We examine the performance of four different methods which are used to measure mass segregation in star-forming regions: the radial variation of the mass function $\mathcal{M}_{\rm MF}$; the minimum spanning tree-based $Λ_{\rm MSR}$ method; the local surface density $Σ_{\rm LDR}$ method; and the $Ω_{\rm GSR}$ technique, which isolates groups of stars and determines whether the most massive star in each group is more centrally concentrated than the average star. All four methods have been proposed in the literature as techniques for quantifying mass segregation, yet they routinely produce contradictory results as they do not all measure the same thing. We apply each method to synthetic star-forming regions to determine when and why they have shortcomings. When a star-forming region is smooth and centrally concentrated, all four methods correctly identify mass segregation when it is present. However, if the region is spatially substructured, the $Ω_{\rm GSR}$ method fails because it arbitrarily defines groups in the hierarchical distribution, and usually discards positional information for many of the most massive stars in the region. We also show that the $Λ_{\rm MSR}$ and $Σ_{\rm LDR}$ methods can sometimes produce apparently contradictory results, because they use different definitions of mass segregation. We conclude that only $Λ_{\rm MSR}$ measures mass segregation in the classical sense (without the need for defining the centre of the region), although $Σ_{\rm LDR}$ does place limits on the amount of previous dynamical evolution in a star-forming region.
We compare the existent methods including the minimum spanning tree based method and the local stellar density based method, in measuring mass segregation of star clusters. We find that the minimum spanning tree method reflects more the compactness, which represents the global spatial distribution of massive stars, while the local stellar density method reflects more the crowdedness, which provides the local gravitational potential information. It is suggested to measure the local and the global mass segregation simultaneously. We also develop a hybrid method that takes both aspects into accou…
We take the end result of smoothed particle hydrodynamics (SPH) simulations of star formation which include feedback from photoionisation and stellar winds and evolve them for a further 10Myr using $N$-body simulations. We compare the evolution of each simulation to a control run without feedback, and to a run with photoionisation feedback only. In common with previous work, we find that the presence of feedback prevents the runaway growth of massive stars, and the resulting star-forming regions are less dense, and preserve their initial substructure for longer. The addition of stellar winds t…
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 prof…
We quantify the structure of a very large number of Galactic open clusters and look for evidence of mass segregation for the most massive stars in the clusters. We characterise the structure and mass segregation ratios of 1276 clusters in the Milky Way Stellar Cluster (MWSC) catalogue containing each at least 40 stars and that are located at a distance of up to $\approx 2$ kpc from the Sun. We use an approach based on the calculation of the minimum spanning tree of the clusters, and for each one of them, we calculate the structure parameter \Q\ and the mass segregation ratio $Λ_{\rm MSR}$. Our…
Recent analyses of mass segregation diagnostics in star forming regions invite a comparison with the output of hydrodynamic simulations of star formation. In this work we investigate the state of mass segregation of 'stars' (i.e. sink particles in the simulations) in the case of hydrodynamical simulations which omit feedback. We first discuss methods to quantify mass segregation in substructured regions, either based on the minimum spanning tree (Allison's Lambda), or through analysis of correlations between stellar mass and local stellar surface number densities. We find that the presence of …
We make use of $N$-body simulations to determine the relationship between two observable parameters that are used to quantify mass segregation and energy equipartition in star clusters. Mass segregation can be quantified by measuring how the slope of a cluster's stellar mass function $α$ changes with clustercentric distance r, and then calculating $δ_α= \frac{d α(r)}{d ln(r/r_m)}$ where $r_m$ is the cluster's half-mass radius. The degree of energy equipartition in a cluster is quantified by $η$, which is a measure of how stellar velocity dispersion $σ$ depends on stellar mass m via $σ(m) \prop…
[abridged] Theoretical investigations have suggested the presence of Intermediate Mass Black Holes (IMBHs, with masses in the 100-10000 Msun range) in the cores of some Globular Clusters (GCs). In this paper we present the first application of a new technique to determine the presence or absence of a central IMBH in globular clusters that have reached energy equipartition via two-body relaxation. The method is based on the measurement of the radial profile for the average mass of stars in the system, using the fact that a quenching of mass segregation is expected when an IMBH is present. Here …
Investigations of mass segregation are of vital interest for the understanding of the formation and dynamical evolution of stellar systems on a wide range of spatial scales. Our method is based on the minimum spanning tree (MST) that serves as a geometry-independent measure of concentration. Compared to previous such approaches we obtain a significant refinement by using the geometrical mean as an intermediate-pass. It allows the detection of mass segregation with much higher confidence and for much lower degrees of mass segregation than other approaches. The method shows in particular very cl…
Massive stellar clusters are the best available laboratories to study the mass function of stars. Based on NTT/SofI near-infrared photometry, we have investigated the properties of the massive young cluster Westerlund 1. From comparison with stellar models, we derived an extinction A_{Ks} = 0.91 +/- 0.05 mag, an age τ= 4 +/- 0.5 Myr and a distance d = 4.0 +/- 0.2 kpc for Westerlund 1, as well as a total mass of M_{Wd1} = 4.91_{-0.49}^{+1.79} x 10^4 M_{sun}. Using spatially dependent completeness corrections we performed a 2D study of the cluster's IMF and, in addition, of the stellar density p…
Primordial Binary Stars, Mass segregation and Fractality Effects on the Early Evolution of Young Open Clusters
Astronomisches Rechen-Institut, Zentrum für Astronomie der Universität Heidelberg（海德堡大学天文学计算研究所）；Department of Physics, New York University Abu Dhabi（阿布扎比纽约大学物理系）；Center for Astrophysics and Space Science (CASS), New York University Abu Dhabi（阿布扎比纽约大学天体物理学与空间科学中心）；Dipartimento di Fisica, Sapienza, Universitá di Roma（罗马智慧大学物理系）；Department of Physics, Xi’an Jiaotong-Liverpool University（西交利物浦大学物理系）；Shanghai Key Laboratory for Astrophysics, Shanghai Normal University（上海师范大学天体物理重点实验室）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Nicolaus Copernicus Astronomical Centre, Polish Academy of Sciences（波兰科学院尼古拉·哥白尼天文学中心）；Main Astronomical Observatory, National Academy of Scien（国家科学院主天文台）
The ability to make meaningful comparisons between theoretical and observational data of star-forming regions is key to understanding the star formation process. In this paper we test the performance of INDICATE, a new method to quantify the clustering tendencies of individual stars in a region, on synthetic star-forming regions with sub-structured, and smooth, centrally concentrated distributions. INDICATE quantifies the amount of stellar affiliation of each individual star, and also determines whether this affiliation is above random expectation for the star-forming region in question. We sh…
We carried out UBVRcIc photometric study of three poorly studied young open clusters IC 1442, King 21, and Trumpler 7 (Tr 7). We obtained 263, 244, and 128 member stars using Gaia DR2 proper motions and parallaxes in IC 1442, King 21, and Tr 7, respectively. The reddening, E(B-V), was derived to be 0.54+/-0.04, 0.76+/-0.06, and 0.38+/-0.04 mag for these clusters. The comparison of observed colour-magnitude diagrams (CMDs) with solar metallicity isochrones yields log(Age) = 7.40+/-0.30, 7.70+/-0.20, and 7.85+/-0.25 yr and corresponding distances 2847+/-238, 2622+/-156, and 1561+/-74 pc for IC 1…
We investigate the effect that the usually large errors associated with ground-based proper motion (PM) components have on the determination of a star cluster's velocity dispersion (\sv). Rather than histograms, we work with PM distribution functions (PMDFs), taking the $1σ$ uncertainties formally into account. In this context, a cluster's intrinsic PMDF is broadened by the error distribution function (eDF) that, given the average error amplitude, has a width usually comparable to the cluster PMDF. Thus, we apply a Richardson-Lucy (RL) deconvolution to the PMDFs of a set of relatively nearby a…
Recent numerical simulations of globular clusters (GCs) have shown that stellar-mass black holes (BHs) play a fundamental role in driving cluster evolution and shaping their present-day structure. Rapidly mass-segregating to the center of GCs, BHs act as a dynamical energy source via repeated super-elastic scattering, delaying onset of core collapse and limiting mass segregation for visible stars. While recent discoveries of BH candidates in Galactic and extragalactic GCs have further piqued interest in BH-mediated cluster dynamics, numerical models show that even if significant BH populations…
We present the results of a comprehensive analysis of the structure and kinematics of six Galactic globular clusters. By comparing the results of the most extensive photometric and kinematical surveys available to date with suited dynamical models, we determine the stellar and dynamical masses of these stellar systems taking into account for the effect of mass segregation, anisotropy and unresolved binaries. We show that the stellar masses of these clusters are on average smaller than those predicted by canonical integrated stellar evolution models because of the shallower slope of their mass …
We investigate the dependence of galaxy clustering at $z \sim 4 - 7$ on UV-luminosity and stellar mass. Our sample consists of $\sim$ 10,000 Lyman-break galaxies (LBGs) in the XDF and CANDELS fields. As part of our analysis, the $M_\star - M_{\rm UV}$ relation is estimated for the sample, which is found to have a nearly linear slope of $d\log_{10} M_\star / d M_{\rm UV} \sim 0.44$. We subsequently measure the angular correlation function and bias in different stellar mass and luminosity bins. We focus on comparing the clustering dependence on these two properties. While UV-luminosity is only r…
It is widely believed that globular clusters evolve over many two-body relaxation times toward a state of energy equipartition, so that velocity dispersion scales with stellar mass as σ~ m^{-η} with η= 0.5. We show that this is incorrect, using direct N-body simulations with a variety of realistic IMFs and initial conditions. No simulated system ever reaches a state close to equipartition. Near the center, the luminous main-sequence stars reach a maximum η_{max} ~ 0.15 \pm 0.03. At large times, all radial bins convergence on an asymptotic value η_{\infty} ~ 0.08 \pm 0.02. The development of th…
We present profiles of temperature (Tx), gas mass, and hydrostatic mass estimated from new and archival X-ray observations of CLASH clusters. We compare measurements derived from XMM and Chandra observations with one another and compare both to gravitational lensing mass profiles derived with CLASH HST and ground-based lensing data. Radial profiles of Chandra and XMM electron density and enclosed gas mass are nearly identical, indicating that differences in hydrostatic masses inferred from X-ray observations arise from differences in Tx measurements. Encouragingly, cluster Txs are consistent w…
