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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 sub-space 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, (RV), based on the Minimum Spanning Tree graph algorithm, which is estimated for a set of radial velocity intervals in the
region. When (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 sub-space of the phase space formed by the coordinates and the 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.
... Star-forming regions form with spatial and kinematic substructure (Larson 1981;Gomez et al. 1993;Cartwright & Whitworth 2004;Sánchez & Alfaro 2009;Alfaro & González 2016), and our simulations are designed to mimic this before any dynamical evolution takes place. For this reason, more stars reside in a high or ambiguous Mahalanobis phase space before dynamical evolution. ...
The architectures of extrasolar planetary systems often deviate considerably from the “standard” model for planet formation, which is largely based on our own solar system. In particular, gas giants on close orbits are not predicted by planet formation theory and so some processes are thought to move the planets closer to their host stars. Recent research has suggested that hot-Jupiter host stars display a different phase space compared to stars that do not host hot Jupiters. This has been attributed to these stars forming in star-forming regions of high stellar density, where dynamical interactions with passing stars have perturbed the planets. We test this hypothesis by quantifying the phase space of planet-hosting stars in dynamical N -body simulations of star-forming regions. We find that stars that retain their planets have a higher phase space than nonhosts, regardless of their initial physical density. This is because an imprint of the kinematic substructure from the regions birth is retained, as these stars have experienced fewer and less disruptive encounters than stars whose planets have been liberated and become free-floating. However, host stars whose planets remain bound but have had their orbits significantly altered by dynamical encounters are also primarily found in high phase space regimes. We therefore corroborate other research in this area that has suggested the high phase space of hot-Jupiter host stars is not caused by dynamical encounters or stellar clustering, but rather reflects an age bias in that these stars are (kinematically) younger than other exoplanet host stars.
... Star-forming regions form with spatial and kinematic substructure (Larson 1981;Gomez et al. 1993;Cartwright & Whitworth 2004;Sánchez & Alfaro 2009;Alfaro & González 2016), and our simulations are designed to mimic this before any dynamical evolution takes place. For this reason, more stars reside in a high or ambiguous Mahalanobis phase space before dynamical evolution. ...
The architectures of extrasolar planetary systems often deviate considerably from the ``standard" model for planet formation, which is largely based on our own Solar System. In particular, gas giants on close orbits are not predicted by planet formation theory and so some process(es) are thought to move the planets closer to their host stars. Recent research has suggested that Hot Jupiter host stars display a different phase space compared to stars that do not host Hot Jupiters. This has been attributed to these stars forming in star-forming regions of high stellar density, where dynamical interactions with passing stars have perturbed the planets. We test this hypothesis by quantifying the phase space of planet-hosting stars in dynamical N-body simulations of star-forming regions. We find that stars that retain their planets have a higher phase space than non-hosts, regardless of their initial physical density. This is because an imprint of the kinematic substructure from the regions birth is retained, as these stars have experienced fewer and less disruptive encounters than stars whose planets have been liberated and become free-floating. However, host stars whose planets remain bound but have had their orbits significantly altered by dynamical encounters are also primarily found in high phase space regimes. We therefore corroborate other research in this area which has suggested the high phase space of Hot Jupiter host stars is not caused by dynamical encounters or stellar clustering, but rather reflects an age bias in that these stars are (kinematically) younger than other exoplanet host stars.
... An alternative method, first proposed by Parker et al. (2011) and since used by other groups (e.g. Alfaro & González 2016;González & Alfaro 2017;Alfaro & Román-Zúñiga 2018), keeps N MST fixed and instead slides through the dataset. For example, one can start with the 10 least massive objects, calculate Λ MSR , and then move to the 11 -20 least massive objects, and so on. ...
The dominant formation mechanism of brown dwarfs and planetary mass objects in star-forming regions is presently uncertain. Do they form like stars, via the collapse and fragmentation of cores in Giant Molecular clouds, or do they form like planets in the discs around stars and are ejected via dynamical interactions? In this paper, we quantify the spatial distribution of substellar objects in NGC1333, in particular focusing on planetary-mass objects that have been the target of recent deep imaging observations. We find that these objects have a spatial distribution that is indistinguishable from the stars, and more massive brown dwarfs. We also analyse N-body simulations and find that a population of ejected planets would have a significantly different spatial and kinematic distribution to stars, and brown dwarfs that also formed through gravitational collapse and fragmentation. We therefore conclude that the low-mass substellar objects in NGC1333 formed more like stars than planets, although we predict that a population of hitherto undetected ejected planetary mass objects may be lurking in this, and other star-forming regions.
... Larson 1995;Cartwright & Whitworth 2004;Gouliermis et al. 2014) and kinematic substructure (e.g. Alfaro & González 2016;Wright et al. 2016). This substructure governs the long-term evolution of these star-forming regions (Parker et al. 2014;Sills et al. 2018), but it is unclear how or why stars inherit these properties from their parent molecular clouds. ...
Observations of pre- and proto-stellar cores in young star-forming regions show them to be mass segregated, i.e. the most massive cores are centrally concentrated, whereas pre-main-sequence stars in the same star-forming regions (and older regions) are not. We test whether this apparent contradiction can be explained by the massive cores fragmenting into stars of much lower mass, thereby washing out any signature of mass segregation in pre-main-sequence stars. Whilst our fragmentation model can reproduce the stellar initial mass function, we find that the resultant distribution of pre-main sequence stars is mass segregated to an even higher degree than that of the cores, because massive cores still produce massive stars if the number of fragments is reasonably low (between one and five). We therefore suggest that the reason cores are observed to be mass segregated and stars are not is likely due to dynamical evolution of the stars, which can move significant distances in star-forming regions after their formation.
... Wright et al. (2016) and Wright & Mamajek (2018) also perform spatial correlation tests to confirm the presence of kinematic substructure in their data sets, but these tests can say little about the distribution of that substructure. ⋆ E-mail: rjarnold1@sheffield.ac.uk Alfaro & González (2016) present a minimum-spanning-treebased method of quantifying kinematic substructure. This method also provides graphical indications of how this substructure is distributed. ...
We present a new method of analysing and quantifying velocity structure in star-forming regions suitable for the rapidly increasing quantity and quality of stellar position–velocity data. The method can be applied to data in any number of dimensions, does not require the centre or characteristic size (e.g. radius) of the region to be determined, and can be applied to regions with any underlying density and velocity structure. We test the method on a variety of example data sets and show it is robust with realistic observational uncertainties and selection effects. This method identifies velocity structures/scales in a region, and allows a direct comparison to be made between regions.
... Larson 1995;Cartwright & Whitworth 2004;Gouliermis et al. 2014) and kinematic substructure (e.g. Alfaro & González 2016;Wright et al. 2016). This substructure governs the long-term evolution of these star-forming regions (Parker et al. 2014;Sills et al. 2018), but it is unclear how or why stars inherit these properties from their parent molecular clouds. ...
Observations of pre-/proto-stellar cores in young star-forming regions show them to be mass segregated, i.e. the most massive cores are centrally concentrated, whereas pre-main sequence stars in the same star-forming regions (and older regions) are not. We test whether this apparent contradiction can be explained by the massive cores fragmenting into stars of much lower mass, thereby washing out any signature of mass segregation in pre-main sequence stars. Whilst our fragmentation model can reproduce the stellar initial mass function, we find that the resultant distribution of pre-main sequence stars is mass segregated to an even higher degree than that of the cores, because massive cores still produce massive stars if the number of fragments is reasonably low (between one and five). We therefore suggest that the reason cores are observed to be mass segregated and stars are not is likely due to dynamical evolution of the stars, which can move significant distances in star-forming regions after their formation.
... Wright et al. (2016) E-mail: rjarnold1@sheffield.ac.uk and Wright & Mamajek (2018) also perform spatial correlation tests to confirm the presence of kinematic substructure in their datasets, but these tests can say little about the distribution of that substructure. Alfaro & González (2016) presents a minimum spanning tree based method of quantifying kinematic substructure. This method also provides graphical indications of how this substructure is distributed. ...
We present a new method of analysing and quantifying velocity structure in star forming regions suitable for the rapidly increasing quantity and quality of stellar position-velocity data. The method can be applied to data in any number of dimensions, does not require the centre or characteristic size (e.g. radius) of the region to be determined, and can be applied to regions with any underlying density and velocity structure. We test the method on a variety of example datasets and show it is robust with realistic observational uncertainties and selection effects. This method identifies velocity structures/scales in a region, and allows a direct comparison to be made between regions.
... If information about the mass of stars is available, then the problem of mass segregation in a cluster can be investigated (Parker & Goodwin 2015). For cases where radial velocity measurements of stars are available, clustering in the third dimension (velocity) can also be analysed enabling the separation of superimposed clusters from the background accurately (Alfaro & Gonzalez 2016). Clusters with extended corona have also been illustrated using radial density profiles by Seleznev (2016). ...
Star cluster studies hold the key to understanding star formation, stellar evolution, and origin of galaxies. The detection and characterization of clusters depend on the underlying background density and the cluster richness. We examine the ability of the Parzen Density Estimation (a.k.a. Parzen Windows) method, which is a generalization of the well-known Star Count method, to detect clusters and measure their properties. We apply it on a range of simulated and real star fields, considering square and circular windows, with and without Gaussian kernel smoothing. Our method successfully identifies clusters and we suggest an optimal standard deviation of the Gaussian Parzen window for obtaining the best estimates of these parameters. Finally, we demonstrate that the Parzen Windows with Gaussian kernels are able to detect small clusters in regions of relatively high background density where the Star Count method fails.
... 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 Λ 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 Λ 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. ...
We quantify the spatial distributions of dense cores in three spatially distinct areas of the Orion B star-forming region. For L1622, NGC2068/NGC2071 and NGC2023/NGC2024 we measure the amount of spatial substructure using the -parameter and find all three regions to be spatially substructured (). We quantify the amount of mass segregation using and find that the most massive cores are mildly mass segregated in NGC2068/NGC2071 (), and very mass segregated in NGC2023/NGC2024 ( for the four most massive cores). Whereas the most massive cores in L1622 are not in areas of relatively high surface density, or deeper gravitational potentials, the massive cores in NGC2068/NGC2071 and NGC2023/NGC2024 are significantly so. Given the low density (10 cores pc) and spatial substructure of cores in Orion B, the mass segregation cannot be dynamical. Our results are also inconsistent with simulations in which the most massive stars form via competitive accretion, and instead hint that magnetic fields may be important in influencing the primordial spatial distributions of gas and stars in star-forming regions.
The dominant formation mechanism of brown dwarfs and planetary mass objects in star-forming regions is presently uncertain. Do they form like stars, via the collapse and fragmentation of cores in Giant Molecular clouds, or do they form like planets in the discs around stars and are ejected via dynamical interactions? In this paper, we quantify the spatial distribution of substellar objects in NGC 1333, in particular focusing on planetary-mass objects that have been the target of recent deep imaging observations. We find that these objects have a spatial distribution that is indistinguishable from the stars, and more massive brown dwarfs. We also analyse N-body simulations and find that a population of ejected planets would have a significantly different spatial and kinematic distribution to stars, and brown dwarfs that also formed through gravitational collapse and fragmentation. We therefore conclude that the low-mass substellar objects in NGC 1333 formed more like stars than planets, although we predict that a population of hitherto undetected ejected planetary mass objects may be lurking in this, and other star-forming regions.
The multi-dimensional phase space density (both position and velocity) of star-forming regions may encode information on the initial conditions of star and planet formation. Recently, a new metric based on the Mahalanobis distance has been used to show that hot Jupiters are more likely to be found around exoplanet host-stars in high 6D phase space density, suggesting a more dynamic formation environment for these planets. However, later work showed that this initial result may be due to a bias in the age of hot Jupiters and the kinematics of their host stars. We test the ability of the Mahalanobis distance and density to differentiate more generally between star-forming regions with different morphologies by applying it to static regions that are either substructured or smooth and centrally concentrated. We find that the Mahalanobis distance is unable to distinguish between different morphologies, and that the initial conditions of the N-body simulations cannot be constrained using only the Mahalanobis distance or density. Furthermore, we find that the more dimensions in the phase space the less effective the Mahalanobis density is at distinguishing between different initial conditions. We show that a combination of the mean three-dimensional (x, y, z) Mahalanobis density and the Q-parameter for a region can constrain its initial virial state. However this is due to the discriminatory power of the Q-parameter and not from any extra information imprinted in the Mahalanobis density. We therefore recommend continued use of multiple diagnostics for determining the initial conditions of star-forming regions, rather than relying on a single multi-dimensional metric.
Context. The young massive cluster Westerlund 1 offers the promise of a grand laboratory for the study of high-mass star evolution, but its basic parameters are still poorly known.
Aims. In this paper, we aim at a better characterisation of the cluster by determining some basic kinematic properties and analysing the area surrounding the cluster and the population in its foreground.
Methods. We have used Gaia early data release 3 (EDR3) data, together with spectra of a large sample of luminous stars in the field surrounding Westerlund 1, to explore the extent of the cluster. We carried out a non-parametric analysis of proper motions and membership determination. We investigated the reddening and proper motions of several dozen OB stars and red supergiants less than one degree away from Westerlund 1.
Results. We identify a population of kinematic members of Westerlund 1 that largely includes the known spectroscopic members. From their EDR3 parallaxes, we derive a distance to the cluster of kpc. We analyse the extinction in this direction, finding that it increases by a large amount around 2.8 kpc, which in all likelihood is due to dark clouds associated with the Scutum-Crux arm. As a consequence, we hardly see any stars at distances comparable (or higher) than that of the cluster. The proper motions of Westerlund 1, however, are very similar to those of stars in the field surrounding it which are – almost without exception – less distant, but distinct. We find a second, astrometrically well-defined population in the foreground ( d ≈ 2 kpc), centred ∼8′ away, which is likely connected to the possible open cluster BH 197. Westerlund 1 is very elongated, an effect that seems real and not driven by the very heavy extinction to the east and south. We find a low-density halo extending to distances up to 10′ from the cluster centre, mainly in the north-west quadrant. A few OB stars at larger distances from the cluster, most notably the luminous blue variable (LBV) MN48, share its proper motions, suggesting that Westerlund 1 has little or no peculiar motion with respect to the field population of the Norma arm. Despite this, we are unable to find any red supergiant that could belong to an extended population related to the cluster, although we observe several dozen such objects in the foreground, demonstrating the richness of the field population along this sightline. We find a substantial population of luminous OB members obscured by several more magnitudes of extinction than most known members. These objects, mostly located in the central region of the cluster, increase the population of OB supergiants by about 25%.
Context. With the third release of the high-precision optical-wavelength Gaia survey, we are in a better position than ever before to study young clusters. However, Gaia is limited in the optical down to G ∼ 21 mag, and therefore it is essential to understand the biases introduced by a magnitude-limited sample on spatial distribution studies.
Aims. We ascertain how sample incompleteness in Gaia observations of young clusters affects the local spatial analysis tool INDICATE and subsequently the perceived spatial properties of these clusters.
Methods. We created a mock Gaia cluster catalogue from a synthetic dataset using the observation generating tool MYOSOTIS. The effect of cluster distance, uniform and variable extinction, binary fraction, population masking by the point spread function wings of high-mass members, and contrast sensitivity limits on the trends identified by INDICATE are explored. A comparison of the typical index values derived by INDICATE for members of the synthetic dataset and their corresponding mock Gaia catalogue observations is made to identify any significant changes.
Results. We typically find only small variations in the pre- and post-observation index values of cluster populations, which can increase as a function of incompleteness percentage and binarity. No significant strengthening or false signatures of stellar concentrations are found, but real signatures may be diluted. Conclusions drawn about the spatial behaviour of Gaia -observed cluster populations that are, and are not, associated with their natal nebulosity are reliable for most clusters, but the perceived behaviours of individual members can change, so INDICATE should be used as a measure of spatial behaviours between members as a function of their intrinsic properties (e.g., mass, age, object type), rather than to draw conclusions about any specific observed member.
Conclusions. INDICATE is a robust spatial analysis tool to reliably study Gaia -observed young cluster populations within 1 kpc, up to a sample incompleteness of 83.3% and binarity of 50%.
Context. The spatial and dynamical structure of star-forming regions can offer insights into stellar formation patterns. The amount of data from current and upcoming surveys calls for robust and objective procedures for detecting structures in order to statistically analyse the various regions and compare them.
Aims. We aim to provide the community with a tool capable of detecting, above random expectations, the small-scale significant structure in star-forming regions that could serve as an imprint of the stellar formation process. The tool makes use of the one-point correlation function to determine an appropriate length scale for ϵ and uses nearest-neighbour statistics to determine a minimum number of points N min for the DBSCAN algorithm in the neighbourhood of ϵ .
Methods. We implemented the procedure and applied it to synthetic star-forming regions of different nature and characteristics to obtain its applicability range. We also applied the method to observed star-forming regions to demonstrate its performance in realistic circumstances and to analyse its results.
Results. The procedure successfully detects significant small-scale substructures in heterogeneous regions, fulfilling the goals it was designed for and providing very reliable structures. The analysis of regions close to complete spatial randomness ( Q ∈ [0.7, 0.87]) shows that even when some structure is present and recovered, it is hardly distinguishable from spurious detection in homogeneous regions due to projection effects. Thus, any interpretation should be done with care. For concentrated regions, we detect a main structure surrounded by smaller ones, corresponding to the core plus some Poisson fluctuations around it. We argue that these structures do not correspond to the small compact regions we are looking for. In some realistic cases, a more complete hierarchical, multi-scale analysis would be needed to capture the complexity of the region.
Conclusions. We carried out implementations of our procedure and devised a catalogue of the Nested Elementary STructures (NESTs) detected as a result in four star-forming regions (Taurus, IC 348, Upper Scorpius, and Carina). This catalogue is being made publicly available to the community. Implementations of the 3D versionsof the procedure, as well as up to 6D versions, including proper movements, are in progress and will be provided in a future work.
We present DECam imaging combined with Gaia DR2 data to study the Canis Major overdensity. The presence of the so-called Blue Plume stars in a low-pollution area of the color-magnitude diagram allows us to derive the distance and proper motions of this stellar feature along the line of sight of its hypothetical core. The stellar overdensity extends on a large area of the sky at low Galactic latitudes, below the plane, and between 230○ < ℓ < 255○. According to the orbit derived for Canis Major, it presents an on-plane rotation around the Milky Way. Moreover, additional overdensities of Blue Plume stars are found around the plane and across the Galaxy, proving that these objects are not only associated with that structure. The spatial distribution of these stars, derived using Gaia astrometric data, confirms that the detection of the Canis Major overdensity results more from the warped structure of the Milky Way disk than from the accretion of a dwarf galaxy.
Star cluster studies hold the key to understanding star formation, stellar evolution, and origin of galaxies. The detection and characterization of clusters depend on the underlying background density and the cluster richness. We examine the ability of the Parzen density estimation (a.k.a. Parzen windows) method, which is a generalization of the well-known star count method, to detect clusters and measure their properties. We apply it on a range of simulated and real star fields, considering square and circular windows, with and without Gaussian kernel smoothing. Our method successfully identifies clusters and we suggest an optimal standard deviation of the Gaussian Parzen window for obtaining the best estimates of these parameters. Finally, we demonstrate that the Parzen windows with Gaussian kernels are able to detect small clusters in regions of relatively high background density, where the star count method fails.
The principal aim of this work is to study the velocity field in the Monoceros star-forming region using the radial velocity data available in the literature, as well as astrometric data from the Gaia first release. This region is a large star-forming complex formed by two associations named Monoceros OB1 and OB2. We have collected radial velocity data for more than 400 stars in the area of 8 × 12 deg² and distance for more than 200 objects. We apply a clustering analysis in the subspace of the phase space formed by angular coordinates and radial velocity or distance data using the Spectrum of Kinematic Grouping methodology. We found four and three spatial groupings in radial velocity and distance variables, respectively, corresponding to the Local arm, the central clusters forming the associations and the Perseus arm, respectively.
We analyse the geometry of the Pipe Nebula, drawn by the distribution (Q-spatial parameter) and hierarchy ( spatial segregation) of column density peaks previously detected and catalogued. By analysing the mass and volume density of the cores, we determine that both variables shown to be spatially segregated and with a high degree of substructure. Given the early evolutionary state of the Pipe Nebula, our results suggest that both, mass and volume-density segregations, may be primordial, in the sense of appearing in the early phases of the chain of physical mechanisms which conform the cluster-formation process. We also propose that volume density, and not mass, is the parameter that most clearly determines the initial spatial distribution of pre-stellar cores.
We propose a method for calculating the radius of an open cluster in an objective way from an astrometric catalogue containing, at least, positions and proper motions. It uses the minimum spanning tree (hereinafter MST) in the proper motion space to discriminate cluster stars from field stars and it quantifies the strength of the cluster-field separation by means of a statistical parameter defined for the first time in this paper. This is done for a range of different sampling radii from where the cluster radius is obtained as the size at which the best cluster-field separation is achieved. The novelty of this strategy is that the cluster radius is obtained independently of how its stars are spatially distributed. We test the reliability and robustness of the method with both simulated and real data from a well-studied open cluster (NGC 188), and apply it to UCAC4 data for five other open clusters with different catalogued radius values. NGC 188, NGC 1647, NGC 6603 and Ruprecht 155 yielded unambiguous radius values of 15.2+/-1.8, 29.4+/-3.4, 4.2+/-1.7 and 7.0+/-0.3 arcmin, respectively. ASCC 19 and Collinder 471 showed more than one possible solution but it is not possible to know whether this is due to the involved uncertainties or to the presence of complex patterns in their proper motion distributions, something that could be inherent to the physical object or due to the way in which the catalogue was sampled.
The main objective of this study is the characterization of the velocity field in the Cygnus OB1 association using the radial velocity data currently available in the literature. This association is part of a larger star-forming complex located in the direction of the Cygnus region, but whose main subsystems may be distributed at different distances from the sun. We have collected radial velocity data for more than 300 stars in the area of 5 x 5 square degrees centred on the Cygnus OB1 association. We present the results of a kinematic clustering analysis in the subspace of the phase space formed by angular coordinates and radial velocity using two independent methodologies. We have found evidence of structure in the phase space with the detection of two main groups, corresponding to different radial velocity and distance values, belonging to the association, and associated with two main shells defined by the Halpha emission. A third grouping well separated from the other two in velocity appears to occupy the whole region associated with what has been called "common shell".
In this work we analyse the structure of a subspace of the phase space of the star-forming region NGC~ 2264 using the Spectrum of Kinematic Groupings (SKG). We show that the SKG can be used to process a collection of star data to find substructure at different scales. We have found structure associated with the NGC~ 2264 region and also with the background area. In the NGC~ 2264 region, a hierarchical analysis shows substructure compatible with that found in previous specific studies of the area but with an objective, compact methodology that allows us to homogeneously compare the structure of different clusters and star-forming regions. Moreover, this structure is compatible with the different ages of the main NGC~ 2264 star-forming populations. The structure found in the field can be roughly associated with giant stars far in the background, dynamically decoupled from NGC~ 2264, which could be related either with the Outer Arm or Monoceros Ring. The results in this paper confirm the relationship between structure in the RV phase-space subspace and different kinds of populations, defined by other variables not necessarily analysed with the SKG, such as age or distance, showing the importance of detecting phase-space substructure in order to trace stellar populations in the broadest sense of the word.
NGC 2548 is a ∼400 − 500 Myr old open cluster with evidence of spatial substructures likely caused by its interaction with
the Galactic disk. In this work we use precise astrometric data from the Carte du Ciel - San Fernando (CdC-SF) catalogue to study the clumpy structure in this cluster. We confirm the fragmented structure of NGC 2548
but, additionally, the relatively high precision of our kinematic data lead us to the first detection of substructures in
the proper motion space of a stellar cluster. There are three spatially separated cores each of which has its own counterpart
in the proper motion distribution. The two main cores lie nearly parallel to the Galactic plane whereas the third one is significantly
fainter than the others and it moves toward the Galactic plane separating from the rest of the cluster. We derive core positions
and proper motions, as well as the stars belonging to each core.
Mass segregation in star clusters is often thought to indicate the onset of energy equipartition, where the most massive stars
impart kinetic energy to the lower-mass stars and brown dwarfs/free floating planets. The predicted net result of this is
that the centrally concentrated massive stars should have significantly lower velocities than fast-moving low-mass objects
on the periphery of the cluster. We search for energy equipartition in initially spatially and kinematically substructured
N-body simulations of star clusters with N = 1500 stars, evolved for 100 Myr. In clusters that show significant mass segregation we find no differences in the proper
motions or radial velocities as a function of mass. The kinetic energies of all stars decrease as the clusters relax, but
the kinetic energies of the most massive stars do not decrease faster than those of lower-mass stars. These results suggest
that dynamical mass segregation – which is observed in many star clusters – is not a signature of energy equipartition from
two-body relaxation.
A large sample of young stellar groups is analysed aiming to investigate
their clustering properties and dynamical evolution. A comparison of the Q
statistical parameter, measured for the clusters, with the fractal dimension
estimated for the projected clouds shows that 52% of the sample has
substructures and tends to follow the theoretically expected relation between
clusters and clouds, according to calculations for artificial distribution of
points. The fractal statistics was also compared to structural parameters
revealing that clusters having radial density profile show a trend of parameter
s increasing with mean surface stellar density. The core radius of the sample,
as a function of age, follows a distribution similar to that observed in
stellar groups of Milky Way and other galaxies. They also have dynamical age,
indicated by their crossing time that is similar to unbound associations. The
statistical analysis allowed us to separate the sample into two groups showing
different clustering characteristics. However, they have the same dynamical
evolution, since the whole sample has been revealed as expanding objects, for
which the substructures seem to have not been erased. These results are in
agreement with simulations that adopt low surface densities and models under
supervirial conditions.
The analysis of the distribution of stars in open clusters may yield
important information on the star formation process and early dynamical
evolution of stellar clusters. Here we address this issue by systematically
characterizing the internal spatial structure of 16 open clusters in the Milky
Way spanning a wide range of ages. Cluster stars have been selected from a
membership probability analysis based on a non-parametric method that uses both
positions and proper motions and does not make any a priori assumption on the
underlying distributions. The internal structure is then characterized by means
of the minimum spanning tree method (Q parameter), King profile fitting, and
the correlation dimension (Dc) for those clusters with fractal patterns. On
average, clusters with fractal-like structure are younger than those exhibiting
radial star density profiles and an apparent trend between Q and age is
observed in agreement with previous ideas about the dynamical evolution of the
internal spatial structure of stellar clusters. However, some new results are
obtained from a more detailed analysis: (a) a clear correlation between Q and
the concentration parameter of the King model for those cluster with radial
density profiles, (b) the presence of spatial substructure in clusters as old
as 100 Myr, and (c) a significant correlation between fractal dimension and age
for those clusters with internal substructure. Moreover, the lowest fractal
dimensions seem to be considerably smaller than the average value measured in
galactic molecular cloud complexes.
We use a Minimum Spanning Tree algorithm to characterize the spatial
distribution of Galactic Far-IR sources and derive their clustering properties.
We aim to reveal the spatial imprint of different types of star forming
processes, e.g. isolated spontaneous fragmentation of dense molecular clouds,
or events of triggered star formation around HII regions, and highlight global
properties of star formation in the Galaxy. We plan to exploit the entire
Hi-GAL survey of the inner Galactic plane to gather significant statistics on
the clustering properties of star forming regions, and to look for possible
correlations with source properties such as mass, temperature or evolutionary
stage. In this paper we present a pilot study based on the two 2x2 square
degree fields centered at longitudes l=30 and l=59 obtained during the Science
Demonstration Phase (SDP) of the Herschel mission. We find that over half of
the clustered sources are associated with HII regions and infrared dark clouds.
Our analysis also reveals a smooth chromatic evolution of the spatial
distribution where sources detected at short-wavelengths, likely proto-stars
surrounded by warm circumstellar material emitting in the far-infrared, tend to
be clustered in dense and compact groups around HII regions while sources
detected at long-wavelengths, presumably cold and dusty density enhancements of
the ISM emitting in the sub-millimeter, are distributed in larger and looser
groups.
We present an expanded kinematic study of the young cluster NGC 2264 based
upon optical radial velocities measured using multi-fiber echelle spectroscopy
at the 6.5 meter MMT and Magellan telescopes. We report radial velocities for
695 stars, of which approximately 407 stars are confirmed or very likely
members. Our results more than double the number of members with radial
velocities from F{\H u}r{\'e}sz et al., resulting in a much better defined
kinematic relationship between the stellar population and the associated
molecular gas.
In particular, we find that there is a significant subset of stars that are
systematically blueshifted with respect to the molecular (CO) gas. The
detection of Lithium absorption and/or infrared excesses in this blue-shifted
population suggests that at least some of these stars are cluster members; we
suggest some speculative scenarios to explain their kinematics. Our results
also more clearly define the redshifted population of stars in the northern end
of the cluster; we suggest that the stellar and gas kinematics of this region
are the result of a bubble driven by the wind from O7 star S Mon. Our results
emphasize the complexity of the spatial and kinematic structure of NGC 2264,
important for eventually building up a comprehensive picture of cluster
formation.
We use the new minimum spanning tree (MST) method to look for mass segregation in the Taurus association. The method computes
the ratio of MST lengths of any chosen subset of objects, including the most massive stars and brown dwarfs, to the MST lengths
of random sets of stars and brown dwarfs in the cluster. This mass segregation ratio (ΛMSR) enables a quantitative measure of the spatial distribution of high- and low-mass stars, and brown dwarfs to be made in Taurus.
We find that the most massive stars in Taurus are inversely mass segregated with ΛMSR= 0.70 ± 0.10 (ΛMSR= 1 corresponds to no mass segregation), which differs from the strong mass segregation signatures found in more dense and
massive clusters such as Orion. The brown dwarfs in Taurus are not mass segregated, although we find evidence that some low-mass
stars are, with an ΛMSR= 1.25 ± 0.15. Finally, we compare our results to previous measures of the spatial distribution of stars and brown dwarfs
in Taurus, and briefly discuss their implications.
We developed a source detection algorithm based on the Minimal Spanning Tree (MST), that is a graph-theoretical method useful
for finding clusters in a given set of points. This algorithm is applied to γ-ray bi-dimensional images where the points correspond
to the arrival direction of photons, and the possible sources are associated with the regions where they clusterize. Some
filters to select these clusters and to reduce the spurious detections are introduced. An empirical study of the statistical
properties of MST on random fields is carried out in order to derive some criteria to estimate the best filter values. We
also introduce two parameters useful to verify the goodness of candidate sources. To show how the MST algorithm works in practice,
we present an application to an EGRET observation of the Virgo field, at high Galactic latitude and with a low and rather
uniform background, in which several sources are detected.
We present an analysis of the spatial distribution of various stellar populations within the Large Magellanic Cloud (LMC). We combine mid-infrared selected young stellar objects, optically selected samples with mean ages between ∼9 and ∼1000 Myr and existing stellar cluster catalogues to investigate how stellar structures form and evolve within the LMC. For the analysis we use Fractured Minimum Spanning Trees, the statistical Q parameter and the two-point correlation function. Restricting our analysis to young massive (OB) stars, we confirm our results obtained for M33, namely that the luminosity function of the groups is well described by a power law with index −2, and that there is no characteristic length-scale of star-forming regions. We find that stars in the LMC are born with a large amount of substructure, consistent with a two-dimensional fractal distribution with dimension and evolve towards a uniform distribution on a time-scale of ∼175 Myr. This is comparable to the crossing time of the galaxy, and we suggest that stellar structure, regardless of spatial scale, will be eliminated in a crossing time. This may explain the smooth distribution of stars in massive/dense young clusters in the Galaxy, while other, less massive, clusters still display large amounts of structure at similar ages. By comparing the stellar and star cluster distributions and evolving time-scales, we show that infant mortality of clusters (or ‘popping clusters’) has a negligible influence on the galactic structure. Finally, we quantify the influence of the elongation, differential extinction and contamination of a population on the measured Q value.
We have previously reported a dimensionless measure, , which can both quantify, and distinguish between, the extent to which a star cluster is centrally concentrated, and the extent to which it contains small-scale subclusters. is the ratio of the normalized correlation length, , (i.e. the mean projected separation between stars, divided by the overall radius of the cluster), to the mean length, , of the segments of a minimal spanning tree (MST) joining all star positions: .
In this paper, we attempt to adapt the correlation-length method to the characterization of gas clouds, with a view to comparing directly the structures of gas clouds and star clusters. We also compare the results of the correlation-length method with fractal dimensions estimated using the more familiar perimeter–area method whereby the lengths of closed contours are plotted against the areas they enclose, on a log–log plot.
We find that the normalized correlation length, when modified to deal with pixellated grey-scale data, is a robust indicator of either central concentration or fractal subclustering of gas clouds, but cannot distinguish between the two types of structure. It is, however, extremely reliable, easy to implement and works accurately at all scales and over all dynamic ranges, even with poorly sampled data. It implicitly incorporates edge effects, so all the data in the complete cloud are used, and it therefore provides a useful method for comparing the structures of molecular clouds and star clusters.
The normalized correlation length produces comparable results to the perimeter–area method when used on molecular cloud data. However, the perimeter–area method is unable to distinguish the degree of clustering in three-dimensional objects with fractal dimensions greater than 2.0. It also suffers from measurement noise and lack of objectivity, particularly if only a few contours are selected for analysis. It cannot be used to compare clouds with star clusters.
It is not found possible to construct an MST algorithm which works reliably for grey-scale data and is immune to scaling problems. The previously reported parameter is therefore not useful when considering gas clouds.
The young stellar population data of the Perseus, Ophiuchus and Serpens molecular clouds are obtained from the Spitzer c2d legacy survey in order to investigate the spatial structure of embedded clusters using the nearest neighbour and minimum spanning tree method. We identify the embedded clusters in these clouds as density enhancements and analyse the clustering parameter Q with respect to source luminosity and evolutionary stage. This analysis shows that the older Class 2/3 objects are more centrally condensed than the younger Class 0/1 protostars, indicating that clusters evolve from an initial hierarchical configuration to a centrally condensed one. Only IC348 and the Serpens core, the older clusters in the sample, shows signs of mass segregation (indicated by the dependence of Q on the source magnitude), pointing to a significant effect of dynamical interactions after a few Myr. The structure of a cluster may also be linked to the turbulent energy in the natal cloud as the most centrally condensed cluster is found in the cloud with the lowest Mach number and vice versa. In general these results agree well with theoretical scenarios of star cluster formation by gravoturbulent fragmentation.
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