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The stellar mass distribution in star-forming regions, stellar clusters and associations, the Initial Mass Function (IMF), appears to be invariant across different star-forming environments, and is consistent with the IMF observed in the Galactic field. Deviations from the field, or standard, IMF, if genuine, would be considered strong evidence for a different set of physics at play during the formation of stars in the birth region in question. We analyse N-body simulations of the evolution of spatially and kinematically substructured star-forming regions to identify the formation of binary star clusters, where two (sub)clusters which form from the same Giant Molecular Cloud orbit a common centre of mass. We then compare the mass distributions of stars in each of the subclusters and compare them to the standard IMF, which we use to draw the stellar masses in the star-forming region from which the binary cluster(s) form. In each binary cluster that forms, the mass distributions of stars in one subcluster deviates from the standard IMF, and drastically so when we apply similar mass resolution limits as for the observed binary clusters. Therefore, if a binary subcluster is observed to have an unusual IMF, this may simply be the result of dynamical evolution, rather than different physical conditions for star formation in these systems., Comment: 6 pages, 4 figures, accepted for publication in MNRAS

The recent discovery of tens of Jupiter-mass binary objects (JuMBOs) in the Orion Nebula Cluster with the James Webb Space Telescope has intensified the debate on the origin of free-floating planetary mass objects within star-forming regions. The JuMBOs have masses below the opacity limit for fragmentation, but have very wide separations (10s - 100s au), suggesting that they did not form in a similar manner to other substellar mass binaries. Here, we propose that the theory of photoerosion of prestellar cores by Lyman continuum radiation from massive stars could explain the JuMBOs in the ONC. We find that for a range of gas densities the final substellar mass is comfortably within the JuMBO mass range, and that the separations of the JuMBOs are consistent with those of more massive (G- and A-type) binaries, that would have formed from the fragmentation of the cores had they not been photoeroded. The photoerosion mechanism is most effective within the HII region(s) driven by the massive star(s). The majority of the observed JuMBOs lie outside of these regions in the ONC, but may have formed within them and then subsequently migrated due to dynamical evolution., Comment: 9 pages, 4 figures, accepted for publication in ApJ

The two main competing theories proposed to explain the formation of massive ($>10$M$_\odot$) stars -- competitive accretion and monolithic core collapse -- make different observable predictions for the environment of the massive stars during, and immediately after, their formation. Proponents of competitive accretion have long predicted that the most massive stars should have a different spatial distribution to lower-mass stars, either through the stars being mass segregated, or being in areas of higher relative densities, or sitting deeper in gravitational potential wells. We test these predictions by analysing a suite of SPH simulations where star clusters form massive stars via competitive accretion with and without feedback. We find that the most massive stars have higher relative densities, and sit in deeper potential wells, only in simulations in which feedback is not present. When feedback is included, only half of the simulations have the massive stars residing in deeper potential wells, and there are no other distinguishing signals in their spatial distributions. Intriguingly, in our simple models for monolithic core collapse, the massive stars may also end up in deeper potential wells, because if massive cores fragment the stars are still massive, and dominate their local environs. We find no robust diagnostic test in the spatial distributions of massive stars that can distinguish their formation mechanisms, and so other predictions for distinguishing between competitive accretion and monolithic collapse are required., Comment: 18 pages, 7 figures, with an Appendix containing a further 18 figures showing all the SPH simulation results. Accepted for publication in ApJ

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., Comment: 11 pages, 4 figures. Accepted for publication in ApJ

Cellulose nanocrystals (CNCs) are bioderived nanoparticles that can be isolated from various sources of natural cellulose via acid hydrolysis. However, the link between particle morphological characteristics and their ensemble behavior is poorly understood, partly because of the difficulties in controlling the CNC morphology during their extraction process. In this work, the impacts of common post-hydrolysis treatments on the CNC morphology are investigated. The results indicate that the centrifugation step commonly applied during CNC purification favors the formation of composite particles made of aligned crystallites, referred to as 'bundles'. Scanning nanobeam electron diffraction reveals that such bundles are associated preferentially along their hydrophobic faces. This is in stark contrast to the formation of misaligned composite particles that can be achieved with ionic treatments, where an uncontrolled aggregation occurs. The functional relevance of these morphological differences is demonstrated by their effect on the cholesteric self-organization of CNCs, with bundles found to exhibit a greater chiral enhancement, whereas the misaligned composite particles found to promote gelation. This study reveals the importance of the often-disregarded purification steps on the final morphology of CNCs and their resulting ensemble properties, thereby unlocking new routes for tailoring this promising material towards a variety of applications.

Observations of star-forming regions provide snapshots in time of the star formation process, and can be compared with simulation data to constrain the initial conditions of star formation. In order to make robust inferences, different metrics must be used to quantify the spatial and kinematic distributions of stars. In this paper, we assess the suitability of the INDICATE (INdex to Define Inherent Clustering And TEndencies) method as a diagnostic to infer the initial conditions of star-forming regions that subsequently undergo dynamical evolution. We use INDICATE to measure the degree of clustering in N-body simulations of the evolution of star-forming regions with different initial conditions. We find that the clustering of individual stars, as measured by INDICATE, becomes significantly higher in simulations with higher initial stellar densities, and is higher in subvirial star-forming regions where significant amounts of dynamical mixing has occurred. We then combine INDICATE with other methods that measure the mass segregation, relative stellar surface density ratio and the morphology (Q-parameter) of star-forming regions, and show that the diagnostic capability of INDICATE increases when combined with these other metrics., Comment: 17 pages (including figures), 12 Figures. Accepted for publication in MNRAS

Whilst the formation of Solar system planets is constrained by meteoritic evidence, the geophysical history of low-mass exoplanets is much less clear. The bulk composition and climate states of rocky exoplanets may vary significantly based on the composition and properties of the planetesimals they form from. An important factor influenced by planetesimal composition is water content, where the desiccation of accreting planetesimals impacts the final water content of the resultant planets. While the inner planets of the Solar system are comparatively water-poor, recent observational evidence from exoplanet bulk densities and planetary formation models suggest that rocky exoplanets engulfed by substantial layers of high-pressure ices or massive steam atmospheres could be widespread. Here we quantify variations in planetesimal desiccation due to potential fractionation of the two short-lived radioisotopes 26Al and 60Fe relevant for internal heating on planetary formation timescales. We focus on how order of magnitude variations in 60Fe can affect the water content of planetesimals, and how this may alter the formation of extrasolar ocean worlds. We find that heating by 26Al is the dominant cause of planetesimal heating in any Solar system analogue scenario, thus validating previous works focussing only on this radioisotope. However, 60Fe can become the primary heating source in the case of high levels of supernova enrichment in massive star-forming regions. These diverging scenarios can affect the formation pathways, bulk volatile budget, and climate diversity of low-mass exoplanets., Comment: 12 pages, 13 figures

Simulations of the effects of stellar fly-bys on planetary systems in star-forming regions show a strong dependence on subtle variations in the initial spatial and kinematic substructure of the regions. For similar stellar densities, the more substructured star-forming regions disrupt up to a factor of two more planetary systems. We extend this work to look at the effects of substructure on stellar binary populations. We present $N$-body simulations of substructured, and non-substructured (smooth) star-forming regions in which we place different populations of stellar binaries. We find that for binary populations that are dominated by close ($<$100au) systems, a higher proportion are destroyed in substructured regions. However, for wider systems ($>$100au), a higher proportion are destroyed in smooth regions. The difference is likely due to the hard-soft, or fast-slow boundary for binary destruction. Hard (fast/close) binaries are more likely to be destroyed in environments with a small velocity dispersion (kinematically substructured regions), whereas soft (slow/wide) binaries are more likely to be destroyed in environments with higher velocity dispersions (non-kinematically substructured regions). Due to the vast range of stellar binary semimajor axes in star-forming regions ($10^{-2} - 10^4$au) these differences are small and hence unlikely to be observable. However, planetary systems have a much smaller initial semimajor axis range (likely $\sim$1 -- 100au for gas giants) and here the difference in the fraction of companions due to substructure could be observed if the star-forming regions that disrupt planetary systems formed with similar stellar densities., Comment: 9 pages, 5 figures, accepted for publication in MNRAS

The presence of short-lived radioisotopes (SLRs) 26-Al and 60-Fe in the Solar system places constraints on the initial conditions of our planetary system. Most theories posit that the origin of 26-Al and 60-Fe is in the interiors of massive stars, and they are either delivered directly to the protosolar disc from the winds and supernovae of the massive stars, or indirectly via a sequential star formation event. However, massive stars that produce SLRs also emit photoionising far and extreme ultraviolet radiation, which can destroy the gas component of protoplanetary discs, possibly precluding the formation of gas giant planets like Jupiter and Saturn. Here, we perfom N-body simulations of star-forming regions and determine whether discs that are enriched in SLRs can retain enough gas to form Jovian planets. We find that discs are enriched and survive the photoionising radiation only when the dust radius of the disc is fixed and not allowed to move inwards due to the photoevaporation, or outwards due to viscous spreading. Even in this optimal scenario, not enough discs survive until the supernovae of the massive stars and so have zero or very little enrichment in 60-Fe. We therefore suggest that the delivery of SLRs to the Solar system may not come from the winds and supernovae of massive stars., Comment: 13 pages, 4 figures, accepted for publication in MNRAS

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., Comment: 11 pages, 8 figures, accepted for publication in MNRAS

Short-lived radioisotopes, in particular 26-Al and 60-Fe, are thought to contribute to the internal heating of the Earth, but are significantly more abundant in the Solar System compared to the Interstellar Medium. The presence of their decay products in the oldest Solar System objects argues for their inclusion in the Sun's protoplanetary disc almost immediately after the star formation event that formed the Sun. Various scenarios have been proposed for their delivery to the Solar System, usually involving one or more core-collapse supernovae of massive stars. An alternative scenario involves the young Sun encountering an evolved Asymptotic Giant Branch (AGB) star. AGBs were previously discounted as a viable enrichment scenario for the Solar System due to the presumed low probability of an encounter between an old, evolved star and a young pre-main sequence star. We report the discovery in Gaia data of an interloping AGB star in the star-forming region NGC2264, demonstrating that old, evolved stars can encounter young forming planetary systems. We use simulations to calculate the yields of 26-Al and 60-Fe from AGBs and their contribution to the long-term geophysical heating of a planet, and find that these are comfortably within the range previously calculated for the Solar System., Comment: 8 pages, 4 figures, accepted for publication in ApJL

The abundance of the short-lived radioisotopes 26-Al and 60-Fe in the early Solar system is usually explained by the Sun either forming from pre-enriched material, or the Sun's protosolar disc being polluted by a nearby supernova explosion from a massive star. Both hypotheses suffer from significant drawbacks: the former does not account for the dynamical evolution of star-forming regions, while in the latter the time for massive stars to explode as supernovae can be similar to, or even longer than, the lifetime of protoplanetary discs. In this paper, we extend the disc enrichment scenario to include the contribution of 26-Al from the winds of massive stars before they explode as supernovae. We use N-body simulations and a post-processing analysis to calculate the amount of enrichment in each disc, and we vary the stellar density of the star-forming regions. We find that stellar winds contribute to disc enrichment to such an extent that the Solar system's 26-Al/60-Fe ratio is reproduced in up to 50 per cent of discs in dense (rho = 1000Msun pc^-3) star-forming regions. When winds are a significant contributor to the SLR enrichment, we find that Solar system levels of enrichment can occur much earlier (before 2.5 Myr) than when enrichment occurs from supernovae, which start to explode at later ages (>4 Myr). We find that Solar system levels of enrichment all but disappear in low-density star-forming regions (rho < 10Msun pc^-3), implying that the Solar system must have formed in a dense, populous star-forming region if 26-Al and 60-Fe were delivered directly to the protosolar disc from massive-star winds and supernovae., Comment: 16 pages, 10 figures, 1 appendix with 3 further figures, accepted for publication in MNRAS

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., Comment: 13 pages + appendices, 10 figures, accepted for publication in MNRAS

Simulations show that the orbits of planets are readily disrupted in dense star-forming regions; planets can be exchanged between stars, become free-floating and then be captured by other stars. However, dense star-forming regions also tend to be populous, containing massive stars that emit photoionising radiation, which can evaporate the gas in protoplanetary discs. We analyse N-body simulations of star-forming regions containing Jovian-mass planets and determine the times when their orbits are altered, when they become free-floating, and when they are stolen or captured. Simultaneously, we perform calculations of the evolution of protoplanetary discs when exposed to FUV radiation fields from massive stars in the same star-forming regions. In almost half (44 per cent) of the planetary systems that are disrupted - either altered, captured, stolen or become free-floating, we find that the radius of the protoplanetary disc evolves inwards, or the gas in the disc is completely evaporated, before the planets' orbits are disrupted. This implies that planets that are disrupted in dense, populous star-forming regions are more likely to be super Earths or mini Neptunes, as Jovian mass planets would not be able to form due to mass loss from photoevaporation. Furthermore, the recent discoveries of distant Jovian mass planets around tightly-packed terrestrial planets argue against their formation in populous star-forming regions, as photoevaporation would preclude gas giant planet formation at distances of more than a few au., Comment: 8 pages, 6 figures, accepted for publication in MNRAS

Exoplanets display incredible diversity, from planetary system architectures around Sun-like stars that are very different to our Solar System, to planets orbiting post-main sequence stars or stellar remnants. Recently the B-star Exoplanet Abundance STudy (BEAST) reported the discovery of at least two super-Jovian planets orbiting massive stars in the Sco Cen OB association. Whilst such massive stars do have Keplerian discs, it is hard to envisage gas giant planets being able to form in such hostile environments. We use N-body simulations of star-forming regions to show that these systems can instead form from the capture of a free-floating planet, or the direct theft of a planet from one star to another, more massive star. We find that this occurs on average once in the first 10Myr of an association's evolution, and that the semimajor axes of the hitherto confirmed BEAST planets (290 and 556au) are more consistent with capture than theft. Our results lend further credence to the notion that planets on more distant (>100au) orbits may not be orbiting their parent star., Comment: 5 pages, 4 figures, published in MNRAS Letters

Protoplanetary discs are crucial to understanding how planets form and evolve, but these objects are subject to the vagaries of the birth environments of their host stars. In particular, photoionising radiation from massive stars has been shown to be an effective agent in disrupting protoplanetary discs. External photoevaporation leads to the inward evolution of the radii of discs, whereas the internal viscous evolution of the disc causes the radii to evolve outwards. We couple N-body simulations of star-forming regions with a post-processing analysis of disc evolution to determine how the radius and mass distributions of protoplanetary discs evolve in young star-forming regions. To be consistent with observations, we find that the initial disc radii must be of order 100au, even though these discs are readily destroyed by photoevaporation from massive stars. Furthermore, the observed disc radii distribution in the Orion Nebula Cluster is more consistent with moderate initial stellar densities (100M$_\odot$ pc$^{-3}$), in tension with dynamical models that posit much higher inital densities for the ONC. Furthermore, we cannot reproduce the observed disc radius distribution in the Lupus star-forming region if its discs are subject to external photoevaporation. A more detailed comparison is not possible due to the well-documented uncertainties in determining the ages of pre-main sequence (disc-hosting) stars., Comment: 17 pages + 2 pages of Appendices, 10 figures, accpeted for publication in MNRAS

We investigate whether spatial-kinematic substructure in young star-forming regions can be quantified using Moran's $I$ statistic. Its presence in young star clusters would provide an indication that the system formed from initially substructured conditions, as expected by the hierarchical model of star cluster formation, even if the cluster were spatially smooth and centrally concentrated. Its absence, on the other hand, would be evidence that star clusters form monolithically. The Moran's $I$ statistic is applied to $N$-body simulations of star clusters with different primordial spatial-velocity structures, and its evolution over time is studied. It is found that this statistic can be used to reliably quantify spatial-kinematic substructure, and can be used to provide evidence as to whether the spatial-kinematic structure of regions with ages $\lesssim$ 6 Myr is best reproduced by the hierarchical or monolithic models of star formation. Moran's $I$ statistic is also able to conclusively say whether the data are $not$ consistent with initial conditions that lack kinematic substructure, such as the monolithic model, in regions with ages up to, and potentially beyond, 10 Myrs. This can therefore provide a kinematic signature of the star cluster formation process that is observable for many Myr after any initial spatial structure has been erased., Comment: 14 pages, 10 figures, accepted for publication in MNRAS

Gravitational interactions in star-forming regions are capable of disrupting and destroying planetary systems, as well as creating new ones. In particular, a planet can be stolen, where it is directly exchanged between passing stars during an interaction; or captured, where a planet is first ejected from its birth system and is free-floating for a period of time, before being captured by a passing star. We perform sets of direct N-body simulations of young, substructured star-forming regions, and follow their evolution for 10 Myr in order to determine how many planets are stolen and captured, and their respective orbital properties. We show that in high density star-forming regions, stolen and captured planets have distinct properties. The semimajor axis distribution of captured planets is significantly skewed to wider orbits compared to the semimajor axis distribution of stolen planets and planets that are still orbiting their parent star (preserved planets). However, the eccentricity and inclination distributions of captured and stolen planets are similar, but in turn very different to the inclination and eccentricity distributions of preserved planets. In low-density star-forming regions these differences are not as distinct but could still, in principle, be used to determine whether observed exoplanets have likely formed in situ or have been stolen or captured. We find that the initial degree of spatial and kinematic substructure in a star-forming region is as important a factor as the stellar density in determining whether a planetary system will be altered, disrupted, captured or stolen., Comment: 15 pages, 10 figures, 1 appendix, accepted for publication in MNRAS

A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are no odd-degree orthogonal constituents. We further show that if the reduction mod p of an ordinary character is orthogonally stable, this determinant is the reduction mod p of the ordinary one. In particular, if the characteristic does not divide the group order, we immediately see in which orthogonal group it lies. We sketch methods for computing this determinant, and give some examples.

Let $G$ be a finite group and $K$ a finite field of characteristic $2$. Denote by $t$ the $2$-rank of the commutator factor group $G/G'$ and by $s$ the number of self-dual simple $KG$-modules. Then the Witt group of equivariant quadratic forms $\WQ (K,G)$ is isomorphic to an elementary abelian $2$-group of rank $s+t$.

We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20 to 450 indicate that a sphere with the precise critical density, higher than the bottom layer density, can display behaviors such as bounce or arrestment after crossing the interface. We experimentally demonstrate that such a critical sphere density increases linearly as the bottom fluid density increases with a fixed top fluid density. Additionally, the critical density approaches the bottom layer fluid density as the thickness of density transition layer increases. We propose an estimation of the critical density based on the potential energy. With assuming the zero layer thickness, the estimation constitutes an upper bound of the critical density with less than 0.043 relative difference within the experimental density regime 0.997 $g/cm^{3}$ $\sim $ 1.11 $g/cm^{3}$ under the zero layer thickness assumption. By matching the experimental layer thickness, we obtain a critical density estimation with less than 0.01 relative difference within the same parameter regime.

We quantify the spatial distribution of stars for two subclusters centred around the massive/intermediate mass stars S Mon and IRS1/2 in the NGC2264 star-forming region. We find that both subclusters are have neither a substructured, nor a centrally concentrated distribution according to the Q-parameter. Neither subcluster displays mass segregation according to the $\Lambda_{\rm MSR}$ ratio, but the most massive stars in IRS1/2 have higher relative surface densities according to the $\Sigma_{\rm LDR}$ ratio. We then compare these quantities to the results of N-body simulations to constrain the initial conditions of NGC2264, which are consistent with having been dense ($\tilde{\rho} \sim 10^4$M$_\odot$pc$^{-3}$), highly substructured and subvirial. These initial conditions were also derived from a separate analysis of the runaway and walkaway stars in the region, and indicate that star-forming regions within 1kpc of the Sun likely have a broad range of initial stellar densities. In the case of NGC2264, its initial stellar density could have been high enough to cause the destruction or truncation of protoplanetary discs and fledgling planetary systems due to dynamical encounters between stars in the early stages of its evolution., Comment: 13 pages, 5 figures, 4 tables, 1 short appendix. Accepted for publication in MNRAS. This paper complements the results from Schoettler et al 2021 (see arXiv:2111.14892)

The ability to make meaningful comparisons between theoretical and observational data of star-forming regions is key to understanding the star formation process. In this paper we test the performance of INDICATE, a new method to quantify the clustering tendencies of individual stars in a region, on synthetic star-forming regions with sub-structured, and smooth, centrally concentrated distributions. INDICATE quantifies the amount of stellar affiliation of each individual star, and also determines whether this affiliation is above random expectation for the star-forming region in question. We show that INDICATE cannot be used to quantify the overall structure of a region due to a degeneracy when applied to regions with different geometries. We test the ability of INDICATE to detect differences in the local stellar surface density and its ability to detect and quantify mass segregation. We then compare it to other methods such as the mass segregation ratio $\Lambda_{\rm{MSR}}$, the local stellar surface density ratio $\Sigma_{\rm{LDR}}$ and the cumulative distribution of stellar positions. INDICATE detects significant differences in the clustering tendencies of the most massive stars when they are at the centre of a smooth, centrally concentrated distribution, corresponding to areas of greater stellar surface density. When applied to a subset of the 50 most massive stars we show INDICATE can detect signals of mass segregation. We apply INDICATE to the following nearby star-forming regions: Taurus, ONC, NGC 1333, IC 348 and $\rho$ Ophiuchi and find a diverse range of clustering tendencies in these regions., Comment: 16 pages + appendices, 10 figures, accepted for publication in MNRAS

Fast, ejected stars have been found around several young star-forming regions, such as the Orion Nebula Cluster (ONC). These ejected stars can be used to constrain the initial density, spatial and kinematic substructure when compared to predictions from $N$-body simulations. We search for runaway and slower walkaway stars using $Gaia$ DR2 within 100 pc of NGC 2264, which contains subclustered regions around higher-mass OB-stars (S Mon, IRS 1 and IRS 2). We find five runaways and nine walkaways that trace back to S Mon and six runaways and five walkaways that trace back to IRS 1/2 based on their 3D-kinematics. We compare these numbers to a range of $N$-body simulations with different initial conditions. The number of runaways/walkaways is consistent with initial conditions with a high initial stellar density ($\sim$10 000 M$_{\odot}$ pc$^{-3}$), a high initial amount of spatial substructure and either a subvirial or virialised ratio for all subclusters. We also confirm the trajectories of our ejected stars using the data from $Gaia$ EDR3, which reduces the number of runaways from IRS 1/2 from six to four but leaves the number of runaways from S Mon unchanged. The reduction in runaways is due to smaller uncertainties in the proper motion and changes in the parallax/distance estimate for these stars in $Gaia$ EDR3. We find further runaway/walkaway candidates based on proper motion alone in $Gaia$ DR2, which could increase these numbers once radial velocities are available. We also expect further changes in the candidate list with upcoming $Gaia$ data releases., Comment: 21 pages, 6 figures, accepted for publication in MNRAS

School value-added models are widely applied to study, monitor, and hold schools to account for school differences in student learning. The traditional model is a mixed-effects linear regression of student current achievement on student prior achievement, background characteristics, and a school random intercept effect. The latter is referred to as the school value-added score and measures the mean student covariate-adjusted achievement in each school. In this article, we argue that further insights may be gained by additionally studying the variance in this quantity in each school. These include the ability to identify both individual schools and school types that exhibit unusually high or low variability in student achievement, even after accounting for differences in student intakes. We explore and illustrate how this can be done via fitting mixed-effects location scale versions of the traditional school value-added model. We discuss the implications of our work for research and school accountability systems.

When pursuing sustainable approaches to fabricate photonic structures, nature can be used as a source of inspiration for both the nanoarchitecture and the constituent materials. Although several biomaterials have been promised as suitable candidates for photonic materials and pigments, their fabrication processes have been limited to the small to medium-scale production of films. Here, by employing a substrate-free process, structurally coloured microparticles are produced via the confined self-assembly of a cholesteric cellulose nanocrystal (CNC) suspension within emulsified microdroplets. Upon drying, the droplets undergo multiple buckling events, which allow for greater contraction of the nanostructure than predicted for a spherical geometry. This buckling, combined with a solvent or thermal post-treatment, enables the production of dispersions of vibrant red, green, and blue cellulose photonic pigments. The hierarchical structure of these pigments enables the deposition of coatings with angular independent colour, offering a consistent visual appearance across a wide range of viewing angles., Comment: 60 pages, 29 figures and 2 tables

Planets are observed to orbit the component star(s) of stellar binary systems on so-called circumprimary or circumsecondary orbits, as well as around the entire binary system on so-called circumbinary orbits. Depending on the orbital parameters of the binary system a planet will be dynamically stable if it orbits within some critical separation of the semimajor axis in the circumprimary case, or beyond some critical separation for the circumbinary case. We present N-body simulations of star-forming regions that contain populations of primordial binaries to determine the fraction of binary systems that can host stable planets at various semimajor axes, and how this fraction of stable systems evolves over time. Dynamical encounters in star-forming regions can alter the orbits of some binary systems, which can induce long-term dynamical instabilities in the planetary system and can even change the size of the habitable zone(s) of the component stars. However, the overall fraction of binaries that can host stable planetary systems is not greatly affected by either the assumed binary population, or the density of the star-forming region. Instead, the critical factor in determining how many stable planetary systems exist in the Galaxy is the stellar binary fraction - the more stars that are born as singles in stellar nurseries, the higher the fraction of stable planetary systems., Comment: 13 pages, 7 figures, 2 short appendices, accepted for publication in MNRAS. A video abstract created by Helena Gibbon is available here: https://youtu.be/76kANnTK9-s