We suggest that a high proportion of brown dwarf (BD) stars are formed by gravitational fragmentation of massive extended discs around Sun-like primary stars. We argue that such discs should arise ...frequently, but should be observed infrequently, precisely because they fragment rapidly. By performing an ensemble of radiation-hydrodynamic simulations, we show that such discs typically fragment within a few thousand years, and produce mainly BD stars, but also planetary-mass (PM) stars and very low-mass hydrogen-burning (HB) stars. Subsequently most of the lower mass stars (i.e. the PM and BD stars) are ejected by mutual interactions. We analyse the statistical properties of these stars, and compare them with observations. After a few hundred thousand years the Sun-like primary is typically left with a close low-mass HB companion, and two much wider companions: a low-mass HB star and a BD star, or a BD–BD binary. The orbits of these companions are highly eccentric, and not necessarily coplanar, either with one another, or with the original disc. There is a BD desert extending out to at least ∼100 au; this is because BDs tend to be formed further out than low-mass HB stars, and then they tend to be scattered even further out, or even into the field. BDs form with discs of a few Jupiter masses and radii of a few tens of au, and they are more likely to retain these discs if they remain bound to the primary star. Binaries form by pairing of the newly formed stars in the disc, giving a low-mass binary fraction of ∼0.16. These binaries include close and wide BD/BD binaries and BD/PM binaries. Binaries can be ejected into the field and survive, even if they have quite wide separations. BDs that remain as companions to Sun-like stars are more likely to be in BD/BD binaries than are BDs ejected into the field. The presence of close and distant companions around Sun-like stars may inhibit planet formation by core accretion. We conclude that disc fragmentation is a robust mechanism for BD formation. Even if only a small fraction of Sun-like stars host the required massive extended discs, this mechanism can produce all the PM stars observed, most of the BD stars and a significant proportion of the very low-mass HB stars.
The time evolution of the probability density function (PDF) of the mass density is formulated and solved for systems in free-fall using a simple approximate function for the collapse of a sphere. We ...demonstrate that a pressure-free collapse results in a power-law tail on the high-density side of the PDF. The slope quickly asymptotes to the functional form P sub(V)(rho) is proportional to rho super(-1.54) for the (volume-weighted) PDF and P sub(M)(rho) is proportional to rho super(-0.54) for the corresponding mass-weighted distribution. From the simple approximation of the PDF we derive analytic descriptions for mass accretion, finding that dynamically quiet systems with narrow density PDFs lead to retarded star formation and low star formation rates (SFRs). Conversely, strong turbulent motions that broaden the PDF accelerate the collapse causing a bursting mode of star formation. Finally, we compare our theoretical work with observations. The measured SFRs are consistent with our model during the early phases of the collapse. Comparison of observed column density PDFs with those derived from our model suggests that observed star-forming cores are roughly in free-fall.
ABSTRACT
We propose a new model for the evolution of a star cluster’s system mass function (SMF). The model involves both turbulent fragmentation and competitive accretion. Turbulent fragmentation ...creates low-mass seed proto-systems (i.e. single and multiple protostars). Some of these low-mass seed proto-systems then grow by competitive accretion to produce the high-mass power-law tail of the SMF. Turbulent fragmentation is relatively inefficient, in the sense that the creation of low-mass seed proto-systems only consumes a fraction, ${\sim }23{{\ \rm per\ cent}}$ (at most ${\sim }50{{\ \rm per\ cent}}$), of the mass available for star formation. The remaining mass is consumed by competitive accretion. Provided the accretion rate on to a proto-system is approximately proportional to its mass (dm/dt ∝ m), the SMF develops a power-law tail at high masses with the Salpeter slope (∼−2.3). If the rate of supply of mass accelerates, the rate of proto-system formation also accelerates, as appears to be observed in many clusters. However, even if the rate of supply of mass decreases, or ceases and then resumes, the SMF evolves homologously, retaining the same overall shape, and the high-mass power-law tail simply extends to ever higher masses until the supply of gas runs out completely. The Chabrier SMF can be reproduced very accurately if the seed proto-systems have an approximately lognormal mass distribution with median mass ${\sim } 0.11 \, {\rm M}_{\odot }$ and logarithmic standard deviation $\sigma _{\log _{10}({M/M}_\odot)}\sim 0.47$).
A star acquires much of its mass by accreting material from a disk. Accretion is probably not continuous but episodic. We have developed a method to include the effects of episodic accretion in ...simulations of star formation. Episodic accretion results in bursts of radiative feedback, during which a protostar is very luminous, and its surrounding disk is heated and stabilized. These bursts typically last only a few hundred years. In contrast, the lulls between bursts may last a few thousand years; during these lulls the luminosity of the protostar is very low, and its disk cools and fragments. Thus, episodic accretion enables the formation of low-mass stars, brown dwarfs, and planetary-mass objects by disk fragmentation. If episodic accretion is a common phenomenon among young protostars, then the frequency and duration of accretion bursts may be critical in determining the low-mass end of the stellar initial mass function.
Protostars grow in mass by accreting material through their discs, and this accretion is initially their main source of luminosity. The resulting radiative feedback heats the environments of young ...protostars, and may thereby suppress further fragmentation and star formation. There is growing evidence that the accretion of material on to protostars is episodic rather than continuous; most of it happens in short bursts that last up to a few hundred years, whereas the intervals between these outbursts of accretion could be thousands of years. We have developed a model to include the effects of episodic accretion in simulations of star formation. Episodic accretion results in episodic radiative feedback, which heats and temporarily stabilizes the disc, suppressing the growth of gravitational instabilities. However, once an outburst has been terminated, the luminosity of the protostar is low, and the disc cools rapidly. Provided that there is enough time between successive outbursts, the disc may become gravitationally unstable and fragment. The model suggests that episodic accretion may allow disc fragmentation if (i) the time between successive outbursts is longer than the dynamical time-scale for the growth of gravitational instabilities (a few kyr), and (ii) the quiescent accretion rate on to the protostar is sufficiently low (at most a few times 10−7 ;M⊙ ;yr−1). We also find that after a few protostars form in the disc, their own episodic accretion events shorten the intervals between successive outbursts, and suppress further fragmentation, thus limiting the number of objects forming in the disc. We conclude that episodic accretion moderates the effect of radiative feedback from young protostars on their environments, and, under certain conditions, allows the formation of low-mass stars, brown dwarfs and planetary-mass objects by fragmentation of protostellar discs.
Thermodynamics play an important role in determining the way a protostellar disc fragments to form planets, brown dwarfs and low-mass stars. We explore the effect that different treatments of ...radiative transfer have in simulations of fragmenting discs. Three prescriptions for the radiative transfer are used: (i) the diffusion approximation of Stamatellos et al.; (ii) the barotropic equation of state (EOS) of Goodwin et al. and (iii) the barotropic EOS of Bate et al. The barotropic approximations capture the general evolution of the density and temperature at the centre of each proto-fragment but (i) they do not make any adjustments for particular circumstances of a proto-fragment forming in the disc and (ii) they do not take into account thermal inertia effects that are important for fast-forming proto-fragments in the outer disc region. As a result, the number of fragments formed in the disc and their properties are different, when a barotropic EOS is used. This is important not only for disc studies but also for simulations of collapsing turbulent clouds, as in many cases in such simulations stars form with discs that subsequently fragment. We also examine the difference in the way proto-fragments condense out in the disc at different distances from the central star using the diffusion approximation and following the collapse of each proto-fragment until the formation of the second core (ρ≃ 10−3 g cm−3). We find that proto-fragments forming closer to the central star tend to form earlier and evolve faster from the first to the second core than proto-fragments forming in the outer disc region. The former have a large pool of material in the inner disc region that they can accrete from and grow in mass. The latter accrete more slowly and they are hotter because they generally form in a quick abrupt event.
The statistical analysis of star clusters Cartwright, Annabel; Whitworth, Anthony P.
Monthly notices of the Royal Astronomical Society,
02/2004, Volume:
348, Issue:
2
Journal Article
Peer reviewed
Open access
We review a range of statistical methods for analysing the structures of star clusters, and derive a new measure , which both quantifies and distinguishes between a (relatively smooth) large-scale ...radial density gradient and multiscale (fractal) subclustering. The distribution of separations p(s) is considered, and the normalized correlation length (i.e. the mean separation between stars, divided by the overall radius of the cluster) is shown to be a robust indicator of the extent to which a smooth cluster is centrally concentrated. For spherical clusters having volume-density n∝r−α (with α between 0 and 2) decreases monotonically with α, from ∼0.8 to ∼0.6. Since reflects all star positions, it implicitly incorporates edge effects. However, for fractal star clusters (with fractal dimension D between 1.5 and 3) decreases monotonically with D (from ∼0.8 to ∼0.6). Hence , on its own, can quantify, but cannot distinguish between, a smooth large-scale radial density gradient and multiscale (fractal) subclustering. The minimal spanning tree (MST) is then considered, and it is shown that the normalized mean edge length i.e. the mean length of the branches of the tree, divided by , A is the area of the cluster and is the number of stars can also quantify, but again cannot on its own distinguish between, a smooth large-scale radial density gradient and multiscale (fractal) subclustering. However, the combination does both quantify and distinguish between a smooth large-scale radial density gradient and multiscale (fractal) subclustering. IC348 has and ρ Ophiuchus has , implying that both are centrally concentrated clusters with, respectively, α≃ 2.2 ± 0.2 and α≃ 1.2 ± 0.3. Chamaeleon and IC2391 have and 0.66, respectively, implying mild substructure with a notional fractal dimension D≃ 2.25 ± 0.25. Taurus has even more substructure, with implying D′≃ 1.55 ± 0.25. If the binaries in Taurus are treated as single systems, increases to 0.58 and D′ increases to 1.9 ± 0.2.
ABSTRACT
The treatment of radiative transfer with multiple radiation sources is a critical challenge in simulations of star formation and the interstellar medium (ISM). In this paper, we present the ...novel TreeRay method for solving general radiative transfer problems, based on reverse ray-tracing combined with tree-based accelerated integration. We implement TreeRay in the adaptive mesh refinement code flash, as a module of the tree solver developed by Wünsch et al. However, the method itself is independent of the host code and can be implemented in any grid-based or particle-based hydrodynamics code. A key advantage of TreeRay is that its computational cost is independent of the number of sources, making it suitable for simulations with many point sources (e.g. massive star clusters) as well as simulations where diffuse emission is important. A very efficient communication and tree-walk strategy enable TreeRay to achieve almost ideal parallel scalings. TreeRay can easily be extended with sub-modules to treat radiative transfer at different wavelengths and to implement related physical processes. Here, we focus on ionizing radiation and use the on-the-spot approximation to test the method and its parameters. The ability to set the tree solver time-step independently enables the speedy calculation of radiative transfer in a multiphase ISM, where the hydrodynamic time-step is typically limited by the sound speed of the hot gas produced in stellar wind bubbles or supernova remnants. We show that complicated simulations of star clusters with feedback from multiple massive stars become feasible with TreeRay.
Most stars are born in clusters and the resulting gravitational interactions between cluster members may significantly affect the evolution of circumstellar disks and therefore the formation of ...planets and brown dwarfs (BDs). Recent findings suggest that tidal perturbations of typical circumstellar disks due to close encounters may inhibit rather than trigger disk fragmentation and so would seem to rule out planet formation by external tidal stimuli. However, the disk models in these calculations were restricted to disk radii of 40 AU and disk masses below 0.1 M{sub sun}. Here, we show that even modest encounters can trigger fragmentation around 100 AU in the sorts of massive ({approx}0.5 M{sub sun}), extended ({>=}100 AU) disks that are observed around young stars. Tidal perturbation alone can do this; no disk-disk collision is required. We also show that very low mass binary systems can form through the interaction of objects in the disk. In our computations, otherwise non-fragmenting massive disks, once perturbed, fragment into several objects between about 0.01 and 0.1 M{sub sun}, i.e., over the whole BD mass range. Typically, these orbit on highly eccentric orbits or are even ejected. While probably not suitable for the formation of Jupiter- or Neptune-type planets, our scenario provides a possible formation mechanism for BDs and very massive planets which, interestingly, leads to a mass distribution consistent with the canonical substellar initial mass function. As a minor outcome, a possible explanation for the origin of misaligned extrasolar planetary systems is discussed.
Guiding the reader through all the stages that lead to the formation of a star such as our Sun, this advanced textbook provides students with a complete overview of star formation. It examines the ...underlying physical processes that govern the evolution from a molecular cloud core to a main-sequence star, and focuses on the formation of solar-mass stars. Each chapter combines theory and observation, helping readers to connect with and understand the theory behind star formation. Beginning with an explanation of the interstellar medium and molecular clouds as sites of star formation, subsequent chapters address the building of typical stars and the formation of high-mass stars, concluding with a discussion of the by-products and consequences of star formation. This is a unique, self-contained text with sufficient background information for self-study, and is ideal for students and professional researchers alike.
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