arXiv subjects

Richard J. Parker

Publications and source records attributed to Richard J. Parker.

At least 73 records · Page 4Linked to original sources

arXiv2016

Isotopic enrichment of forming planetary systems from supernova pollution

Heating by short-lived radioisotopes (SLRs) such as aluminum-26 and iron-60 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 disk 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 aluminum-26 and iron-60 based on N-body simulations of typical to large clusters (1000-10000 stars) with a range of initial conditions. We quantify the pollution of protoplanetary disks 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.

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arXiv2016

Mass segregation in star clusters is not energy equipartition

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.

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arXiv2016

Dynamical evolution of star forming regions - II. Basic kinematics

We follow the dynamical evolution of young star-forming regions with a wide range of initial conditions and examine how the radial velocity dispersion, $σ$, evolves over time. We compare this velocity dispersion to the theoretically expected value for the velocity dispersion if a region were in virial equilibrium, $σ_{\rm vir}$ and thus assess the virial state ($σ/ σ_{\rm vir}$) 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, $σ$, 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, $σ_{\rm vir}$. 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 $\sim$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 $σ$, or the ratio of $σ$ 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.

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arXiv2015

Did the Solar System form in a sequential triggered star formation event?

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 SPH 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.

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arXiv2015

On the spatial distributions of stars and gas in numerical simulations of molecular clouds

We compare the spatial distribution of stars which form in hydrodynamical simulations to the spatial distribution of the gas, using the $\mathcal{Q}$-parameter. The $\mathcal{Q}$-parameter enables a self-consistent comparison between the stars and gas because it uses a pixelated image of the gas as a distribution of points, in the same way that the stars (sink particles in the simulations) are a distribution of points. We find that, whereas the stars have a substructured, or hierarchical spatial distribution ($\mathcal{Q} \sim 0.4 - 0.7$), the gas is dominated by a smooth, concentrated component and typically has $\mathcal{Q} \sim 0.9$. We also find no statistical difference between the structure of the gas in simulations that form with feedback, and those that form without, despite these two processes producing visually different distributions. These results suggest that the link between the spatial distributions of gas, and the stars which form from them, is non-trivial.

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arXiv2015

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

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arXiv2015

The M-dwarfs in Multiples (MinMs) survey - I. Stellar multiplicity among low-mass stars within 15 pc

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 $\sim$1 au to 100 au, while digitised wide-field archival plates were searched for wide companions from $\sim$100 au to 10,000 au. With sensitivity to the bottom of the main sequence over a separation range of 3 au 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 co-moving stellar companions and find a companion star fraction of $23.5 \pm 3.2$ 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 characterisation 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 disks and planets.

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arXiv2014

Primordial mass segregation in simulations of star formation?

We take the end result of smoothed particle hydrodynamics (SPH) simulations of star formation which include feedback from photoionisation and stellar winds and evolve them for a further 10Myr using $N$-body simulations. We compare the evolution of each simulation to a control run without feedback, and to a run with photoionisation 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 photoionisation 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.

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arXiv2014

Dynamics versus structure: breaking the density degeneracy in star formation

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, $ρ$ Oph and Corona Australis - are consistent with having evolved from the Kroupa universal initial period distribution and a binary fraction of unity.

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arXiv2014

Binaries in the field: fossils of the star formation process?

Recent observations of binary stars in the Galactic field show that the binary fraction and the mean orbital separation both decrease as a function of decreasing primary mass. We present $N$-body simulations of the effects of dynamical evolution in star-forming regions on primordial binary stars to determine whether these observed trends can be explained by the dynamical processing of a common binary population. We find that dynamical processing of a binary population with an initial binary fraction of unity and an initial excess of intermediate/wide separation (100 - 10$^4$ au) binaries does not reproduce the observed properties in the field, even in initially dense ($\sim 10^3$M$_\odot$ pc$^{-3}$) star-forming regions. If instead we adopt a field-like population as the initial conditions, most brown dwarf and M-dwarf binaries are dynamically hard and their overall fractions and separation distributions are unaffected by dynamical evolution. G-dwarf and A-star binaries in the field are dynamically intermediate in our simulated dense regions and dynamical processing does destroy some systems with separations $>$100 au. However, the formation of wide binaries through the dissolution of supervirial regions is a strong function of primary mass, and the wide G-dwarf and A-star binaries that are destroyed by dynamical evolution in subvirial regions are replenished by the formation of binaries in supervirial regions. We therefore suggest that the binary population in the field is $indicative$ of the primordial binary population in star-forming regions, at least for systems with primary masses in the range 0.02 - 3.0M$_\odot$.

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arXiv2014

Probing brown dwarf formation mechanisms with Gaia

One of the fundamental questions in star formation is whether or not brown dwarfs form in the same way as stars, or more like giant planets. If their formation scenarios are different, we might expect brown dwarfs to have a different spatial distribution to stars in nearby star-forming regions. In this contribution, we discuss methods to look for differences in their spatial distributions and show that in the only nearby star-forming region with a significantly different spatial distribution (the Orion Nebula Cluster), this is likely due to dynamical evolution. We then present a method for unravelling the past dynamical history of a star-forming region, and show that in tandem with Gaia, we will be able to discern whether observed differences are due to distinct formation mechanisms for brown dwarfs compared to stars.

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arXiv2014

Spatial differences between stars and brown dwarfs: a dynamical origin?

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, $Σ_{\rm LDR}$, and we compare the global spatial distributions using the $Λ_{\rm MSR}$ method. From a suite of twenty initially statistically identical simulations, 6/20 attain $\mathcal{R}_{\rm SSR} << 1$ $and$ $Σ_{\rm LDR} << 1$ $and$ $Λ_{\rm MSR} << 1$, 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 ($Σ_{\rm LDR} << 1$), but their global spatial distributions are indistinguishable ($Λ_{\rm MSR} = 1$) 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.

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arXiv2013

Constraints on Massive Star Formation: Cygnus OB2 was always an Association

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 Mo this result suggests that very massive stars can be born in relatively low-density environments. This would imply that the massive stars in Cyg OB2 did not form by competitive accretion, or by mergers.

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arXiv2013

Dynamical evolution of star forming regions

We model the dynamical evolution of star forming regions with a wide range of initial properties. We follow the evolution of the regions' substructure using the Q-parameter, we search for dynamical mass segregation using the Lambda_MSR technique, and we also quantify the evolution of local density around stars as a function of mass using the Sigma_LDR method. The amount of dynamical mass segregation measured by Lambda_MSR is generally only significant for subvirial and virialised, substructured regions - which usually evolve to form bound clusters. The Sigma_LDR method shows that massive stars attain higher local densities than the median value in all regions, even those that are supervirial and evolve to form (unbound) associations. We also introduce the Q-Sigma_LDR plot, which describes the evolution of spatial structure as a function of mass-weighted local density in a star forming region. Initially dense (>1000 stars pc^{-2}), bound regions always have Q >1, Sigma_LDR > 2 after 5Myr, whereas dense unbound regions always have Q < 1, Sigma_LDR > 2 after 5Myr. Less dense regions (<100 stars pc^{-2}) do not usually exhibit Sigma_LDR > 2 values, and if relatively high local density around massive stars arises purely from dynamics, then the Q-Sigma_LDR plot can be used to estimate the initial density of a star forming region.

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arXiv2013

Supernova enrichment and dynamical histories of solar-type stars in clusters

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 25M_Sun star which is expected to explode as a supernova at about 6.6Myr. We determine the number of Solar (G)-type stars that are within 0.1 - 0.3pc of the 25M_Sun 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-100au encounters, and which also do not suffer strong dynamical perturbations. The evolution of a suite of twenty 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 1 - 2 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 6.6Myr. If we sum together simulations with identical initial conditions, then ~1 per cent of all G-dwarfs in our simulations are enriched, unperturbed singletons.

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arXiv2013

On the frequency of planetary systems around G-dwarfs

We determine the fraction of G-dwarf stars that could host stable planetary systems based on the observed properties of binaries in the Galactic field, and in various postulated primordial binary populations, which assume that the primordial binary fraction is higher than that in the field. We first consider the frequency of Solar System analogues - planetary systems that form either around a single G-dwarf star, or a binary containing a G-dwarf where the binary separation exceeds 100-300au. If the primordial binary fraction and period distribution is similar to that in the field, then up to 63 per cent of G-dwarf systems could potentially host a Solar System analogue. However, if the primordial binary fraction is higher, the fraction of G-dwarf systems that could host a planetary system like our own is lowered to 38 per cent. We extend our analysis to consider the fraction of G-dwarf systems (both single and binary) that can host either circumprimary planets (orbiting the primary star of the binary) or circumbinary planets (orbiting both stars in the binary) for fiducial planetary separations between 1 - 100au. Depending on the assumed binary population, in the circumprimary case between 65 and 95 per cent of systems can host a planet at 1au, decreasing to between 20 and 65 per cent of systems that can host a planet at 100au. In the circumbinary case, between 5 and 59 per cent of systems can host a planet at 1au, increasing to between 34 and 75 per cent of systems that can host a planet at 100au. Our results suggest that the assumed binary fraction is the key parameter in determining the fraction of potentially stable planetary systems in G-dwarf systems and that using the present-day value may lead to significant overestimates if the binary fraction was initially higher.

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arXiv2013

The binary companion mass ratio distribution: an imprint of the star formation process?

We explore the effects of dynamical evolution in dense clusters on the companion mass ratio distribution (CMRD) of binary stars. Binary systems are destroyed by interactions with other stars in the cluster, lowering the total binary fraction and significantly altering the initial semi-major axis distribution. However, the shape of the CMRD is unaffected by dynamics; an equal number of systems with high mass ratios are destroyed compared to systems with low mass ratios. We might expect a weak dependence of the survivability of a binary on its mass ratio because its binding energy is proportional to both the primary and secondary mass components of the system. However, binaries are broken up by interactions in which the perturbing star has a significantly higher energy (by a factor of >10, depending on the particular binary properties) than the binding energy of the binary, or through multiple interactions in the cluster. We therefore suggest that the shape of the observed binary CMRD is an outcome of the star formation process, and should be measured in preference to the distributions of orbital parameters, such as the semi-major axis distribution.

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arXiv2013

Imprints of feedback in young gasless clusters?

We present the results of N-body simulations in which we take the masses, positions and velocities of sink particles from five pairs of hydrodynamical simulations of star formation by Dale et al. (2012, 2013) and evolve them for a further 10Myr. We compare the dynamical evolution of star clusters that formed under the influence of mass-loss driven by photoionization feedback, to the evolution of clusters that formed without feedback. We remove any remaining gas and follow the evolution of structure in the clusters (measured by the Q-parameter), half-mass radius, central density, surface density and the fraction of bound stars. There is little discernible difference in the evolution of clusters that formed with feedback compared to those that formed without. The only clear trend is that all clusters which form without feedback in the hydrodynamical simulations lose any initial structure over 10Myr, whereas some of the clusters which form with feedback retain structure for the duration of the subsequent N-body simulation. This is due to lower initial densities (and hence longer relaxation times) in the clusters from Dale et al. (2012, 2013) which formed with feedback, which prevents dynamical mixing from erasing substructure. However, several other conditions (such as supervirial initial velocities) also preserve substructure, so at a given epoch one would require knowledge of the initial density and virial state of the cluster in order to determine whether star formation in a cluster has been strongly influenced by feedback.

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