Myr (Kim, Morris & Lee 1999; Portegies Zwart et al. 2002). The initial mass of the cluster has been determined from N-body simulations; however, different results have been obtained by different authors: Kim et al. (2000) found that their best model for the Arches cluster had a total mass of about 2 104 M ; Portegies Zwart et al. (2002), on the other hand, came to the conclusion that the cluster was initially more massive than 4 104 M . The initial mass function (IMF), a key aspect of star formation, seems to be uniform throughout the Universe (Bastian, Covey & Meyer 2010). This universal IMF can be described by the power law found by Salpeter (1955) for stars in the solar neighbourhood and is valid from 0.5 M to the highest masses. Below 0.5 M , the IMF is significantly flattened (e.g. Kroupa 2002). Determining the IMF of young clusters from observations is not a straightforward process. Uncertainties can arise from the measured luminosities, the estimated age of the cluster, the completeness of the observed sample and the stellar evolution models. In addition, the non-linear dynamical evolution of the cluster has to be taken into account as shown in Fig. 1: as the star cluster evolves, more massive stars (star symbols) will move towards the cluster centre and low-mass stars (points) will move in the opposite direction (indicated by the arrows in the left-hand image). If the detection of cluster members is radially limited (dashed circle), it will result in an observed mass function (MF) in the mass-segregated cluster (right-hand image), which is different from the IMF. This effect is visualized in Fig. 1 by the ratio of low- to high-mass stars inside the dashed circles, before and after mass segregation. In case of the Arches cluster, observations have revealed that the slope of the observed MF for R 0.4 pc is significantly flattened with 0.9 0.15 with respect to the standard Salpeter IMF ( = 1.35) (Figer et al. 1999b; Stolte et al. 2002, 2005) and therefore the Arches cluster has been regarded as a possible case against the universality of the IMF. More recently, however, Espinoza et al. (2009) derived a slope of = 1.1 0.2 in R < 0.4 pc and concluded that a standard Salpeter IMF cannot be ruled out for the Arches cluster. In addition to the radial variation in AV , these authors also accounted for differential extinction variations, which can severely affect the incompleteness and may have biased the earlier results. Large uncertainties in the slope still remain, revealing the necessity to compare the observed cluster MF with simulations. In addition to the flattened slope, there has been some debate whether the IMF of the Arches cluster is truncated at the low-mass end as the result of the extreme conditions at the Galactic Centre, where the cluster has formed. Possible evidence for a turnover in the present-day MF was reported by Stolte et al. (2005), who determined a low- and intermediate-mass depleted MF in the cluster core (R < 0.2 pc) with a turnover at 67 M . This truncation in the MF was not seen by Kim et al. (2006). They only found a local bump in the MF at 6 M . Even if the MF is truncated at the low-mass end, it remains unclear whether this would be the result of a truncated IMF or a dynamical effect, such as tidal stripping of low-mass stars. With the aim to account for tidal stripping and mass-loss in the Galactic Centre potential, several studies have been done to determine the global IMF of the Arches cluster using numerical simulations, again coming to different conclusions: the model favoured by Kim et al. (2000) started with a flat IMF with a slope of = 0.75 close to the observed one. Portegies Zwart et al. (2002) found that the observed MF is the result of the dynamical evolution of the cluster and observational selection effects (namely radius-limited selection). They argued that the observed flat MF in the cluster core is therefore consistent with a global Salpeter IMF. The same effect is seen by Kim et al. (2006); however, they suggested that the slope of the IMF was 1 to 1.1, slightly shallower than Salpeter. The Arches cluster also exhibits other clear signs of mass segregation. The slope of the observed MF for stars in different annuli changes with distance from the cluster centre. Towards the centre, the slope becomes shallower and farther out, the slope is closer to Salpeter (Stolte et al. 2005; Kim et al. 2006). Most recently, Espinoza et al. (2009) have reported = 0.9 for R < 0.2 pc and = 1.3 in the 0.20.4 pc annulus. Portegies Zwart et al. (2007) have found the same characteristics in numerical N-body models and concluded that the central flattening is the result of mass segregation. Furthermore, they claimed that the MF near the centre of the Arches cluster can be best described by a broken power law, with a turning point at 56 M (at the position of the bump reported by Kim et al. 2006). Based on these findings, they determined that the Arches cluster is about half-way to core co (...truncated)