Using the minimum spanning tree to trace mass segregation

Allison, Richard J.; Goodwin, S. P.; Parker, R. J.; Zwart, Simon F. Portegies; Grijs, Richard de; Kouwenhoven, M. B. N.

doi:10.1111/j.1365-2966.2009.14508.x

Cited by 231 publications

(314 citation statements)

References 26 publications

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“…Because the sensitivity of the MST to the completeness of a sample is not fully understood (Allison et al 2009), we cannot draw firm conclusions. We note however that two independent methods, profile fitting and MST analysis, both point towards mass segregation, as can be expected for the most massive stars in such a cluster.…”

Section: Mass Segregationmentioning

confidence: 98%

A MAD view of Trumpler 14

Sana

Momany

Gieles³

et al. 2010

A&A

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We present adaptive optics (AO) near-infrared observations of the core of the Tr 14 cluster in the Carina region obtained with the ESO multi-conjugate AO demonstrator, MAD. Our campaign yields AO-corrected observations with an image quality of about 0.2 across the 2 field of view, which is the widest AO mosaic ever obtained. We detected almost 2000 sources spanning a dynamic range of 10 mag. The pre-main sequence (PMS) locus in the colour−magnitude diagram is well reproduced by Palla & Stahler isochrones with an age of 3 to 5 × 10 5 yr, confirming the very young age of the cluster. We derive a very high (deprojected) central density n 0 ∼ 4.5(±0.5) × 10 4 pc −3 and estimate the total mass of the cluster to be about ∼4.3 +3.3 −1.5 × 10 3 M , although contamination of the field of view might have a significant impact on the derived mass. We show that the pairing process is largely dominated by chance alignment so that physical pairs are difficult to disentangle from spurious ones based on our single epoch observation. Yet, we identify 150 likely bound pairs, 30% of these with a separation smaller than 0.5 (∼1300 AU). We further show that at the 2σ level massive stars have more companions than lower-mass stars and that those companions are respectively brighter on average, thus more massive. Finally, we find some hints of mass segregation for stars heavier than about 10 M . If confirmed, the observed degree of mass segregation could be explained by dynamical evolution, despite the young age of the cluster.

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Section: Mass Segregationmentioning

confidence: 98%

A MAD view of Trumpler 14

Sana

Momany

Gieles³

et al. 2010

A&A

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“…A statistical method to probe spatial compactness is the minimum spanning tree (MST) method (Prim 1957). This (see also Allison et al 2009;Parker et al 2011) consists in computing the minimum path-length required to connect all points of a given sample in a network of direct point-to-point links with no closed loops. Shorter MST lengths will thus identify, to a certain degree of confidence, more compact populations.…”

Section: A Spatial Mapping Of Accretion Properties In Ngc 2264mentioning

confidence: 99%

Mapping accretion and its variability in the young open cluster NGC 2264: a study based onu-band photometry

Venuti

Bouvier

Flaccomio

et al. 2014

A&A

138

261

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Context. The accretion process has a central role in the formation of stars and planets. Aims. We aim at characterizing the accretion properties of several hundred members of the star-forming cluster NGC 2264 (3 Myr).Methods. We performed a deep ugri mapping as well as a simultaneous u-band+r-band monitoring of the star-forming region with CFHT/MegaCam in order to directly probe the accretion process onto the star from UV excess measurements. Photometric properties and stellar parameters are determined homogeneously for about 750 monitored young objects, spanning the mass range ∼0.1-2 M . About 40% of the sample are classical (accreting) T Tauri stars, based on various diagnostics (H α , UV and IR excesses). The remaining non-accreting members define the (photospheric + chromospheric) reference UV emission level over which flux excess is detected and measured. Results. We revise the membership status of cluster members based on UV accretion signatures, and report a new population of 50 classical T Tauri star (CTTS) candidates. A large range of UV excess is measured for the CTTS population, varying from a few times 0.1 to ∼3 mag. We convert these values to accretion luminosities and accretion rates, via a phenomenological description of the accretion shock emission. We thus obtain mass accretion rates ranging from a few 10 −10 to ∼10 −7 M /yr. Taking into account a mass-dependent detection threshold for weakly accreting objects, we find a >6σ correlation between mass accretion rate and stellar mass. A power-law fit, properly accounting for censored data (upper limits), yieldsṀ acc ∝ M 1.4±0.3 * . At any given stellar mass, we find a large spread of accretion rates, extending over about 2 orders of magnitude. The monitoring of the UV excess on a timescale of a couple of weeks indicates that its variability typically amounts to 0.5 dex, i.e., much smaller than the observed spread in accretion rates. We suggest that a non-negligible age spread across the star-forming region may effectively contribute to the observed spread in accretion rates at a given mass. In addition, different accretion mechanisms (like, e.g., short-lived accretion bursts vs. more stable funnel-flow accretion) may be associated to differentṀ acc regimes. Conclusions. A huge variety of accretion properties is observed for young stellar objects in the NGC 2264 cluster. While a definite correlation seems to hold between mass accretion rate and stellar mass over the mass range probed here, the origin of the large intrinsic spread observed in mass accretion rates at any given mass remains to be explored.

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“…As a proxy for mass segregation we extend the method M Λ MST developed by Allison et al (2009b) (see also Cartwright & Whitworth 2004;Schmeja & Klessen 2006). In summary, the authors use the minimum spanning tree (MST), the graph which connects all vertices within a given sample with the lowest possible sum of edges and no closed loops (Gower & Ross 1969).…”

Section: Geometrical Minimum Spanning Tree γ Mstmentioning

confidence: 99%

“…Our method M Γ MST involves two crucial modifications of M Λ MST that make it computationally much more effective and boost its sensitivity. First, unlike Allison et al (2009b) we do not calculate the separations between all possible pairs of stars but determine the MST (in two dimensions) in a three-step procedure: first we use a 2D Delaunay triangulation (from the software package GEOMPACK: Joe 1991) to construct a useful graph of stellar positions projected onto a plane, then we sort the edges of the triangles in ascending order, and finally adapt Kruskal's algorithm (Kruskal 1956) with an efficient union-find-algorithm to construct the MST.…”

Section: Geometrical Minimum Spanning Tree γ Mstmentioning

confidence: 99%

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A highly efficient measure of mass segregation in star clusters

Olczak

Spurzem

Henning

2011

A&A

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Context. 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. A consistent analysis requires a robust measure among different objects and well-defined comparison with theoretical expectations. Various methods have been used for this purpose but usually with limited significance, quantifiability, and application to both simulations and observations. Aims. We aim at developing a measure of mass segregation with as few parameters as possible, robustness against peculiar configurations, independence of mass determination, simple implementation, stable algorithm, and that is equally well adoptable for data from either simulations or observations. Methods. 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. Results. The geometrical mean boosts the sensitivity compared to previous applications of the MST. It thus 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 clear signatures even when applied to small subsets of the entire population. We confirm with high significance strong mass segregation of the five most massive stars in the Orion nebula cluster (ONC). Conclusions. Our method is the most sensitive general measure of mass segregation so far and provides robust results for both data from simulations and observations. As such it is ideally suited for tracking mass segregation in young star clusters and to investigate the long standing paradigm of primordial mass segregation by comparison of simulations and observations.

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Using the minimum spanning tree to trace mass segregation

Cited by 231 publications

References 26 publications

A MAD view of Trumpler 14

A MAD view of Trumpler 14

Mapping accretion and its variability in the young open cluster NGC 2264: a study based onu-band photometry

A highly efficient measure of mass segregation in star clusters

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