Dense, star-forming cores of molecular clouds are observed to be significantly magnetized. A realistic magnetic field of moderate strength has been shown to suppress, through catastrophic magnetic ...braking, the formation of a rotationally supported disk (RSD) during the protostellar accretion phase of low-mass star formation in the ideal MHD limit. We address, through two-dimensional (axisymmetric) simulations, the question of whether realistic levels of non-ideal effects, computed with a simplified chemical network including dust grains, can weaken the magnetic braking enough to enable an RSD to form. We find that ambipolar diffusion (AD), the dominant non-ideal MHD effect over most of the density range relevant to disk formation, does not enable disk formation, at least in two dimensions. The reason is that AD allows the magnetic flux that would be dragged into the central stellar object in the ideal MHD limit to pile up instead in a small circumstellar region, where the magnetic field strength (and thus the braking efficiency) is greatly enhanced. We also find that, on the scale of tens of AU or more, a realistic level of Ohmic dissipation does not weaken the magnetic braking enough for an RSD to form, either by itself or in combination with AD. The Hall effect, the least explored of these three non-ideal MHD effects, can spin up the material close to the central object to a significant, supersonic rotation speed, even when the core is initially non-rotating, although the spun-up material remains too sub-Keplerian to form an RSD. The problem of catastrophic magnetic braking that prevents disk formation in dense cores magnetized to realistic levels remains unresolved. Possible resolutions of this problem are discussed.
Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. In the simplest case of a laminar (non-turbulent) core with the magnetic field aligned with the ...rotation axis, both analytic considerations and numerical simulations have shown that the formation of a large, 10 super(2) AU scale, rotationally supported protostellar disk is suppressed by magnetic braking in the ideal MHD limit for a realistic level of core magnetization. This theoretical difficulty in forming protostellar disks is termed the "magnetic braking catastrophe." A possible resolution to this problem, proposed by Hennebelle & Ciardi and Joos et al., is that misalignment between the magnetic field and rotation axis may weaken the magnetic braking enough to enable disk formation. We evaluate this possibility quantitatively through numerical simulations. We confirm the basic result of Joos et al. that the misalignment is indeed conducive to disk formation. In relatively weakly magnetized cores with dimensionless mass-to-flux ratio > ~ 4, it enabled the formation of rotationally supported disks that would otherwise be suppressed if the magnetic field and rotation axis are aligned. For more strongly magnetized cores, disk formation remains suppressed, however, even for the maximum tilt angle of 90degrees. If dense cores are as strongly magnetized as indicated by OH Zeeman observations (with a mean dimensionless mass-to-flux ratio ~2), it would be difficult for the misalignment alone to enable disk formation in the majority of them. We conclude that, while beneficial to disk formation, especially for the relatively weak field case, misalignment does not completely solve the problem of catastrophic magnetic braking in general.
Abstract Using general relativistic magnetohydrodynamic simulations, it has been suggested that the rotational energy of a rapidly rotating black hole (BH) is preferentially extracted along the ...magnetic field lines threading the event horizon in the middle and lower latitudes. Applying this angle-dependent Poynting flux to the jet downstream, we demonstrate that the jets exhibit limb-brightened structures at various viewing angles, as observed from Mrk 501, M87, and Cyg A between 5° and 75°, and that the limb brightening is enhanced when the jet is collimated strongly. It is also found that the jet width perpendicular to the propagation direction shrinks at the projected distance of the altitude where the jet collimates from a conical shape (near the BH) to a parabolic one (in the jet). Comparing with Very Long Baseline Interferometry observations, we show that this collimation takes place within the deprojected altitude of 100 Schwarzschild radii from the BH in the case of the M87 jet.
Abstract
Astrochemical simulations are a powerful tool for revealing chemical evolution in the interstellar medium. Astrochemical calculations require efficient processing of large matrices for the ...chemical networks. The large chemical reaction networks often present bottlenecks for computation because of time derivatives of chemical abundances. We propose an efficient algorithm using a stoichiometry matrix approach in which this time-consuming part is expressed as a loop, unlike the algorithm used in previous studies. Since stoichiometry matrices are sparse in general, the performances of simulations with our algorithm depend on which sparse-matrix storage format is used. We conducted a performance comparison experiment using the common storage formats, including the coordinate format, the compressed column storage format, the compressed row storage (CRS) format, and the sliced ELLPACK format. Experimental results showed that the simulations with the CRS format are the most suitable for astrochemical simulations and about a factor of 2 faster than those with the algorithm used in previous studies. In addition, our algorithm significantly reduces not only the computation time but also the compilation time. We also explore the beneficial effects of parallelization and sparse-matrix reordering in these algorithms.
Abstract
We examine the temporary evolution of axisymmetric magnetospheres around rapidly rotating black holes (BHs), by applying our two-dimensional particle-in-cell simulation code. Assuming a ...stellar-mass BH, we find that the created pairs fail to screen the electric field along the magnetic field, provided that the mass accretion rate is much small compared to the Eddington limit. Magnetic islands are created by reconnection near the equator and migrate toward the event horizon, expelling magnetic flux tubes from the BH vicinity during a large fraction of time. When the magnetic islands stick to the horizon due to redshift and virtually vanish, a strong magnetic field penetrates the horizon, enabling efficient extraction of energy from the BH. During this flaring phase, a BH gap appears around the inner light surface with a strong meridional return current toward the equator within the ergosphere. If the mass accretion rate is 0.025% of the Eddington limit, the BH’s spin-down luminosity becomes 16–19 times greater than its analytical estimate during the flares, although its long-term average is only 6% of it. We demonstrate that the extracted energy flux concentrates along the magnetic field lines threading the horizon in the middle latitudes. It is implied that this meridional concentration of the Poynting flux may result in the formation of limb-brightened jets from low-accreting BH systems.
Abstract
Pseudodisks are dense structures formed perpendicular to the direction of the magnetic field during the gravitational collapse of a molecular cloud core. Numerical simulations of the ...formation of pseudodisks are usually computationally expensive with conventional CPU codes. To demonstrate the proof of concept of a fast computing method for this numerically costly problem, we explore the GPU-powered MHD code Astaroth, a sixth-order finite difference method with low adjustable finite resistivity implemented with sink particles. The formation of pseudodisks is physically and numerically robust and can be achieved with a simple and clean setup for this newly adopted numerical approach for science verification. The method’s potential is illustrated by evidencing the dependence on the initial magnetic field strength of specific physical features accompanying the formation of pseudodisks, e.g., the occurrence of infall shocks and the variable behavior of the mass and magnetic flux accreted on the central object. As a performance test, we measure both weak and strong scaling of our implementation to find the most efficient way to use the code on a multi-GPU system. Once suitable physics and problem-specific implementations are realized, the GPU-accelerated code is an efficient option for 3D magnetized collapse problems.
The formation of rotationally supported protostellar disks is suppressed in ideal MHD in non-turbulent cores with aligned magnetic fields and rotation axes. A promising way to resolve this so-called ..."magnetic braking catastrophe" is through turbulence. The reason for the turbulence-enabled disk formation is usually attributed to the turbulence-induced magnetic reconnection, which is thought to reduce the magnetic flux accumulated in the disk-forming region. We advance an alternative interpretation, based on magnetic decoupling-triggered reconnection of severely pinched field lines close to the central protostar and turbulence-induced warping of the pseudodisk of Galli and Shu. Such reconnection weakens the central split magnetic monopole that lies at the heart of the magnetic braking catastrophe under flux freezing. We show, through idealized numerical experiments, that the pseudodisk can be strongly warped, but not completely destroyed, by a subsonic or sonic turbulence. The warping decreases the rates of angular momentum removal from the pseudodisk by both magnetic torque and outflow, making it easier to form a rotationally supported disk. More importantly, the warping of the pseudodisk out of the disk-forming, equatorial plane greatly reduces the amount of magnetic flux threading the circumstellar, disk-forming region, further promoting disk formation. The beneficial effects of pseudodisk warping can also be achieved by a misalignment between the magnetic field and rotation axis. These two mechanisms of disk formation, enabled by turbulence and field-rotation misalignment respectively, are thus unified. We find that the disks formed in turbulent magnetized cores are rather thick and significantly magnetized. Implications of these findings, particularly for the thick young disk inferred in L1527, are briefly discussed.
Stars form in dense cores of molecular clouds that are observed to be significantly magnetized. A dynamically important magnetic field presents a significant obstacle to the formation of protostellar ...disks. Recent studies have shown that magnetic braking is strong enough to suppress the formation of rotationally supported disks in the ideal MHD limit. Whether non-ideal MHD effects can enable disk formation remains unsettled. We carry out a first study on how disk formation in magnetic clouds is modified by the Hall effect, the least explored of the three non-ideal MHD effects in star formation (the other two being ambipolar diffusion and Ohmic dissipation). For illustrative purposes, we consider a simplified problem of a non-self-gravitating, magnetized envelope collapsing onto a central protostar of fixed mass. We find that the Hall effect can spin up the inner part of the collapsing flow to Keplerian speed, producing a rotationally supported disk. The disk is generated through a Hall-induced magnetic torque. Disk formation occurs even when the envelope is initially non-rotating, provided that the Hall coefficient is large enough. When the magnetic field orientation is flipped, the direction of disk rotation is reversed as well. The implication is that the Hall effect can in principle produce both regularly rotating and counter-rotating disks around protostars. The Hall coefficient expected in dense cores is about one order of magnitude smaller than that needed for efficient spin-up in these models. We conclude that the Hall effect is an important factor to consider in studying the angular momentum evolution of magnetized star formation in general and disk formation in particular.
HH 212 is a nearby (400 pc) Class 0 protostellar system showing several components that can be compared with theoretical models of core collapse. We have mapped it in the 350 GHz continuum and ...HCO{sup +} J = 4-3 emission with ALMA at up to ∼0.''4 resolution. A flattened envelope and a compact disk are seen in the continuum around the central source, as seen before. The HCO{sup +} kinematics shows that the flattened envelope is infalling with small rotation (i.e., spiraling) into the central source, and thus can be identified as a pseudodisk in the models of magnetized core collapse. Also, the HCO{sup +} kinematics shows that the disk is rotating and can be rotationally supported. In addition, to account for the missing HCO{sup +} emission at low-redshifted velocity, an extended infalling envelope is required, with its material flowing roughly parallel to the jet axis toward the pseudodisk. This is expected if it is magnetized with an hourglass B-field morphology. We have modeled the continuum and HCO{sup +} emission of the flattened envelope and disk simultaneously. We find that a jump in density is required across the interface between the pseudodisk and the disk. A jet is seen in HCO{sup +} extending out to ∼500 AU away from the central source, with the peaks upstream of those seen before in SiO. The broad velocity range and high HCO{sup +} abundance indicate that the HCO{sup +} emission traces internal shocks in the jet.
Abstract
Kinematic signatures of the jet, winds, multicavities, and episodic shells arising in the unified model of bipolar outflows developed in Shang et al. (Paper I), in which an outflow forms by ...radially directed, wide-angle toroidally magnetized winds interacting with magnetized isothermal toroids, are extracted in the form of position–velocity diagrams. Elongated outflow lobes, driven by magnetized winds and their interplay with the environment, are dominated by extended bubble structures with mixing layers beyond the conventional thin-shell models. The axial cylindrically stratified density jet carries a broad profile near the base, across the projected velocity of the wide-angle wind, and narrows down along the axis with the collimated flow. The reverse shock encloses the magnetized free wind, forms an innermost cavity, and deflects the flow pattern. Shear, Kelvin–Helmholtz instabilities, and pseudopulses add fine and distinctive features between the jet–shell components, and the fluctuating jet velocities. The broad webbed velocity features connect the extremely high and the low velocities across the multicavities, mimicking nested outflowing slower-wind components. Rings and ovals in the perpendicular cuts trace multicavities at different heights, and the compressed ambient gap regions enrich the low-velocity features with protruding spikes. Our kinematic signatures capture the observed systematics of the high-, intermediate-, and low-velocity components from Class 0 to II jet–outflow systems in molecular and atomic lines. The nested shells observed in HH 212, HH 30, and DG Tau B are naturally explained. Outflows as bubbles are ubiquitous and form an inevitable integrative outcome of the interaction between wind and ambient media.
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