Slow MHD Research Articles

Plasma Motions and Compressive Wave Energetics in the Solar Corona and Solar Wind from Radio Wave Scattering Observations

Radio signals propagating via the solar corona and solar wind are significantly affected by compressive waves, impacting the properties of solar bursts as well as sources viewed through the turbulent solar atmosphere. While static fluctuations scatter radio waves elastically, moving, turbulent, or oscillating density irregularities act to broaden the frequency of the scattered waves. Using a new anisotropic density fluctuation model from the kinetic scattering theory for solar radio bursts, we deduce the plasma velocities required to explain observations of spacecraft signal frequency broadening. The inferred velocities are consistent with motions that are dominated by the solar wind at distances ≳10 R ⊙, but the levels of frequency broadening for ≲10 R ⊙ require additional radial speeds ∼(100–300) km s−1 and/or transverse speeds ∼(20–70) km s−1. The inferred radial velocities also appear consistent with the sound or proton thermal speeds, while the speeds perpendicular to the radial direction are consistent with nonthermal motions measured via coronal Doppler-line broadening, interpreted as Alfvénic fluctuations. Landau damping of parallel propagating ion-sound (slow MHD) waves allows an estimate of the proton heating rate. The energy deposition rates due to ion-sound wave damping peak at a heliocentric distance of ∼(1–3) R ⊙ are comparable to the rates available from a turbulent cascade of Alfvénic waves at large scales, suggesting a coherent picture of energy transfer, via the cascade or/and parametric decay of Alfvén waves to the small scales where heating takes place.

Analytical and numerical solution of sausage MHD wave oscillation in a thin magnetic flux tube

<p>The aim of the present study is to investigate the damping of slow sausage MHD waves propagating in a gravitationally-stratified magnetic cylindrical structure when the plasma is strongly partially ionised. The problem is treated as an initial value problem and the analysis deals with the temporal evolution of waves in an asymptotic sense, i.e., large values of time compared to the period of waves. The plasma is assumed to be collision-dominated, i.e., we employ a two-fluid approximation. The set of equations describing the plasma dynamics is reduced to a coupled partial differential equations. Our findings show that the slow wave of charged species is affected by the presence of a cut-off. The mode associated with the neutral fluid propagates without any cut-off and decay very quickly due to collisions between particles.</p>

The Effect of Mass Flow on Slow MHD Oscillations of Curved Solar Coronal Loops

The Effect of Mass Flow on Slow MHD Oscillations of Curved Solar Coronal Loops

The Effect of Flow and Magnetic Twist on Resonant Absorption of Slow MHD Waves in Magnetic Flux Tubes

Observations show that there are twisted magnetic flux tubes and plasma flow throughout the solar atmosphere. The main purpose of this work is to obtain the damping rate of sausage modes in the presence of magnetic twist and plasma flow. We obtain the dispersion relation for sausage modes in slow continuity in an inhomogeneous layer under the conditions of magnetic pores, then we solve it numerically. For the selected density profile, the magnetic field, and the plasma flow as a function of radius across the inhomogeneous layer, we show that the effect of the twisted magnetic field on the resonance absorption at low speed of the plasma flow is greater than one at high speed.

Propagating Oscillations in the Lower Atmosphere Under Coronal Holes

The subject of this study is oscillations in the lower atmosphere in coronal-hole regions, where the conditions are favorable for propagation between the atmospheric layers. Based on spectroscopic observations in photospheric and chromospheric lines, we analysed the features of the oscillations that show signs of propagation between layers of the solar atmosphere. Using the cross-spectrum wavelet algorithm, we found that both chromospheric and photospheric signals under coronal holes share a range of significant oscillations of periods around five minutes, while the signals outside of coronal holes show no mutual oscillations in the photosphere and chromosphere. The phase shift between the layers indicates a predominantly upward propagation with partial presence of standing waves. We also tested the assumption that torsional Alfv\'en waves propagating in the corona originate in the lower atmosphere. However, the observed line-width oscillations, although similar in period to the Alfv\'en waves observed earlier in the corona of open-field regions, seem to be associated with other MHD modes. If we assume that the oscillations that we observed are related to Alfv\'en waves, then perhaps this is only through the mechanisms of the slow MHD wave transformation.

The Effect of Flow on the Resonance Absorption of Slow MHD Waves in Magnetic Flux Tubes

Abstract In this paper, we study kink and sausage oscillations in the presence of longitudinal background flow. We study the resonance absorption of kink and sausage modes in the slow continuum, under magnetic pore conditions, in the presence of flow. We determine the dispersion relation, and solve it numerically to find the frequencies and damping rates of the slow kink and sausage surface modes. We also obtain an analytical solution for the damping rate of the slow surface mode in the long wavelength limit. We show that in the presence of plasma flow, resonance absorption can result in strong damping for forward waves, and can be considered as an efficient mechanism to justify the extremely rapid damping of slow surface sausage waves observed in magnetic pores. Moreover, the plasma flow reduces the efficiency of resonance absorption to damp backward waves. With respect to pore conditions, resonance instability is avoided in our model.

Transverse bifurcation of viscous slow MHD shocks

We study by a combination of analytical and numerical Evans function techniques multi-D viscous and inviscid stability and associated transverse bifurcation of planar slow Lax MHD shocks in a channel with periodic boundary conditions. Notably, this includes the first multi-D numerical Evans function study for viscous MHD. Our results suggest that, rather than a planar shock, a nonplanar traveling wave with the same normal velocity is the typical mode of propagation in the slow Lax mode. Moreover, viscous and inviscid stability transitions appear to agree, answering (for this particular model and setting) an open question of Zumbrun and Serre.

Hall-magnetohydrodynamic waves in flowing ideal incompressible solar-wind plasmas: reconsidered

It is well established that the magnetically structured solar atmosphere supports the propagation of MHD waves along various kind of jets including also the solar wind. It is well-known as well that under some conditions, namely high enough jet speeds, the propagating MHD modes can become unstable against to the most common Kelvin--Helmholtz instability (KHI). In this article, we explore how the propagation and instability characteristics of running along a slow solar wind MHD modes are affected when they are investigated in the framework of the ideal Hall-magnetohydrodynamics. Hall-MHD is applicable if the jet width is shorter than or comparable to the so called Hall parameter $l_\mathrm{Hall} = c/\omega_\mathrm{pi}$ (where $c$ is the speed of light and $\omega_\mathrm{pi}$ is the ion plasma frequency). We model the solar wind as a moving with velocity $\vec{v}_0$ cylindrical flux tube of radius $a$, containing incompressible plasma with density $\rho_\mathrm{i}$ permeated by a constant magnetic field $\vec{B}_\mathrm{i}$. The surrounding plasma is characterized with its density $\rho_\mathrm{e}$ and magnetic field $\vec{B}_\mathrm{e}$. The dispersion relation of MHD waves is derived in the framework of both standard and Hall-MHD and is numerically solved with input parameters: the density contrast $\eta = \rho_\mathrm{e}/\rho_\mathrm{i}$, the magnetic fields ratio $b = {B}_\mathrm{e}/{B}_\mathrm{i}$, and the Hall scale parameter $l_\mathrm{Hall}/a$. It is found that the Hall current, at moderate values of $l_\mathrm{Hall}/a$, stimulates the emerging of KHI of the kink ($m = 1)$ and high-mode ($m \geqslant 2$) MHD waves, while for the sausage wave ($m = 0$) the trend is just the opposite---the KHI is suppressed.

Local sunspot oscillations and umbral dots

Data analysis of sunspot oscillations based on a 6-hr SDO run of an observation showed that low frequency () oscillations are locally similar to three and five minute oscillations. The oscillations in the sunspot are concentrated in cells of a few arcsec, each of which has its own oscillation spectrum. The analysis of two scenarios for sunspot oscillations leads to a conclusion that local sunspot oscillations occur due to a subphotospheric resonator for slow MHD waves. Empirical models of a sunspot atmosphere and the theory of slow waves in thin magnetic flux tubes are applied to modeling the subphotospheric resonator. The spectrum of local oscillations consists of a great number of lines. This kind of spectrum can occur only if the subphotospheric resonator is a magnetic tube with a rather weak magnetic field. Magnetic tubes of this sort are umbral dots that appear due to the convective tongues in monolithic sunspots. The interrelation of local oscillations with umbral dots and wavefronts of traveling waves in sunspots is discussed.

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.

Probing the Sunspot Atmosphere with Three-Minute Oscillations

We present a seismological method to probe the solar atmosphere above sunspot umbrae with three-minute oscillations. Our technique allows us to estimate both the vertical distance between atmospheric layers and the wave-propagation speed without specifying any extra parameters, in particular, the phase speed of the wave or the emission formation heights. Our method uses the projected wave paths of slow MHD waves propagating through the atmospheric layers of different heights and guided by the magnetic field. The length of the projected wave path depends upon the distance between the layers and the inclination angle of the magnetic field with respect to the line of sight, allowing us to estimate the distance between the layers from measured projected wave paths and the local magnetic-field vector. In turn, the wave-propagation delay registered at different heights allows for the calculation of the phase speed. We estimated the vertical distance between the emission layers at the temperature minimum (1600 {\AA}) and transition region (304 {\AA}), as well as the average phase speed above the sunspot umbrae, for three active regions. We found that the distance between the 1600 {\AA} emission layer and the transition region above the sunspot umbrae lies in the range of 500 -- 800 km. The average phase speed between these layers was found to be about 30 km/s giving the sound speed of 6 km/s. The temperature between the layers has been roughly estimated as 3000 K and corresponds to the region of the temperature minimum. The results obtained are consistent with the semiempirical model of the sunspot umbrae atmosphere by Fontenla, 2009. The manuscript has been accepted for publication in Solar Physics journal.

Longitudinal expansion of field line dipolarization

We examine the substorm expansions that started at 1155 UT 10 August 1994 in the midnight sector focusing on the longitudinal (eastward) expansion of field line dipolarization in the auroral zone. Eastward expansion of the dipolarization region was observed in all of the H, D, and Z components. The dipolarization that started at 1155 UT (0027 MLT) from 260° of geomagnetic longitude (CMO) expanded to 351°(PBQ) in about 48 min. The expansion velocity was 0.03–0.04°/s, or 1.9 km/s at 62°N of geomagnetic latitude. The dipolarization region expanding to the east was accompanied by a bipolar event at the leading edge of the expansion in latitudes equatorward of the westward electrojet (WEJ). In the midnight sector at the onset meridian, the Magnetospheric Plasma Analyzer (MAP) on board geosynchronous satellite L9 measured electrons and ions between 10 eV and 40 keV. We conclude from the satellite observations that this dipolarization was characterized by the evolution of temperature anisotropies, an increase of the electron and ion temperatures, and a rapid change in the symmetry axis of the temperature tensor. The field line dipolarization and its longitudinal expansion were interpreted in terms of the slow MHD mode triggered by the current disruption. We propose a new magnetosphere-ionosphere coupling (MI-coupling) mechanism based on the scenario that transmitted westward electric fields from the magnetosphere in association with expanding dipolarization produced electrostatic potential (negative) in the ionosphere through differences in the mobility of collisional ions and collisionless electrons. The field-aligned currents that emerged from the negative potential region are arranged in a concentric pattern around the negative potential region, upward toward the center and downward on the peripheral.

THREE-DIMENSIONAL MAGNETOGRADIENT WAVES IN THE UPPER ATMOSPHERE

General dispersion equation has been obtained for three-dimensional electromagnetic planetary waves, from which follows, as particular case Khantadze results in one-dimension case. It was shown that partial magnetic field line freezing-in as in one-dimension case lead to the excitation of both “fast” and “slow” planetary waves, in two-liquid approximation (i.e. at ion drag by neutral particles) they are represent oscillations of magnetized electrons and partially magnetized ions in E region of the ionosphere. In F region of the ionosphere using one-liquid approximation only “fast” planetary wave will be generated representing oscillation of medium as a whole. Hence, it was shown that three-dimension magnetogradient planetary waves are exist in all components of the ionosphere, and as exact solutions, with well-known slow short-wave MHD waves, are simple mathematical consequence of the MHD equations for the ionosphere.

SHOCKFIND - an algorithm to identify magnetohydrodynamic shock waves in turbulent clouds

The formation of stars occurs in the dense molecular cloud phase of the interstellar medium. Observations and numerical simulations of molecular clouds have shown that supersonic magnetised turbulence plays a key role for the formation of stars. Simulations have also shown that a large fraction of the turbulent energy dissipates in shock waves. The three families of MHD shocks --- fast, intermediate and slow --- distinctly compress and heat up the molecular gas, and so provide an important probe of the physical conditions within a turbulent cloud. Here we introduce the publicly available algorithm, SHOCKFIND, to extract and characterise the mixture of shock families in MHD turbulence. The algorithm is applied to a 3-dimensional simulation of a magnetised turbulent molecular cloud, and we find that both fast and slow MHD shocks are present in the simulation. We give the first prediction of the mixture of turbulence-driven MHD shock families in this molecular cloud, and present their distinct distributions of sonic and Alfvenic Mach numbers. Using subgrid one-dimensional models of MHD shocks we estimate that ~0.03 % of the volume of a typical molecular cloud in the Milky Way will be shock heated above 50 K, at any time during the lifetime of the cloud. We discuss the impact of this shock heating on the dynamical evolution of molecular clouds.

Propagation and damping of slow MHD waves in a flowing viscous coronal plasma

We investigate the propagation of slow MHD waves in a flowing viscous solar coronal plasma. The compressive viscosity and steady flow along and opposite to the wave propagation are taken into account to study the damping of slow waves. We numerically solve the MHD equations by MacCormack method to examine the effect of steady flow on the damping of slow MHD waves in viscous solar coronal plasma. Amplitude of velocity perturbation and damping time of slow waves decrease with the increase in the value of Mach number. Flow causes a phase shift in the perturbed velocity amplitude and an increase in wave period. The damping of slow waves in flowing viscous plasma is stronger than the damping of waves in viscous plasma. Slow wave in backward flow damps earlier than the wave in forward flow.

Standing Slow MHD Waves in Radiatively Cooling Coronal Loops

The standing slow magneto-acoustic oscillations in cooling coronal loops are investigated. There are two damping mechanisms which are considered to generate the standing acoustic modes in coronal magnetic loops, namely, thermal conduction and radiation. The background temperature is assumed to change temporally due to optically thin radiation. In particular, the background plasma is assumed to be radiatively cooling. The effects of cooling on longitudinal slow MHD modes is analytically evaluated by choosing a simple form of radiative function, that ensures the temperature evolution of the background plasma due to radiation, coincides with the observed cooling profile of coronal loops. The assumption of low-beta plasma leads to neglecting the magnetic field perturbation and, eventually, reduces the MHD equations to a 1D system modelling longitudinal MHD oscillations in a cooling coronal loop. The cooling is assumed to occur on a characteristic time scale, much larger than the oscillation period that subsequently enables using the WKB theory to study the properties of standing wave. The governing equation describing the time-dependent amplitude of waves is obtained and solved analytically. The analytically derived solutions are numerically evaluated to give further insight into the evolution of the standing acoustic waves. We find that the plasma cooling gives rise to a decrease in the amplitude of oscillations. In spite of the reduction in damping rate caused by rising the cooling, the damping scenario of slow standing MHD waves strongly increases in hot coronal loops.

STUDIES OF THE JET IN BL LACERTAE. II. SUPERLUMINAL ALFVÉN WAVES

We study the kinematics of ridge lines on the pc-scale jet of the active galactic nucleus BL Lac. We show that the ridge lines display transverse patterns that move superluminally downstream, and that the moving patterns are analogous to waves on a whip. Their apparent speeds $\beta_\mathrm{app}$ (units of $c$) range from 3.9 to 13.5, corresponding to $\beta_\mathrm{wave}^\mathrm{gal}= 0.981 - 0.998$ in the galaxy frame. We show that the magnetic field in the jet is well-ordered with a strong transverse component, and assume that it is helical and that the transverse patterns are Alfv\'en waves propagating downstream on the longitudinal component of the magnetic field. The wave-induced transverse speed of the jet is non-relativistic ($\beta_\mathrm{tr}^\mathrm{gal} \lesssim 0.09$). In 2010 the wave activity subsided and the jet then displayed a mild wiggle that had a complex oscillatory behaviour. The Alfv\'en waves appear to be excited by changes in the position angle of the recollimation shock, in analogy to exciting a wave on a whip by shaking the handle. A simple model of the system with plasma sound speed $\beta_\mathrm{s}=0.3$ and apparent speed of a slow MHD wave $\beta_\mathrm{app,S}=4$ yields Lorentz factor of the beam $\Gamma_\mathrm{beam} \sim 4.5$, pitch angle of the helix (in the beam frame) $\alpha\sim 67^\circ$, Alfv\'en speed $\beta_\mathrm{A}\sim 0.64$, and magnetosonic Mach number $M_\mathrm{ms}\sim 4.7$. This describes a plasma in which the magnetic field is dominant and in a rather tight helix, and Alfv\'en waves are responsible for the moving transverse patterns.

Can slow solar shock waves heat the corona?

Based on the solution to a generalized Riemann-Kotchine problem, the appearance of dissipative slow shock waves in the plasma of the solar corona, which occur when rotational discontinuities are refracted at a contact discontinuity in the transition region between the chromosphere and corona, is studied. The oblique interaction between a solar rotational discontinuity A and stationary contact discontinuity C in the transition region is considered in the scope of the magnetohydrodynamic model. Here, due to the presence of a large number of nonlinear Alfven waves, there is a real possibility of the appearance of a rotational discontinuity moving to the solar corona in the chromosphere. The appearance of dissipative slow MHD shock waves with an insignificant change in the magnetic field as a result of refraction of nondissipative rotational discontinuities at a contact discontinuity in the transition region is proved. It is supposed that a wave source of plasma heating can exist in upper layers of the corona because of the motion of slow shock waves undergoing the Landau damping. Thus, a new model of heat transfer from the chromosphere to the solar corona is proposed.

Model of local oscillations in sunspots

We have analyzed the properties of oscillations in a sunspot based on SDO observations with a duration of 6 h. The 3-min oscillation spectrum has turned out to consist of dozens of spectral lines. The line widths are at the spectral resolution limit. The oscillations in a sunspot have been broken down into individual areas with a size of a few arcseconds, each having its own oscillation spectrum. These oscillation properties cannot be explained in terms of the existing models based on the assumption that the sunspot oscillates as a whole. We propose a model of local oscillations that explains the complex spectrum of the oscillations and their locality. We show that in addition to the chromospheric resonator, there exists a subphotospheric resonator for slow MHD waves. The existence of this resonance layer allows the locality of the oscillations and their complex spectrum to be explained in terms of Parker’s model.

Resonant Damping of Propagating Kink Waves in Time-Dependent Magnetic Flux Tube

We explore the notion of resonant absorption in a dynamic time-dependent magnetised plasma background. Very many works have investigated resonance in the Alfven and slow MHD continua under both ideal and dissipative MHD regimes. Jump conditions in static and steady systems have been found in previous works, connecting solutions at both sides of the resonant layer. Here, we derive the jump conditions in a temporally dependent, magnetised, inhomogeneous plasma background to leading order in the Wentzel–Kramers–Billouin (WKB) approximation. Next, we exploit the results found in Williamson and Erdelyi (Solar Phys.289, 899, 2014) to describe the evolution of the jump condition in the dynamic model considered. The jump across the resonant point is shown to increase exponentially in time. We determined the damping as a result of the resonance over the same time period and investigated the temporal evolution of the damping itself. We found that the damping coefficient, as a result of the evolution of the resonance, decreases as the density gradient across the transitional layer decreases. This has the consequence that in such time-dependent systems resonant absorption may not be as efficient as time progresses.