Comparisons between different techniques for measuring mass segregation

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 $\Lambda_{\rm MSR}$ method; the local surface density $\Sigma_{\rm LDR}$ method; and the $\Omega_{\rm GSR}$ 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 $\Omega_{\rm GSR}$ 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 $\Lambda_{\rm MSR}$ and $\Sigma_{\rm LDR}$ methods can sometimes produce apparently contradictory results, because they use different definitions of mass segregation. We conclude that only $\Lambda_{\rm MSR}$ measures mass segregation in the classical sense (without the need for defining the centre of the region), although $\Sigma_{\rm LDR}$ does place limits on the amount of previous dynamical evolution in a star-forming region

No preferential spatial distribution for massive stars expected from their formation

We analyse N-body and Smoothed Particle Hydrodynamic (SPH) simulations of young star-forming regions to search for differences in the spatial distributions of massive stars compared to lower-mass stars. The competitive accretion theory of massive star formation posits that the most massive stars should sit in deeper potential wells than lower-mass stars. This may be observable in the relative surface density or spatial concentration of the most massive stars compared to other, lower-mass stars. Massive stars in cool–collapse N-body models do end up in significantly deeper potentials, and are mass segregated. However, in models of warm (expanding) star-forming regions, whilst the massive stars do come to be in deeper potentials than average stars, they are not mass segregated. In the purely hydrodynamical SPH simulations, the massive stars do come to reside in deeper potentials, which is due to their runaway growth. However, when photoionisation and stellar winds are implemented in the simulations, these feedback mechanisms regulate the mass of the stars and disrupt the inflow of gas into the clouds’ potential wells. This generally makes the potential wells shallower than in the control runs, and prevents the massive stars from occupying deeper potentials. This in turn results in the most massive stars having a very similar spatial concentration and surface density distribution to lower-mass stars. Whilst massive stars do form via competitive accretion in our simulations, this rarely translates to a different spatial distribution and so any lack of primordial mass segregation in an observed star-forming region does not preclude competitive accretion as a viable formation mechanism for massive stars

Kinematic signatures of cluster formation from cool collapse in the Lagoon Nebula cluster NGC 6530

We examine the mass dependence of the velocity dispersion of stars in the young cluster NGC 6530 to better understand how it formed. Using a large sample of members we find that the proper motion velocity dispersion increases with stellar mass. While this trend is the opposite of that predicted if the cluster were developing energy equipartition, it is in agreement with recent N-body simulations that find such a trend develops because of the Spitzer instability. In these simulations the massive stars sink to the centre of the cluster and form a self-gravitating system with a higher velocity dispersion. If the cluster has formed by the cool collapse of an initially substructured distribution, then this occurs within 1–2 Myr, in agreement with our observations of NGC 6530. We therefore conclude that NGC 6530 formed from much more extended initial conditions and has since collapsed to form the cluster we see now. This cluster formation model is inconsistent with the idea that all stars form in dense, compact clusters and provides the first dynamical evidence that star clusters can form by hierarchical mergers between subclusters

On the mass segregation of cores and stars

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

Dynamical evolution of fractal structures in star-forming regions

The Q-parameter is used extensively to quantify the spatial distributions of stars and gas in star-forming regions as well as older clusters and associations. It quantifies the amount of structure using the ratio of the average length of a minimum spanning tree, m¯⁠, to the average length within the complete graph, s¯⁠. The interpretation of the Q-parameter often relies on comparing observed values of Q⁠, m¯⁠, and s¯ to idealised synthetic geometries, where there is little or no match between the observed star-forming regions and the synthetic regions. We measure Q⁠, m¯⁠, and s¯ over 10 Myr in N-body simulations which are compared to IC 348, NGC 1333, and the ONC. For each star-forming region we set up simulations that approximate their initial conditions for a combination of different virial rations and fractal dimensions. We find that dynamical evolution of idealised fractal geometries can account for the observed Q⁠, m¯⁠, and s¯ values in nearby star-forming regions. In general, an initially fractal star-forming region will tend to evolve to become more smooth and centrally concentrated. However, we show that initial conditions, as well as where the edge of the region is defined, can cause significant differences in the path that a star-forming region takes across the m¯−s¯ plot as it evolves. We caution that the observed Q-parameter should not be directly compared to idealised geometries. Instead, it should be used to determine the degree to which a star-forming region is either spatially substructured or smooth and centrally concentrated

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

We examine the level of substructure and mass segregation in the massive, young cluster Westerlund 1. We find that it is relatively smooth, with little or no mass segregation, but with the massive stars in regions of significantly higher than average surface density. While an expanding or bouncing-back scenario for the evolution of Westerlund 1 cannot be ruled out, we argue that the most natural model to explain these observations is one in which Westerlund 1 formed with no primordial mass segregation and at a similar or larger size than we now observe

Was Planet 9 captured in the Sun’s natal star-forming region?

The presence of an unseen ‘Planet 9’ on the outskirts of the Solar system has been invoked to explain the unexpected clustering of the orbits of several Edgeworth–Kuiper Belt Objects. We use N-body simulations to investigate the probability that Planet 9 was a free-floating planet (FFLOP) that was captured by the Sun in its birth star formation environment. We find that only 1–6 per cent of FFLOPs are ensnared by stars, even with the most optimal initial conditions for capture in star-forming regions (one FFLOP per star, and highly correlated stellar velocities to facilitate capture). Depending on the initial conditions of the star-forming regions, only 5–10 of 10 000 planets are captured on to orbits that lie within the constraints for Planet 9. When we apply an additional environmental constraint for Solar system formation – namely the injection of short-lived radioisotopes into the Sun’s protoplanetary disc from supernovae – we find the probability for the capture of Planet 9 to be almost zero

Structure and mass segregation in Galactic stellar clusters

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 characterize 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 ≈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 MSR. Our findings indicate that most clusters possess a Q parameter that falls in the range 0.7–0.8 and are thus neither strongly concentrated nor do they show significant substructure. Only 27 per cent can be considered centrally concentrated with Q values >0.8. Of the 1276 clusters, only 14 per cent show indication of significant mass segregation (MSR > 1.5). Furthermore, no correlation is found between the structure of the clusters or the degree of mass segregation with their position in the Galaxy. A comparison of the measured Q values for the young open clusters in the MWSC to N-body numerical simulations that follow the evolution of the Q parameter over the first 10 Myr of the clusters life suggests that the young clusters found in the MWSC catalogue initially possessed local mean volume densities of ρ∗ ≈ 10–100 M� pc−3

Unlocking Galactic Wolf–Rayet stars with Gaia DR2 – II. Cluster and association membership

Galactic Wolf–Rayet (WR) star membership of star-forming regions can be used to constrain the formation environments of massive stars. Here, we utilize Gaia DR2 parallaxes and proper motions to reconsider WR star membership of clusters and associations in the Galactic disc, supplemented by recent near-infrared studies of young massive clusters. We find that only 18–36 per cent of 553 WR stars external to the Galactic Centre region are located in clusters, OB associations or obscured star-forming regions, such that at least 64 per cent of the known disc WR population are isolated, in contrast with only 13 per cent of O stars from the Galactic O star Catalogue. The fraction located in clusters, OB associations or star-forming regions rises to 25–41 per cent from a global census of 663 WR stars including the Galactic Centre region. We use simulations to explore the formation processes of isolated WR stars. Neither runaways, nor low-mass clusters, are numerous enough to account for the low cluster membership fraction. Rapid cluster dissolution is excluded as mass segregation ensures WR stars remain in dense, well-populated environments. Only low-density environments consistently produce WR stars that appeared to be isolated during the WR phase. We therefore conclude that a significant fraction of WR progenitors originate in low-density association-like surroundings which expand over time. We provide distance estimates to clusters and associations host to WR stars, and estimate cluster ages from isochrone fitting

The early dynamical evolution of cool, clumpy star clusters

Observations and theory both suggest that star clusters form sub-virial (cool) with highly sub-structured distributions. We perform a large ensemble of N-body simulations of moderate-sized (N = 1000) cool, fractal clusters to investigate their early dynamical evolution. We find that cool, clumpy clusters dynamically mass segregate on a short timescale, that Trapezium-like massive higher-order multiples are commonly formed, and that massive stars are often ejected from clusters with velocities > 10 km s−1 (c.f. the average escape velocity of 2.5 km s−1 ). The properties of clusters also change rapidly on very short timescales. Young clusters may also undergo core collapse events, in which a dense core containing massive stars is hardened due to energy losses to a halo of lower-mass stars. Such events can blow young clusters apart with no need for gas expulsion. The warmer and less substructured a cluster is initially, the less extreme its evolution