Fast Magnetosonic Speed Research Articles

GLOBAL CORONAL SEISMOLOGY IN THE EXTENDED SOLAR CORONA THROUGH FAST MAGNETOSONIC WAVES OBSERVED BYSTEREOSECCHI COR1

We present global coronal seismology for the first time, which allows us to determine inhomogeneous magnetic field strength in the extended corona. From the measurements of the propagation speed of a fast magnetosonic wave associated with a coronal mass ejection (CME) and the coronal background density distribution derived from the polarized radiances observed by the STEREO SECCHI COR1, we determined the magnetic field strengths along the trajectories of the wave at different heliocentric distances. We found that the results have an uncertainty less than 40%, and are consistent with values determined with a potential field model and reported in previous works. The characteristics of the coronal medium we found are that (1) the density, magnetic field strength, and plasma β are lower in the coronal hole region than in streamers; (2) the magnetic field strength decreases slowly with height but the electron density decreases rapidly so that the local fast magnetosonic speed increases while plasma β falls off with height; and (3) the variations of the local fast magnetosonic speed and plasma β are dominated by variations in the electron density rather than the magnetic field strength. These results imply that Moreton and EIT waves are downward-reflected fast magnetosonic waves from the upper solar corona, rather than freely propagating fast magnetosonic waves in a certain atmospheric layer. In addition, the azimuthal components of CMEs and the driven waves may play an important role in various manifestations of shocks, such as type II radio bursts and solar energetic particle events.

A slow bow shock ahead of the heliosphere

Current estimates of plasma parameters in the local interstellar medium indicate that the speed of the interstellar wind, i.e., the relative speed of the local interstellar cloud with respect to the Sun, is most likely less than both the fast magnetosonic speed (subfast) and the Alfvén speed (sub‐Alfvénic) but greater than the slow magnetosonic speed (superslow). In this peculiar parameter regime, MHD theory postulates a slow magnetosonic shock ahead of the heliosphere, provided that the angle between the interstellar magnetic field and the interstellar plasma flow velocity is quite small (e.g., 15° to 30°). In this likely scenario, our multifluid MHD model of the heliospheric interface self‐consistently produces a spatially confined quasi‐parallel slow bow shock. Voyager 1 is heading toward the slow bow shock, while Voyager 2 is not, which means that the two spacecraft are expected to encounter different interstellar plasma populations beyond the heliopause. The slow bow shock also affects the density and spatial extent of the neutral hydrogen wall.

STEREOOBSERVATIONS OF FAST MAGNETOSONIC WAVES IN THE EXTENDED SOLAR CORONA ASSOCIATED WITH EIT/EUV WAVES

We report white-light observations of a fast magnetosonic wave associated with a coronal mass ejection observed by STEREO/SECCHI/COR1 inner coronagraphs on 2011 August 4. The wave front is observed in the form of density compression passing through various coronal regions such as quiet/active corona, coronal holes, and streamers. Together with measured electron densities determined with STEREO COR1 and Extreme UltraViolet Imager (EUVI) data, we use our kinematic measurements of the wave front to calculate coronal magnetic fields and find that the measured speeds are consistent with characteristic fast magnetosonic speeds in the corona. In addition, the wave front turns out to be the upper coronal counterpart of the EIT wave observed by STEREO EUVI traveling against the solar coronal disk; moreover, stationary fronts of the EIT wave are found to be located at the footpoints of deflected streamers and boundaries of coronal holes, after the wave front in the upper solar corona passes through open magnetic field lines in the streamers. Our findings suggest that the observed EIT wave should be in fact a fast magnetosonic shock/wave traveling in the inhomogeneous solar corona, as part of the fast magnetosonic wave propagating in the extended solar corona.

BIPOLAR JETS LAUNCHED FROM MAGNETICALLY DIFFUSIVE ACCRETION DISKS. I. EJECTION EFFICIENCY VERSUS FIELD STRENGTH AND DIFFUSIVITY

We investigate the launching of jets and outflows from magnetically diffusive accretion disks. Using the PLUTO code we solve the time-dependent resistive MHD equations taking into account the disk and jet evolution simultaneously. The main question we address is which kind of disks do launch jets and which kind of disks do not? In particular, we study how the magnitude and distribution of the (turbulent) magnetic diffusivity affect mass loading and jet acceleration. We have applied a turbulent magnetic diffusivity based on \alpha-prescription, but have also investigate examples where the scale height of diffusivity is larger than that of the disk gas pressure. We further investigate how the ejection efficiency is governed by the magnetic field strength. Our simulations last for up to 5000 dynamical time scales corresponding to 900 orbital periods of the inner disk. As a general result we observe a continuous and robust outflow launched from the inner part of the disk, expanding into a collimated jet of super fast magneto-sonic speed. For long time scales the disk internal dynamics changes, as due to outflow ejection and disk accretion the disk mass decreases. For magneto-centrifugally driven jets we find that for i) less diffusive disks, ii) a stronger magnetic field, iii) a low poloidal diffusivity, or a iv) lower numerical diffusivity (resolution), the mass loading of the outflow is increased - resulting in more powerful jets with high mass flux. For weak magnetization the (weak) outflow is driven by the magnetic pressure gradient. We further investigate the jet asymptotic velocity and the jet rotational velocity in respect of the different launching scenarios. We find a lower degree of jet collimation than previous studies, most probably due to our revised outflow boundary condition.

The onset of impulsive bursty reconnection at a two-dimensional current layer

The sudden reconnection of a non-force free 2D current layer, embedded in a low-beta plasma, triggered by the onset of an anomalous resistivity, is studied in detail. The resulting behaviour consists of two main phases. First, a transient reconnection phase, in which the current in the layer is rapidly dispersed and some flux is reconnected. This dispersal of current launches a family of small amplitude magnetic and plasma perturbations, which propagate away from the null at the local fast and slow magnetosonic speeds. The vast majority of the magnetic energy released in this phase goes into internal energy of the plasma, and only a tiny amount is converted into kinetic energy. In the wake of the outwards propagating pulses, an imbalance of Lorentz and pressure forces creates a stagnation flow which drives a regime of impulsive bursty reconnection, in which fast reconnection is turned on and off in a turbulent manner as the current density exceeds and falls below a critical value. During this phase, the null current density is continuously built up above a certain critical level, then dissipated very rapidly, and built up again, in a stochastic manner. Interestingly, the magnetic energy converted during this quasi-steady phase is greater than that converted during the initial transient reconnection phase. Again essentially all the energy converted during this phase goes directly to internal energy. These results are of potential importance for solar flares and coronal heating, and set a conceptually important reference for future 3D studies.

Propagation of Moreton Waves

Abstract With the Flare-Monitoring Telescope (FMT) and Solar Magnetic Activity Research Telescope (SMART) at Hida observatory of Kyoto University, 13 events of Moreton waves were captured at H$\alpha$ center, H$\alpha$$\pm$0.5 Å, and H$\alpha$$\pm$0.8 Å wavebands since 1997. With such samples, we have studied the statistical properties of the propagation of Moreton waves. Moreton waves were all restricted in sectorial zones with a mean value of 92$^\circ$. However, their accompanying EIT waves, observed simultaneously with SOHO/EIT at extreme-ultraviolet wavelength, were very isotropic with a quite extended scope of 193$^\circ$. The average propagation speeds of the Moreton waves and the corresponding EIT waves were 664 km s$^{-1}$ and 205 km s$^{-1}$, respectively. Moreton waves propagated either under large-scale close magnetic flux loops, or firstly in the sectorial region where two sets of magnetic loops separated from each other and diverged, and then stopped before the open magnetic flux region. The location swept by Moreton waves had a relatively weak magnetic field as compared to the magnetic fields at their sidewalls. The ratio of the magnetic flux density between the sidewall and the path falls in the range of 1.4 to 3.7 at a height of 0.01 solar radii. Additionally, we roughly estimated the distribution of the fast magnetosonic speed between the propagating path and sidewalls in an event on 1997 November 3, and found a relatively low-fast magnetosonic speed in the path. We also found that the propagating direction of Moreton waves coincided with the direction of filament eruption in a few well-observed events. This favors an interpretation of the “Piston” model, although further studies are necessary for any definitive conclusion.

Comparing Solar Minimum 23/24 with Historical Solar Wind Records at 1 AU

Based on the variations of sunspot numbers, we choose a 1-year interval at each solar minimum from the beginning of the acquisition of solar wind measurements in the ecliptic plane and at 1 AU. We take the period of July 2008 - June 2009 to represent the solar minimum between Solar Cycles 23 and 24. In comparison with the previous three minima, this solar minimum has the slowest, least dense, and coolest solar wind, and the weakest magnetic field. As a result, the solar wind dynamic pressure, dawn-dusk electric field, and geomagnetic activity during this minimum are the weakest among the four min- ima. The weakening trend had already appeared during solar minimum 22/23, and it may continue into the next solar minimum. During this minimum, the galactic cosmic ray inten- sity reached the highest level in the space age, while the number of solar energetic proton events and the ground level enhancement events were the least. Using solar wind measure- ments near the Earth over 1995 - 2009, we have surveyed and characterized the large-scale solar wind structures, including fast-slow stream interaction regions (SIRs), interplanetary coronal mass ejections (ICMEs), and interplanetary shocks. Their solar cycle variations over the 15 years are studied comprehensively. In contrast with the previous minimum, we find that there are more SIRs and they recur more often during this minimum, probably because more low- and mid-latitude coronal holes and active regions emerged due to the weaker so- lar polar field than during the previous minimum. There are more shocks during this solar minimum, probably caused by the slower fast magnetosonic speed of the solar wind. The SIRs, ICMEs, and shocks during this minimum are generally weaker than during the pre- vious minimum, but did not change as much as did the properties of the undisturbed solar wind.

CORONAL SEISMOLOGY USING EIT WAVES: ESTIMATION OF THE CORONAL MAGNETIC FIELD STRENGTH IN THE QUIET SUN

Coronal EIT waves have been observed for many years. The nature of EIT waves is still contentious, however, there is strong evidence that some of them might be fast magnetosonic waves, or at least have a fast magnetosonic wave component. The fast magnetosonic wave speed is formed from two components; the Alfven speed (magnetic) and the sound speed (thermal). By making measurements of the wave speed, coronal density and temperature it is possible to calculate the quiet-Sun coronal magnetic field strength through coronal seismology. In this paper, we investigate an EIT wave observed on 2009 February 13 by the SECCHI/EUVI instruments on board the STEREO satellites. The wave epicenter was observed at disk center in the STEREO B (Behind) satellite. At this time, the STEREO satellites were separated by approximately 90°, and as a consequence the STEREO A (Ahead) satellite observed the wave on the solar limb. These observations allowed us to make accurate speed measurements of the wave. The background coronal density was derived through Hinode/Extreme-ultraviolet Imaging Spectrometer observations of the quiet Sun and the temperature was estimated through the narrow temperature response in the EUVI bandpasses. The density, temperature, and speed measurements allowed us to estimate the quiet-Sun coronal magnetic field strength to be approximately 0.7 ± 0.7 G.

STUDYING EXTREME ULTRAVIOLET WAVE TRANSIENTS WITH A DIGITAL LABORATORY: DIRECT COMPARISON OF EXTREME ULTRAVIOLET WAVE OBSERVATIONS TO GLOBAL MAGNETOHYDRODYNAMIC SIMULATIONS

In this work, we describe our effort to explore the signatures of large-scale extreme ultraviolet (EUV) transients in the solar corona (EUV waves) using a three-dimensional thermodynamic magnetohydrodynamic model. We conduct multiple simulations of the 2008 March 25 EUV wave (~18:40 UT), observed both on and off of the solar disk by the STEREO-A and B spacecraft. By independently varying fundamental parameters thought to govern the physical mechanisms behind EUV waves in each model, such as the ambient magneto-sonic speed, eruption free energy, and eruption handedness, we are able to assess their respective contributions to the transient signature. A key feature of this work is the ability to synthesize the multi-filter response of the STEREO Extreme UltraViolet Imagers directly from model data, which gives a means for direct interpretation of EUV observations with full knowledge of the three-dimensional magnetic and thermodynamic structures in the simulations. We discuss the implications of our results with respect to some commonly held interpretations of EUV waves (e.g., fast-mode magnetosonic wave, plasma compression, reconnection front, etc.) and present a unified scenario which includes both a wave-like component moving at the fast magnetosonic speed and a coherent driven compression front related to the eruptive event itself.

Rotational Asymmetry of Earth's Bow Shock

AbstractIn terms of global magnetohydrodynamic (MHD) simulations of the solar wind‐magnetosphere‐ionosphere system, this paper investigates the rotational asymmetry of the Earth's bow shock with respect to the Sun‐Earth line. We are limited to simple cases in which the solar wind is along the Sun‐Earth Line; and both the Earth's magnetic dipole moment and the interplanetary magnetic field (IMF) are perpendicular to the Sun‐Earth line. It is shown that even for the case of vanishing IMF strength the bow shock is not rotationally symmetric with respect to the Sun‐Earth line: the east‐west width of the cross section of the bow shock exceeds the north‐south width by about 9%~11% on the terminator plane (dawn‐dusk meridian plane) and its sunward side, and becomes smaller than the north‐south width by about 8% on the tailward side of the terminator plane. In the presence of the IMF, the configuration of the bow shock is affected by both the shape of the magnetopause and the anisotropy of fast magnetosonic wave speed. The magnetopause expands outward, being stretched along the IMF, and the extent of its expansion and stretch increases when the IMF rotates from north to south. In the magnetosheath, the fast magnetosonic wave speed is higher in the direction perpendicular to the magnetic field than that in the parallel direction. Therefore, the stretch direction of the magnetopause is perpendicular to the maximum direction of the fast magnetosonic wave speed, and their effects on the bow shock position are exactly opposite. The eventual shape of the bow shock depends on which effect dominates. On the tailward side of the terminator plane, the anisotropy of fast magnetosonic wave speed dominates, so the cross section of the bow shock is wider in the direction perpendicular to the IMF. On the terminator plane and its sunward side, the shape of the bow shock cross section depends on the orientation of the IMF: the bow shock cross section is still wider in the direction perpendicular to the IMF under generic northward or dawn‐dusk IMF cases, but it becomes narrower in the direction perpendicular to the IMF instead under generic southward IMF cases. In light of the intimate relationship between the shape of the bow shock and the orientation of the IMF, it is proposed to take the IMF as the datum direction so as to extract the parallel half width Rb// and the perpendicular half width Rb┴ as the scale parameters. In comparison with the commonly used east‐west half width yb and the north‐west half width zb, these parameters provide a more reasonable description of the geometry of the bow shock. Simulation data show that under the assumption of isotropic orientation of the IMF, the statistical averages of yb/zb and Rb‌‌/Rb┴ are both smaller than 1 on the terminator plane, which agrees with relevant observational conclusions.

STEREO QUADRATURE OBSERVATIONS OF THE THREE-DIMENSIONAL STRUCTURE AND DRIVER OF A GLOBAL CORONAL WAVE

We present the first observations of a global coronal wave ("EIT wave") from the two Solar Terrestrial Relations Observatory (STEREO) satellites in quadra- ture. The wave's initiation site was at the disk center in STEREO-B and precisely on the limb in STEREO-A. These unprecedented observations from the STEREO Extreme Ultraviolet Imaging (EUVI) instruments enable us to gain insight into the wave's kinematics, initiation and 3D structure. The wave propagates globally over the whole solar hemisphere visible to STEREO-B with a constant velocity of 263+/-16 km/s. From the two STEREO observations we derive a height of the wave in the range of 80-100 Mm. Comparison of the wave kinematics with the early phase of the erupting CME structure indicates that the wave is initiated by the CME lateral expansion, and then propagates freely with a velocity close to the fast magnetosonic speed in the quiet solar corona.

Sub-Alfvenic inlet boundary conditions for axisymmetric MHD nozzles

There are numerous electromagnetic accelerator concepts which require plasma expansion through a magnetic nozzle. If the inlet flow is slower than one or all of the outgoing characteristics, namely, the Alfven, slow and fast magnetosonic speeds, then the number of inlet conditions which could be arbitrarily specified are reduced by the number of outgoing characteristics (up to three). We derive the axisymmetric compatibility equations using the method of projected characteristics for the inlet conditions in the z-plane to assure the boundary conditions being consistent with flow properties. We make simplifications to the equations assuming that the inlet Alfven speed is much faster than the sonic and slow magnetosonic speeds. We compare results for various inlet boundary conditions, including a modified Lax–Wendroff implementation of the compatibility equations, first order extrapolation and arbitrarily specifying the inlet conditions, in order to assess the stability and accuracy of various approaches.

Solar Energetic Particles and Radio‐silent Fast Coronal Mass Ejections

Both solar flares and shock waves driven by fast coronal mass ejections (CMEs) can accelerate charged particles in the solar corona and create transient enhancements of solar energetic particle fluxes in interplanetary space (SEP events). Fast CMEs and flares often occur together, which makes it difficult to directly identify the actual source of SEP events detected near Earth orbit. In this paper, we attempt to single out fast CMEs without any signature of particle acceleration related to a flare. We choose meter-wave radio emission from energetic electrons as a tracer of flare-related particle acceleration. In truly radio-silent fast CMEs, the only source of SEP acceleration should be the CME shock. The SOHO LASCO catalog by St. Cyr et al. contains 24 fast CMEs (V > 900 km s-1) located above the western solar limb that occurred between 1996 July and 1998 June. Of these, only three are radio-silent. Comparison of their speeds with the fast magnetosonic speed in the corona shows that these three CMEs very likely drive coronal shock waves. Their properties do not depart significantly from a reference set of SEP-associated fast CMEs, except for their smaller angular width. Although one, possibly two of these three CMEs are accompanied by weak enhancements of the electron and proton fluxes (Ep < 20 MeV; SOHO COSTEP and ACE EPAM), none produces a conspicuous SEP event. This suggests that either CME shocks accelerate particles over much smaller angular ranges than generally believed or that they are less efficient accelerators at energies above ~10 MeV than often thought.

A model of the Alfvén speed in the solar corona

We present an analytic model of the Alfven speed vA in the solar corona. The coronal magnetic field is modeled by a radial component representing the global field and by a dipole representing an active region. The free parameters of the model are constrained by actual observations of solar magnetic fields and coronal electron densities. The coronal magnetic field strength in the quiet Sun is determined by coronal seismology, using EIT waves as proxies for the fast magnetosonic speed vms, and thus for the magnetic field strength. Depending on the orientation of the dipole, we find local minima of vA (and vms )a t the coronal base at distances of 0.2-0.3 solar radii from the center of the modelled active region (AR), as well as above the AR at comparable heights. For all dipole orientations, a global maximum is found at 3.5 solar radii. We apply our model to the study of the formation and propagation of coronal shock waves which are observed as flare waves and as type II radio bursts, using a sample of eight solar events. We find that flare waves are initially highly supermagnetosonic (with magnetosonic Mach numbers of Mms ≈ 2-3). During their propagation, they decelerate until Mms = 1 is reached. This behavior can be explained by a strong shock or large-amplitude simple wave that decays to an ordinary fast magnetosonic wave. The observed starting frequencies and Mach numbers of the associated type II bursts are consistent with the predictions of the model.

Interaction of EIT Waves with Coronal Active Regions

Large-scale coronal waves associated with flares were first observed by the Solar and Heliospheric Observatory (SOHO) Extreme ultraviolet Imaging Telescope (EIT). We present the first three-dimensional MHD modeling of the interaction of the EIT waves with active regions and the possibility of destabilization of an active region by these waves. The active region is modeled by an initially force-free, bipolar magnetic configuration with gravitationally stratified density. We include finite thermal pressure and resistive dissipation in our model. The EIT wave is launched at the boundary of the region, as a short time velocity pulse that travels with the local fast magnetosonic speed toward the active region. We find that the EIT wave undergoes strong reflection and refraction, in agreement with observations, and induces transient currents in the active region. The resulting Lorentz force leads to the dynamic distortion of the magnetic field and to the generation of secondary waves. The resulting magnetic compression of the plasma induces flows, which are particularly strong in the current-carrying active region. We investigate the effect of the magnetic field configuration and find that the current-carrying active region is destabilized by the impact of the wave. Analysis of the three-dimensional interaction between EIT waves and active regions can serve as a diagnostic of the active region coronal magnetic structure and stability.

Near‐Sun and near‐Earth manifestations of solar eruptions

We compare the near‐Sun and near‐Earth manifestations of solar eruptions that occurred during November 1994 to June 1998. We compared white‐light coronal mass ejections, metric type II radio bursts, and extreme ultraviolet wave transients (near the Sun) with interplanetary (IP) signatures such as decameter‐hectometric type II bursts, kilometric type II bursts, IP ejecta, and IP shocks. We did a two‐way correlation study to (1) look for counterparts of metric type II bursts that occurred close to the central meridian and (2) look for solar counterparts of IP shocks and IP ejecta. We used data from Wind and Solar and Heliospheric Observatory missions along with metric radio burst data from ground‐based solar observatories. Analysis shows that (1) most (93%) of the metric type II bursts did not have IP signatures, (2) most (80%) of the IP events (IP ejecta and shocks) did not have metric counterparts, and (3) a significant fraction (26%) of IP shocks were detected in situ without drivers. In all these cases the drivers (the coronal mass ejections) were ejected transverse to the Sun‐Earth line, suggesting that the shocks have a much larger extent than the drivers. Shocks originating from both limbs of the Sun arrived at Earth, contradicting earlier claims that shocks from the west limb do not reach Earth. These shocks also had good type II radio burst association. We provide an explanation for the observed relation between metric, decameter‐hectometric, and kilometric type II bursts based on the fast mode magnetosonic speed profile in the solar atmosphere.

Relativistic Jet Flow from a One Dimensional Magnetic Nozzle—Analytic Solutions

AbstractMagnetohydrodynamic devices that can accelerate plasmas to speeds of the order of hundreds of kilometres per second have been designed and built for nearly forty years. Up to the time of writing, however, the theory for such devices has been exclusively non-relativistic. In this paper we derive the special relativistic magnetohydrodynamic (SRMHD) equations and use them to obtain the relativistic, magnetic nozzle equation which describes the production of jet flows with speeds approaching the speed of light.We obtain analytic solutions to this equation and show that, in principle, magnetic field gradients can accelerate a plasma to highly relativistic speeds. We also show that the exit kinetic energy, EK, of a particle is given by the equation EK = m0C2FR, where m0 is the rest mass of the particle and CFR is the fast magnetosonic speed at the start of the flow.The relativistic nozzle differs in a number of ways from the non-relativistic case.A non-relativistic nozzle has a relatively symmetric converging/diverging shape, while a highly relativistic nozzle converges in the usual manner, but diverges, in an abrupt fashion, at the very end of the nozzle. The gentle divergence of non-relativistic nozzles causes the exit plasma densities and magnetic fields of the flow to have values that are small relative to their values at the start of the nozzle. The abrupt divergence of a highly relativistic nozzle implies that, for a less than perfect nozzle, the exit values of the mass density and the magnetic field strength are comparable to their initial values. This unexpected dichotomy in behaviour may have future application in understanding the ‘radio-loud’ and ‘radio-quiet’ relativistic jets that are produced from astrophysical sources.

Gasdynamic Analogies in Problems of the Oblique Interaction of MHD Shock Waves

Gasdynamic analogies are constructed for the oblique interaction of MHD shock waves (counter colliding or overtaking). These analogies fairly adequately describe the complex dependences of the gas dynamic parameters of the medium on the magnetic field strength and inclination. The complete gas dynamic analogy in which the MHD interaction is simulated by the interaction of two gas dynamic shock waves with Mach numbers calculated on the basis of the fast magnetosonic speeds adequately describe the state of the medium for weak and moderate magnetic fields. The “hybrid” model, in which the state behind the interacting shock wave is calculated from the MHD relations on discontinuities and the gas dynamic analogy is then used, gives satisfactory results in a stronger field.

Magnetocentrifugally Driven Winds: Comparison of MHD Simulations with Theory

Stationary MHD outflows from a rotating accretion disk are investigated numerically by time-dependent axisymmetric simulations. The initial magnetic field is taken to be a split-monopole poloidal field configuration frozen into the disk. The disk is treated as a perfectly conducting, time-independent density boundary [?(r)] in Keplerian rotation. The outflow velocity from this surface is not specified but rather is determined self-consistently from the MHD equations. The temperature of the matter outflowing from the disk is small in the region where the magnetic field is inclined away from the symmetry axis (cv) but relatively high (c v) at very small radii in the disk, where the magnetic field is not inclined away from the axis. We have found a large class of stationary MHD winds. Within the simulation region, the outflow accelerates from thermal velocity ( ~cs) to a much larger asymptotic poloidal flow velocity of the order of ?, where M is the mass of the central object and ri is the inner radius of the disk. This asymptotic velocity is much larger than the local escape speed and is larger than fast magnetosonic speed by a factor of ~1.75. The acceleration distance for the outflow, over which the flow accelerates from ~0% to, say, 90% of the asymptotic speed, occurs at a flow distance of about 80ri. The outflows are approximately spherical, with only small collimation within the simulation region. The collimation distance over which the flow becomes collimated (with divergence less than, say, 100) is much larger than the size of our simulation region. Close to the disk the outflow is driven by the centrifugal force, while at all larger distances the flow is driven by the magnetic force, which is proportional to -(rB)2, where B is the toroidal field. Our stationary numerical solutions allow us to (1) compare the results with MHD theory of stationary flows, (2) investigate the influence of different outer boundary conditions on the flows, and (3) investigate the influence of the shape of the simulation region on the flows. Different comparisons were made with the theory. The ideal MHD integrals of motion (constants on flux surfaces) were calculated along magnetic field lines and were shown to be constants with an accuracy of 5%-15%. Other characteristics of the numerical solutions were compared with the theory, including conditions at the Alfv?n surface. Different outer boundary conditions on the toroidal component of the magnetic field were investigated. We conclude that the commonly used free boundary condition on the toroidal field leads to artificial magnetic forces on the outer boundaries, which can significantly influence to the calculated flows. New outer boundary conditions are proposed and investigated that do not give artificial forces. We show that simulated flows may depend on the shape of the simulation region. Namely, if the simulation region is elongated in the z-direction, then Mach cones on the outer cylindrical boundary may be partially directed inside the simulation region. Because of this, the boundary can have an artificial influence on the calculated flow. This effect is reduced if the computational region is approximately square or if it is spherical. Simulations of MHD outflows with an elongated computational region can lead to artificial collimation of the flow.

Collimation of Highly Variable Magnetohydrodynamic Disturbances around a Rotating Black Hole

We have studied non-stationary and non-axisymmetric perturbations of a magnetohydrodynamic accretion onto a rotating (Kerr) black hole. Assuming that the magnetic field dominates the plasma accretion, we find that the accretion suffers a large radial acceleration resulting from the Lorentz force, and becomes highly variable compared with the electromagnetic field there. In fact, we further find an interesting perturbed structure of the plasma velocity with a large peak in some narrow region located slightly inside of the fast-magnetosonic surface. This is due to the concentrated propagation of the fluid disturbances in the form of fast-magnetosonic waves along the separatrix surface. If the fast-magnetosonic speed is smaller in the polar regions than in the equatorial regions, the critical surface has a prolate shape for radial poloidal field lines. In this case, only the waves that propagate towards the equator can escape from the super-fast-magnetosonic region and collimate polewards as they propagate outwards in the sub-fast-magnetosonic regions. We further discuss the capabilities of such collimated waves in accelerating particles due to cyclotron resonance in an electron-positron plasma.