ALBERT

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

Description: The presence and abundance of the short-lived radioisotopes (SLRs) 26 Al and 60 Fe during the formation of the Solar system is difficult to explain unless the Sun formed in the vicinity of one or more massive star(s) that exploded as supernovae. Two different scenarios have been proposed to explain the delivery of SLRs to the protosolar nebula: (i) direct pollution of the protosolar disc by supernova ejecta, and (ii) the formation of the Sun in a sequential star formation event in which supernovae shockwaves trigger further star formation which is enriched in SLRs. The sequentially triggered model has been suggested as being more astrophysically likely than the direct pollution scenario. In this paper, we investigate this claim by analysing a combination of N -body and smoothed particle hydrodynamics simulations of star formation. We find that sequential star formation would result in large age spreads (or even bi-modal age distributions for spatially coincident events) due to the dynamical relaxation of the first star formation event(s). Secondly, we discuss the probability of triggering spatially and temporally discrete populations of stars and find this to be only possible in very contrived situations. Taken together, these results suggest that the formation of the Solar system in a triggered star formation event is as improbable, if not more so, than the direct pollution of the protosolar disc by a supernova.

Description: Heating by short-lived radioisotopes (SLRs) such as 26 Al and 60 Fe fundamentally shaped the thermal history and interior structure of Solar system planetesimals during the early stages of planetary formation. The subsequent thermo-mechanical evolution, such as internal differentiation or rapid volatile degassing, yields important implications for the final structure, composition and evolution of terrestrial planets. SLR-driven heating in the Solar system is sensitive to the absolute abundance and homogeneity of SLRs within the protoplanetary disc present during the condensation of the first solids. In order to explain the diverse compositions found for extrasolar planets, it is important to understand the distribution of SLRs in active planet formation regions (star clusters) during their first few Myr of evolution. By constraining the range of possible effects, we show how the imprint of SLRs can be extrapolated to exoplanetary systems and derive statistical predictions for the distribution of 26 Al and 60 Fe based on N -body simulations of typical to large clusters (10 3 –10 4 stars) with a range of initial conditions. We quantify the pollution of protoplanetary discs by supernova ejecta and show that the likelihood of enrichment levels similar to or higher than the Solar system can vary considerably, depending on the cluster morphology. Furthermore, many enriched systems show an excess in radiogenic heating compared to Solar system levels, which implies that the formation and evolution of planetesimals could vary significantly depending on the birth environment of their host stars.

Description: We present a large-scale, volume-limited companion survey of 245 late-K to mid-M (K7-M6) dwarfs within 15 pc. Infrared adaptive optics (AO) data were analysed from the Very Large Telescope, Subaru Telescope, Canada–France–Hawaii Telescope, and MMT Observatory to detect close companions to the sample from ~ 1 to 100 au, while digitized wide-field archival plates were searched for wide companions from ~ 100 to 10 000 au. With sensitivity to the bottom of the main sequence over a separation range of 3 to 10 000 au, multiple AO and wide-field epochs allow us to confirm candidates with common proper motions, minimize background contamination, and enable a measurement of comprehensive binary statistics. We detected 65 comoving stellar companions and find a companion star fraction of 23.5 ± 3.2 per cent over the 3 au to 10 000 au separation range. The companion separation distribution is observed to rise to a higher frequency at smaller separations, peaking at closer separations than measured for more massive primaries. The mass ratio distribution across the q  = 0.2–1.0 range is flat, similar to that of multiple systems with solar-type primaries. The characterization of binary and multiple star frequency for low-mass field stars can provide crucial comparisons with star-forming environments and hold implications for the frequency and evolutionary histories of their associated discs and planets.

Description: We follow the dynamical evolution of young star-forming regions with a wide range of initial conditions and examine how the radial velocity dispersion, , evolves over time. We compare this velocity dispersion to the theoretically expected value for the velocity dispersion if a region were in virial equilibrium, vir and thus assess the virial state (/ vir ) of these systems. We find that in regions that are initially subvirial, or in global virial equilibrium but subvirial on local scales, the system relaxes to virial equilibrium within several million years, or roughly 25–50 crossing times, according to the measured virial ratio. However, the measured velocity dispersion, , appears to be a bad diagnostic of the current virial state of these systems as it suggests that they become supervirial when compared to the velocity dispersion estimated from the virial mass, vir . We suggest that this discrepancy is caused by the fact that the regions are never fully relaxed, and that the early non-equilibrium evolution is imprinted in the one-dimensional velocity dispersion at these early epochs. If measured early enough (〈2 Myr in our simulations, or ~20 crossing times), the velocity dispersion can be used to determine whether a region was highly supervirial at birth without the risk of degeneracy. We show that combining , or the ratio of to the interquartile range (IQR) dispersion, with measures of spatial structure, places stronger constraints on the dynamical history of a region than using the velocity dispersion in isolation.

Description: We examine substructure and mass segregation in the massive OB association Cygnus OB2 to better understand its initial conditions. Using a well-understood Chandra X-ray selected sample of young stars, we find that Cyg OB2 exhibits considerable physical substructure and has no evidence for mass segregation, both indications that the association is not dynamically evolved. Combined with previous kinematical studies we conclude that Cyg OB2 is dynamically very young, and what we observe now is very close to its initial conditions: Cyg OB2 formed as a highly substructured, unbound association with a low volume density (〈100 stars pc –3 ). This is inconsistent with the idea that all stars form in dense, compact clusters. The massive stars in Cyg OB2 show no evidence for having formed particularly close to one another, nor in regions of higher than average density. Since Cyg OB2 contains stars as massive as ~100 M , this result suggests that very massive stars can be born in relatively low-density environments. This would imply that massive stars in Cyg OB2 did not form by competitive accretion, or by mergers.

Description: We use N -body simulations of star cluster evolution to explore the hypothesis that short-lived radioactive isotopes found in meteorites, such as 26 Al, were delivered to the Sun's protoplanetary disc from a supernova at the epoch of Solar system formation. We cover a range of star cluster formation parameter space and model both clusters with primordial substructure and those with smooth profiles. We also adopt different initial virial ratios – from cool, collapsing clusters to warm, expanding associations. In each cluster, we place the same stellar population; the clusters each have 2100 stars and contain one massive 25 M star which is expected to explode as a supernova at about 6.6 Myr. We determine the number of solar (G)-type stars that are within 0.1–0.3 pc of the 25 M star at the time of the supernova, which is the distance required to enrich the protoplanetary disc with the 26 Al abundances found in meteorites. We then determine how many of these G-dwarfs are unperturbed ‘singletons’; stars which are never in close binaries, nor suffer sub-100 au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of 20 initially identical clusters is highly stochastic, with the supernova enriching over 10 G-dwarfs in some clusters, and none at all in others. Typically, only ~25 per cent of clusters contain enriched, unperturbed singletons, and usually only one to two per cluster (from a total of 96 G-dwarfs in each cluster). The initial conditions for star formation do not strongly affect the results, although a higher fraction of supervirial (expanding) clusters would contain enriched G-dwarfs if the supernova occurred earlier than 6.6 Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.

Description: We use N -body simulations to compare the evolution of spatial distributions of stars and brown dwarfs in young star-forming regions. We use three different diagnostics: the ratio of stars to brown dwarfs as a function of distance from the region's centre, $\mathcal {R}_{\rm SSR}$ , the local surface density of stars compared to brown dwarfs, LDR , and we compare the global spatial distributions using the MSR method. From a suite of 20 initially statistically identical simulations, 6/20 attain $\mathcal {R}_{\rm SSR} \ll 1$ and LDR  〈〈 1 and MSR  〈〈 1, indicating that dynamical interactions could be responsible for observed differences in the spatial distributions of stars and brown dwarfs in star-forming regions. However, many simulations also display apparently contradictory results – for example, in some cases the brown dwarfs have much lower local densities than stars ( LDR  〈〈 1), but their global spatial distributions are indistinguishable ( MSR  = 1) and the relative proportion of stars and brown dwarfs remains constant across the region ( $\mathcal {R}_{\rm SSR} = 1$ ). Our results suggest that extreme caution should be exercised when interpreting any observed difference in the spatial distribution of stars and brown dwarfs, and that a much larger observational sample of regions/clusters (with complete mass functions) is necessary to investigate whether or not brown dwarfs form through similar mechanisms to stars.

Description: The initial density of individual star-forming regions (and by extension the birth environment of planetary systems) is difficult to constrain due to the ‘density degeneracy problem’: an initially dense region expands faster than a more quiescent region due to two-body relaxation and so two regions with the same observed present-day density may have had very different initial densities. We constrain the initial densities of seven nearby star-forming regions by folding in information on their spatial structure from the $\mathcal {Q}$ -parameter and comparing the structure and present-day density to the results of N -body simulations. This in turn places strong constraints on the possible effects of dynamical interactions and radiation fields from massive stars on multiple systems and protoplanetary discs. We apply our method to constrain the initial binary population in each of these seven regions and show that the populations in only three – the Orion Nebula Cluster, Oph, and Corona Australis – are consistent with having evolved from the Kroupa universal initial period distribution and a binary fraction of unity.

Description: We take the end result of smoothed particle hydrodynamics (SPH) simulations of star formation which include feedback from photoionization and stellar winds and evolve them for a further 10 Myr using N -body simulations. We compare the evolution of each simulation to a control run without feedback, and to a run with photoionization 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 to the feedback produces only marginal differences compared to the simulations with just photoionization feedback. We search for mass segregation at different stages in the simulations; before feedback is switched on in the SPH runs, at the end of the SPH runs (before N -body integration) and during the N -body evolution. Whether a simulation is primordially mass segregated (i.e. before dynamical evolution) depends extensively on how mass segregation is defined, and different methods for measuring mass segregation give apparently contradictory results. Primordial mass segregation is also less common in the simulations when star formation occurs under the influence of feedback. Further dynamical mass segregation can also take place during the subsequent (gas-free) dynamical evolution. Taken together, our results suggest that extreme caution should be exercised when interpreting the spatial distribution of massive stars relative to low-mass stars in simulations.