Vertical Flux Tubes Research Articles

Open and Closed Magnetic Configurations of Twisted Flux Tubes

We construct two classes of magnetohydrostatic (MHS) equilibria for an axisymmetric vertical flux tube spanning from the photosphere to the lower part of the transition region within a realistic stratified solar atmosphere subject to solar gravity. We assume a general quadratic expression of the magnetic flux function for the gas pressure and poloidal current and solve the Grad-Shafranov equation analytically. The solution is a combination of a homogeneous and a particular part where the former is separable by a Coulomb function in $r$ and exponential in $z$, while the particular part is an open configuration that has no $z$ dependence. We also present another open field solution by using a self-similar formulation with two different profile functions and incorporating stratified solar gravity to maintain the magnetohydrostatic equilibria, which is a modification of earlier self-similar models with a twist. We study the admitted parameter space that is consistent with the conditions in the solar atmosphere and derive magnetic and the thermodynamic structures inside the flux tube that are reasonably consistent with the photospheric magnetic bright points (MBPs) for both open and closed field Coulomb function and self-similar models as estimated from observations and simulations. The obtained open and closed field flux tube solutions can be used as the background conditions for the numerical simulations for the study of the wave propagation through the flux tubes. The solutions can also be used to construct realistic magnetic canopies.

Wave modes excited by photosphericp-modes and mode conversion in a multi-loop system

Context. Waves are ubiquitous in the solar corona and there are indications that they are excited by photosphericp-modes. However, it is unclear howp-modes in coronal loops are converted to sausage modes and transverse (kink) modes, which are observed in the corona.Aims. We aim to investigate how those wave modes are excited in the lower corona by photospheric acoustic waves.Methods. We built 3D magnetohydrostatic loop systems with multiple inclinations spanning from the photosphere to the lower corona. We then simulated these atmospheres with the MANCHA code, in which we perturb the equilibrium with ap-mode driver at the bottom of the domain. By splitting the velocity perturbation into components longitudinal, normal, and azimuthal to the magnetic flux surfaces we can study wave behavior.Results. In vertical flux tubes, we find that deformed fast sausage surface waves and slow sausage body waves are excited. In inclined flux tubes fast kink surface waves, slow sausage body waves, and either a fast sausage surface wave or a plane wave are excited. In addition, we calculate a wave conversion factor (0 ≤ C ≤ 1) from acoustic to magnetic wave behavior by taking the ratio of the mean magnetic energy flux to the sum of the mean magnetic and acoustic energy flux and compare it to a commonly used theoretical conversion factor. We find that between magnetic field inclinations of 10° to 30° those two methods lie within 40%. For smaller inclinations the absolute deviation is smaller than 0.1.

The dark side of solar photosphericG-band bright points

Bright small-scale magnetic elements found mainly in intergranular lanes at the solar surface are named bright points (BPs). They show high contrasts in Fraunhofer G-band observations and are described by nearly vertical slender flux tubes or sheets. A recent comparison between BP observations in the ultraviolet (UV) and visible spectral range recorded with the balloon-borne observatory SUNRISE and state-of-the-art magnetohydrodynamical (MHD) simulations revealed a kiloGauss magnetic field for 98% of the synthetic BPs. Here we address the opposite question, namely which fraction of pixels hosting kiloGauss fields coincides with an enhanced G-band brightness. We carried out 3D radiation MHD simulations for three magnetic activity levels (corresponding to the quiet Sun, weak and strong plage) and performed a full spectral line synthesis in the G-band. Only 7% of the kiloGauss pixels in our quiet-Sun simulation coincide with a brightness lower than the mean quiet-Sun intensity, while 23% of the pixels in the weak-plage simulation and even 49% in the strong-plage simulation are associated with a local darkening. Dark strong-field regions are preferentially found in the cores of larger flux patches that are rare in the quiet Sun, but more common in plage regions, often in the vertices of granulation cells. The significant brightness shortfall in the core of larger flux patches coincide with a slight magnetic field weakening. KiloGauss elements in the quiet Sun are on average brighter than similar features in plage regions. Almost all strong-field pixels display a more or less vertical magnetic field orientation. Hence in the quiet Sun, G-band BPs correspond almost one-to-one with kiloGauss elements. In weak plage the correspondence is still very good, but not perfect.

Magnetohydrostatics of a vertical flux tube in the solar atmosphere: Coronal loops, a model of a ring flare filament

The magnetohydrostatic theory of a twisted magnetic flux tube (rope) immersed in a realistic solar atmosphere is presented in a closed analytical form for the first time. General formulas that allow the equilibrium plasma density, pressure, and temperature distributions inside an axisymmetric vertical flux tube to be calculated from its magnetic structure, which is assumed to be known (fixed), have been derived. An analytical model of the external hydrostatic medium free of a magnetic field, the solar atmosphere, where the temperature profile of the semi-empirical tabulated Avrett-Loeser model is used, has been constructed. The distribution of plasma parameters in a twisted magnetic flux tube at small deviations of its internal magnetic structure from the force-free one has been calculated as an example of applying the general theoretical formulas. Since the tube cross section does not change with height, the constructed model can be applied to describe the vertical parts of coronal loops. It has been found that the plasma density in the magnetic flux tube rises when the field twisting exceeds the force-free level and falls with decreasing field twisting compared to the force-free level. This property of a twisted magnetic flux tube is of fundamental importance for justifying the mechanism of flare energy release in magnetic flux ropes. A model of a flare in a ring chromospheric configuration is considered.

Formation of magnetic flux tubes in cylindrical wedge geometry

Three-dimensional (3D) MHD numerical simulations have not been able to demonstrate convincingly the spontaneous formation of large vertical flux tubes. Two-dimensional (2D) magnetoconvection in axisymmetric cylinders forms a central magnetic flux tube surrounded by annular convection rings. To study the robustness of this type of solution in three dimensions, the nonlinear resistive MHD equations are solved numerically in a 3D cylindrical wedge from an initially uniform vertical magnetic field. It is shown that the 2D result is retrieved for small domain radii. However, for larger radii the central axis loses its importance and in this case many convection cells form in the numerical domain. Magnetic flux is captured between cells where flow converges and the reduced amount of flux that congregates at the central axis is eroded by the surrounding convection.

Hall instability of solar flux tubes in the presence of shear flows

The magnetic network which consists of vertical flux tubes located in intergranular lanes is dominated by Hall drift in the photosphere-lower chromosphere region ($\lesssim 1 Mm$). In the internetwork regions, Hall drift dominates above $0.25 Mm$ in the photosphere and below $2.5 Mm$ in the chromosphere. Although Hall drift does not cause any dissipation in the ambient plasma, it can destabilise the flux tubes and magnetic elements in the presence of azimuthal shear flow. The physical mechanism of this instability is quite simple: the shear flow twists the radial magnetic field and generates azimuthal field; torsional oscillations of the azimuthal field in turn generates the radial field completing feedback loop. The maximum growth rate of Hall instability is proportional to the absolute value of the shear gradient and is dependent on the ambient diffusivity. The diffusivity also determines the most unstable wavelength which is smaller for weaker fields. We apply the result of local stability analysis to the network and internetwork magnetic elements and show that the maximum growth rate for kilogauss field occurs around $0.5 Mm$ and decreases with increasing altitude. However, for a $120 G$ field, the maximum growth rate remains almost constant in the entire photosphere-lower chromosphere except in a small region of lower photosphere. For shear flow gradient $\sim 0.01 s^{-1}$, the Hall growth time is 10 minute near the footpoint. Therefore, network fields are likely to be unstable in the photosphere, whereas internetwork fields could be unstable in the entire photosphere-chromosphere. Thus the Hall instability can play an important role in generating low frequency turbulence which can heat the chromosphere.

Magnetic Field Structures in a Facular Region Observed by THEMIS and Hinode

The main objective of this paper is to build and compare vector magnetic maps obtained by two spectral polarimeters, i.e. THEMIS/MTR and Hinode SOT/SP, using two inversion codes (UNNOFIT and MELANIE) based on the Milne-Eddington solar atmosphere model. To this end, we used observations of a facular region within active region NOAA 10996 on 23 May 2008, and found consistent results concerning the field strength, azimuth and inclination distributions. Because SOT/SP is free from the seeing effect and has better spatial resolution, we were able to resolve small magnetic polarities with sizes of 1" to 2", and we could detect strong horizontal magnetic fields, which converge or diverge in negative or positive facular polarities. These findings support models which suggest the existence of small vertical flux tube bundles in faculae. A new method is proposed to get the relative formation heights of the multi-lines observed by MTR assuming the validity of a flux tube model for the faculae. We found that the Fe 1 6302.5 \AA line forms at a greater atmospheric height than the Fe 1 5250.2 \AA line.

Discriminant analysis of solar bright points and faculae

While photospheric magnetic elements appear mainly as Bright Points (BPs) at the disk center and as faculae near the limb, high-resolution images reveal the coexistence of BPs and faculae over a range of heliocentric angles. This is not explained by a "hot wall" effect through vertical flux tubes, and suggests that the transition from BPs to faculae needs to be quantitatively investigated. To achieve this, we made the first recorded attempt to discriminate BPs and faculae, using a statistical classification approach based on Linear Discriminant Analysis(LDA). This paper gives a detailed description of our method, and shows its application on high-resolution images of active regions to retrieve a center-to-limb distribution of BPs and faculae. Bright "magnetic" features were detected at various disk positions by a segmentation algorithm using simultaneous G-band and continuum information. By using a selected sample of those features to represent BPs and faculae, suitable photometric parameters were identified in order to carry out LDA. We thus obtained a Center-to-Limb Variation (CLV) of the relative number of BPs and faculae, revealing the predominance of faculae at all disk positions except close to disk center (mu > 0.9). Although the present dataset suffers from limited statistics, our results are consistent with other observations of BPs and faculae at various disk positions. The retrieved CLV indicates that at high resolution, faculae are an essential constituent of active regions all across the solar disk. We speculate that the faculae near disk center as well as the BPs away from disk center are associated with inclined fields.

ESTIMATION OF SPICULE MAGNETIC FIELD USING OBSERVED MHD WAVES BY THE HINODE SOT

Using the MHD coronal seismology technique, we estimated the magnetic field for three spicules observed in 2008 June. For this study, we used the high resolution Ca II H line (<TEX>$3968.5\;{\AA}$</TEX>) images observed by the Hinode SOT and considered a vertical thin flux tube as a spicule model. To our knowledge, this is the first attempt to estimate the spicule magnetic field using the Hinode observation. From the observed oscillation properties, we determined the periods, amplitudes, minimum wavelengths, and wave speeds. We interpreted the observed oscillations as MHD kink waves propagating through a vertical thin flux tube embedded in a uniform field environment. Then we estimated spicule magnetic field assuming spicule densities. Major results from this study are as follows : (1) we observed three oscillating spicules having durations of 5-7 minutes, oscillating periods of 2-3 minutes, and transverse displacements of 700-1000 km. (2) The estimated magnetic field in spicules is about 10-18 G for lower density limit and about 43-76 G for upper density limit. (3) In this analysis, we can estimate the minimum wavelength of the oscillations, such as 60000 km, 56000 km, and 45000 km. This may be due to the much longer wavelength comparing with the height of spicules. (4) In the first event occurred on 2008 June 03, the oscillation existed during limited time (about 250 s). This means that the oscillation may be triggered by an impulsive mechanism (like low atmospheric reconnection), not continuous. Being compared with the ground-based observations of spicule oscillations, our observation indicates quite different one, i.e., more than one order longer in wavelength, a factor of 3-4 larger in wave speed, and 2-3 times longer in period.

The Magnetic Landscape of the Sun's Polar Region

We present observations of the magnetic landscape of the polar region of the Sun that are unprecedented in terms of spatial resolution, field of view, and polarimetric precision. They were carried out with the Solar Optical Telescope aboard Hinode. Using a Milne-Eddington inversion, we find many vertically oriented magnetic flux tubes with field strengths as strong as 1 kG scattered in latitude between 70° and 90°. They all have the same polarity, consistent with the global polarity of the polar region. The field vectors are observed to diverge from the centers of the flux elements, consistent with a view of magnetic fields that are expanding and fanning out with height. The polar region is also found to have ubiquitous horizontal fields. The polar regions are the source of the fast solar wind, which is channeled along unipolar coronal magnetic fields whose photospheric source is evidently rooted in the strong-field, vertical patches of flux. We conjecture that vertical flux tubes with large expansion around the photospheric-coronal boundary serve as efficient chimneys for Alfven waves that accelerate the solar wind.

Modeling Penumbral Microjets by Two-Fluid Simulations

We investigate how penumbral microjets, recently observed by the Hinode satellite, can be produced within sunspot penumbra. We consider two penumbral filaments with axial currents and axial flows. We assume that a vertical magnetic flux tube exists between two horizontal penumbral filaments. We also assume that the axial flows are not steady; a high-velocity axial flow is imposed on the background slow axial flow. We find that this high-velocity axial flow can trigger magnetic reconnection between one penumbral filament and the vertical flux tube. As a result, inclined bidirectional jetlike flows, driven by the magnetic reconnection, propagate along the vertical magnetic flux tube. Strong proton heating, up to 25 times their original temperature, is observed in these generated jets. Conversely, the neutral-hydrogen particles are only very weakly heated. We propose that these plasma jets explain the phenomenon of penumbral microjets, recently observed by the Hinode satellite.

Processes in the magnetized chromosphere of the Sun

AbstractWe review physical processes in magnetized chromospheres on the Sun. In the quiet chromosphere, it is useful to distinguish between the magnetic network on the boundaries of supergranules, where strong magnetic fields are organized in mainly vertical flux tubes and internetwork regions in the cell interiors, which have traditionally been associated with weak magnetic fields. Recent observations from Hinode, however, suggest that there is a significant amount of horizontal magnetic flux in the cell interior with large field strength. Furthermore, processes that heat the magnetic network have not been fully identified. Is the network heated by wave dissipation and if so, what is the nature of these waves? These and other aspects related to the role of spicules will also be highlighted. A critical assessment will be made on the challenges facing theory and observations, particularly in light of the new space experiments and the planned ground facilities.

The properties of penumbral microjets inclination

We investigate the dependence of penumbral microjets inclination on the position within penumbra. The high cadence observations taken on 10 November 2006 with the Hinode satellite through the \ion{Ca}{ii} H and G--band filters were analysed to determine the inclination of penumbral microjets. The results were then compared with the inclination of the magnetic field determined through the inversion of the spectropolarimetric observations of the same region. The penumbral microjet inclination is increasing towards the outer edge of the penumbra. The results suggest that the penumbral microjet follows the opening magnetic field lines of a vertical flux tube that creates the sunspot.

Hinode Observations of Horizontal Quiet Sun Magnetic Flux and the “Hidden Turbulent Magnetic Flux”

We present observations of magnetic fields of the very quiet Sun near disk center using the Spectro-Polarimeter of the Solar Optical Telescope aboard the Hinode satellite. These observations reveal for the first time the ubiquitous presence of horizontal magnetic fields in the internetwork regions. The horizontal fields are spatially distinct from the vertical fields, demonstrating that they are not arising mainly from buffeting of vertical flux tubes by the granular convection. The horizontal component has an average “apparent flux density” of 55 Mxcm$^{-2}$ (assuming the horizontal field structures are spatially resolved), in contrast to the average apparent vertical flux density of 11 Mxcm$^{-2}$. The vertical fields reside mainly in the intergranular lanes, whereas the horizontal fields occur mainly over the bright granules, with a preference to be near the outside edge of the bright granules. The large apparent imbalance of vertical and horizontal flux densities is discussed, and several scenarios are presented to explain this imbalance.

Slow magnetohydrodynamic waves in stratified and viscous plasmas

The propagation of slow magnetohydrodynamic waves in vertical thin flux tubes embedded in a vertically stratified plasma in the presence of viscosity is shown here to be governed by the Klein-Gordon-Burgers (KGB) equation, which is solved in two limiting cases assuming an isothermal medium in hydrostatic equilibrium surrounded by a quiescent environment. The results presented here can be applied to, e.g., study the propagation of slow magnetohydrodynamic waves generated by the granular buffeting motion in thin magnetic photospheric tubes. When the variation in the reduced velocity occurs over typical lengths much larger than the gravitational scale height, the KGB equation can be reduced to a Klein-Gordon equation describing the propagation of an impulse followed by a wake oscillating with the frequency reduced by viscosity and the solution has no spatial or temporal decay. However, in the other limiting case, i.e., typical variations in the reduced velocity occur over characteristic lengths much smaller than the gravitational scale height, waves have a temporal and spatial decay.

Bright rings around sunspots

There are two possible explanations for why sunspots are dark: the partial suppression by the sunspot magnetic fields of convective energy transport from the underlying layers1, or the removal of energy from the sunspot by enhanced hydromagnetic wave radiation2. Both processes would reduce the energy emitted radiatively. The first explanation is currently favoured3, and predicts that the blocked energy should show up as a bright ring around the spot2, with the actual brightness of the ring sensitive to details of solar convective transport and sunspot structure4. Previous searches5 for these bright rings were inconclusive because of the presence of bright, vertical magnetic flux tubes near the spots, and a lack of sufficient precision in the observations. Here we report high-photometric-precision observations of bright rings around eight sunspots. The rings are about 10 K warmer than the surrounding photosphere and extend at least one sunspot radius out from the penumbra. About 10% of the radiative energy missing from the sunspots is emitted through the bright rings. We also report observations of a second set of sunspots, for which simultaneous magnetic field measurements demonstrate that the rings are not associated with vertical flux tubes.

Excitation of Oscillations in Photospheric Flux Tubes through Buffeting by External Granules

We examine the excitation of transverse (kink) and longitudinal (sausage) waves in magnetic flux tubes by granules in the solar photosphere. The investigation is motivated by the interpretation of network oscillations in terms of flux tube waves. We model the interaction between a granule, with a specified transverse velocity, and a vertical flux tube in terms of the Klein-Gordon equation, which we solve analytically as an initial value problem for both wave modes, assuming the same external impulse. The calculations show that for magnetic field strengths typical of the network, the energy flux in transverse waves is higher than in longitudinal waves by an order of magnitude, in agreement with the chromospheric power spectrum of network oscillations observed by Lites, Rutten, & Kalkofen. But for weaker fields, such as those that might be found in internetwork regions, the energy fluxes in the two modes are comparable. This result implies that if there are internetwork oscillations in magnetic flux tubes, they must show the cutoff periods of both longitudinal and transverse modes at 3 minutes and at 7 minutes or longer. We also find that granules with speeds of about 2 km s-1 can efficiently excite transverse oscillations in frequent short-duration (typically 1 minute) bursts that can heat the corona.

On the stability of stationary flows in thin magnetic flux tubes

Based on the almost fibril state of magnetic flux in astrophysical bodies we present a study of the stability of magnetic flux tubes which are described by the thin flux tube approximation. A stationary flow is allowed in the tube which in equilibrium lies in a vertical plane, while the surroundings are assumed to be static. This complements earlier studies with external but no internal flows. The equations governing small adiabatic displacements are given in a canonical form which allows the proof that operators are Hermitian. This form is derived for the first time. The character of operators allows powerful conclusions about the eigensolutions, sufficient conditions for stability as well as the application of variational techniques. The velocity may potentially lead to the phenomenon of overstability. Special cases are discussed analytically. These cover the local approximation, binormal perturbations, static equilibria, and horizontal and vertical flux tubes. Stability of siphon flows along arch-shaped flux tubes describing the Evershed effect in penumbrae of sunspots is analyzed numerically. A standard model is found to be stable. Increasing the flow speed or decreasing the magnetic field strength however leads to monotonic instability. Further astrophysical applications are mentioned.

Implications of rapid footpoint motions of photospheric flux tubes for coronal heating

Some recent observations at Pic-du-Midi (Mulleret al., 1992a) suggest that the photospheric footpoints of coronal magnetic field lines occasionally move rapidly with typical velocities of the order 3 km s–1 for about 3 or 4 min. We argue that such occasional rapid footpoint motions could have a profound impact on the heating of the quiet corona. Qualitative estimates indicate that these occasional rapid motions can account for the entire energy flux needed to heat the quiet corona. We therefore carry out a mathematical analysis to study in detail the response of a vertical thin flux tube to photospheric footpoint motions in terms of a superposition of linear kink modes for an isothermal atmosphere. We find the resulting total energy that is asymptotically injected into an isothermal atmosphere (i.e., an atmosphere without any back reflection). By using typical parameter values for fast and slow footpoint motions, we show that, even if the footpoints spend only 2.5% of the time undergoing rapid motions, still these rapid motions could be more efficient in transporting energy to the corona than the slow motions that take place most of the time.

Effects of fibril magnetic fields on solar p-modes. II - Calculation of mode frequency shifts

The effect of magnetic flux tubes in the solar convection zone on p-mode oscillations is investigated analytically using WKB ray theory, extending the results of Bogdan and Zweibel (1985) to the case of propagation not perpendicular to the tubes. Results for the frequency shift in polytropic slabs with vertical or horizontal flux tubes are presented in graphs and discussed.