We numerically evolve turbulence driven by the magnetorotational instability (MRI) in a 3D, unstratified shearing box and study its structure using two-point correlation functions. We confirm Fromang and Papaloizou's result that shearing box models with zero net magnetic flux are not converged; the dimensionless shear stress $α$ is proportional to the grid scale. We find that the two-point correlation of the magnetic field shows that it is composed of narrow filaments that are swept back by differential rotation into a trailing spiral. The correlation lengths along each of the correlation function principal axes decrease monotonically with the grid scale. For mean azimuthal field models, which we argue are more relevant to astrophysical disks than the zero net field models, we find that: $α$ increases weakly with increasing resolution at fixed box size; $α$ increases slightly as the box size is increased; $α$ increases linearly with net field strength, confirming earlier results; the two-point correlation function of the magnetic field is resolved and converged, and is composed of narrow filaments swept back by the shear; the major axis of the two-point increases slightly as the box size is increased; these results are code independent, based on a comparison of ATHENA and ZEUS runs. The velocity, density, and magnetic fields decorrelate over scales larger than $\sim H$, as do the dynamical terms in the magnetic energy evolution equations. We conclude that MHD turbulence in disks is localized, subject to the limitations imposed by the absence of vertical stratification, the use of an isothermal equation of state, finite box size, finite run time, and finite resolution
We address the turbulent fragmentation scenario for the origin of the stellar initial mass function (IMF), using a large set of numerical simulations of randomly driven supersonic MHD turbulence. The turbulent fragmentation model successfully predicts the main features of the observed stellar IMF assuming an isothermal equation of state without any stellar feedback. As a test of the model, we focus on the case of a magnetized isothermal gas, neglecting stellar feedback, while pursuing a large dynamic range in both space and timescales covering the full spectrum of stellar masses from brown dwa…
C-type shocks are believed to be ubiquitous in turbulent molecular clouds thanks to ambipolar diffusion. We investigate whether the drag instability in 1D isothermal C-shocks, inferred from the local linear theory of Gu & Chen, can appear in non-ideal magnetohydrodynamic simulations. Two C-shock models (with narrow and broad steady-state shock widths) are considered to represent the typical environment of star-forming clouds. The ionization-recombination equilibrium is adopted for the one-fluid approach. In the 1D simulation, the inflow gas is continuously perturbed by a sinusoidal density flu…
We investigate the effect of numerical magnetic diffusion in magnetohydrodynamic simulations of magnetically supported molecular clouds. To this end, we have performed numerical studies on adaptive mesh isothermal simulations of marginally sub-critical molecular clouds. We find that simulations with low and intermediate resolutions collapse, contrary to what is theoretically expected. However, the simulation with the highest numerical resolution oscillates around an equilibrium state without collapsing. In order to quantify the numerical diffusion of the magnetic field, we ran a second suit of…
Context. An essential facet of turbulence is the space-time intermittency of the cascade of energy that leads to coherent structures of high dissipation. Aims. In this work, we attempt to investigate systematically the physical nature of the intense dissipation regions in decaying isothermal magnetohydrodynamical (MHD) turbulence. Methods. We probe the turbulent dissipation with grid based simulations of compressible isothermal decaying MHD turbulence. We take unprecedented care at resolving and controlling dissipation: we design methods to locally recover the dissipation due to the numerical …
We investigated the effect of magnetic fields on the collision process between dense molecular cores. We performed three-dimensional magnetohydrodynamic simulations of collisions between two self-gravitating cores using the Enzo adaptive mesh refinement code. The core was modeled as a stable isothermal Bonnor-Ebert (BE) sphere immersed in uniform magnetic fields. Collisions were characterized by the offset parameter $b$, Mach number of the initial core $\mathcal{M}$, magnetic field strength $B_{0}$, and angle $θ$ between the initial magnetic field and collision axis. For head-on ($b = 0$) coll…
Magnetic and kinetic energy in ideal incompressible MHD are not global invariants and, therefore, it had been justified to discuss only the cascade of their sum, total energy. We provide a physical argument based on scale-locality of the cascade, along with compelling evidence that at high Reynolds numbers, magnetic and kinetic energy budgets statistically decouple beyond a transitional "conversion" range. This arises because magnetic field-line stretching is a large-scale process which vanishes on average at intermediate and small scales within the inertial-inductive range, thereby allowing e…
We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify non-linear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies …
We investigate collapse of magnetic protostellar clouds of mass $10$ and $1 M_{\odot}$. The collapse is simulated numerically using the two-dimensional magnetohydrodynamic (MHD) code `Enlil'. The simulations show that protostellar clouds acquire a hierarchical structure by the end of the isothermal stage of collapse. Under the action of the electromagnetic force, the protostellar cloud takes the form of an oblate envelope with the half-thickness to radius ratio $Z/R \sim (0.20-0.95)$. A geometrically and optically thin primary disk with radius $0.2-0.7 R_0$ and $Z/R \sim (10^{-2}-10^{-1})$ for…
MRI Turbulence versus $α$-Viscosity in Circumbinary Disks: Implications for Gravitational-Wave Dephasing and Accretion Variability
Center for Cosmology and Particle Physics, Physics Department, New York University（纽约大学物理系宇宙学与粒子物理中心）；Center for Computational Astrophysics, Flatiron Institute（西蒙斯平顿研究所计算天体物理学中心）
We perform a linear analysis of the stability of isothermal, rotating, magnetic, self-gravitating sheets that are weakly ionized. The magnetic field and rotation axis are perpendicular to the sheet. We include a self-consistent treatment of thermal pressure, gravitational, rotational, and magnetic (pressure and tension) forces together with two nonideal magnetohydrodynamic (MHD) effects (Ohmic dissipation and ambipolar diffusion) that are treated together for their influence on the properties of gravitational instability for a rotating sheet-like cloud or disk. Our results show that there is a…
The collapse of the magnetic rotating protostellar cloud with mass of $10\,M_{\odot}$ is numerically studied. The initial ratios of the thermal, magnetic, and rotational energies of the cloud to the modulus of its gravitational energy are 0.3, 0.2 and 0.01, respectively. The emphasis is on the evolution and properties of the quasi-magnetostatic primary disk formed at the isothermal stage of the collapse. Simulations show that the primary disk size and mass increase during evolution from $1500$ au to $7400$ au and from $0.3\,M_{\odot}$ to $5.2\,M_{\odot}$, respectively. Magnetic field is quasi-…
We numerically model the collapse of magnetic rotating protostellar clouds with mass of 10 $M_{sun}$. The simulations are carried out with the help of 2D MHD code Enlil. The structure of the cloud at the isothermal stage of the collapse is investigated for the cases of weak, moderate, and strong initial magnetic field. Simulations reveal the universal hierarchical structure of collapsing protostellar clouds, consisting of flattened envelope with the qausi-magnetostatc disk inside and the first core in its center. The size of the primary disk increases with the initial magnetic energy of the cl…
