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

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

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

Extending the Latent Multinomial Model with Complex Error Processes and Dynamic Markov Bases

The latent multinomial model (LMM) model of Link et al. (2010) provided a general framework for modelling mark-recapture data with potential errors in identification. Key to this approach was a Markov chain Monte Carlo (MCMC) scheme for sampling possible configurations of the counts true capture histories that could have generated the observed data. This MCMC algorithm used vectors from a basis for the kernel of the linear map between the true and observed counts to move between the possible configurations of the true data. Schofield and Bonner (2015) showed that a strict basis was sufficient for some models of the errors, including the model presented by Link et al. (2010), but a larger set called a Markov basis may be required for more complex models. We address two further challenges with this approach: 1) that models with more complex error mechanisms do not fit easily within the LMM and 2) that the Markov basis can be difficult or impossible to compute for even moderate sized studies. We address these issues by extending the LMM to separately model the capture/demographic process and the error process and by developing a new MCMC sampling scheme using dynamic Markov bases. Our work is motivated by a study of Queen snakes (Regina septemvittata) in Kentucky, USA, and we use simulation to compare the use of PIT tags, with perfect identification, and brands, which are prone to error, when estimating survival rates

Investigating prescriptions for artificial resistivity in smoothed particle magnetohydrodynamics

In numerical simulations, artificial terms are applied to the evolution equations for stability. To prove their validity, these terms are thoroughly tested in test problems where the results are well known. However, they are seldom tested in production-quality simulations at high resolution where they interact with a plethora of physical and numerical algorithms. We test three artificial resistivities in both the Orszag-Tang vortex and in a star formation simulation. From the Orszag-Tang vortex, the Price et. al. (2017) artificial resistivity is the least dissipative thus captures the density and magnetic features; in the star formation algorithm, each artificial resistivity algorithm interacts differently with the sink particle to produce various results, including gas bubbles, dense discs, and migrating sink particles. The star formation simulations suggest that it is important to rely upon physical resistivity rather than artificial resistivity for convergence.Comment: 8 pages, 7 figures. Proceedings of the "12th international SPHERIC workshop", Ourense, Spain, 13-15 June 201

An evaluation of the quality of statistical design and analysis of published medical research : results from a systematic survey of general orthopaedic journals

Background: The application of statistics in reported research in trauma and orthopaedic surgery has become ever more important and complex. Despite the extensive use of statistical analysis, it is still a subject which is often not conceptually well understood, resulting in clear methodological flaws and inadequate reporting in many papers. Methods: A detailed statistical survey sampled 100 representative orthopaedic papers using a validated questionnaire that assessed the quality of the trial design and statistical analysis methods. Results: The survey found evidence of failings in study design, statistical methodology and presentation of the results. Overall, in 17% (95% confidence interval; 10–26%) of the studies investigated the conclusions were not clearly justified by the results, in 39% (30–49%) of studies a different analysis should have been undertaken and in 17% (10–26%) a different analysis could have made a difference to the overall conclusions. Conclusion: It is only by an improved dialogue between statistician, clinician, reviewer and journal editor that the failings in design methodology and analysis highlighted by this survey can be addressed

The impact of magnetic fields on single and binary star formation

We have performed magnetohydrodynamic (MHD) simulations of the collapse and fragmentation of molecular cloud cores using a new algorithm for MHD within the smoothed particle hydrodynamics (SPH) method, that enforces the zero magnetic divergence constraint. We find that the support provided by magnetic fields over thermal pressure alone has several important effects on fragmentation and the formation of binary and multiple systems, and on the properties of massive circumstellar discs. The extra support suppresses the tendency of molecular cloud cores to fragment due to either initial density perturbations or disc fragmentation. Furthermore, unlike most previous studies, we find that magnetic pressure plays the dominant role in inhibiting fragmentation rather than magnetic tension or magnetic braking. In particular, we find that if the magnetic field is aligned with the rotation axis of the molecular cloud core, the effects of the magnetic field on fragmentation and disc structure are almost entirely due to magnetic pressure, while if the rotation axis is initially perpendicular to the magnetic field, magnetic tension plays a greater role and can actually aid fragmentation. Despite these effects, and contrary to several past studies, we find that strongly-perturbed molecular cloud cores are able to fragment to form wide binary systems even in the presence of quite strong magnetic fields. For massive circumstellar discs, we find that slowing of the collapse caused by the magnetic support decreases the mass infall rate on to the disc and, thus, weakens gravitational instabilities in young massive circumstellar discs. This not only reduces the likelihood that they will fragment, but also decreases the importance of spiral density waves in providing angular momentum transport and in promoting planet formation.Comment: 15 pages, 12 figures, accepted for publication in MNRAS. Images degraded to fit size requirements. High res version and pretty movies for this paper can be found at http://www.astro.ex.ac.uk/people/dprice/pubs/magsf/index1.htm

Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure

A crucial aspect of mass-mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present results from a new method that reconstructs maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type $\ell_1$-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass-mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets of the Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of individual local massive substructure at significant confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data