arXiv subjects

A. P. Whitworth

Publications and source records attributed to A. P. Whitworth.

At least 55 records · Page 3Linked to original sources

arXiv2016

Forming isolated brown dwarfs by turbulent fragmentation

We use Smoothed Particle Hydrodynamics to explore the circumstances under which an isolated very-low-mass prestellar core can be formed by colliding turbulent flows and collapse to form a brown-dwarf. Our simulations suggest that the flows need not be very fast, but do need to be very strongly convergent, i.e. the gas must flow in at comparable speeds from all sides, which seems rather unlikely. We therefore revisit the object Oph-B11, which Andre, Ward-Thompson and Greaves (2012) have identified as a prestellar core with mass between $\sim 0.020\,\mathrm{M_\odot}$ and $\sim 0.030\,\mathrm{M_\odot}$. We reanalyse the observations using a Markov-chain Monte Carlo method that allows us (i) to include the uncertainties on the distance, temperature and dust mass opacity, and (ii) to consider different Bayesian prior distributions of the mass. We estimate that the posterior probability that Oph-B11 has a mass below the hydrogen burning limit at $\sim 0.075\,\mathrm{M_\odot}$, is between 0.66 and 0.86. We conclude that, if Oph-B11 is destined to collapse, it probably will form a brown dwarf. However, the flows required to trigger this appear to be so contrived that it is difficult to envisage this being the only way, or even a major way, of forming isolated brown dwarfs. Moreover, Oph-B11 could easily be a transient, bouncing, prolate core, seen end-on; there could, indeed should, be many such objects masquerading as very low-mass prestellar cores.

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arXiv2015

The Role of Discs in the Collapse and Fragmentation of Prestellar Cores

Disc fragmentation provides an important mechanism for producing low mass stars in prestellar cores. Here, we describe Smoothed Particle Hydrodynamics simulations which show how populations of prestellar cores evolve into stars. We find the observed masses and multiplicities of stars can be recovered under certain conditions. First, protostellar feedback from a star must be episodic. The continuous accretion of disc material on to a central protostar results in local temperatures which are too high for disc fragmentation. If, however, the accretion occurs in intense outbursts, separated by a downtime of $\sim10^4\,\mathrm{years}$, gravitational instabilities can develop and the disc can fragment. Second, a significant amount of the cores' internal kinetic energy should be in solenoidal turbulent modes. Cores with less than a third of their kinetic energy in solenoidal modes have insufficient angular momentum to form fragmenting discs. In the absence of discs, cores can fragment but results in a top heavy distribution of masses with very few low mass objects.

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arXiv2015

Temperature as a third dimension in column-density mapping of dusty astrophysical structures associated with star formation

We present PPMAP, a Bayesian procedure that uses images of dust continuum emission at multiple wavelengths to produce resolution-enhanced image cubes of differential column-density as a function of dust temperature and position. PPMAP is based on the generic 'point process' formalism, whereby the system of interest (in this case, a dusty astrophysical structure such as a filament or prestellar core) is represented by a collection of points in a suitably defined state space. It can be applied to a variety of observational data, such as Herschel images, provided only that the image intensity is delivered by optically thin dust in thermal equilibrium. PPMAP takes full account of the instrumental point spread functions and does not require all images to be degraded to the same resolution. We present the results of testing using simulated data for a prestellar core and a fractal turbulent cloud, and demonstrate its performance with real data from the Hi-GAL survey. Specifically, we analyse observations of a large filamentary structure in the CMa OB1 giant molecular cloud. Histograms of differential column-density indicate that the warm material (T > 13 K) is distributed log-normally, consistent with turbulence, but the column-densities of the cooler material are distributed as a high density tail, consistent with the effects of self-gravity. The results illustrate the potential of PPMAP to aid in distinguishing between different physical components along the line of sight in star-forming clouds, and aid the interpretation of the associated PDFs of column density.

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arXiv2015

Star Formation triggered by cloud-cloud collisions

We present the results of SPH simulations in which two clouds, each having mass $M_{_{\rm{o}}}\!=\!500\,{\rm M}_{_\odot}$ and radius $R_{_{\rm{o}}}\!=\!2\,{\rm pc}$, collide head-on at relative velocities of $Δv_{_{\rm{o}}} =2.4,\;2.8,\;3.2,\;3.6\;{\rm and}\;4.0\,{\rm km}\,{\rm s}^{-1}$. There is a clear trend with increasing $Δv_{_{\rm{o}}}$. At low $Δv_{_{\rm{o}}}$, star formation starts later, and the shock-compressed layer breaks up into an array of predominantly radial filaments; stars condense out of these filaments and fall, together with residual gas, towards the centre of the layer, to form a single large-$N$ cluster, which then evolves by competitive accretion, producing one or two very massive protostars and a diaspora of ejected (mainly low-mass) protostars; the pattern of filaments is reminiscent of the hub and spokes systems identified recently by observers. At high $Δv_{_{\rm{o}}}$, star formation occurs sooner and the shock-compressed layer breaks up into a network of filaments; the pattern of filaments here is more like a spider's web, with several small-$N$ clusters forming independently of one another, in cores at the intersections of filaments, and since each core only spawns a small number of protostars, there are fewer ejections of protostars. As the relative velocity is increased, the {\it mean} protostellar mass increases, but the {\it maximum} protostellar mass and the width of the mass function both decrease. We use a Minimal Spanning Tree to analyse the spatial distributions of protostars formed at different relative velocities.

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arXiv2015

Are the majority of Sun-like stars single?

It has recently been suggested that, in the field, $\sim\!\!56\%$ of Sun-like stars ($0.8\,{\rm M}_{_\odot}\lesssim M_\star\lesssim 1.2\,{\rm M}_{_\odot}$) are single. We argue here that this suggestion may be incorrect, since it appears to be based on the multiplicity frequency of systems with Sun-like primaries, and therefore takes no account of Sun-like stars that are secondary (or higher-order) components in multiple systems. When these components are included in the reckoning, it seems likely that only $\sim\!46\%$ of Sun-like stars are single. This estimate is based on a model in which the system mass function has the form proposed by Chabrier, with a power-law Salpeter extension to high masses; there is a flat distribution of mass ratios; and the probability that a system of mass $M$ is a binary is $\,0.50 + 0.46\log_{_{10}}\!\left(M/{\rm M}_{_\odot}\right)\,$ for $\,0.08\,{\rm M}_{_\odot}\leq M\leq 12.5\,{\rm M}_{_\odot}$, $\,0\,$ for $\,M<0.08\,{\rm M}_{_\odot}$, and $\,1\,$ for $\,M>12.5\,{\rm M}_{_\odot}$. The constants in this last relation are chosen so that the model also reproduces the observed variation of multiplicity frequency with primary mass. However, the more qualitative conclusion, that a minority of Sun-like stars are single, holds up for virtually all reasonable values of the model parameters. Parenthetically, it is still likely that the majority of {\it all} stars in the field are single, but that is because most M Dwarfs probably are single.

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arXiv2015

On the effects of solenoidal and compressive turbulence in prestellar cores

We present the results of an ensemble of SPH simulations that follow the evolution of prestellar cores for $0.2\,{\rm Myr}$. All the cores have the same mass, and start with the same radius, density profile, thermal and turbulent energy. Our purpose is to explore the consequences of varying the fraction of turbulent energy, $δ_\mathrm{sol}$, that is solenoidal, as opposed to compressive; specifically we consider $δ_\mathrm{sol}=1,\,2/3,\,1/3,\,1/9\;{\rm and}\;0$. For each value of $δ_\mathrm{sol}$, we follow ten different realisations of the turbulent velocity field, in order also to have a measure of the stochastic variance blurring any systematic trends. With low $δ_\mathrm{sol}(<\!1/3)$ filament fragmentation dominates and delivers relatively high mass stars. Conversely, with high values of $δ_\mathrm{sol}(>\!1/3)$ disc fragmentation dominates and delivers relatively low mass stars. There are no discernible systematic trends in the multiplicity statistics obtained with different $δ_\mathrm{sol}$.

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arXiv2014

Simulations of star formation in Ophiuchus, II: Multiplicity

Lomax et al. have constructed an ensemble of 60 prestellar cores having masses, sizes, projected shapes, temperatures and non-thermal radial velocity dispersions that match, statistically, the cores in Ophiuchus; and have simulated the evolution of these cores using SPH. Each core has been evolved once with no radiative feedback from stars, once with continuous radiative feedback, and once with episodic radiative feedback. Here we analyse the multiplicity statistics from these simulations. With episodic radiative feedback, (i) the multiplicity frequency is ~60% higher than in the field; (ii) the multiplicity frequency and the mean semi-major axis both increase with primary mass; (iii) one third of multiple systems are hierarchical systems with more than two components; (iv) in these hierarchical systems the inner pairings typically have separations of a few au and mass ratios concentrated towards unity, whereas the outer pairings have separations of order 100 au and a flatter distribution of mass ratios. The binary statistics are compatible with observations of young embedded populations, and -- if wider orbits are disrupted preferentially by external perturbations -- with observations of mature field populations. With no radiative feedback, the results are similar to those from simulations with episodic feedback. With continuous radiative feedback, brown dwarfs are under-produced, the number of multiple systems is too low, and the statistical properties of multiple systems are at variance with observation. This suggests that star formation in Ophiuchus may only be representative of global star formation if accretion onto protostars, and hence radiative feedback, is episodic.

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arXiv2014

Simulating star formation in Ophiuchus

We have simulated star formation in prestellar cores, using SPH and initial conditions informed by observations of the cores in Ophiuchus. Because the observations are limited to two spatial dimensions plus radial velocity, we cannot infer initial conditions for the collapse of a particular core. However, with a minimum of assumptions (isotropic turbulence with a power-law spectrum, a thermal mix of compressive and solenoidal modes, a critical Bonnor-Ebert density profile) we can generate initial conditions that match, in a statistical sense, the distributions of mass, projected size and aspect ratio, thermal and non-thermal one-dimensional velocity dispersion, observed in Ophiuchus. The time between core-core collisions in Ophiuchus is sufficiently long, that we can simulate single cores evolving is isolation, and therefore we are able to resolve masses well below the opacity limit. We generate an ensemble of 100 cores, and evolve them with no radiative feedback from the stars formed, then with continuous radiative feedback, and finally with episodic radiative feedback. With no feedback the simulations produce too many brown dwarfs, and with continuous feedback too few. With episodic radiative feedback, both the peak of the protostellar mass function (at ~ 0.2 M_sun) and the ratio of H-burning stars to brown dwarfs are consistent with observations. The mass of a star is not strongly related to the mass of the core in which it forms. Low-mass cores (M ~ 0.1 M_sun) tend to collapse into single objects, whereas high-mass cores (1 > M_sun) usually fragment into several objects with a broad mass range.

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arXiv2013

Clumps and triggered star formation in ionised molecular clouds

Infrared shells and bubbles are ubiquitous in the Galaxy and can generally be associated with HII regions formed around young, massive stars. In this paper, we use high-resolution 3D SPH simulations to explore the effect of a single O7 star emitting photons at 10^49 1/s and located at the centre of a molecular cloud with mass 10^4 M_sun and radius 6.4 pc; the internal structure of the cloud is characterised by its fractal dimension, D (with 2.0 <= D <= 2.8), and the variance of its (log-normal) density distribution, sigma_0^2 (with 0.36 <= sigma_0^2 <= 1.42). Our study focuses on the morphology of the swept-up cold gas and the distribution and statistics of the resulting star formation. If the fractal dimension is low, the border of the HII region is dominated by extended shell-like structures, and these break up into a small number of massive high-density clumps which then spawn star clusters; star formation occurs relatively quickly, and delivers somewhat higher stellar masses. Conversely, if the fractal dimension is high, the border of the HII region is dominated by a large number of pillars and cometary globules, which contain compact dense clumps and tend to spawn single stars or individual multiple systems; star formation occurs later, the stellar masses are somewhat lower, and the stars are more widely distributed.

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arXiv2013

Mapping the core mass function onto the stellar IMF: multiplicity matters

Observations indicate that the central portions of the Present-Day Prestellar Core Mass Function (CMF) and the Stellar Initial Mass Function (IMF) both have approximately log-normal shapes, but that the CMF is displaced to higher mass than the IMF by a factor F = 4+/-1. This has lead to suggestions that the shape of the IMF is directly inherited from the shape of the CMF - and therefore, by implication, that there is a self-similar mapping from the CMF onto the IMF. If we assume a self-similar mapping, it follows (i) that F = N0/eta, where eta is the mean fraction of a core's mass that ends up in stars, and N0 is the mean number of stars spawned by a single core; and (ii) that the stars spawned by a single core must have an approximately log-normal distribution of relative masses, with universal standard deviation sigma0. Observations can be expected to deliver ever more accurate estimates of F, but this still leaves a degeneracy between eta and N0; and sigma0 is also unconstrained by observation. Here we show that these parameters can be estimated by invoking binary statistics. Specifically, if (a) each core spawns one long-lived binary system, and (b) the probability that a star of mass M is part of this long-lived binary is proportional to M^alpha, current observations of the binary frequency as a function of primary mass and the distribution of mass ratios strongly favour eta = 1.0 +/- 0.3, N0 = 4.3 +/- 0.4, sigma0 = 0.3 +/- 0.03 and alpha = 0.9 +/- 0.6. The mapping from CMF to IMF is not necessarily self-similar - there are many possible motivations for a non self-similar mapping - but if it is not, then the shape of the IMF cannot be inherited from the CMF. Given the limited observational constraints currently available and the ability of a self-similar mapping to satisfy them, the possibility that the shape of the IMF is inherited from the CMF cannot be ruled out at this juncture.

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arXiv2013

Simulations of the non-linear thin shell instability

We use three-dimensional smoothed particle hydrodynamics simulations to study the non-linear thin shell instability (NTSI) in supersonic colliding flows. We show that for flows with monochromatic perturbations and for flows with white-noise perturbations, growth speeds approximate quite well to the analytic predictions of Vishniac (1994). For flows with subsonic turbulence, growth speeds match Vishniac's predictions only at short wavelengths where the turbulence is weaker. We find that supersonic turbulence, of a lower Mach number than the colliding flows, completely suppresses the NTSI. Our results provide a diagnostic for identifying the presence of the NTSI in colliding flows with turbulence.

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arXiv2013

An improved sink particle algorithm for SPH simulations

Numerical simulations of star formation frequently rely on the implementation of sink particles, (a) to avoid expending computational resource on the detailed internal physics of individual collapsing protostars, (b) to derive mass functions, binary statistics and clustering kinematics (and hence to make comparisons with observation), and (c) to model radiative and mechanical feedback; sink particles are also used in other contexts, for example to represent accreting black holes in galactic nuclei. We present a new algorithm for creating and evolving sink particles in SPH simulations, which appears to represent a significant improvement over existing algorithms {\refrpt -- particularly in situations where sinks are introduced after the gas has become optically thick to its own cooling radiation and started to heat up by adiabatic compression}. (i) It avoids spurious creation of sinks. (ii) It regulates the accretion of matter onto a sink so as to mitigate non-physical perturbations in the vicinity of the sink. (iii) Sinks accrete matter, but the associated angular momentum is transferred back to the surrounding medium. With the new algorithm -- and modulo the need to invoke sufficient resolution to capture the physics preceding sink formation -- the properties of sinks formed in simulations are essentially independent of the user-defined parameters of sink creation, or the number of SPH particles used.

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arXiv2012

Dispersal of molecular clouds by ionising radiation

The role of feedback from massive stars is believed to be a key element in the evolution of molecular clouds. We use high-resolution 3D SPH simulations to explore the dynamical effects of a single O7 star located at the centre of a molecular cloud with mass 10^4M_sun and radius 6.4pc. The initial internal structure of the cloud is characterised by its fractal dimension, D=2.0 - 2.8, and its log-normal density PDF. (i) As regards star formation, in the short term ionising feedback is positive, in the sense that star formation occurs much more quickly in gas that is compressed by the high pressure of the ionised gas. However, in the long term ionising feedback is negative, in the sense that most of the cloud is dispersed with an outflow rate of up to ~0.01M_sun/yr, on a timescale comparable with the sound-crossing time for the ionised gas (~1-2Myr), and triggered star formation is therefore limited to a few percent of the cloud's mass. (ii) As regards the morphology of the ionisation fronts (IFs) bounding the HII region and the systematics of outflowing gas, we distinguish two regimes. For low D<=2.2, the initial cloud is dominated by large-scale structures, so the neutral gas tends to be swept up into a few extended coherent shells, and the ionised gas blows out through a few large holes between these shells; we term these HII regions "shell-dominated". Conversely, for high D>=2.6, the initial cloud is dominated by small-scale structures, and these are quickly overrun by the advancing IF, thereby producing neutral pillars whilst the ionised gas blows out through a large number of small holes between the pillars; we term these HII regions "pillar-dominated". (iii) As regards the injection of bulk kinetic energy, by ~1Myr, the expansion of the HII region has delivered a rms velocity of ~6km/s; this represents less than 0.1% of the total energy radiated by the O7 star.

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arXiv2012

Interactions between brown-dwarf binaries and Sun-like stars

Several mechanisms have been proposed for the formation of brown dwarfs, but there is as yet no consensus as to which -- if any -- are operative in nature. Any theory of brown dwarf formation must explain the observed statistics of brown dwarfs. These statistics are limited by selection effects, but they are becoming increasingly discriminating. In particular, it appears (a) that brown dwarfs that are secondaries to Sun-like stars tend to be on wide orbits, $a\ga 100\,{\rm AU}$ (the Brown Dwarf Desert), and (b) that these brown dwarfs have a significantly higher chance of being in a close ($a\la 10\,{\rm AU}$) binary system with another brown dwarf than do brown dwarfs in the field. This then raises the issue of whether these brown dwarfs have formed {\it in situ}, i.e. by fragmentation of a circumstellar disc; or have formed elsewhere and subsequently been captured. We present numerical simulations of the purely gravitational interaction between a close brown-dwarf binary and a Sun-like star. These simulations demonstrate that such interactions have a negligible chance ($<0.001$) of leading to the close brown-dwarf binary being captured by the Sun-like star. Making the interactions dissipative by invoking the hydrodynamic effects of attendant discs might alter this conclusion. However, in order to explain the above statistics, this dissipation would have to favour the capture of brown-dwarf binaries over single brown-dwarfs, and we present arguments why this is unlikely. The simplest inference is that most brown-dwarf binaries -- and therefore possibly also most single brown dwarfs -- form by fragmentation of circumstellar discs around Sun-like protostars, with some of them subsequently being ejected into the field.

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arXiv2011

The influence of the turbulent perturbation scale on prestellar core fragmentation and disk formation

The collapse of weakly turbulent prestellar cores is a critical stage in the process of star formation. Being highly non-linear and stochastic, the outcome of collapse can only be explored theoretically by performing large ensembles of numerical simulations. Standard practice is to quantify the initial turbulent velocity field in a core in terms of the amount of turbulent energy (or some equivalent) and the exponent in the power spectrum (n \equiv -d log Pk /d log k). In this paper, we present a numerical study of the influence of the details of the turbulent velocity field on the collapse of an isolated, weakly turbulent, low-mass prestellar core. We show that, as long as n > 3 (as is usually assumed), a more critical parameter than n is the maximum wavelength in the turbulent velocity field, λ_MAX. This is because λ_MAX carries most of the turbulent energy, and thereby influences both the amount and the spatial coherence of the angular momentum in the core. We show that the formation of dense filaments during collapse depends critically on λ_MAX, and we explain this finding using a force balance analysis. We also show that the core only has a high probability of fragmenting if λ_MAX > 0.5 R_CORE (where R_CORE is the core radius); that the dominant mode of fragmentation involves the formation and break-up of filaments; and that, although small protostellar disks (with radius R_DISK <= 20 AU) form routinely, more extended disks are rare. In turbulent, low-mass cores of the type we simulate here, the formation of large, fragmenting protostellar disks is suppressed by early fragmentation in the filaments.

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arXiv2011

The initial conditions of isolated star formation - X. A suggested evolutionary diagram for prestellar cores

We propose an evolutionary path for prestellar cores on the radius-mass diagram, which is analogous to stellar evolutionary paths on the Hertzsprung-Russell Diagram. Using James Clerk Maxwell Telescope (JCMT) observations of L1688 in the Ophiuchus star-forming complex, we analyse the HCO+ (J=4\rightarrow3) spectral line profiles of prestellar cores. We find that of the 58 cores observed, 14 show signs of infall in the form of a blue-asymmetric double-peaked line profile. These 14 cores all lie beyond the Jeans mass line for the region on a radius-mass plot. Furthermore another 10 cores showing tentative signs of infall, in their spectral line profile shapes, appear on or just over the Jeans mass line. We therefore propose the manner in which a prestellar core evolves across this diagram. We hypothesise that a core is formed in the low-mass, low-radius region of the plot. It then accretes quasistatically, increasing in both mass and radius. When it crosses the limit of gravitational instability it begins to collapse, decreasing in radius, towards the region of the diagram where protostellar cores are seen.

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arXiv2011

SEREN - A new SPH code for star and planet formation simulations

We present SEREN, a new hybrid Smoothed Particle Hydrodynamics and N-body code designed to simulate astrophysical processes such as star and planet formation. It is written in Fortran 95/2003 and has been parallelised using OpenMP. SEREN is designed in a flexible, modular style, thereby allowing a large number of options to be selected or disabled easily and without compromising performance. SEREN uses the conservative `grad-h' formulation of SPH, but can easily be configured to use traditional SPH or Godunov SPH. Thermal physics is treated either with a barotropic equation of state, or by solving the energy equation and modelling the transport of cooling radiation. A Barnes-Hut tree is used to obtain neighbour lists and compute gravitational accelerations efficiently, and an hierarchical time-stepping scheme is used to reduce the number of computations per timestep. Dense gravitationally bound objects are replaced by sink particles, to allow the simulation to be evolved longer, and to facilitate the identification of protostars and the compilation of stellar and binary properties. At the termination of a hydrodynamical simulation, SEREN has the option of switching to a pure N-body simulation, using a 4th-order Hermite integrator, and following the ballistic evolution of the sink particles (e.g. to determine the final binary statistics once a star cluster has relaxed). We describe in detail all the algorithms implemented in SEREN and we present the results of a suite of tests designed to demonstrate the fidelity of SEREN and its performance and scalability. Further information and additional tests of SEREN can be found at the web-page http://www.astro.group.shef.ac.uk/seren.

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arXiv2010

Statistical comparison of clouds and star clusters

The extent to which the projected distribution of stars in a cluster is due to a large-scale radial gradient, and the extent to which it is due to fractal sub-structure, can be quantified -- statistically -- using the measure ${\cal Q} = \bar{m}/\bar{s}$. Here $\bar{m}$ is the normalized mean edge length of its minimum spanning tree (i.e. the shortest network of edges connecting all stars in the cluster) and $\bar{s}$ is the correlation length (i.e. the normalized mean separation between all pairs of stars). We show how ${\cal Q}$ can be indirectly applied to grey-scale images by decomposing the image into a distribution of points from which $\bar{m}$ and $\bar{s}$ can be calculated. This provides a powerful technique for comparing the distribution of dense gas in a molecular cloud with the distribution of the stars that condense out of it. We illustrate the application of this technique by comparing ${\cal Q}$ values from simulated clouds and star clusters.

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