Collapse of a Molecular Cloud Core to Stellar Densities: The First Three-Dimensional Calculations

We present results from the first three-dimensional calculations ever to follow the collapse of a molecular cloud core (~ 10^{-18} g cm^{-3}) to stellar densities (> 0.01 g cm^{-3}). The calculations resolve structures over 7 orders of magnitude in spatial extent (~ 5000 AU - 0.1 R_\odot), and over 17 orders of magnitude in density contrast. With these calculations, we consider whether fragmentation to form a close binary stellar system can occur during the second collapse phase. We find that, if the quasistatic core that forms before the second collapse phase is dynamically unstable to the growth of non-axisymmetric perturbations, the angular momentum extracted from the central regions of the core, via gravitational torques, is sufficient to prevent fragmentation and the formation of a close binary during the subsequent second collapse.Comment: ApJ Letters, in press (will appear in Nov 20 issue; available from the ApJ Rapid Release web page). 7 pages, incl. 5 figures. Also available at http://www.mpia-hd.mpg.de/theory/bat

Magnetic fields and radiative feedback in the star formation process

Star formation is a complex process involving the interplay of many physical effects, including gravity, turbulent gas dynamics, magnetic fields and radiation. Our understanding of the process has improved substantially in recent years, primarily as a result of our increased ability to incorporate the relevant physics in numerical calculations of the star formation process. In this contribution we present an overview of our recent studies of star cluster formation in turbulent, magnetised clouds using self-gravitating radiation-magnetohydrodynamics calculations (Price and Bate 2008, 2009). Our incorporation of magnetic fields and radiative transfer into the Smoothed Particle Hydrodynamics method are discussed. We highlight how magnetic fields and radiative heating of the gas around newborn stars can solve several of the key puzzles in star formation, including an explanation for why star formation is such a slow and inefficient process. However, the presence of magnetic fields at observed strengths in collapsing protostellar cores also leads to problems on smaller scales, including a difficulty in forming protostellar discs and binary stars (Price and Bate 2007, Hennebelle and Teyssier 2008), which suggests that our understanding of the role of magnetic fields in star formation is not yet complete.Comment: 14 pages aip conf. format, 5 figures, submitted to AIP conf proc. of "Plasmas in the Laboratory and in the Universe: Interactions, Patterns and Turbulence", Como, Italy 1st-4th Dec 2009, eds. Bertin et al. Relevant movies at http://users.monash.edu.au/~dprice/mclusterRT/index.html#movie

The effect of magnetic fields on star cluster formation

We examine the effect of magnetic fields on star cluster formation by performing simulations following the self-gravitating collapse of a turbulent molecular cloud to form stars in ideal MHD. The collapse of the cloud is computed for global mass-to-flux ratios of infinity, 20, 10, 5 and 3, that is using both weak and strong magnetic fields. Whilst even at very low strengths the magnetic field is able to significantly influence the star formation process, for magnetic fields with plasma beta < 1 the results are substantially different to the hydrodynamic case. In these cases we find large-scale magnetically-supported voids imprinted in the cloud structure; anisotropic turbulent motions and column density structure aligned with the magnetic field lines, both of which have recently been observed in the Taurus molecular cloud. We also find strongly suppressed accretion in the magnetised runs, leading to up to a 75% reduction in the amount of mass converted into stars over the course of the calculations and a more quiescent mode of star formation. There is also some indication that the relative formation efficiency of brown dwarfs is lower in the strongly magnetised runs due to the reduction in the importance of protostellar ejections.Comment: 16 pages, 9 figures, 8 very pretty movies, MNRAS, accepted. Version with high-res figures + movies available from http://www.astro.ex.ac.uk/people/dprice/pubs/mcluster/index.htm

Smoothed particle magnetohydrodynamic simulations of protostellar outflows with misaligned magnetic field and rotation axes

We have developed a modified form of the equations of smoothed particle magnetohydrodynamics which are stable in the presence of very steep density gradients. Using this formalism, we have performed simulations of the collapse of magnetised molecular cloud cores to form protostars and drive outflows. Our stable formalism allows for smaller sink particles (< 5 AU) than used previously and the investigation of the effect of varying the angle, {\theta}, between the initial field axis and the rotation axis. The nature of the outflows depends strongly on this angle: jet-like outflows are not produced at all when {\theta} > 30{\deg}, and a collimated outflow is not sustained when {\theta} > 10{\deg}. No substantial outflows of any kind are produced when {\theta} > 60{\deg}. This may place constraints on the geometry of the magnetic field in molecular clouds where bipolar outflows are seen.Comment: Accepted for publication in MNRAS, 13 pages, 14 figures. Animations can be found at http://www.astro.ex.ac.uk/people/blewis/research/outflows_misaligned_fields.htm

Modelling circumstellar discs with 3D radiation hydrodynamics

We present results from combining a grid-based radiative transfer code with a Smoothed Particle Hydrodynamics code to produce a flexible system for modelling radiation hydrodynamics. We use a benchmark model of a circumstellar disc to determine a robust method for constructing a gridded density distribution from SPH particles. The benchmark disc is then used to determine the accuracy of the radiative transfer results. We find that the SED and the temperature distribution within the disc are sensitive to the representation of the disc inner edge, which depends critically on both the grid and SPH resolution. The code is then used to model a circumstellar disc around a T-Tauri star. As the disc adjusts towards equilibrium vertical motions in the disc are induced resulting in scale height enhancements which intercept radiation from the central star. Vertical transport of radiation enables these perturbations to influence the mid-plane temperature of the disc. The vertical motions decay over time and the disc ultimately reaches a state of simultaneous hydrostatic and radiative equilibrium.Comment: MNRAS accepted; 15 pages; 17 figures, 4 in colou

Constrained hyperbolic divergence cleaning in smoothed particle magnetohydrodynamics with variable cleaning speeds

We present an updated constrained hyperbolic/parabolic divergence cleaning algorithm for smoothed particle magnetohydrodynamics (SPMHD) that remains conservative with wave cleaning speeds which vary in space and time. This is accomplished by evolving the quantity $\psi / c_h$ instead of $\psi$. Doing so allows each particle to carry an individual wave cleaning speed, $c_h$, that can evolve in time without needing an explicit prescription for how it should evolve, preventing circumstances which we demonstrate could lead to runaway energy growth related to variable wave cleaning speeds. This modification requires only a minor adjustment to the cleaning equations and is trivial to adopt in existing codes. Finally, we demonstrate that our constrained hyperbolic/parabolic divergence cleaning algorithm, run for a large number of iterations, can reduce the divergence of the field to an arbitrarily small value, achieving $\nabla \cdot B=0$ to machine precision.Comment: 23 pages, 16 figures, accepted for publication in Journal of Computational Physic

Measurements on fully wetted and ventilated ring wing hydrofoils

Force measurements and visual observations were made in a water tunnel on fully wetted and ventilated flows past a family of conical ring wings having a flat plate section geometry. The diameter-chord ratio was varied from one to three, and the total included cone angle was 12 degrees. The fully wetted flows all exhibited separation from the leading edge except for the largest diameter-chord ratio, a result which was in agreement with previous work. The effect of ventilation is to reduce markedly the lift curve slope. Pressure distribution measurements were also made under ventilating conditions for one member of this series. The effect of ventilation over only a portion of the circumference of the ring was also briefly investigated. Large cross forces were developed by such ventilation and some comparisons are made between this method of obtaining control forces and more conventional methods

The efficiency of star formation in clustered and distributed regions

We investigate the formation of both clustered and distributed populations of young stars in a single molecular cloud. We present a numerical simulation of a 10,000 solar mass elongated, turbulent, molecular cloud and the formation of over 2500 stars. The stars form both in stellar clusters and in a distributed mode which is determined by the local gravitational binding of the cloud. A density gradient along the major axis of the cloud produces bound regions that form stellar clusters and unbound regions that form a more distributed population. The initial mass function also depends on the local gravitational binding of the cloud with bound regions forming full IMFs whereas in the unbound, distributed regions the stellar masses cluster around the local Jeans mass and lack both the high-mass and the low-mass stars. The overall efficiency of star formation is ~ 15 % in the cloud when the calculation is terminated, but varies from less than 1 % in the the regions of distributed star formation to ~ 40 % in regions containing large stellar clusters. Considering that large scale surveys are likely to catch clouds at all evolutionary stages, estimates of the (time-averaged) star formation efficiency for the giant molecular cloud reported here is only ~ 4 %. This would lead to the erroneous conclusion of 'slow' star formation when in fact it is occurring on a dynamical timescale.Comment: 9 pages, 8 figures, MNRAS in pres

Competitive accretion in embedded stellar cluster

We investigate the physics of gas accretion in young stellar clusters. Accretion in clusters is a dynamic phenomenon as both the stars and the gas respond to the same gravitational potential. Accretion rates are highly non-uniform with stars nearer the centre of the cluster, where gas densities are higher, accreting more than others. This competitive accretion naturally results in both initial mass segregation and a spectrum of stellar masses. Accretion in gas-dominated clusters is well modelled using a tidal-lobe radius instead of the commonly used Bondi-Hoyle accretion radius. This works as both the stellar and gas velocities are under the influence of the same gravitational potential and are thus comparable. The low relative velocity that results means that the tidal radius is smaller than the Bondi-Hoyle radius in these systems. In contrast, when the stars dominate the potential and are virialised, the Bondi-Hoyle radius is smaller than the tidal radius and thus Bondi-Hoyle accretion is a better fit to the accretion rates.Comment: 11 pages, 11 figures, MNRAS in pres