Looking for phase-space structures in star-forming regions: an MST-based methodology

Abstract

We present a method for analysing the phase space of star-forming regions. In particular we are searching for clumpy structures in the 3D subspace formed by two position coordinates and radial velocity. The aim of the method is the detection of kinematic segregated radial velocity groups, that is, radial velocity intervals whose associated stars are spatially concentrated. To this end we define a kinematic segregation index,Λ(RV), based on the Minimum Spanning Tree (MST) graph algorithm, which is estimated for a set of radial velocity intervals in the region. WhenΛ(RV) is significantly greater than 1 we consider that this bin represents a grouping in the phase space. We split a star-forming region into radial velocity bins and calculate the kinematic segregation index for each bin, and then we obtain the spectrum of kinematic groupings, which enables a quick visualization of the kinematic behaviour of the region under study. We carried out numerical models of different configurations in the subspace of the phase space formed by the coordinates and the radial velocity that various case studies illustrate. The analysis of the test cases demonstrates the potential of the new methodology for detecting different kind of groupings in phase space.

On the spatial distributions of dense cores in Orion B

“…This determination prevents a single outlying object from heavily influencing the uncertainty, which could be an issue if using the Gaussian dispersion as the uncertainty estimator. If MSR > 1, then the most massive cores are more spatially concentrated than the average cores, and we designate this as significant if the lower error bar also exceeds unity (see also Alfaro & González 2016;González & Alfaro 2017). Parker & Goodwin (2015) show that MSR can sometimes be too sensitive in that it sometimes finds that random fluctuations in low-number distributions lead to mass segregation according to our definition.…”

Analysis of the kinematic structure of the Cygnus OB1 association

“…The method proposed and tested in Alfaro & González (2016) to look for kinematic segregation in stellar systems is based on calculating the kinematic index (Λ) and the Spectrum of Kinematic Groupings (SKG). The kinematic index Λ measures whether a target group (in this case, a group associated with a particular velocity channel) is more spatially concentrated than an average group with the same number of stars taken from the full sample.…”

“…The SKG methodology detects a third grouping whose morphology looks like a filament (see Alfaro & González 2016, for more details of the analysed test-cases), which lies in the main diagonal form of the Cygnus OB1 association (Fig. 4bottom -right).…”

NGC 2548: clumpy spatial and kinematic structure in an intermediate-age Galactic cluster

“…The search of patterns or substructures in the velocity phase space requires further improvement both in specific searching tools (e.g. Alfaro & González 2016) and in the precision of the kinematic data. Precise radial velocity measurements have allowed to resolve clumpy structures in four clusters: NGC 2264 (Fűrész et al 2006;Tobin et al 2015), Orion Nebula Cluster (Fűrész et al 2008), Gamma Velorum (Jeffries et al 2014) and NGC 2547 (Sacco et al 2015).…”