Photospheric granulation may excite transverse kink pulses in anchored vertical magnetic flux tubes. The pulses propagate upwards along the tubes with the kink speed, while oscillating wakes are formed behind the wave front in a stratified atmosphere. The wakes oscillate at the kink cut-off frequency of stratified medium and gradually decay in time. When two or more consecutive kink pulses with different polarizations propagate in the same thin tube, then the wakes corresponding to different pulses may superimpose. The superposition sets up helical motions of magnetic flux tubes in the photosphere/chromosphere as seen by recent Hinode movies. The energy carried by the pulses is enough to heat the solar chrmosphere/corona and accelerate the solar wind.
Analytical solution of $α$-dynamo equation representing strongly torsioned helical dynamo is obtained in the thin twisted Riemannian flux tubes approximation. The $α$ factor possesses a fundamental contribution from torsion which is however weaken in the thin tubes approximation. It is shown that assuming that the poloidal component of the magnetic field is in principle time-independent, the toroidal magnetic field component grows very fast in time, actually it possesses a linear time dependence, while the poloidal component grows under the influence of torsion or twist of the flux tube. The t…
The mean value of the normalized current helicity in solar active regions is on the order of 1e-8 1/m, negative in the northern hemisphere, positive in the southern hemisphere. Observations indicate that this helicity has a subsurface origin. Possible mechanisms leading to a twist of this amplitude in magnetic flux tubes include the solar dynamo, convective buffeting of rising flux tubes, and the accretion of weak external poloidal flux by a rising toroidal flux tube. After briefly reviewing the observational and theoretical constraints on the origin of helicity, we present a recently develope…
We show that the atmospheric and magnetic height variations are coupled in general MHS equilibria with gravity when isolated thin non-force-free flux tubes are present. In gas-dominated environments, as in stellar photospheres, flux tubes must expand rapidly with height to maintain pressure balance with the cool surroundings. But in magnetically dominated environments, as in stellar coronae, the large-scale background magnetic field determines the average spreading of embedded flux tubes, and rigidly held flux tubes {\it require} a specific surrounding atmosphere with a unique temperature prof…
We report two-dimensional MHD simulations which demonstrate that photospheric 5-min oscillations can leak into the chromosphere inside small-scale vertical magnetic flux tubes. The results of our numerical experiments are compatible with those inferred from simultaneous spectropolarimetric observations of the photosphere and chromosphere obtained with the Tenerife Infrared Polarimeter (TIP) at 10830 A. We conclude that the efficiency of energy exchange by radiation in the solar photosphere can lead to a significant reduction of the cut-off frequency and may allow for the propagation of the 5 m…
For a magnetic flux tube, or indeed any flux, to emerge into the Solar corona from the convection zone it must pass through the partially ionised layers of the lower atmosphere: the photosphere and the chromosphere. In such regions the ion-neutral collisions lead to an increased resistivity for currents flowing across magnetic field lines. This Cowling resistivity can exceed the Spitzer resistivity by orders of magnitude and in 2.5D simulations has been shown to be sufficient to remove all cross field current from emerging flux. Here we extend this modelling into 3D. Once again it is found tha…
Analytical solution of first order torsion $α$-effect in twisted magnetic flux tubes representing a flux tube dynamo in Riemannian space is presented. Toroidal and poloidal component of the magnetic field decays as $r^{-1}$, while grow exponentially in time. The rate of speed of the helical dynamo depends upon the value of Frenet curvature of the tube. The $α$ factor possesses a fundamental contribution from constant torsion tube approximation. It is also assumed that the curvature of the magnetic axis of the tube is constant. Though $α$-effect dynamo equations are rather more complex in Riema…
In the past few years suggestions have emerged that the solar magnetic field might have a bi-helical component with oppositely polarized magnetic fields at large and small scales, and that the shedding of such fields may be crucial for the operation of the dynamo. It is shown that, if a bi-helical field is shed into the solar wind, positive and negative contributions of the magnetic helicity spectrum tend to mix and decay. Even in the absence of turbulence, mixing and decay can occur on a time scale faster than the resistive one provided the two signs of magnetic helicity originate from a sing…
We employ a 3-dimensional magnetohydrostatic model of a horizontal flux tube, embedded in a magnetic surrounding atmosphere, to successfully reproduce the azimuthal and center-to-limb variations of the Net Circular Polarization observed in sunspot penumbrae. This success is partly due to the realistic modeling of the interaction between the flux tube and the surrounding magnetic field.
3D numerical simulations of a horizontal magnetic flux tube emergence with different twist are carried out in a computational domain spanning the upper layers of the convection zone to the lower corona. We use the Oslo Staggered Code to solve the full MHD equations with non-grey and non-LTE radiative transfer and thermal conduction along the magnetic field lines. The emergence of the magnetic flux tube input at the bottom boundary into a weakly magnetized atmosphere is presented. The photospheric and chromospheric response is described with magnetograms, synthetic images and velocity field dis…
Aims: We investigate the formation of flux ropes in a flux emergence region and their rise into the outer atmosphere of the Sun. Methods: We perform 3D numerical experiments solving the time-dependent and resistive MHD equations. Results: A sub-photospheric twisted flux tube rises from the solar interior and expands into the corona. A flux rope is formed within the expanding field, due to shearing and reconnection of field lines at low atmospheric heights. If the tube emerges into a non-magnetized atmosphere, the flux rope rises, but remains confined inside the expanding magnetized volume. On …
First results of the inversion of Stokes I and V profiles from plage regions near disk center are presented. Both low and high spatial resolution spectra of FeI 6301.5 and FeI 6302.5 A obtained with the Advanced Stokes Polarimeter (ASP) have been considered for analysis. The thin flux tube approximation, implemented in an LTE inversion code based on response functions, is used to describe unresolved magnetic elements. The code allows the simultaneous and consistent inference of all atmospheric quantities determining the radiative transfer with the sole assumption of hydrostatic equilibrium. By…
Recent observations of coronal-loop waves by TRACE and within the corona as a whole by CoMP clearly indicate that the dominant oscillation period is 5 minutes, thus implicating the solar p modes as a possible source. We investigate the generation of tube waves within the solar convection zone by the buffeting of p modes. The tube waves--in the form of longitudinal sausage waves and transverse kink waves--are generated on the many magnetic fibrils that lace the convection zone and pierce the solar photosphere. Once generated by p-mode forcing, the tube waves freely propagate up and down the tub…
A new antidynamo theorem for non-stretched twisted magnetic flux tube dynamo is obtained. Though Riemannian curvature cannot be neglected since one considers curved magnetic flux tube axis, the stretch can be neglect since one only considers the limit of thin magnetic flux tubes. The theorem states that marginal or slow dynamos along curved (folded), torsioned (twisted) and non-stretched flux tubes endowed with diffusionless plasma flows, if a constraint is imposed on the relation between poloidal and toroidal magnetic fields in the helical dynamo case. A formula for the stretch of flux tubes …
Two examples of the use of differential geometry in plasma physics are given: The first is the computation and solution of the constraint equations obtained from the Riemann metric isometry of the twisted flux tube. In this case a constraint between the Frenet torsion and curvature is obtained for inhomogeneous helical magnetic flux tube axis. In the second one, geometrical and topological constraints on the current-carrying solar loops are obtained by assuming that the plasma filament is stable. This is analogous to early computations by Liley [(Plasma Physics (1964)] in the case of hydromagn…
Propagation of torsional Alfvén waves along magnetic flux tubes has been extensively studied for many years but no conclusive results regarding the existence of a cutoff frequency for these waves have been obtained. The main purpose of this paper is to derive new wave equations that describe the propagation of linear torsional Alfvén waves along thin and isothermal magnetic flux tubes, and use these wave equations to demonstrate that the torsional wave propagation is not affected by any cutoff frequency. It is also shown that this cutoff-free propagation is independent of different choices of …
We study the magnetohydrostatic equilibrium of magnetic flux tubes with circular cross sections embedded in a magnetic surrounding atmosphere. We solve the static momentum equation in 2.5D to obtain the thermodynamics that are consistent with a prescribed velocity and magnetic fields. We show that force balance is roughly satisfied if the flux tube's magnetic field is aligned with its axis. Equilibrium is guaranteed if this magnetic field possesses a transverse component. Several forms of this transverse field are investigated. The resulting magnetic field configurations are critically reviewe…
In the first part of these lecture notes, new high-resolution observations of small-scale magnetic flux concentrations are presented and compared to results from new three-dimensional magnetohydrodynamic simulations. Special attention is paid to the physics of faculae and to new three-dimensional radiation magnetohydrodynamic simulations of the integral layers from the top of the convection zone to the mid-chromosphere. The second part is devoted to a few basic properties of magnetic flux tubes, which can be considered to be an abstraction of the more complicated flux concentrations known from…
Vector magnetograms taken at Huairou Solar Observing Station (HSOS) and Mees Solar Observatory (MSO) reveal that the super active region (AR) NOAA 10486 was a complex region containing current helicity flux of opposite signs. The main positive sunspots were dominated by negative helicity fields, while positive helicity patches persisted both inside and around the main positive sunspots. Based on a comparison of two days of deduced current helicity density, pronounced changes were noticed which were associated with the occurrence of an X10 flare that peaked at 20:49 UT, 2003 October 29. The ave…
Over the last few years, numerical models of the behavior of solar magnetic flux tubes have gone from using methods that were essentially one-dimensional (i.e. the thin flux tube approximation), over more or less idealized two-dimensional simulations, to becoming ever more realistic three-dimensional case studies. Along the way a lot of new knowledge has been picked up as to the e.g. the likely topology of the flux tubes, and the instabilities that they are subjected to etc. Within the context of what one could call the ``flux tube solar dynamo paradigm,'' I will discuss recent results of effo…
Based on the Meso-Structured Magnetic Atmosphere (MESMA) approximation, recently introduced by Carroll & Kopf (2007), we present first results of an inversion of spectropolarimetric observations obtained from solar internetwork regions. To cope with the inherent complexity of the mostly unresolved magnetic field in the solar photosphere the MESMA approach provides a statistical description of the underlying atmosphere in terms of a random Markov field. This statistical model allows us to derive a stochastic transfer equation for polarized light. The stochastic transfer equation explicitly acco…
Relying on the assumption that the interchange convection of magnetic flux tubes is the physical cause for the existence of sunspot penumbrae, we propose a model in which the dynamical evolution of a thin magnetic flux tube reproduces the Evershed effect and the penumbral fine structure such as bright and dark filaments and penumbral grains. According to our model, penumbral grains are the manifestation of the footpoints of magnetic flux tubes, along which hot subphotospheric plasma flows upwards with a few km/s. Above the photosphere the hot plasma inside the tube is cooled by radiative losse…
We present results of non-linear, 2D, numerical simulations of magneto-acoustic wave propagation in the photosphere and chromosphere of small-scale flux tubes with internal structure. Waves with realistic periods of three to five minutes are studied, after applying horizontal and vertical oscillatory perturbations to the equilibrium model. Spurious reflections of shock waves from the upper boundary are minimized thanks to a special boundary condition. This has allowed us to increase the duration of the simulations and to make it long enough to perform a statistical analysis of oscillations. Th…
We use G-band and Ca II H image sequences from the Dutch Open Telescope (DOT) to study magnetic elements that appear as bright points in internetwork parts of the quiet solar photosphere and chromosphere. We find that many of these bright points appear recurrently with varying intensity and horizontal motion within longer-lived magnetic patches. We develop an algorithm for detection of the patches and find that all patches identified last much longer than the granulation. The patches outline cell patterns on mesogranular scales, indicating that magnetic flux tubes are advected by granular flow…
Context: Sunspot penumbrae harbor highly structured magnetic fields and flows. The moving flux tube model offers an explanation for several observed phenomena, e.g. the Evershed effect and bright penumbral grains. Aims: A wealth of information can be extracted from spectropolarimetric observations. In order to deduce the structure of the magnetic field in sunspot penumbrae, detailed forward modeling is necessary. On the one hand, it gives insight into the sensitivity of various spectral lines to different physical scenarios. On the other hand, it is a very useful tool to guide inversion techni…
