Collapse, outflows and fragmentation of massive, turbulent and magnetized prestellar barotropic cores

Stars and more particularly massive stars, have a drastic impact on galaxy evolution. Yet the conditions in which they form and collapse are still not fully understood. In particular, the influence of the magnetic field on the collapse of massive clumps is relatively unexplored, it is thus of great relevance in the context of the formation of massive stars to investigate its impact. We perform high resolution, MHD simulations of the collapse of hundred solar masses, turbulent and magnetized clouds, using the adaptive mesh refinement code RAMSES. We compute various quantities such as mass distribution, magnetic field and angular momentum within the collapsing core and study the episodic outflows and the fragmentation that occurs during the collapse. The magnetic field has a drastic impact on the cloud evolution. We find that magnetic braking is able to substantially reduce the angular momentum in the inner part of the collapsing cloud. Fast and episodic outflows are being launched with typical velocities of the order of 3-5 km s$^{-1}$ although the highest velocities can be as high as 30-40 km s$^{-1}$. The fragmentation in several objects, is reduced in substantially magnetized clouds with respect to hydrodynamical ones by a factor of the order of 1.5-2. We conclude that magnetic fields have a significant impact on the evolution of massive clumps. In combination with radiation, magnetic fields largely determine the outcome of massive core collapse. We stress that numerical convergence of MHD collapse is a challenging issue. In particular, numerical diffusion appears to be important at high density therefore possibly leading to an over-estimation of the number of fragments.Comment: accepted for publication in A&

A Simple Law of Star Formation

We show that supersonic MHD turbulence yields a star formation rate (SFR) as low as observed in molecular clouds (MCs), for characteristic values of the free-fall time divided by the dynamical time, $t_{\rm ff}/t_{\rm dyn}$, the alfv\'{e}nic Mach number, ${\cal M}_{\rm a}$, and the sonic Mach number, ${\cal M}_{\rm s}$. Using a very large set of deep adaptive-mesh-refinement simulations, we quantify the dependence of the SFR per free-fall time, $\epsilon_{\rm ff}$, on the above parameters. Our main results are: i) $\epsilon_{\rm ff}$ decreases exponentially with increasing $t_{\rm ff}/t_{\rm dyn}$, but is insensitive to changes in ${\cal M}_{\rm s}$, for constant values of $t_{\rm ff}/t_{\rm dyn}$ and ${\cal M}_{\rm a}$. ii) Decreasing values of ${\cal M}_{\rm a}$ (stronger magnetic fields) reduce $\epsilon_{\rm ff}$, but only to a point, beyond which $\epsilon_{\rm ff}$ increases with a further decrease of ${\cal M}_{\rm a}$. iii) For values of ${\cal M}_{\rm a}$ characteristic of star-forming regions, $\epsilon_{\rm ff}$ varies with ${\cal M}_{\rm a}$ by less than a factor of two. We propose a simple star-formation law, based on the empirical fit to the minimum $\epsilon_{\rm ff}$, and depending only on $t_{\rm ff}/t_{\rm dyn}$: $\epsilon_{\rm ff} \approx \epsilon_{\rm wind} \exp(-1.6 \,t_{\rm ff}/t_{\rm dyn})$. Because it only depends on the mean gas density and rms velocity, this law is straightforward to implement in simulations and analytical models of galaxy formation and evolution.Comment: ApJ Letters - in pres

Passage of Time in a Planck Scale Rooted Local Inertial Structure

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations--suppressed quadratically by the Planck energy--from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts.Comment: 17 pages; Diagram depicting "the objective flow of time" is replaced with a much-improved diagra

Testing Low Complexity Affine-Invariant Properties

Invariance with respect to linear or affine transformations of the domain is arguably the most common symmetry exhibited by natural algebraic properties. In this work, we show that any low complexity affine-invariant property of multivariate functions over finite fields is testable with a constant number of queries. This immediately reproves, for instance, that the Reed-Muller code over F_p of degree d < p is testable, with an argument that uses no detailed algebraic information about polynomials except that low degree is preserved by composition with affine maps. The complexity of an affine-invariant property P refers to the maximum complexity, as defined by Green and Tao (Ann. Math. 2008), of the sets of linear forms used to characterize P. A more precise statement of our main result is that for any fixed prime p >=2 and fixed integer R >= 2, any affine-invariant property P of functions f: F_p^n -> [R] is testable, assuming the complexity of the property is less than p. Our proof involves developing analogs of graph-theoretic techniques in an algebraic setting, using tools from higher-order Fourier analysis.Comment: 38 pages, appears in SODA '1

Efficient white noise sampling and coupling for multilevel Monte Carlo with non-nested meshes

When solving stochastic partial differential equations (SPDEs) driven by additive spatial white noise, the efficient sampling of white noise realizations can be challenging. Here, we present a new sampling technique that can be used to efficiently compute white noise samples in a finite element method and multilevel Monte Carlo (MLMC) setting. The key idea is to exploit the finite element matrix assembly procedure and factorize each local mass matrix independently, hence avoiding the factorization of a large matrix. Moreover, in a MLMC framework, the white noise samples must be coupled between subsequent levels. We show how our technique can be used to enforce this coupling even in the case of non-nested mesh hierarchies. We demonstrate the efficacy of our method with numerical experiments. We observe optimal convergence rates for the finite element solution of the elliptic SPDEs of interest in 2D and 3D and we show convergence of the sampled field covariances. In a MLMC setting, a good coupling is enforced and the telescoping sum is respected.Comment: 28 pages, 10 figure

Improved chemistry restraints for crystallographic refinement by integrating the Amber force field into Phenix.

The refinement of biomolecular crystallographic models relies on geometric restraints to help to address the paucity of experimental data typical in these experiments. Limitations in these restraints can degrade the quality of the resulting atomic models. Here, an integration of the full all-atom Amber molecular-dynamics force field into Phenix crystallographic refinement is presented, which enables more complete modeling of biomolecular chemistry. The advantages of the force field include a carefully derived set of torsion-angle potentials, an extensive and flexible set of atom types, Lennard-Jones treatment of nonbonded interactions and a full treatment of crystalline electrostatics. The new combined method was tested against conventional geometry restraints for over 22 000 protein structures. Structures refined with the new method show substantially improved model quality. On average, Ramachandran and rotamer scores are somewhat better, clashscores and MolProbity scores are significantly improved, and the modeling of electrostatics leads to structures that exhibit more, and more correct, hydrogen bonds than those refined using traditional geometry restraints. In general it is found that model improvements are greatest at lower resolutions, prompting plans to add the Amber target function to real-space refinement for use in electron cryo-microscopy. This work opens the door to the future development of more advanced applications such as Amber-based ensemble refinement, quantum-mechanical representation of active sites and improved geometric restraints for simulated annealing

Phenomenology of loop quantum cosmology

After introducing the basic ingredients of Loop Quantum Cosmology, I will briefly discuss some of its phenomenological aspects. Those can give some useful insight about the full Loop Quantum Gravity theory and provide an answer to some long-standing questions in early universe cosmology.Comment: 16 pages, 3 figures; Invited talk in the First Mediterranean Conference on Classical and Quantum Gravity (Crete, Greece

Multi-scale initial conditions for cosmological simulations

We discuss a new algorithm to generate multi-scale initial conditions with multiple levels of refinements for cosmological "zoom-in" simulations. The method uses an adaptive convolution of Gaussian white noise with a real space transfer function kernel together with an adaptive multi-grid Poisson solver to generate displacements and velocities following first (1LPT) or second order Lagrangian perturbation theory (2LPT). The new algorithm achieves RMS relative errors of order 10^(-4) for displacements and velocities in the refinement region and thus improves in terms of errors by about two orders of magnitude over previous approaches. In addition, errors are localized at coarse-fine boundaries and do not suffer from Fourier-space induced interference ringing. An optional hybrid multi-grid and Fast Fourier Transform (FFT) based scheme is introduced which has identical Fourier space behaviour as traditional approaches. Using a suite of re-simulations of a galaxy cluster halo our real space based approach is found to reproduce correlation functions, density profiles, key halo properties and subhalo abundances with per cent level accuracy. Finally, we generalize our approach for two-component baryon and dark-matter simulations and demonstrate that the power spectrum evolution is in excellent agreement with linear perturbation theory. For initial baryon density fields, it is suggested to use the local Lagrangian approximation in order to generate a density field for mesh based codes that is consistent with Lagrangian perturbation theory instead of the current practice of using the Eulerian linearly scaled densities.Comment: 22 pages, 24 figures. MNRAS in press. Updated affiliation