Mass segregation and fractal substructure in young massive clusters - I. The McLuster code and method calibration

Abstract

By analysing models of the young massive cluster R136 in 30 Doradus, set‐up using the herewith introduced and publicly made available code McLuster, we investigate and compare different methods for detecting and quantifying mass segregation and substructure in non‐seeing limited N‐body data. For this purpose we generate star cluster models with different degrees of mass segregation and fractal substructure and analyse them. We quantify mass segregation by measuring, from the projected 2D model data, the mass function slope in radial annuli, by looking for colour gradients in radial colour profiles, by measuring Allison’s Λ parameter and by determining the local stellar surface density around each star. We find that these methods for quantifying mass segregation often produce ambiguous results. Most reliable for detecting mass segregation is the mass function slope method, whereas the colour‐gradient method is the least practical in an R136‐like configuration. The other two methods are more sensitive to low degrees of mass segregation but are computationally much more demanding. We also discuss the effect of binaries on these measures. Moreover, we quantify substructure by looking at the projected radial stellar density profile, by comparing projected azimuthal stellar density profiles and by determining Cartwright & Whitworth’s Q parameter. We find that only high degrees of substructure affect the projected radial density profile, whereas the projected azimuthal density profile is very sensitive to substructure. The Q parameter is also sensitive to substructure but its absolute value shows a dependence on the radial density gradient of the cluster and is strongly influenced by binaries. Thus, in terms of applicability and comparability for large sets of N‐body data, the mass function slope method and the azimuthal density profile method seem to be the best choices for quantifying the degree of mass segregation and substructure, respectively. The other methods are computationally too demanding to be practically feasible for large data sets.

Hierarchical formation of Westerlund 1: a collapsing cluster with no primordial mass segregation?

“…The median density of the chosen subset of stars is then compared to the median density for the entire distribution (Küpper et al 2011;Parker et al 2014) to obtain the local surface density ratio, ΣLDR:…”

Radial variation in the stellar mass functions of star clusters

“…Leigh et al (2013), Webb & Leigh (2015) 2 Leigh et al (2013), Webb & Leigh (2015) To explore how other initial parameters may affect the evolution of α(r), we have run simulations of the standard tidally filling and under-filling cases but with a range of IMFs, initial degrees of mass segregation (S), initial binary fractions ( N B,i Ntot ), masses, orbits, and black hole retention fractions ( N BH,retained N BH,created ). (Küpper et al 2011) to simulate clusters with power law IMFs (α0 = 1.85, α0 = 2.35), a Kroupa (2001) IMF (K01), and a broken power law (BPL) IMF (α0 = −0.9 for 0.1 < m < 0.5M⊙ and α0 = −2.3 for 0.5 m 50M⊙). McLuster was also used to generate primordially mass segregated clusters, which were assumed to have a Kroupa (2001) IMF so they could be compared to the aforementioned K01 model.…”

Globular clusters with Gaia

“…The simulated clusters were computed with the McLuster code 12 (Küpper et al 2011), that is designed to produce initial conditions for N-body simulations. We used the code version (mcluster sse) which implements the stellar evolution recipes by Hurley, Pols, & Tout (2000).…”