We examine the effects of self-gravity and magnetic fields on supersonic turbulence in isothermal molecular clouds with high resolution simulations and adaptive mesh refinement. These simulations use large root grids (512 3 ) to capture turbulence and four levels of refinement to capture high density, for an effective resolution of 8, 196 3 . Three Mach 9 simulations are performed, two super-Alfvénic and one trans-Alfvénic. We find that gravity splits the clouds into two populations, one low density turbulent state and one high density collapsing state. The low density state exhibits properties similar to non-self-gravitating in this regime, and we examine the effects of varied magnetic field strength on statistical properties: the density probability distribution function is approximately lognormal; velocity power spectral slopes decrease with field strength; alignment between velocity and magnetic field increases with field; the magnetic field probability distribution can be fit to a stretched exponential. The high density state is characterized by self-similar spheres; the density PDF is a power-law; collapse rate decreases with increasing mean field; density power spectra have positive slopes, P (ρ, k) ∝ k; thermal-to-magnetic pressure ratios are unity for all simulations; dynamic-to-magnetic pressure ratios are larger than unity for all simulations; magnetic field distribution is a power-law. The high Alfvén Mach numbers in collapsing regions explain recent observations of magnetic influence decreasing with density. We also find that the high density state is found in filaments formed by converging flows, consistent with recent Herschel observations. Possible modifications to existing star formation theories are explored.

Many astrophysical applications involve magnetized turbulent flows with shock waves. Ab initio star formation simulations require a robust representation of supersonic turbulence in molecular clouds on a wide range of scales imposing stringent demands on the quality of numerical algorithms. We employ simulations of supersonic super-Alfvénic turbulence decay as a benchmark test problem to assess and compare the performance of nine popular astrophysical MHD methods actively used to model star formation. The set of nine codes includes: ENZO, FLASH, KT-MHD, LL-MHD, PLUTO, PPML, RAMSES, STAGGER, and ZEUS. These applications employ a variety of numerical approaches, including both split and unsplit, finite difference and finite volume, divergence preserving and divergence cleaning, a variety of Riemann solvers, a range of spatial reconstruction and time integration techniques. We present a comprehensive set of statistical measures designed to quantify the effects of numerical dissipation in these MHD solvers. We compare power spectra for basic fields to determine the effective spectral bandwidth of the methods and rank them based on their relative effective Reynolds numbers. We also compare numerical dissipation for solenoidal and dilatational velocity components to check for possible impacts of the numerics on small-scale density statistics. Finally, we discuss convergence of various characteristics for the turbulence decay test and impacts of various components of numerical schemes on the accuracy of solutions. The nine codes gave qualitatively the same results, implying that they are all performing reasonably well and are useful for scientific applications. We show that the best performing codes employ a consistently high order of accuracy for spatial reconstruction of the evolved fields, transverse gradient interpolation, conservation law update step, and Lorentz force computation. The best results are achieved with divergence-free evolution of the magnetic field using the constrained transport method, and using little to no explicit artificial viscosity. Codes which fall short in one or more of these areas are still useful, but they must compensate higher numerical dissipation with higher numerical resolution. This paper is the largest, most comprehensive MHD code comparison on an application-like test problem to date. We hope this work will help developers improve their numerical algorithms while helping users to make informed choices in picking optimal applications for their specific astrophysical problems.

We explore the structure and statistics of multiphase, magnetized ISM turbulence in the local Milky Way by means of driven periodic box numerical MHD simulations. Using the higher order-accurate piecewise-parabolic method on a local stencil (PPML), we carry out a small parameter survey varying the mean magnetic field strength and density while fixing the rms velocity to observed values. We quantify numerous characteristics of the transient and steady-state turbulence, including its thermodynamics and phase structure, kinetic and magnetic energy power spectra, structure functions, and distribution functions of density, column density, pressure, and magnetic field strength. The simulations reproduce many observables of the local ISM, including molecular clouds, such as the ratio of turbulent to mean magnetic field at 100 pc scale, the mass and volume fractions of thermally stable HI, the lognormal distribution of column densities, the mass-weighted distribution of thermal pressure, and the linewidth-size relationship for molecular clouds. Our models predict the shape of magnetic field probability density functions (PDFs), which are strongly non-Gaussian, and the relative alignment of magnetic field and density structures. Finally, our models show how the observed low rates of star formation per free-fall time are controlled by the multiphase thermodynamics and largescale turbulence.To explore this complexity, we develop self-consistent models based on very idealized numerical experiments, linking together scales relevant to molecular cloud formation and fragmentation. We exploit the concept of self-organization in nonequilibrium nonlinear dissipative systems [14] in application to the ISM, which is long overdue [15]. We treat interstellar turbulence as an agent that imposes 'order' in the form of coherent structures and correlations between flow fields emerging in a simple periodic box simulation when a statistically stationary state fully develops. In this case, the details of initial conditions are no longer important. Instead the steady state provides realistic initial conditions for star formation. Unlike various flavors of the popular converging flow scenario [16][17][18][19], this approach allows us to reproduce basic ISM observables, including properties of local molecular clouds, with only a few control parameters. The model can be readily extended to include more physics (e.g., radiative transfer and chemistry), to augment the range of resolved scales, and to close the star formation feedback loop.The paper is organized as follows. Section 2 contains the details of our numerical models, including equations, initial and boundary conditions, and parameters. Section 3 presents the results of statistical analysis and comparison with observations for a number of ISM diagnostics. Section 3.1 describes the transition to turbulence and global properties of the statistically stationary state. Section 3.2 summarizes the evolution of magnetic field under the action of random large-scale external forcing. In section 3...

Context. According to time-distance helioseismology, information about internal fluid motions is encoded in the travel times of solar waves. The inverse problem consists of inferring three-dimensional vector flows from a set of travel-time measurements. While only few tests of the inversions have been done, it is known that the retrieval of the small-amplitude vertical flow velocities is problematic. A thorough study of biases and noise has not been carried out in realistic conditions. Aims. Here we investigate the potential of time-distance helioseismology to infer three-dimensional convective velocities in the near-surface layers of the Sun. We developed a new subtractive optimally localised averaging (SOLA) code suitable for pipeline pseudo-automatic processing. Compared to its predecessor, the code was improved by accounting for additional constraints in order to get the right answer within a given noise level. The main aim of this study is to validate results obtained by our inversion code. Methods. We simulate travel-time maps using a snapshot from a numerical simulation of solar convective flows, realistic Born traveltime sensitivity kernels, and a realistic model of travel-time noise. These synthetic travel times are inverted for flows and the results compared with the known input flow field. Additional constraints are implemented in the inversion: cross-talk minimization between flow components and spatial localization of inversion coefficients. Results. Using modes f , p 1 through p 4 , we show that horizontal convective flow velocities can be inferred without bias, at a signal-tonoise ratio greater than one in the top 3.5 Mm, provided that observations span at least four days. The vertical component of velocity (v z ), if it were to be weak, is more difficult to infer and is seriously affected by cross-talk from horizontal velocity components. We emphasise that this cross-talk must be explicitly minimised in order to retrieve v z in the top 1 Mm. We also show that statistical averaging over many different areas of the Sun allows for reliably measuring of average properties of all three flow components in the top 5.5 Mm of the convection zone.

We show that simulations of magnetohydrodynamic turbulence in the multiphase interstellar medium yield an E/B ratio for polarized emission from Galactic dust in broad agreement with recent Planck measurements. In addition, the B-mode spectra display a scale dependence that is consistent with observations over the range of scales resolved in the simulations. The simulations present an opportunity to understand the physical origin of the E/B ratio and a starting point for more refined models of Galactic emission of use for both current and future cosmic microwave background experiments.