Fast MHD Waves Research Articles

On the properties and implications of collapse-driven MHD turbulence

ABSTRACT We investigate the driving of MHD turbulence by gravitational contraction using simulations of an initially spherical, isothermal, magnetically supercritical molecular cloud core with transonic and trans-Alfvénic turbulence. We perform a Helmholtz decomposition of the velocity field, and investigate the evolution of its solenoidal and compressible parts, as well as of the velocity component along the gravitational acceleration vector, a proxy for the infall component of the velocity field. We find that (1) In spite of being supercritical, the core first contracts to a sheet perpendicular to the mean magnetic field, and the sheet itself collapses. (2) The solenoidal component of the turbulence remains at roughly its initial level throughout the simulation, while the compressible component increases continuously, implying that turbulence does not dissipate towards the centre of the core. (3) The distribution of simulation cells in the B–ρ plane occupies a wide triangular region at low densities, bounded below by the expected trend for fast MHD waves (B ∝ ρ, applicable for high-local Alfvénic Mach number MA) and above by the trend expected for slow waves (B ∼ constant, applicable for low local MA). At high densities, the distribution follows a single trend $B \propto \rho ^{\gamma _{\rm eff}}$, with 1/2 < γeff < 2/3, as expected for gravitational compression. (4) The mass-to-magnetic flux ratio λ increases with radius r due to the different scalings of the mass and magnetic flux with r. At a fixed radius, λ increases with time due to the accretion of material along field lines. (5) The solenoidal energy fraction is much smaller than the total turbulent component, indicating that the collapse drives the turbulence mainly compressibly, even in directions orthogonal to that of the collapse.

Nonlinear Fast Magnetosonic Waves in Solar Prominence Pillars

We investigate the properties of nonlinear fast magnetosonic (NFM) waves in a solar prominence, motivated by recent high-resolution and high-cadence Hinode/Solar Optical Telescope (SOT) observations of small-scale oscillations in a prominence pillar. As an example, we analyze the details of the 2012 February 14 Hinode/SOT observations of quasi-periodic propagating features consistent with NFM waves, imaged in emission in Ca ii and in the far blue wing of Hα. We perform wavelet analysis and find oscillations in the 1–3 minutes period range. Guided by these observations, we model the NFM waves with a three-dimensional magnetohydrodynamics (3D MHD) model, extending previous 2.5D MHD studies. The new model includes the structure of the high-density, low-temperature material of the prominence pillar embedded in the hot corona, in both potential and non-force-free sheared magnetic field configurations. The nonlinear model demonstrates the effects of mode coupling and the propagating density compressions associated with linear and NFM waves. The guided fast magnetosonic waves, together with density compressions and currents, are reproduced in the 3D pillar structure. We demonstrate for the first time the dynamic effects of the Lorentz force due to the magnetic shear in the non-force-free field on the pillar structure and on the propagation of the waves. The insights gained from the 3D MHD modeling are useful for improving the coronal seismology of prominence structures that exhibit fast MHD wave activity.

Effects of Background Periodic Flow on MHD Fast-wave Propagation to a Coronal Loop

This paper investigates the propagation of MHD fast waves into a cylindrical coronal loop through an inhomogeneous stationary flow region. The background flow is assumed to have a small, spatially periodic structure in addition to a constant speed. This study focuses on the absorption of the wave energy in Alfvén resonance, comparing it with the constant flow case. A new flow (absorption) regime is induced by the periodic flow structure, which enhances the absorption for the antiparallel flow and inverse absorption (overreflection) for the parallel flow with respect to the axial wavevector, depending on the transitional layer and flow profiles. A giant overreflection and anomalous absorption behavior arises for some flow configurations. In the other flow regimes, its effect on the absorption is shown to be weak.

PRIMARY DISKS AND THEIR OBSERVATIONAL APPEARANCE IN COLLAPSING MAGNETIC ROTATING PROTOSTELLAR CLOUDS

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-radial in the cloud envelope and quasi-uniform within the primary disk. A toroidal magnetic field is generated behind the front of the fast shock MHD wave propagating from the primary disk boundary and in the region of the outflow formed near the first hydrostatic core. The hierarchical structure of collapsing protostellar clouds can be revealed in observations in terms of the magnetic field geometry and the angular momentum distribution.

Magnetically coupled atmosphere, fast sausage MHD waves, and forced magnetic field reconnection during the SOL2014-09-10T17:45 flare

Aims.We study the physical properties and behaviour of the solar atmosphere during the GOES X1.6 solar flare on 2014 September 10.Methods.The steady plasma flows and the fast sausage MHD waves were analysed with the wavelet separation method. The magnetically coupled atmosphere and the forced magnetic field reconnection were studied with the help of the Vertical-Current Approximation Non-linear Force-Free Field code.Results.We studied a mechanism of MHD wave transfer from the photosphere without dissipation or reflection before reaching the corona and a mechanism of the wave energy distribution over the solar corona. We report a common behaviour of (extreme)ultraviolet steady plasma flows (speed of 15.3 → 10.9 km s−1) and fast sausage MHD waves (Alfvén speed of 13.7 → 10.3 km s−1and characteristic periods of 1587 → 1607 s), propagating in cylindrical plasma waveguides of the individual atmospheric layers (photosphere → corona) observed by SDO/AIA/HMI and IRIS space instruments. A magnetically coupled solar atmosphere by a magnetic field flux tube above a sunspot umbra and a magnetic field reconnection forced by the waves were analysed. The solar seismology with trapped, leakage, and tunnelled modes of the waves, dissipating especially in the solar corona, is discussed with respect to its possible contribution to the outer atmosphere heating.Conclusions.We demonstrate that a dispersive nature of fast sausage MHD waves, which can easily generate the leaky and other modes propagating outside of their waveguide, and magnetic field flux tubes connecting the individual atmospheric layers can distribute the magnetic field energy across the active region. This mechanism can contribute to the coronal energy balance and to our knowledge on how the coronal heating is maintained.

Reversals in the Direction of Polarization Rotation in OJ 287

Abstract We have obtained a smooth time series for the electric vector position angle (EVPA) of the blazar OJ 287 at centimeter wavelengths, by making ±nπ adjustments to archival values from 1974 to 2016. The data display rotation reversals in which the EVPA rotates counterclockwise for ∼180° and then rotates clockwise by a similar amount. The timescale of the rotations is a few weeks to a year, and the scale for a double rotation, including the reversal, is 1–3 yr. We have seen four of these events in 40 yr. A model consisting of two successive outbursts in polarized flux density, with EVPAs counterrotating, superposed on a steady polarized jet, can explain many of the details of the observations. Polarization images support this interpretation. The model can also help to explain similar events seen at optical wavelengths. The outbursts needed for the model can be generated by the supermagnetosonic jet model of Nakamura et al. and Nakamura & Meier, which requires a strong helical magnetic field. This model produces forward and reverse pairs of fast and slow MHD waves, and the plasma inside the two fast/slow pairs rotates around the jet axis, but in opposite directions.

Resistively-limited current sheet implosions in planar anti-parallel (1D) and null-point containing (2D) magnetic field geometries

Implosive formation of current sheets is a fundamental plasma process. Previous studies focused on the early time evolution, while here our primary aim is to explore the longer-term evolution, which may be critical for determining the efficiency of energy release. To address this problem, we investigate two closely related problems, namely: (i) 1D, pinched anti-parallel magnetic fields and (ii) 2D, null point containing fields which are locally imbalanced (“null-collapse” or “X-point collapse”). Within the framework of resistive MHD, we simulate the full nonlinear evolution through three distinct phases: the initial implosion, its eventual halting mechanism, and subsequent evolution post-halting. In a parameter study, we find that the scaling with resistivity of current sheet properties at the halting time is in good agreement—in both geometries—with that inferred from a known 1D similarity solution. We find that the halting of the implosions occurs rapidly after reaching the diffusion scale by sudden Ohmic heating of the dense plasma within the current sheet, which provides a pressure gradient sufficient to oppose further collapse and decelerate the converging flow. This back-pressure grows to exceed that required for force balance and so the post-implosion evolution is characterised by the consequences of the current sheet “bouncing” outwards. These are: (i) the launching of propagating fast MHD waves (shocks) outwards and (ii) the width-wise expansion of the current sheet itself. The expansion is only observed to stall in the 2D case, where the pressurisation is relieved by outflow in the reconnection jets. In the 2D case, we quantify the maximum amount of current sheet expansion as it scales with resistivity and analyse the structure of the reconnection region, which forms post-expansion, replete with Petschek-type slow shocks and fast termination shocks.

Control of ULF Wave Accessibility to the Inner Magnetosphere by the Convection of Plasma Density

AbstractDuring periods of storm activity and enhanced convection, the plasma density in the afternoon sector of the magnetosphere is highly dynamic due to the development of plasmaspheric drainage plume (PDP) structure. This significantly affects the local Alfvén speed and alters the propagation of ULF waves launched from the magnetopause. Therefore, it can be expected that the accessibility of ULF wave power for radiation belt energization is sensitively dependent on the recent history of magnetospheric convection and the stage of development of the PDP. This is investigated using a 3‐D model for ULF waves within the magnetosphere in which the plasma density distribution is evolved using an advection model for cold plasma, driven by a (VollandStern) convection electrostatic field (resulting in PDP structure). The wave model includes magnetic field day/night asymmetry and extends to a paraboloid dayside magnetopause, from which ULF waves are launched at various stages during the PDP development. We find that the plume structure significantly alters the field line resonance location, and the turning point for MHD fast waves, introducing strong asymmetry in the ULF wave distribution across the noon meridian. Moreover, the density enhancement within the PDP creates a waveguide or local cavity for MHD fast waves, such that eigenmodes formed allow the penetration of ULF wave power to much lower L within the plume than outside, providing an avenue for electron energization.

Generation of sheet currents by high frequency fast MHD waves

The evolution of fast magnetosonic waves of high frequency propagating into an axisymmetric equilibrium plasma is studied. By using the methods of weakly nonlinear geometrical optics, it is shown that the perturbation travels in the equatorial plane while satisfying a transport equation which enables us to predict the time and location of formation of shock waves. For plasmas of large magnetic Prandtl number, this would result into the creation of sheet currents which may give rise to magnetic reconnection and destruction of the original equilibrium.

EIGENMODES OF THREE-DIMENSIONAL MAGNETIC ARCADES IN THE SUN’S CORONA

We develop a model of coronal-loop oscillations that treats the observed bright loops as an integral part of a larger 3-D magnetic structure comprised of the entire magnetic arcade. We demonstrate that magnetic arcades within the solar corona can trap MHD fast waves in a 3-D waveguide. This is accomplished through the construction of a cylindrically symmetric model of a magnetic arcade with a potential magnetic field. For a magnetically dominated plasma, we derive a governing equation for MHD fast waves and from this equation we show that the magnetic arcade forms a 3-D waveguide if the Alfv\'en speed increases monotonically beyond a fiducial radius. Both magnetic pressure and tension act as restoring forces, instead of just tension as is generally assumed in 1-D models. Since magnetic pressure plays an important role, the eigenmodes involve propagation both parallel and transverse to the magnetic field. Using an analytic solution, we derive the specific eigenfrequencies and eigenfunctions for an arcade possessing a discontinuous density profile. The discontinuity separates a diffuse cylindrical cavity and an overlying shell of denser plasma that corresponds to the bright loops. We emphasize that all of the eigenfunctions have a discontinuous axial velocity at the density interface; hence, the interface can give rise to the Kelvin-Helmholtz instability. Further, we find that all modes have elliptical polarization with the degree of polarization changing with height. However, depending on the line of sight, only one polarization may be clearly visible.

Three‐dimensional lunar wake reconstructed from ARTEMIS data

AbstractData from the two‐spacecraft Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun mission to the Moon have been exploited to characterize the lunar wake with unprecedented fidelity. The differences between measurements made by a spacecraft in the solar wind very near the Moon and concurrent measurements made by a second spacecraft in the near lunar wake are small but systematic. They enabled us to establish the perturbations of plasma density, temperature, thermal, magnetic and total pressure, field, and flow downstream of the Moon to distances of 12 lunar radii (RM). The wake disturbances are initiated immediately behind the Moon by the diamagnetic currents at the lunar terminator. Rarefaction waves propagate outward at fast MHD wave velocities. Beyond ~6.5 RM, all plasma and field parameters are poorly structured which suggests the presence of instabilities excited by counter‐streaming particles. Inward flowing plasma accelerated through pressure gradient force and ambipolar electric field compresses the magnetic field and leads to continuous increase in magnitude of magnetic perturbations. Besides the downstream distance, the field perturbation magnitude is also a function of the solar wind ion beta and the angle between the solar wind and the interplanetary magnetic field (IMF). Both ion and electron temperatures increase as a consequence of an energy dispersion effect, whose explanation requires fully kinetic models. Downstream of the Moon, the IMF field lines are observed to bulge toward the Moon, which is unexpected and may be caused by a plasma pressure gradient force or/and the pickup of heavy charged dust grains behind the Moon.

STUDIES OF THE JET IN BL LACERTAE. I. RECOLLIMATION SHOCK AND MOVING EMISSION FEATURES

Parsec-scale VLBA images of BL Lac at 15 GHz show that the jet contains a permanent quasi-stationary emission feature 0.26 mas (0.34 pc projected) from the core, along with numerous moving features. In projection, the tracks of the moving features cluster around an axis at position angle -166.6 deg that connects the core with the standing feature. The moving features appear to emanate from the standing feature in a manner strikingly similar to the results of numerical 2-D relativistic magneto-hydrodynamic (RMHD) simulations in which moving shocks are generated at a recollimation shock. Because of this, and the close analogy to the jet feature HST-1 in M87, we identify the standing feature in BL Lac as a recollimation shock. We assume that the magnetic field dominates the dynamics in the jet, and that the field is predominantly toroidal. From this we suggest that the moving features are compressions established by slow and fast mode magneto-acoustic MHD waves. We illustrate the situation with a simple model in which the slowest moving feature is a slow-mode wave, and the fastest feature is a fast-mode wave. In the model the beam has Lorentz factor about 3.5 in the frame of the host galaxy, and the fast mode wave has Lorentz factor about 1.6 in the frame of the beam. This gives a maximum apparent speed for the moving features 10c. In this model the Lorentz factor of the pattern in the galaxy frame is approximately 3 times larger than that of the beam itself.

Three-dimensional, two-species magnetohydrodynamic studies of the early time behaviors of the Combined Release and Radiation Effects Satellite G2 barium release

We present a three-dimensional, two-species (Ba+ and H+) MHD model to study the early time behaviors of a barium release at about 1 RE like Combined Release and Radiation Effects Satellite G2, with emphasis placed on the three-dimensional evolution of the barium cloud and its effects on the ambient plasma environment. We find that the perturbations caused by the cloud are the combined results of the initial injection, the radial expansion, and the diamagnetic effect and propagate as fast MHD waves in the magnetosphere. In return, the transverse expansion and the cross-B motion of barium ions are constrained by the magnetic force, which lead to a field-aligned striation of ions and the decoupling of these ions from the neutrals. Our simulation shows the formation and collapse of the diamagnetic cavity in the barium cloud. The estimated time scale for the cavity evolution might be much shorter if photoionization time scale and field aligned expansion of barium ions are considered. In addition, our two species MHD simulation also finds the snowplow effect resulting from the momentum coupling between barium ions and background H+, which creates density hole and bumps in the background H+ when barium ions expanding along the magnetic field lines.

AN INTERPRETATION OF FLARE-INDUCED AND DECAYLESS CORONAL-LOOP OSCILLATIONS AS INTERFERENCE PATTERNS

We present an alternative model of coronal-loop oscillations which considers that the waves are trapped in a 2D waveguide formed by the entire arcade of field lines. This differs from the standard 1D model which treats the waves as the resonant oscillations of just the visible bundle of field lines. Within the framework of our 2D model, the two types of oscillations that have been observationally identified, flare-induced waves and "decayless" oscillations, can both be attributed to MHD fast waves. The two components of the signal differ only because of the duration and spatial extent of the source that creates them. The flare-induced waves are generated by strong localized sources of short duration, while the decayless background can be excited by a continuous, stochastic source. Further, the oscillatory signal arising from a localized, short-duration source can be interpreted as a pattern of interference fringes produced by waves that have traveled diverse routes of various pathlengths through the waveguide. The resulting amplitude of the fringes slowly decays in time with an inverse square root dependence. The details of the interference pattern depend on the shape of the arcade and the spatial variation of the Alfv\'en speed. The rapid decay of this wave component, which has previously been attributed to physical damping mechanisms that remove energy from resonant oscillations, occurs as a natural consequence of the interference process without the need for local dissipation.

MAGNETOHYDRODYNAMIC WAVES IN TWO-DIMENSIONAL PROMINENCES EMBEDDED IN CORONAL ARCADES

Solar prominence models used so far in the analysis of MHD waves in such structures are quite elementary. In this work, we calculate numerically magnetohydrostatic models in two-dimensional configurations under the presence of gravity. Our interest is in models that connect the magnetic field to the photosphere and include an overlying arcade. The method used here is based on a relaxation process and requires solving the time-dependent nonlinear ideal MHD equations. Once a prominence model is obtained, we investigate the properties of MHD waves superimposed on the structure. We concentrate on motions purely two-dimensional neglecting propagation in the ignorable direction. We demonstrate how by using different numerical tools we can determine the period of oscillation of stable waves. We find that vertical oscillations, linked to fast MHD waves, are always stable and have periods in the 4-10 min range. Longitudinal oscillations, related to slow magnetoacoustic-gravity waves, have longer periods in the range of 28-40 min. These longitudinal oscillations are strongly influenced by the gravity force and become unstable for short magnetic arcades.

Linear MHD Wave Propagation in Time-Dependent Flux Tube

MHD waves and oscillations in sharply structured magnetic plasmas have been studied for static and steady systems in the thin tube approximation over many years. This work will generalize these studies by introducing a slowly varying background density in time, in order to determine the changes to the wave parameters introduced by this temporally varying equilibrium, i.e. to investigate the amplitude, frequency, and wavenumber for the kink and higher order propagating fast magnetohydrodynamic wave in the leading order approximation to the WKB approach in a zero-β plasma representing the upper solar atmosphere. To progress, the thin tube and over-dense loop approximations are used, restricting the results found here to the duration of a number of multiples of the characteristic density change timescale. Using such approximations it is shown that the amplitude of the kink wave is enhanced in a manner proportional to the square of the Alfven speed, \(V_{\mathrm{A}}^{2}\). The frequency of the wave solution tends to the driving frequency of the system as time progresses; however, the wavenumber approaches zero after a large multiple of the characteristic density change timescale, indicating an ever increasing wavelength. For the higher order fluting modes the changes in amplitude are dependent upon the wave mode; for the m=2 mode the wave is amplified to a constant level; however, for all m≥3 the fast MHD wave is damped within a relatively small multiple of the characteristic density change timescale. Understanding MHD wave behavior in time-dependent plasmas is an important step towards a more complete model of the solar atmosphere and has a key role to play in solar magneto-seismological applications.

Large‐scale flow vortices following a magnetospheric sudden impulse

Global MHD simulations predict the generation of flow vortices on the magnetospheric flanks near the equatorial plane after the impact of solar wind dynamic pressure pulses on the magnetosphere. These vortices are associated with field‐aligned currents, having similar senses to those responsible for the main impulse, i.e., the second impulse of the well‐known sudden impulse variations at high geomagnetic latitudes. We investigate the evolution of the vortices and show that they result from the interaction of a fast MHD wave and the inner (near‐Earth) boundary of numerical models. Near the inner boundary, the Ampere force decelerates plasma flow resulting in two closely related phenomena: the generation of flow vortices and the launch of a reflected fast wave moving sunward. The vortices propagate antisunward and split into several parts during several minutes. The reflected wave interacts with the magnetopause and bow shock and changes its velocity. The interaction between the reflected wave and bow shock results in two new discontinuities moving earthward through the magnetosheath. The first is either a very weak fast rarefaction wave or a weak fast shock, and the second is either a tangential discontinuity or a compound discontinuity with a decrease of the density and magnetic field and an increase of the temperature. We speculate that the inner boundary in simulations may correspond to either the plasmasphere or ionosphere.

Numerical MHD Simulations of Solar Magnetoconvection and Oscillations in Inclined Magnetic Field Regions

The sunspot penumbra is a transition zone between the strong vertical magnetic field area (sunspot umbra) and the quiet Sun. The penumbra has a fine filamentary structure that is characterized by magnetic field lines inclined toward the surface. Numerical simulations of solar convection in inclined magnetic field regions have provided an explanation of the filamentary structure and the Evershed outflow in the penumbra. In this paper, we use radiative MHD simulations to investigate the influence of the magnetic field inclination on the power spectrum of vertical velocity oscillations. The results reveal a strong shift of the resonance mode peaks to higher frequencies in the case of a highly inclined magnetic field. The frequency shift for the inclined field is significantly greater than that in vertical field regions of similar strength. This is consistent with the behavior of fast MHD waves.

Acoustic power absorption and enhancement generated by slow and fast MHD waves

We used long duration, high quality, unresolved (Sun-as-a star) observations collected by the ground based network BiSON and by the instruments GOLF and VIRGO on board the ESA/NASA SOHO satellite to search for solar-cycle-related changes in mode characteristics in velocity and continuum intensity for the frequency range between 2.5 mHz <ν< 6.8 mHz. Over the ascending phase of solar cycle 23 we found a suppression in the p-mode amplitudes both in the velocity and intensity data between 2.5 mHz <ν <4.5 mHz with a maximum suppression for frequencies in the range between 2.5 mHz <ν< 3.5 mHz. The size of the amplitude suppression is 13 ± 2 per cent for the velocity and 9 ± 2 per cent for the intensity observations. Over the range of 4.5 mHz <ν < 5.5 mHz the findings hint within the errors to a null change both in the velocity and intensity amplitudes. At still higher frequencies, in the so called High-frequency Interference Peaks (HIPs) between 5.8 mHz <ν< 6.8 mHz, we found an enhancement in the velocity amplitudes with the maximum 36 ± 7 per cent occurring for 6.3 mHz <ν< 6.8 mHz. However, in intensity observations we found a rather smaller enhancement of about 5± 2 per cent in the same interval. There is evidence that the frequency dependence of solar-cycle velocity amplitude changes is consistent with the theory behind the mode conversion of acoustic waves in a non-vertical magnetic field, but there are some problems with the intensity data, which may be due to the height in the solar atmosphere at which the VIRGO data are taken.

Propagating magneto-hydrodynamic waves in a cooling homogenous coronal plasma

Aims. We present an investigation into how the cooling of the background plasma influences the propagation of slow and fast MHD wave modes supported by an unbounded, homogenous plasma. Previous investigations have suggested that the cooling of the plasma and a reduction in density could lead to the damping of fast magneto-acoustic oscillations. We aim to investigate whether cooling of the background plasma at a constant density may be responsible for the damping of slow and fast modes. Methods. The plasma is assumed homogeneous and the background temperature (pressure) is decreasing with time. The temperature change is assumed to be due to optically thin radiation. A special case of the radiative function is chosen to allow an analytical assessment of the effects of cooling on magneto-acoustic MHD modes and ensures the temperature evolution of the background plasma due to this radiation also matches the observed cooling profile of coronal loops. Results. A time-dependent dispersion relation is obtained on the slow timescale of cooling and full time-dependent solutions are found. Leading order equations for the amplitude of the waves are obtained and solved analytically for the slow and fast MHD modes. The cooling of the plasma is found to cause the frequency of the magneto-acoustic modes to decrease with time. The slow modes are found to experience a greater change in frequency than the fast modes. More importantly, the radiative losses also provide a significant damping of the slow mode and a small damping of the component of the fast mode perpendicular to the magnetic field. The damping of the slow mode is found to be strong within typical lifetimes of oscillations observed in coronal structures. Cooling could have important consequences and needs to be assessed when trying to determine what mechanism is responsible for the observed damping of coronal oscillations.