Solar Magnetic Flux Tubes Research Articles

The effect of linear background rotational flows on magnetoacoustic modes of a photospheric magnetic flux tube

ABSTRACT Magnetoacoustic waves in solar magnetic flux tubes may be affected by the presence of background rotational flows. Here, we investigate the behaviour of m = 0 and m = ±1 modes of a magnetic flux tube in the presence of linear background rotational flows embedded in a photospheric environment. We show that the inclusion of a background rotational flow is found to have little effect on the obtained eigensolutions for the axisymmetric m = 0 sausage mode. However, solutions for the kink mode are dependent on the location of the flow resonance modified by the slow frequency. A background rotational flow causes the modified flow resonances to possess faster phase speeds in the thin-tube (TT) limit for the case m = 1. This results in solutions for the slow body and slow surface kink modes to follow this trajectory, changing their dispersive behaviour. For a photospheric flux tube in the TT limit, we show that it becomes difficult to distinguish between the slow surface and fast surface kink (m = 1) modes upon comparison of their eigenfunctions. 2D velocity field plots demonstrate how these waves, in the presence of background rotational flows, may appear in observational data. For slow body kink modes, a swirling pattern can be seen in the total pressure perturbation. Furthermore, the tube boundary undergoes a helical motion from the breaking of azimuthal symmetry, where the m = 1 and m = −1 modes become out of phase, suggesting the resulting kink wave is circularly polarized. These results may have implications for the seismology of magnetohydrodynamic waves in solar magnetic vortices.

Large scale coherent magnetohydrodynamic oscillations in a sunspot

Although theoretically predicted, the simultaneous excitation of several resonant modes in sunspots has not been observed. Like any harmonic oscillator, a solar magnetic flux tube can support a variety of resonances, which constitute the natural response of the system to external forcing. Apart from a few single low order eigenmodes in small scale magnetic structures, several simultaneous resonant modes were not found in extremely large sunspots. Here we report the detection of the largest-scale coherent oscillations observed in a sunspot, with a spectrum significantly different from the Sun’s global acoustic oscillations, incorporating a superposition of many resonant wave modes. Magnetohydrodynamic numerical modeling agrees with the observations. Our findings not only demonstrate the possible excitation of coherent oscillations over spatial scales as large as 30–40 Mm in extreme magnetic flux regions in the solar atmosphere, but also paves the way for their diagnostic applications in other astrophysical contexts.

Magnetohydrodynamic Wave Modes of Solar Magnetic Flux Tubes with an Elliptical Cross Section

Abstract The purpose of this paper is to study the behavior of magnetohydrodynamic (MHD) wave modes that propagate in compressible magnetic flux tubes with an elliptical cross section embedded in a magnetic environment. The dispersion relation that describes the behavior of MHD wave modes permitted in an elliptical magnetic flux tube is solved numerically. Distortion of the spatial structure of the purely real eigenmodes from the well-known circular flux tube model has been considered. It has been studied under both photospheric and coronal conditions. It has been shown that (i) solutions in the form of even Mathieu functions are more sensitive to the value of eccentricity than solutions with the form of odd Mathieu functions; (ii) if the ellipticity of the cross section of the magnetic flux tube increases, a sausage mode (m = 0) cannot be easily identified; (iii) even solutions that correspond to the fluting mode (m = 3) can be misinterpreted as a kink mode (m = 1) due to their similarities. In contrast to the fluting modes that are polarized along the major axis and strongly depend on the ellipticity of the magnetic flux tube, the kink and sausage surface modes are practically unaffected by ellipticity. Several examples of the spatial structure of the eigenmodes permitted in the pores and sunspots have been visualized. The solutions obtained in the approximation of cylindrical symmetry are in agreement with previous studies.

New cutoff frequency for torsional Alfv́en waves propagating along wide solar magnetic flux tubes

An isolated, isothermal, and wide magnetic flux tube embedded either in the solar chromosphere or in the lower solar corona is considered, and the propagation of linear torsional Alfv'en waves is investigated. It is shown that the wideness of the tube leads to a new cutoff frequency, which is a local quantity that gives the conditions for the wave propagation at different atmospheric heights. The cutoff is used to establish the ranges of frequencies for the propagating and reflected waves in the solar chromosphere and lower solar corona. The obtained results are compared to those previously obtained for thin magnetic flux tubes and the differences are discussed. Moreover, the results are also compared to some current observational data, and used to establish the presence of propagating waves in the data at different atmospheric heights; this has profound implications on the energy and momentum transfer by the waves in the solar atmosphere, and the role of linear torsional Alfv'en waves in the atmospheric heating and wind acceleration.

Analysis of dayside magnetosphere of Mars: High mass loading case as observed on MAVEN spacecraft

MAVEN spacecraft provides new opportunities for analysis of Martian environment and physical process in near-Mars space. One of interesting regions of near-Mars space is the Martian magnetosphere that is formed from mass-loaded magnetic flux tubes. There is quite detailed knowledge of the night-side magnetosphere of Mars, however the number of publications on the dayside magnetosphere are quite limited. We analyze the plasma and magnetic structure and properties of Martian magnetosphere at strong mass-loading conditions as observed on MAVEN at Mars at the solar-zenith angle of ∼80° on January 4, 2015. This strong mass loading of upstream flow was apparently associated with plume ions ejected from upper part of Martian magnetosphere by the solar wind motional electric field. The magnetosphere is defined by two current layers separating it from the magnetosheath at higher altitudes and from ionosphere plasma at lower altitudes. It is characterized by dominance of planetary ions which number density increases by two orders of magnitude from upper boundary to lower one. There is approximate equipartition between magnetic, ion thermal and kinetic energies through magnetosphere. The data suggest that the boundary of the magnetosphere is in pressure equilibrium with magnetosheath flow. The total energy of ion flow above (in the magnetosheath) and below (in the region of accelerated ionospheric ions) magnetosphere exceeds the magnetic energy. The upper boundary of magnetosphere was located at the place where the ratio of heavy ions and protons number densities reached ∼0.4. Within magnetosphere this ratio continued to rise and increased by about 2 orders of magnitude at the inner boundary of magnetosphere. The heavy ion number density profile within magnetosphere suggests that it was formed by the solar wind magnetic flux tubes that reached Mars in a narrow region near the subsolar point, and then drifted around Mars to the terminator region, mass-loaded by UV-ionized upper atmosphere neutrals during this drift.

Kink mode m = 1 in a thin plasma filament with discontinuous vertical magnetic field

In this paper, we study the conditions of realization and stability of kink modes with azimuthal wave numbers m = ±1 in a cylindrical plasma filament with a twisted magnetic field and a homogeneous current along its axis. We assume that there are vertical constant magnetic fields inside and outside of the filament; the filament is surrounded by current-free plasma; and outside of its boundary, the azimuthal magnetic field decreases inversely in proportion to the distance from the filament’s border. The dispersion equations for stable and unstable modes are obtained in the approximation of “thin” plasma filament. The analysis of the equations for the case of discontinuous vertical magnetic field at the filament’s boundary is provided. The conditions of propagation of the wave modes have been defined. We have obtained that the unstable modes with m = ±1 cannot be realized. The results of this work can be applied to the interpretation of the solar magnetic flux tubes’ behavior using measurements provided by the spacecrafts.

Asymmetric penetration of shocked solar wind down to 400 km altitudes at Mars

AbstractThe penetration boundary of shocked solar wind (magnetosheath) into the Martian upper atmosphere is typically located at altitudes above 800 km. However, magnetosheath plasma occasionally penetrates into low altitudes below 400 km. Here we used Mars Global Surveyor magnetic field and electron observations from April 1999 to November 2006 to investigate the magnetosheath penetration events. We identified 1145 events and found that both solar wind dynamic pressure (Pdyn) and the orientation of the interplanetary magnetic field (IMF) control the occurrence of the events. The magnetosheath penetration events during low Pdyn periods tend to be distributed in low latitudes of the northern hemisphere or where the crustal magnetic field is weak, while the event locations are widely distributed in terms of the latitude under high Pdyn conditions. During low Pdyn periods, a remarkable feature is that the observational probability is approximately 2.4 times larger during periods of the “away” IMF sector than during the “toward” sector. The northern hemisphere during the away sector corresponds to the upward electric field hemisphere due to the convection of draping solar wind origin magnetic flux tubes. These results thus indicate that the magnetosheath penetrations into Martian upper atmosphere more often occur in the upward electric field hemisphere than the downward hemisphere during low Pdyn periods. Large‐amplitude undulation excited by the Kelvin‐Helmholtz instability in the upward electric field hemisphere is a candidate process to cause the asymmetric penetration during low Pdyn periods. Another possibility might be the mirror‐mode instability by the asymmetric distribution of planetary pickup ions.

Torsional Alfvén waves in solar magnetic flux tubes of axial symmetry

Aims: Propagation and energy transfer of torsional Alfv\'en waves in solar magnetic flux tubes of axial symmetry is studied. Methods: An analytical model of a solar magnetic flux tube of axial symmetry is developed by specifying a magnetic flux and deriving general analytical formulae for the equilibrium mass density and a gas pressure. The main advantage of this model is that it can be easily adopted to any axisymmetric magnetic structure. The model is used to simulate numerically the propagation of nonlinear Alfv\'en waves in such 2D flux tubes of axial symmetry embedded in the solar atmosphere. The waves are excited by a localized pulse in the azimuthal component of velocity and launched at the top of the solar photosphere, and they propagate through the solar chromosphere, transition region, and into the solar corona. Results: The results of our numerical simulations reveal a complex scenario of twisted magnetic field lines and flows associated with torsional Alfv\'en waves as well as energy transfer to the magnetoacoustic waves that are triggered by the Alfv\'en waves and are akin to the vertical jet flows. Alfv\'en waves experience about 5 % amplitude reflection at the transition region. Magnetic (velocity) field perturbations experience attenuation (growth) with height is agreement with analytical findings. Kinetic energy of magnetoacoustic waves consists of 25 % of the total energy of Alfv\'en waves. The energy transfer may lead to localized mass transport in the form of vertical jets, as well as to localized heating as slow magnetoacoustic waves are prone to dissipation in the inner corona.

MAGNETOHYDRODYNAMIC KINK WAVES IN NONUNIFORM SOLAR FLUX TUBES: PHASE MIXING AND ENERGY CASCADE TO SMALL SCALES

Magnetohydrodynamic (MHD) kink waves are ubiquitously observed in the solar atmosphere. The propagation and damping of these waves may play relevant roles for the transport and dissipation of energy in the solar atmospheric medium. However, in the atmospheric plasma dissipation of transverse MHD wave energy by viscosity or resistivity needs very small spatial scales to be efficient. Here, we theoretically investigate the generation of small scales in nonuniform solar magnetic flux tubes due to phase mixing of MHD kink waves. We go beyond the usual approach based on the existence of a global quasi-mode that is damped in time due to resonant absorption. Instead, we use a modal expansion to express the MHD kink wave as a superposition of Alfv\'en continuum modes that are phase mixed as time evolves. The comparison of the two techniques evidences that the modal analysis is more physically transparent and describes both the damping of global kink motions and the building up of small scales due to phase mixing. In addition, we discuss that the processes of resonant absorption and phase mixing are intimately linked. They represent two aspects of the same underlying physical mechanism: the energy cascade from large scales to small scales due to naturally occurring plasma and/or magnetic field inhomogeneities. This process may provide the necessary scenario for efficient dissipation of transverse MHD wave energy in the solar atmospheric plasma.

Prominence seismology using the period ratio of transverse thread oscillations

The ratio of the period of the fundamental mode to that of the first overtone of kink oscillations, from here on the "period ratio", is a seismology tool that can be used to infer information about the spatial variation of density along solar magnetic flux tubes. The period ratio is 2 in longitudinally homogeneous thin tubes, but it differs from 2 due to longitudinal inhomogeneity. In this paper we investigate the period ratio in longitudinally inhomogeneous prominence threads and explore its implications for prominence seismology. We numerically solve the two-dimensional eigenvalue problem of kink oscillations in a model of a prominence thread. We take into account three nonuniform density profiles along the thread. In agreement with previous works that used simple piecewise constant density profiles, we find that the period ratio is larger than 2 in prominence threads. When the ratio of the central density to that at the footpoints is fixed, the period ratio depends strongly on the form of the density profile along the thread. The more concentrated the dense prominence plasma near the center of the tube, the larger the period ratio. However, the period ratio is found to be independent of the specific density profile when the spatially averaged density in the thread is the same for all the profiles. An empirical fit of the dependence of the period ratio on the average density is given and its use for prominence seismology is discussed.

CORONAL HEATING DRIVEN BY A MAGNETIC GRADIENT PUMPING MECHANISM IN SOLAR PLASMAS

The solar coronal heating is a longstanding mystery in astrophysics. Considering that the solar magnetic field is spatially inhomogeneous with considerable magnetic gradient from solar surface to the corona, this work proposes a magnetic gradient pumping (MGP) mechanism and try to explain the formation of hot plasma upflows, such as the hot type II spicules and hot plasma ejections, etc. In MGP mechanism, the magnetic gradients drive the energetic particles to move upwards from the underlying solar atmosphere and form hot upflows. These upflow energetic particles deposit in corona and make it becoming very hot. Roughly estimations indicate that the solar corona can be heated to above 1 million degrees, and the upflow velocity is about 40 km/s in chromosphere and about 130 km/s in the corona. The solar magnetic flux tubes act as pumpers to extract energetic particles from the underlying thermal photosphere, convey them and deposit in the corona. The deposition of energetic particles will make the corona become hot, and their escaping from the photosphere will make the underlying photosphere a bit cold. This mechanism present a natural explanation to the mystery of solar coronal heating.

Numerical simulations of three-dimensional magnetic swirls in a solar flux-tube

We aim to numerically study evolution of Alfvén waves that accompany short-lasting swirl events in a solar magnetic flux-tube that can be a simple model of a magnetic pore or a sunspot. With the use of the FLASH code we numerically solve three-dimensional ideal magnetohydrodynamic equations to simulate twists which are implemented at the top of the photosphere in magnetic field lines of the flux-tube. Our numerical results exhibit swirl events and Alfvén waves with associated clockwise and counterclockwise rotation of magnetic lines, with the largest values of vorticity at the bottom of the chromosphere, and a certain amount of energy flux.

THE TRANSVERSE AND ROTATIONAL MOTIONS OF MAGNETOHYDRODYNAMIC KINK WAVES IN THE SOLAR ATMOSPHERE

Magnetohydrodynamic (MHD) kink waves have now been observed to be ubiquitous throughout the solar atmosphere. With modern instruments, they have now been detected in the chromosphere, interface region, and corona. The key purpose of this paper is to show that kink waves do not only involve purely transverse motions of solar magnetic flux tubes, but the velocity field is a spatially and temporally varying sum of both transverse and rotational motion. Taking this fact into account is particularly important for the accurate interpretation of varying Doppler velocity profiles across oscillating structures such as spicules. It has now been shown that, as well as bulk transverse motions, spicules have omnipresent rotational motions. Here we emphasize that caution should be used before interpreting the particular MHD wave mode/s responsible for these rotational motions. The rotational motions are not necessarily signatures of the classic axisymmetric torsional Alfven wave alone, because kink motion itself can also contribute substantially to varying Doppler velocity profiles observed across these structures. In this paper, the displacement field of the kink wave is demonstrated to be a sum of its transverse and rotational components, both for a flux tube with a discontinuous density profile at its boundary, and one with a more realistic density continuum between the internal and external plasma. Furthermore, the Doppler velocity profile of the kink wave is forward modeled to demonstrate that, depending on the line of sight, it can either be quite distinct or very similar to that expected from a torsional Alfven wave.

Effect of partial ionization on wave propagation in solar magnetic flux tubes

Observations show that waves are ubiquitous in the solar atmosphere and may play an important role for plasma heating. The study of waves in the solar corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully ionized plasma. However, the plasma in the photosphere and the chromosphere is only partially ionized. Here we investigate theoretically the impact of partial ionization on MHD wave propagation in cylindrical flux tubes in the two-fluid model. We derive the general dispersion relation that takes into account the effects of neutral-ion collisions and the neutral gas pressure. We take the neutral-ion collision frequency as an arbitrary parameter. Particular results for transverse kink modes and slow magnetoacoustic modes are shown. We find that the wave frequencies only depend on the properties of the ionized fluid when the neutral-ion collision frequency is much lower that the wave frequency. For high collision frequencies realistic of the solar atmosphere ions and neutrals behave as a single fluid with an effective density corresponding to the sum of densities of both fluids and an effective sound velocity computed as the average of the sound velocities of ions and neutrals. The MHD wave frequencies are modified accordingly. The neutral gas pressure can be neglected when studying transverse kink waves but it has to be taken into account for a consistent description of slow magnetoacoustic waves. The MHD waves are damped due to neutral-ion collisions. The damping is most efficient when the wave frequency and the collision frequency are of the same order of magnitude. For high collision frequencies slow magnetoacoustic waves are more efficiently damped than transverse kink waves. In addition, we find the presence of cut-offs for certain combinations of parameters that cause the waves to become non-propagating.

Solar magnetic flux tube simulations with time-dependent ionization

In the present work we expand the study of time-dependent ionization previously identified to be of pivotal importance for acoustic waves in solar magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known to be an important heating agent of solar magnetic regions. Our models also consider new results of wave energy generation as well as an updated determination of the mixing length of convection now identified as 1.8 scale heights in the upper solar convective layers. We present 1-D wave simulations for the solar chromosphere by studying tubes of different spreading as function of height aimed at representing tubes in environments of different magnetic filling factors. Multi-level radiative transfer has been applied to correctly represent the total chromospheric emission function. The effects of time-dependent ionization are significant in all models studied. They are most pronounced behind strong shocks and in low density regions, i.e., the middle and high chromosphere. Concerning our models of different tube spreading, we attained pronounced differences between the various types of models, which were largely initiated by different degrees of dilution of the wave energy flux as well as the density structure partially shaped by strong shocks, if existing. Models showing a quasi-steady rise of temperature with height are obtained via monochromatic waves akin to previous acoustic simulations. However, longitudinal flux tube waves are identified as insufficient to heat the solar transition region and corona in agreement with previous studies.

THREE-DIMENSIONAL SIMULATIONS OF MAGNETOHYDRODYNAMIC WAVES IN MAGNETIZED SOLAR ATMOSPHERE

We present results of three-dimensional numerical simulations of magnetohydrodynamic (MHD) wave propagation in a solar magnetic flux tube. Our study aims at understanding the properties of a range of MHD wave modes generated by different photospheric motions. We consider two scenarios observed in the lower solar photosphere, namely, granular buffeting and vortex-like motion, among the simplest mechanism for the generation of waves within a strong, localized magnetic flux concentration. We show that granular buffeting is likely to generate stronger slow and fast magnetoacoustic waves as compared to swirly motions. Correspondingly, the energy flux transported differs as a result of the driving motions. We also demonstrate that the waves generated by granular buffeting are likely to manifest in stronger emission in the chromospheric network. We argue that different mechanisms of wave generation are active during the evolution of a magnetic element in the intergranular lane, resulting in temporally varying emission at chromospheric heights.

Selective spatial damping of propagating kink waves due to resonant absorption

There is observational evidence of propagating kink waves driven by photospheric motions. These disturbances, interpreted as kink magnetohydrodynamic (MHD) waves are attenuated as they propagate upwards in the solar corona. In this paper we show that resonant absorption provides a simple explanation to the spatial damping of these waves. Kink MHD waves are studied using a cylindrical model of solar magnetic flux tubes which includes a non-uniform layer at the tube boundary. Assuming that the frequency is real and the longitudinal wavenumber complex, the damping length and damping per wavelength produced by resonant absorption are analytically calculated. The damping length of propagating kink waves due resonant absorption is a monotonically decreasing function of frequency. For kink waves with low frequencies the damping length is exactly inversely proportional to frequency and we denote this as the TGV relation. When moving to high frequencies the TGV relation continues to be an exceptionally good approximation of the actual dependency of the damping length on frequency. This dependency means that resonant absorption is selective as it favours low frequency waves and can efficiently remove high frequency waves from a broad band spectrum of kink waves. It is selective as the damping length is inversely proportional to frequency so that the damping becomes more severe with increasing frequency. This means that radial inhomogeneity can cause solar waveguides to be a natural low-pass filter for broadband disturbances. Hence kink wave trains travelling along, e.g., coronal loops, will have a greater proportion of the high frequency components dissipated lower down in the atmosphere. This could have important consequences with respect to the spatial distribution of wave heating in the solar atmosphere.

Are the umbral dots, penumbral grains, and G band bright points formed by the same type of magnetic flux tubes?

AbstractToday's Solar Physics comes across of different type of fine structures in solar atmosphere including umbral dots and penumbral grains in sunspots, and G-band bright points in quiet Sun. In this report, we present evidence that umbral dots, penumbral grains, and, possibly, G band bright points are related to a common type of features in solar atmosphere magnetic flux tubes.

The heating of solar magnetic flux tubes II. Nonadiabatic longitudinal tube waves

The formation of shocks and shock heating by radiatively damped longitudinal waves in solar magnetic flux tubes of different filling factors is studied. We consider three flux tubes of filling factors: 1%, 20%, and exponentially spreading which represent normal, enhanced network regions and the interior of supergranulation cells respectively. Monochromatic waves with periods 60 s and energy fluxes of 4.0 · 10 8 erg cm −2 s −1 are assumed to propagate in the tubes. We find that the H −-continuum losses and the Mg II line emission are much reduced in the tube of small filling factor while the mean temperatures are roughly similar in both tubes. The exponential flux tube shows little or no shock heating and no radiation damping. Shocks form earlier in the tube of high filling factor, and have larger strength.

Formation of Solar Magnetic Flux Tubes with Kilogauss Field Strength Induced by Convective Instability

Convective instability has been a mechanism used to explain the formation of solar photospheric flux tubes with kG field strength. However, the turbulence of the Earth's atmosphere has prevented ground-based observers from examining the hypothesis with precise polarimetric measurement on the subarcsecond scale flux tubes. Here we discuss observational evidence of this scenario based on observations with the Solar Optical Telescope (SOT) aboard Hinode. The cooling of an equipartition field strength flux tube precedes a transient downflow reaching 6 km s−1 and the intensification of the field strength to 2 kG. These observations agree very well with the theoretical predictions.