Weak Vertical Magnetic Field Research Articles

Jets with a Twist: The Emergence of FR0 Jets in a 3D GRMHD Simulation of Zero-angular-momentum Black Hole Accretion

Spinning supermassive black holes (BHs) in active galactic nuclei magnetically launch relativistic collimated outflows, or jets. Without angular momentum supply, such jets are thought to perish within 3 orders of magnitude in distance from the BH, well before reaching kiloparsec scales. We study the survival of such jets at the largest scale separation to date, via 3D general relativistic magnetohydrodynamic simulations of rapidly spinning BHs immersed into uniform zero-angular-momentum gas threaded by a weak vertical magnetic field. We place the gas outside the BH sphere of influence, or the Bondi radius, chosen to be much larger than the BH gravitational radius, R B = 103 R g. The BH develops dynamically important large-scale magnetic fields, forms a magnetically arrested disk (MAD), and launches relativistic jets that propagate well outside R B and suppress BH accretion to 1.5% of the Bondi rate, ṀB . Thus, low-angular-momentum accretion in the MAD state can form large-scale jets in Fanaroff–Riley (FR) type I and II galaxies. Subsequently, the disk shrinks and exits the MAD state: barely a disk (BAD), it rapidly precesses, whips the jets around, globally destroys them, and lets 5%–10% of ṀB reach the BH. Thereafter, the disk starts rocking back and forth by angles 90°–180°: the rocking accretion disk (RAD) launches weak intermittent jets that spread their energy over a large area and suppress BH accretion to ≲2% ṀB . Because the BAD and RAD states tangle up the jets and destroy them well inside R B, they are promising candidates for the more abundant, but less luminous, class of FR0 galaxies.

Effects of magnetic field, fluid properties, and geometric parameters on double-diffusive convection of liquid metals

<sec>Thermal convection in conducting fluids under the influence of a magnetic field is a hot research topic. In this study, a high-precision and high-resolution numerical method is used to directly simulate the double-diffusive convection of liquid metal in a two-dimensional cavity. The study covers the effects of magnetic field strength (<i>Ha</i>), Prandtl number (<i>Pr</i>), Lewis number (<i>Le</i>), and aspect ratio on the dynamics of flow and heat/mass transfer under both horizontal magnetic field and vertical magnetic field. The study considers magnetic field intensities ranging from 0 to 100, Prandtl numbers from 0.01 to 1, Lewis numbers varying from 1 to 100, and aspect ratios spanning from 1 to 12. Within these specified parameter ranges, the outcomes under conditions of no magnetic field (<i>Ha</i> = 0), weak magnetic field (<i>Ha</i> = 10), and strong magnetic field (<i>Ha</i> = 50) are compared with each other.</sec><sec>The results show that the magnetic field primarily suppresses flow, heat transfer, and mass transfer. Under the same strength of the magnetic field, the horizontal magnetic field has a greater suppressing effect than the vertical magnetic field. However, the cases of weak magnetic field and strong magnetic field, their effects on heat and mass transfer are similar. Regardless of the orientation and strength of the magnetic field, the heat transfer efficiency and mass transfer efficiency always increase with Prandtl number increasing. The application of a magnetic field can reduce the increase in heat and mass transfer, and when the magnetic field strength reaches a certain level, the Lorentz force predominates, making the influence of the Prandtl number on heat and mass transfer very small. In the presence of a magnetic field, a bifurcation phenomenon is observed around <i>Pr</i> = 0.9.</sec><sec>Additionally, as the Lewis number increases, the flow transforms from steady flow to periodic flow, and the influence on mass transfer efficiency becomes more significant. For example, under a horizontal magnetic field, the mass transfer efficiency at the maximum Lewis number is about six times that at the minimum Lewis number. Similarly, under a weak vertical magnetic field, the mass transfer efficiency is about nine times higher. The influence of Lewis number on heat transfer efficiency is relatively minor.</sec><sec>Within the range of considered aspect ratios, the heat transfer efficiency and mass transfer efficiency exhibit oscillatory behavior under no magnetic field and weak magnetic field as the aspect ratio increases. However, the heat transfer efficiency and mass transfer efficiency under a strong magnetic field are less affected by the aspect ratio. For flows with the same number of vortices, lower aspect ratio can lead to stronger heat and mass transfer.</sec>

MHD in a Cylindrical Shearing Box. II. Intermittent Bursts and Substructures in MRI Turbulence

By performing ideal magnetohydrodynamical (MHD) simulations with weak vertical magnetic fields in unstratified cylindrical shearing boxes with modified boundary treatment, we investigate MHD turbulence excited by magnetorotational instability. The cylindrical simulation exhibits extremely large temporal variation in the magnetic activity compared with the simulation in a normal Cartesian shearing box, although the time-averaged field strengths are comparable in the cylindrical and Cartesian setups. Detailed analysis of the terms describing magnetic energy evolution with “triangle diagrams” surprisingly reveals that in the cylindrical simulation the compression of toroidal magnetic field is unexpectedly as important as the winding due to differential rotation in amplifying magnetic fields and triggering intermittent magnetic bursts, which are not seen in the Cartesian simulation. The importance of the compressible amplification is also true for a cylindrical simulation with tiny curvature; the evolution of magnetic fields in the nearly Cartesian shearing box simulation is fundamentally different from that in the exact Cartesian counterpart. The radial gradient of epicyclic frequency, κ, which cannot be considered in the normal Cartesian shearing box model, is the cause of this fundamental difference. An additional consequence of the spatial variation of κ is continuous and ubiquitous formation of narrow high-density (low-density) and weak-field (strong-field) localized structures; seeds of these ring gap structures are created by the compressible effect and subsequently amplified and maintained under the marginally unstable condition regarding “viscous-type” instability.

Bridging the Bondi and Event Horizon Scales: 3D GRMHD Simulations Reveal X-shaped Radio Galaxy Morphology

X-shaped radio galaxies (XRGs) produce misaligned X-shaped jet pairs and make up ≲10% of radio galaxies. XRGs are thought to emerge in galaxies featuring a binary supermassive black hole (SMBH), SMBH merger, or large-scale ambient medium asymmetry. We demonstrate that XRG morphology can naturally form without such special, preexisting conditions. Our 3D general-relativistic magnetohydrodynamic (GRMHD) simulation for the first time follows magnetized rotating gas from outside the SMBH sphere of influence of radius R B to the SMBH of gravitational radius R g at the largest scale separation, R B/R g = 103, to date. Initially, our axisymmetric system of constant-density hot gas contains a weak vertical magnetic field and rotates in the equatorial plane of a rapidly spinning SMBH. We seed the gas with small-scale 2% level pressure perturbations. Infalling gas forms an accretion disk, and the SMBH launches relativistically magnetized collimated jets reaching well outside R B. Under the pressure of the infalling gas, the jets intermittently turn on and off, erratically wobble, and inflate pairs of cavities in different directions, resembling an X-shaped jet morphology. Synthetic X-ray images reveal multiple pairs of jet-powered shocks and cavities. Large-scale magnetic flux accumulates on the SMBH, becomes dynamically important, and leads to a magnetically arrested disk state. The SMBH accretes at 2% of the Bondi rate ( for M87*) and launches twin jets at η = 150% efficiency. These jets are powerful enough (P jets ≃ 2 × 1044 erg s−1) to escape along the SMBH spin axis and end the short-lived intermittent jet state, whose transient nature can account for the rarity of XRGs.

Origin of Weak Turbulence in the Outer Regions of Protoplanetary Disks

Abstract The mechanism behind angular momentum transport in protoplanetary disks, and whether this transport is turbulent in nature, is a fundamental issue in planet formation studies. Recent ALMA observations have suggested that turbulent velocities in the outer regions of these disks are less than ∼0.05– , contradicting theoretical predictions of turbulence driven by the magnetorotational instability (MRI). These observations have generally been interpreted to be consistent with a large-scale laminar magnetic wind driving accretion. Here, we carry out local, shearing-box simulations with varying ionization levels and background magnetic field strengths in order to determine which parameters produce results consistent with observations. We find that even when the background magnetic field launches a strong largely laminar wind, significant turbulence persists and is driven by localized regions of vertical magnetic field (the result of zonal flows) that are unstable to the MRI. The only conditions for which we find turbulent velocities below the observational limits are weak background magnetic fields and ionization levels well below that usually assumed in theoretical studies. We interpret these findings within the context of a preliminary model in which a large-scale magnetic field, confined to the inner disk, hinders ionizing sources from reaching large radial distances, e.g., through a sufficiently dense wind. Thus, in addition to such a wind, this model predicts that for disks with weakly turbulent outer regions, the outer disk will have significantly reduced ionization levels compared to standard models and will harbor only a weak vertical magnetic field.

Effects of a small magnetic field on homoclinic bifurcations in a low-Prandtl-number fluid.

Effects of a uniform magnetic field on homoclinic bifurcations in Rayleigh-Bénard convection in a fluid of Prandtl number Pr = 0.01 are investigated using direct numerical simulations (DNS). A uniform magnetic field is applied either in the vertical direction or in the horizontal direction. For a weak vertical magnetic field, the possibilities of both forward and backward homoclinic bifurcations are observed leading to a spontaneous gluing of two limit cycles into one as well as a spontaneous breaking of a limit cycle into two for lower values of the Chandrasekhar's number ( Q≤5). A slightly stronger magnetic field makes the convective flow time independent giving the possibility of stationary patterns at the secondary instability. For horizontal magnetic field, the x⇋y symmetry is destroyed and neither a homoclinic gluing nor a homoclinic breaking is observed. Two low-dimensional models are also constructed: one for a weak vertical magnetic field and another for a weak horizontal magnetic field. The models qualitatively capture the features observed in DNS and help understanding the unfolding of bifurcations close to the onset of magnetoconvection.

Magneto-rotational instability with the effect of cosmic rays

AbstractCosmic ray (CR) is an important component of the interstellar medium. It interacts with plasma via embedded magnetic irregularities. We study the magneto-rotational instability (MRI) in the presence of CRs. We analyse the effect of CRs including their diffusion using both linear stability analysis and MHD simulations. Two models are studied. (1) In the shearing box model, uniform initial state is adopted. Linear analysis shows that the growth rate of MRI is not sensitive to the value of CR diffusion coefficient. (2) In the differentially rotating cylinder model, the initial state is taken as a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both linear results are confirmed by MHD simulations.

ANALYSIS OF MAGNETOROTATIONAL INSTABILITY WITH THE EFFECT OF COSMIC-RAY DIFFUSION

We present the results obtained from linear stability analysis and 2.5-dimensional magnetohydrodynamic (MHD) simulations of the magnetorotational instability (MRI), including the effects of cosmic rays (CRs). We took into account of the CR diffusion along the magnetic field but neglect the cross-field-line diffusion. Two models are considered in this paper: shearing box model and differentially rotating cylinder model. We studied how MRI is affected by the initial CR pressure (i.e., energy) distribution. In the shearing box model, the initial state is uniform distribution. Linear analysis shows that the growth rate of MRI does not depend on the value of CR diffusion coefficient. In the differentially rotating cylinder model, the initial state is a constant angular momentum polytropic disk threaded by weak uniform vertical magnetic field. Linear analysis shows that the growth rate of MRI becomes larger if the CR diffusion coefficient is larger. Both results are confirmed by MHD simulations. The MHD simulation results show that the outward movement of matter by the growth of MRI is not impeded by the CR pressure gradient, and the centrifugal force which acts to the concentrated matter becomes larger. Consequently, the growth rate of MRI is increased. On the other hand, if the initial CR pressure is uniform, then the growth rate of the MRI barely depends on the value of the CR diffusion coefficient.

MAGNETOHYDRODYNAMIC SIMULATIONS OF GLOBAL ACCRETION DISKS WITH VERTICAL MAGNETIC FIELDS

(Abridged) We report results of three dimensional MHD simulations of global accretion disks threaded with weak vertical magnetic fields. We perform the simulations in the spherical coordinates with different temperature profiles and accordingly different rotation profiles. In the cases with a spatially constant temperature, because the rotation frequency is vertically constant in the equilibrium condition, general properties of the turbulence are quantitatively similar to those obtained in local shearing box simulations. On the other hand, in the cases with a radially variable temperature profile, the vertical differential rotation, which is inevitable in the equilibrium condition, winds up the magnetic field lines, in addition to the usual radial differential rotation. As a result, the coherent wound magnetic fields contribute to the Maxwell stress in the surface regions. We obtain nondimensional density and velocity fluctuations ~0.1-0.2 at the midplane. The azimuthal power spectra of the magnetic fields show shallow slopes, ~m^0- m^{-1}, than those of velocity and density. We observe intermittent and structured disk winds driven by the Poynting flux associated with the MHD turbulence. The Poynting flux originating from magnetic tension is injected from the regions above a scale height towards both the midplane and the surfaces. Related to this, sound waves are directed to the midplane from the surface regions. The mass accretion mainly occurs near the surfaces and the gas near the midplane slowly moves outward, which causes large-scale meridional circulations. The vertical magnetic fields are also dragged inward in the surface regions, while they stochastically move outward and inward around the midplane. We also discuss an observational implication of induced spiral structure in the simulated turbulent disks to protoplanetary disks.

DRIVING DISK WINDS AND HEATING HOT CORONAE BY MRI TURBULENCE

We investigate the formation of hot coronae and vertical outflows in accretion disks by magneto-rotational turbulence. We perform local three-dimensional (3D) MHD simulations with the vertical stratification by explicitly solving an energy equation with various effective ratios of specific heats, gamma. Initially imposed weak vertical magnetic fields are effectively amplified by magnetorotational instability (MRI) and winding due to the differential rotation. In the isothermal case (gamma=1), the disk winds are mainly driven by the Poynting flux associated with the MHD turbulence and show quasi-periodic intermittency. On the other hand, in the non-isothermal cases with gamma >~ 1.1, the regions above 1-2 scale heights from the midplane are effectively heated up to form coronae with the temperature of ~ 50 times of the initial value, which are connected to the cooler midplane region through the pressure-balanced transition regions. As a result, the disk winds are mainly driven by the gas pressure with exhibiting more time-steady nature, although the nondimensional time-averaged mass loss rates are similar to that of the isothermal case. Sound-like waves are confined in the cool midplane region in these cases, and the amplitude of the density fluctuations is larger than that of the isothermal case.

Revisiting linear dynamics of non-axisymmetric perturbations in weakly magnetized accretion discs

We investigate linear dynamics of non-axisymmetric perturbations in incompressible, vertically stratified Keplerian discs with a weak vertical magnetic field in the shearing box approximation. Perturbations are decomposed into shearing waves whose evolution is followed via numerical integration of the linearized ideal MHD equations. There are two basic modes in the system -- inertia-gravity waves and magnetic mode, which displays the magnetorotational instability (MRI). As distinct from previous studies, we introduce `eigenvariables' characterizing each (counter-propagating) component of the inertia-gravity and magnetic modes, which are governed by a set of four first order coupled ordinary differential equations. This allowed us to identify a new process of linear coupling of the two above non-axisymmetric modes due to the disc's differential rotation. We did a comparative analysis of the dynamics of non-axisymmetric and axisymmetric magnetic mode perturbations. It is shown that the growth of optimal and close-to-optimal non-axisymmetric harmonics of this mode, having transient nature, can prevail over the exponential growth of axisymmetric ones (i.e., over the axisymmetric MRI) during dynamical time. A possible implication of this result for axisymmetric channel solutions is discussed. Specifically, the formation of the channel may be affected/impeded by non-axisymmetric modes already at the early linear stage leading to its untimely disruption -- the outcome strongly depends on the amplitude and spectrum of initial perturbation. So, this competition may result in an uncertainty in the magnetic mode's non-linear dynamics. It is also shown that a maximum non-axisymmetric growth is at vertical wavelengths close to the scale-height for which compressibility effects are important. This indirectly suggests that compressibility plays a role in the dynamics of the non-axisymmetric MRI.

Local outflows from turbulent accretion disks

The aim of this paper is to investigate the properties of accretion disks threaded by a weak vertical magnetic field, with a particular focus on the interplay between MHD turbulence driven by the magnetorotational instability (MRI) and outflows that might be launched from the disk. For that purpose, we use a set of numerical simulations performed with the MHD code RAMSES in the framework of the shearing box model. We concentrate on the case of a rather weak vertical magnetic field such that the initial ratio beta0 of the thermal and magnetic pressures in the disk midplane equals 10^4. As reported recently, we find that MHD turbulence drives an efficient outflow out of the computational box. We demonstrate a strong sensitivity of that result to the box size: enlargements in the radial and vertical directions lead to a reduction of up to an order of magnitude in the mass-loss rate. Such a dependence prevents any realistic estimates of disk mass-loss rates being derived using shearing-box simulations. We find however that the flow morphology is robust and independent of the numerical details of the simulations. Its properties display some features and approximate invariants that are reminiscent of the Blandford & Payne launching mechanism, but differences exist. For the magnetic field strength considered in this paper, we also find that angular momentum transport is most likely dominated by MHD turbulence, the saturation of which scales with the magnetic Prandtl number, the ratio of viscosity and resistivity, in a way that is in good agreement with expectations based on unstratified simulations. This paper thus demonstrates for the first time that accretion disks can simultaneously exhibit MRI-driven MHD turbulence along with magneto-centrifugally accelerated outflows.

Growth oxygen-containing defects in silicon grown in a weak vertical magnetic field

Properties of silicon (M-Si) prepared by the Czochralski growth technique in a vertical magnetic field of 0.05 T applied to a melt are studied by measuring IR absorption spectra, microindentation, and selective etching. The effect of increasing the concentration of interstitial oxygen upon the thermal treatment of M-Si is found. It is shown that microhardness of M-Si is higher than that of silicon grown by the traditional Czochralski technique by ∼8%. The features in the behavior of M-Si are attributed to the formation of oxygen-containing defect-impurity complexes during the growth. Upon thermal treatment at 900°C in the hydrogen flow, these complexes decompose with the extraction of interstitial oxygen, which suppresses thermal hardening typical of the silicon single crystals grown by the traditional Czochralski technique.

Numerical simulations of magnetic structures

AbstractWe use 3D radiative MHD simulations of the upper turbulent convection layer for investigation of physical mechanisms of formation of magnetic structures on the Sun. The simulations include all essential physical processes, and are based of the LES (Large-Eddy Simulations) approach for describing the sub-grid scale turbulence. The simulation domain covers the top layer of the convection zone and the lower atmosphere. The results reveal a process of spontaneous formation of stable magnetic structures from an initially weak vertical magnetic field, uniformly distributed in the simulation domain. The process starts concentration of magnetic patches at the boundaries of granular cells, which are subsequently merged together into a stable large-scale structure by converging downdrafts below the surface. The resulting structure represents a compact concentration of strong magnetic field, reaching 6 kG in the interior. It has a cluster-like internal structurization, and is maintained by strong downdrafts extending into the deep layers.

MECHANISM OF SPONTANEOUS FORMATION OF STABLE MAGNETIC STRUCTURES ON THE SUN

One of the puzzling features of solar magnetism is formation of long-living compact magnetic structures; such as sunspots and pores, in the highly turbulent upper layer of the solar convective zone. We use realistic radiative 3D MHD simulations to investigate the interaction between magnetic field and turbulent convection. In the simulations, a weak vertical uniform magnetic field is imposed in a region of fully developed granular convection; and the total magnetic flux through the top and bottom boundaries is kept constant. The simulation results reveal a process of spontaneous formation of stable magnetic structures, which may be a key to understanding of the magnetic self-organization on the Sun and formation of pores and sunspots. This process consists of two basic steps: 1) formation of small-scale filamentary magnetic structures associated with concentrations of vorticity and whirlpool-type motions, and 2) merging of these structures due to the vortex attraction, caused by converging downdrafts around magnetic concentration below the surface. In the resulting large-scale structure maintained by the converging plasma motions, the magnetic field strength reaches ~1.5 kG at the surface and ~6 kG in the interior; and the surface structure resembles solar pores. The magnetic structure remains stable for the whole simulation run of several hours with no sign of decay.

Large scale magnetic fields in viscous resistive accretion disks

<i>Aims. <i/>Cold steady-state disk wind theory from near Keplerian accretion disks requires a large scale magnetic field at near equipartition strength. However the minimum magnetization has never been tested with time dependent simulations. We investigate the time evolution of a Shakura-Sunyaev accretion disk threaded by a weak vertical magnetic field. The strength of the field is such that the disk magnetization falls off rapidly with radius.<i>Methods. <i/>Four 2.5D numerical simulations of viscous resistive accretion disk are performed using the magnetohydrodynamic code PLUTO. In these simulations, a mean field approach is used and turbulence is assumed to give rise to anomalous transport coefficients (alpha prescription). <i>Results. <i/>The large scale magnetic field introduces only a small perturbation to the disk structure, with accretion driven by the dominant viscous torque. However, a super fast magnetosonic jet is observed to be launched from the innermost regions and remains stationary over more than 953 Keplerian orbits. This is the longest accretion-ejection simulation ever carried out. The self-confined jet is launched from a finite radial zone in the disk which remains constant over time. Ejection is made possible because the magnetization reaches unity at the disk surface, due to the steep density decrease. However, no ejection is reported when the midplane magnetization becomes too small. The asymptotic jet velocity remains nevertheless too low to explain observed jets. This is because of the negligible power carried away by the jet.<i>Conclusions. <i/>Astrophysical disks with superheated surface layers could drive analogous outflows even if their midplane magnetization is low. Sufficient angular momentum would be extracted by the turbulent viscosity to allow the accretion process to continue. The magnetized outflows would be no more than byproducts, rather than a fundamental driver of accretion. However, if the midplane magnetization increases towards the center, a natural transition to an inner jet dominated disk could be achieved.

DISK WINDS DRIVEN BY MAGNETOROTATIONAL INSTABILITY AND DISPERSAL OF PROTOPLANETARY DISKS

By performing local three-dimensional MHD simulations of stratified accretion disks, we investigate disk winds driven by MHD turbulence. Initially given weak vertical magnetic fields are effectively amplified by magnetorotational instability and winding due to differential rotation. Large scale channel flows develop most effectively at 1.5 - 2 times the scale heights where the magnetic pressure is comparable to but slightly smaller than the gas pressure. The breakup of these channel flows drives structured disk winds by transporting the Poynting flux to the gas. These features are universally observed in the simulations of various initial fields. This disk wind process should play an essential role in the dynamical evaporation of proto-planetary disks. The breakup of channel flows also excites the momentum fluxes associated with Alfvenic and (magneto-)sonic waves toward the mid-plane, which possibly contribute to the sedimentation of small dust grains in protoplanetary disks.

Magnetic Buoyancy Instabilities of a Shear‐generated Magnetic Layer

We discuss a series of high-resolution fully nonlinear MHD numerical simulations relevant to processes that are expected to operate in the solar tachocline. We study the generation of a strong toroidal magnetic field by the stretching action of velocity shear on a weak background poloidal magnetic field, a process often referred to in solar dynamotheoryasthe-effect.Herewespecificallystudythegenerationof astronglayerof horizontalmagneticfield by the action of vertical shear on weak vertical magnetic field in a subadiabatically stratified atmosphere, and we examinethebuoyancypropertiesof theresultingmagneticconfigurations.Wefindthatmagneticlayerscanindeedbe generated, and that magnetic buoyancy instabilities of this layer can exist and lead to rising magnetic structures that resemble arching tubes. However, the conditions for the instabilities to occur are much more demanding than might be anticipated from previous results where a magnetic layer was initially prescribed, rather than shear-generated. Furthermore, the magnetic flux transport by the buoyancy instabilities in this case is decidedly inefficient. These issues, stemming from the feedback of strong magnetic field on the generating shear, raise serious questions for the efficacy of this process in the current solar dynamo paradigm. Subject headingg hydrodynamics — MHD — Sun: magnetic fields

The Acceleration Mechanism of Resistive Magnetohydrodynamic Jets Launched from Accretion Disks

We analyzed the results of nonlinear resistive magnetohydrodynamic (MHD) simulations of jet formation to study the acceleration mechanism of axisymmetric, resistive MHD jets. The initial state is a constant angular momentum, polytropic torus threaded by weak uniform vertical magnetic fields. The time evolution of the torus is simulated by applying the CIP-MOCCT scheme extended for resistive MHD equations. We carried out simulations up to 50 rotation periods at the innermost radius of the disk created by accretion from the torus. The acceleration forces and the characteristics of resistive jets were studied by computing forces acting on Lagrangian test particles. Since the angle between the rotation axis of the disk and magnetic field lines is smaller in resistive models than in ideal MHD models, magnetocentrifugal acceleration is smaller. The effective potential along a magnetic field line has a maximum around z ~ 0.5r0 in resistive models, where r0 is the radius at which the density of the initial torus is maximum. Jets are launched after the disk material is lifted to this height by pressure gradient force. Even in this case, the main acceleration force around the slow magnetosonic point is the magnetocentrifugal force. The power of the resistive MHD jet is comparable to the mechanical energy liberated in the disk by mass accretion. Joule heating is not essential for the formation of jets.

Spin switching in semiconductor quantum dots through spin-orbit coupling

The spin-orbit coupling influences the total spin of semiconductor quantum dots. We analyze the theoretical prediction for the combined effects of spin-orbit coupling, weak vertical magnetic fields and deformation of the dot. Our results allow the characterization of the quantum dots as spin switches, controllable with electric gates.