arXiv subjects

A. P. Whitworth

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

At least 91 records · Page 5Linked to original sources

arXiv2005

Binary star formation from ring fragmentation

We present a simple model of binary star formation based on the assumption that rotating prestellar cores collapse to form rings and these rings then fragment into protostars. We assume that each ring spawns a small number (N <= 6) of protostars, and that the condensation of the protostars is sufficiently rapid that they can subsequently be treated as point masses. We simulate the dynamical evolution of a ring of N stars and record the properties of the single stars, binaries and higher multiples that form as a result of the dissolution of the ring. The masses of the individual stars in a ring are drawn from a log-normal distribution with dispersion σ. This part of the model is perfomed for many different realizations of the ring, to obtain good statistics. The second part of the model is to convolve the results of these dimensionless simulations, first with the distribution of core masses, which yields the distributions of multiplicity,mass ratio and eccentricity, as a function of primary mass; and second with the distribution of core angular momenta, which yields the distributions of semi-major axis and period, again as a function of primary mass. Using the observed distribution of core masses, and the observed distribution of core angular momenta, our model is able to reproduce the observed IMF, the observed high multiplicity frequency of pre-Main Sequence stars, the observed distribution of separations, and -- for long-period systems -- the observed distributions of eccentricity and mass-ratio, provided we invoke N = 4 or 5 and $σ= 0.6$. We presume that the reduced multiplicity frequency in the field, compared with young clusters, is the result of dynamical interactions between stars formed in different cores but the same cluster, following ring dissolution.

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arXiv2004

The Minimum Mass for Opacity-Limited Fragmentation in Turbulent Cloud Cores

We present a new analysis of the minimum mass for star formation, based on opacity-limited fragmentation. Our analysis differs from the standard one, which considers hierarchical fragmentation of a 3-D medium, and yields $M_{_{\rm MIN}} \sim 0.007 {\rm to} 0.010 M_\odot$ for Population I star formation. Instead we analyse the more realistic situation in which there is one-shot fragmentation of a shock-compressed layer, of the sort which arises in turbulent star-forming clouds. In this situation, $M_{_{\rm MIN}}$ can be smaller than $0.003 M_\odot$. Our analysis is more stringent than the standard one in that (a) it requires fragments to have condensation timescales shorter than all competing mass scales, and (b) it takes into acount that a fragment grows by accretion whilst it is condensing out, and has to radiate away the energy dissipated in the associated accretion shock. It also accords with the recent detection, in young star clusters, of free-floating star-like objects having masses as low as $0.003 {\rm M}_\odot$.

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arXiv2004

The Formation of Free-Floating Brown Dwarves and Planetary-Mass Objects by Photo-Erosion of Prestellar Cores

We explore the possibility that, in the vicinity of an OB star, a prestellar core which would otherwise have formed an intermediate or low-mass star may form a free-floating brown dwarf or planetary-mass object, because the outer layers of the core are eroded by the ionizing radiation from the OB star before they can accrete onto the protostar at the centre of the core. The masses of objects formed in this way are given approximately by $\sim 0.010 M_\odot (a_{\rm I} / 0.3 {\rm km} {\rm s}^{-1})^6 (\dot{\cal N}_{\rm Lyc} / 10^{50} {\rm s}^{-1})^{-1/3} (n_{\rm 0} / 10^3 {\rm cm}^{-3})^{-1/3} $, where $a_{\rm I}$ is the isothermal sound speed in the neutral gas of the core, $\dot{\cal N}_{\rm Lyc}$ is the rate of emission of Lyman continuum photons from the OB star (or stars), and $n_{\rm 0}$ is the number-density of protons in the HII region surrounding the core. We conclude that the formation of low-mass objects by this mechanism should be quite routine, because the mechanism operates over a wide range of conditions ($10^{50} {\rm s}^{-1} \la \dot{\cal N}_{\rm Lyc} \la 10^{52} {\rm s}^{-1}$, $10 {\rm cm}^{-3} \la n_0 \la 10^5 {\rm cm}^{-3}$, $0.2 {\rm km} {\rm s}^{-1} \la a_{\rm I} \la 0.6 {\rm km} {\rm s}^{-1}$) and is very effective. However, it is also a rather wasteful way of forming low-mass objects, in the sense that it requires a relatively massive initial core to form a single low-mass object. The effectiveness of photo-erosion also implies that that any intermediate-mass protostars which have formed in the vicinity of a group of OB stars must already have been well on the way to formation before the OB stars switched on their ionizing radiation; otherwise these protostars would have been stripped down to extremely low mass.

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arXiv2004

The Origin of the IMF from Core Mass Functions

We examine the initial mass functions (IMFs) of stars produced by different molecular core mass functions. Simulations suggest that more massive cores produce more stars, so we propose a model in which the average number of stars formed in a core is equal to the initial number of Jeans masses in that core. Small-$N$ systems decay through dynamical interactions, ejecting low-mass stars and brown dwarfs which populate the low-mass tail of the IMF. Stars which remain in cores are able to competitively accrete more gas and become more massive. We deduce the forms of the core mass functions required to explain the IMFs of Taurus, Orion, IC 348 and NGC 2547. These core mass functions fall into two categories - one which peaks at a few $M_\odot$ to explain Taurus and NGC 2547, and one that peaks at around $0.2 M_\odot$ to explain Orion and IC 348.

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arXiv2004

Dust temperatures in asymmetric prestellar cores

We present 2D Monte Carlo radiative transfer simulations of flattened prestellar cores. We argue the importance of observing prestellar cores near the peak of their emission spectra, and we point out observable characteristic features on isophotal maps of asymmetric cores at FIR wavelengths that are indicative of the cores' density and temperature structure. These features are on scales 1/5 to 1/3 of the overall core size, and so high resolution observations are needed to observe them. Finally, we discuss the importance of determining the temperatures of prestellar cores with high accuracy.

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arXiv2004

Radiative transfer models of non-spherical prestellar cores

We present 2D Monte Carlo radiative transfer simulations of prestellar cores. We consider two types of asymmetry: disk-like asymmetry, in which the core is denser towards the equatorial plane than towards the poles; and axial asymmetry, in which the core is denser towards the south pole than the north pole. We limit our treatment to cores with mild asymmetries, which are exposed directly to the interstellar radiation field or are embedded inside molecular clouds. The isophotal maps of a core depend strongly on the viewing angle. Maps at wavelengths longer than the peak of the SED (e.g. 850 micron) essentially trace the column-density. Thus, for instance, cores with disk-like asymmetry appear elongated when mapped at 850 micron from close to the equatorial plane. However, at wavelengths near the peak of the SED (e.g. 200 micron), the emissivity is more strongly dependent on the temperature, and therefore, at particular viewing angles, there are characteristic features which reflect a more complicated convolution of the density and temperature fields within the core. These characteristic features are on scales 1/5 to 1/3 of the overall core size, and so high resolution observations are needed to observe them. They are also weaker if the core is embedded in a molecular cloud (because the range of temperature within the core is then smaller), and so high sensitivity is needed to detect them. Herschel, to be launched in 2007, will in principle provide the necessary resolution and sensitivity at 170 to 250 micron.

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arXiv2004

An explanation for the unusual IMF in Taurus

In comparison with other well studied star formation regions, Taurus is unusual in several respects. (i) Its stellar initial mass function (IMF) peaks at relatively high mass ($\sim 0.8 M_\odot$), but contains very few stars much more massive than $1 M_\odot$, and is relatively deficient in brown dwarfs. (ii) It has a higher binary fraction, particularly at large separations. (iii) Its core mass function is strongly peaked at a few $M_\odot$, and the cores have extended envelopes and relatively low levels of turbulence. We present here the results of an ensemble of hydrodynamic simulations which suggest that the unusual stellar IMF in Taurus is a direct consequence of the unusual properties of the cores there. By following the collapse and fragmentation of cores having properties typical of Taurus, we find that roughly 50% of the objects formed in a core, predominantly the low-mass ones, are ejected from the core to form a population of low-mass stars and brown dwarfs with a flat mass function. The remaining objects form multiple systems within the core, accreting until their masses approach $1 M_\odot$; this produces a population of intermediate-mass stars whose mass function peaks at $\sim 0.8 M_\odot$. Together these two populations reproduce the IMF in Taurus very well. This demonstrates, for the first time, a direct causal link between the core mass function and the stellar IMF in a star formation region.

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arXiv2003

The dynamical evolution of fractal star clusters: the survival of substructure

We simulate the dynamics of fractal star clusters, in order to investigate the evolution of substructure in recently formed clusters. The velocity dispersion is found to be the key parameter determining the survival of substructure. In clusters with a low initial velocity dispersion, the ensuing collapse of the cluster tends to erase substructure, although some substructure may persist beyond the collapse phase. In clusters with virial ratios of 0.5 or higher, initial density substructure survives for several crossing times, in virtually all cases. Even an initially homogeneous cluster can develop substructure, if it is born with coherent velocity dispersion. These results suggest that the simple initial conditions used for many sophisticated $N$-body simulations could be missing a very important and dramatic phase of star cluster evolution.

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arXiv2003

Triggered massive-star formation at the border of the HII region Sh 104

We present millimetre-line imaging of the Galactic HII region Sh 104. We show that it is surrounded by a ring of molecular gas and dust. Four large molecular condensations are regularly spaced around the ring. These condensations are themselves fragmented and contain several massive dense cores. A deeply embedded cluster is observed in the near IR towards the largest condensation. It contains at least one massive star ionizing an ultra-compact HII region. The Sh 104 region is a good illustration of the `collect and collapse' model for star formation triggered by the expansion of an HII region.

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arXiv2003

Why do starless cores appear more flattened than protostellar cores?

We evaluate the intrinsic three dimensional shapes of molecular cores, by analysing their projected shapes. We use the recent catalogue of molecular line observations of Jijina et al. and model the data by the method originally devised for elliptical galaxies. Our analysis broadly supports the conclusion of Jones et al. that molecular cores are better represented by triaxial intrinsic shapes (ellipsoids) than biaxial intrinsic shapes (spheroids). However, we find that the best fit to all of the data is obtained with more extreme axial ratios ($1:0.8:0.4$) than those derived by Jones et al. More surprisingly, we find that starless cores have more extreme axial ratios than protostellar cores -- starless cores appear more `flattened'. This is the opposite of what would be expected from modeling the freefall collapse of triaxial ellipsoids. The collapse of starless cores would be expected to proceed most swiftly along the shortest axis - as has been predicted by every modeller since Zel'dovich - which should produce more flattened cores around protostars, the opposite of what is seen.

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arXiv2003

Monte Carlo Radiative Transfer in Embedded Prestellar Cores

We implement a Monte Carlo radiative transfer method, that uses a large number of monochromatic luminosity packets to represent the radiation transported through a system. These packets are injected into the system and interact stochastically with it. We test our code against various benchmark calculations and determine the number of packets required to obtain accurate results under different circumstances. We then use this method to study cores that are directly exposed to the interstellar radiation field (non-embedded cores) and find similar results with previous studies. We also explore a large number of models of cores that are embedded in the centre of a molecular cloud. Our study indicates that the temperature profiles in embedded cores are less steep than those in non-embedded cores. Deeply embedded cores (ambient cloud with visual extinction larger than 15-25) are almost isothermal at around 7-8 K. The temperature inside cores surrounded by an ambient cloud of even moderate thickness (Av~5) is less than 12 K, which is lower than previous studies have assumed. Thus, previous mass calculations of embedded cores (for example in the rho Ophiuchi protocluster), based on mm continuum observations, may underestimate core masses by up to a factor of 2. Our study shows that the best wavelength region to observe embedded cores is between 400 and 500 microns, where the core is quite distinct from the background. We also predict that very sensitive observations (~1-3 MJy/sr) at 170-200 microns can be used to estimate how deeply a core is embedded in its parent molecular cloud. The upcoming HERSCHEL mission (ESA, 2007) will, in principle, be able to detect these features and test our models.

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arXiv2003

Radiative Transfer in Prestellar Cores: A Monte Carlo Approach

We use our Monte Carlo radiative transfer code to study non-embedded prestellar cores and cores that are embedded at the centre of a molecular cloud. Our study indicates that the temperature inside embedded cores is lower than in isolated non-embedded cores, and generally less than 12 K, even when the cores are surrounded by an ambient cloud of small visual extinction (Av~5). Our study shows that the best wavelength region to observe embedded cores is between 400 and 500 microns, where the core is quite distinct from the background. We also predict that very sensitive observations (~1-3 MJy/sr) at 170-200 microns can be used to estimate how deeply a core is embedded in its parent molecular cloud. Finally, we present preliminary results of asymmetric models of non-embedded cores.

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arXiv2002

Protostellar Collapse Induced by Compression

We present numerical simulations of the evolution of low-mass, isothermal, molecular cores which are subjected to an increase in external pressure $P\xt$. If $P\xt$ increases very slowly, the core approaches instability quite quasistatically. However, for larger (but still quite modest) $dP\xt/dt$ a compression wave is driven into the core, thereby triggering collapse from the outside in. If collapse of a core is induced by increasing $P\xt$, this has a number of interesting consequences. (i) The density profile is approximately flat in the centre during the prestellar phase (i.e. before the compression wave converges on the centre creating the central protostar). (ii) During the prestellar phase there are (subsonic) inward velocities in the outer layers of the core, whilst the inner parts are still approximately at rest. (iii) There is an initial short phase of rapid accretion (notionally the Class 0 phase), followed by a longer phase of slower accretion (the Class I phase). All these features accord well with observation, but are at variance with the predictions of the standard theory of star formation based on the inside-out collapse of a singular isothermal sphere. We note that the setting up of a coherent inward velocity field appears to be a generic feature of compression waves; and we speculate that interactions and interference between such velocity fields may play a crucial rôle in initiating the fragmentation of cores and the genesis of multiple star systems.

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arXiv2002

Smoothed Particle Hydrodynamics with particle splitting, applied to self-gravitating collapse

We describe and demonstrate a method for increasing the resolution locally in a Smoothed Particle Hydrodynamic (SPH) simulation, by splitting particles. We show that in simulations of self-gravitating collapse (of the sort which are presumed to occur in star formation) the method is stable, and affords great savings in computer time and memory. When applied to the standard Boss & Bodenheimer test -- which has been shown to depend critically on fulfilment of the Jeans Condition -- the results are comparable both with those obtained using Adaptive Mesh Refinement, and with those obtained using a standard high-resolution SPH simulation, but they are achieved with considerably less computational resource. Further development and testing is required before the method can safely be applied to more general flows.

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arXiv2001

Hydrodynamics of photoionized columns in the Eagle Nebula, M 16

We present hydrodynamical simulations of the formation, structure and evolution of photoionized columns, with parameters based on those observed in the Eagle Nebula. On the basis of these simulations we argue that there is no unequivocal evidence that the dense neutral clumps at heads of the columns were cores in the pre-existing molecular cloud. In our simulations, a variety of initial conditions leads to the formation and maintenance of near-equilibrium columns. Therefore, it is likely that narrow columns will often occur in regions with large-scale inhomogeneities, but that observations of such columns can tell us little about the processes by which they formed. The manner in which the columns in our simulations develop suggests that their evolution may result in extended sequences of radiation-induced star formation.

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arXiv2000

An empirical model for protostellar collapse

We propose a new analytic model for the initial conditions of protostellar collapse in relatively isolated regions of star formation. The model is non-magnetic, and is based on a Plummer-like radial density profile as its initial condition. It fits: the observed density profiles of pre-stellar cores and Class 0 protostars; recent observations in pre-stellar cores of roughly constant contraction velocities over a wide range of radii; and the lifetimes and accretion rates derived for Class 0 and Class I protostars. However, the model is very simple, having in effect only 2 free parameters, and so should provide a useful framework for interpreting observations of pre-stellar cores and protostars, and for calculations of radiation transport and time-dependent chemistry. As an example, we model the pre-stellar core L1544.

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arXiv1998

The structure of young star clusters

We analyse and compare the clustering of young stars in Chamaeleon I and Taurus. We compute the mean surface-density of companion stars \bar{N} as a function of angular displacement θfrom each star. We then fit \bar{N}(θ) with two simultaneous power laws. For Chamaeleon I, the exponents of the power laws are 1.97 and 0.28, with the elbow at ~0.011 degrees. For Taurus, we obtain 2.02 and 0.87, with the elbow at ~0.013 deg. For both star clusters the observational data make quite large systematic excursions from the best fitting curve in the binary regime. These excursions may be attributable to evolutionary effects of the types discussed recently by Nakajima et al. and Bate et al. In the clustering regime the data conform to the best fitting curve very well. We also calculate the box-dimensions for the two star clusters. However, the limited dynamic range makes these estimates simply descriptors of the large-scale clustering, and not admissible evidence for fractality. We also propose two algorithms for objectively generating maps of constant stellar surface-density in young star clusters. Such maps are useful for comparison with molecular-line and dust-continuum maps of star-forming clouds, and with the results of numerical simulations. These maps retain information which is suppressed in the evaluation of \bar{N}(θ). Analyzing such maps can be used to discriminate between fractal structure and single-level clustering, and to determine the degree of central condensation in small-N clusters. Algorithm I uses a universal smoothing length, and therefore has a restricted dynamic range, but it is implicitly normalized. Algorithm II uses a local smoothing length, which gives it much greater dynamic range, but it has to be normalized explicitly.

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arXiv1998

Numerical simulations of protostellar encounters I. Star-disc encounters

It appears that most stars are born in clusters, and that at birth most stars have circumstellar discs which are comparable in size to the separations between the stars. Interactions between neighbouring stars and discs are therefore likely to play a key role in determining disc lifetimes, stellar masses, and the separations and eccentricities of binary orbits. Such interactions may also cause fragmentation of the discs, thereby triggering the formation of additional stars. We have carried out a series of simulations of disc-star interactions using an SPH code which treats self-gravity, hydrodynamic and viscous forces. We find that interactions between discs and stars provide a mechanism for removing energy from, or adding energy to, the orbits of the stars, and for truncating the discs. However, capture during such encounters is unlikely to be an important binary formation mechanism. A more significant consequence of such encounters is that they can trigger fragmentation of the disc, via tidally and compressionally induced gravitational instabilities, leading to the formation of additional stars. When the disc-spins and stellar orbits are randomly oriented, encounters lead to the formation of new companions to the original star in 20% of encounters. If most encounters are prograde and coplanar, as suggested by simulations of dynamically-triggered star formation, then new companions are formed in approximately 50% of encounters.

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