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 minutes waves vertically into the chromosphere.
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…
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 photosp…
The interaction of magnetic fields and convection is investigated in the context of the coronal heating problem. We study the motions of photospheric magnetic elements using filtergrams obtained at the Swedish Vacuum Solar Telescope at La Palma. We use potential-field modeling to extrapolate the magnetic and velocity fields to larger height. We find that the velocity in the chromosphere can be locally enhanced at the separatrix surfaces between neighboring flux tubes. The predicted velocities are several km/s, significantly larger than those of the photospheric flux tubes, which may have impor…
The effects of radiative energy exchange on the convective instability of a weak field magnetic structure, which lead to a prediction and a physical explanation of the magnetic flux dependent field strength, are examined in detail using a real model stratification for the photospheric and convection zone structure of the Sun. Adopting the generalised Eddington approximation for the radiative transfer, which is valid both in the optically thick and the thin limits, we model the lateral radiative energy exchange by the tube with the external medium with a self-consistent inclusion of vertical ra…
The concept of hyperbolic flux tubes (HFTs) is a generalization of the concept of separator field lines for coronal magnetic fields with a trivial magnetic topology. An effective mechanism of a current layer formation in HFTs is proposed. This mechanism is called magnetic pinching and it is caused by large-scale shearing motions applied to the photospheric feet of HFTs in a way as if trying to twist the HFT. It is shown that in the middle of an HFT such motions produce a hyperbolic flow that causes an exponentially fast growth of the current density in a thin force-free current layer. The magn…
We studied the radiative properties of small magnetic elements (active region faculae and the network) during the rising phase of solar cycle 23 from 1996 to 2001, determining their contrasts as a function of heliocentric angle, magnetogram signal, and the solar cycle phase. We combined near-simultaneous full disk images of the line-of-sight magnetic field and photospheric continuum intensity provided by the MDI instrument on board the SOHO spacecraft. Sorting the magnetogram signal into different ranges allowed us to distinguish between the contrast of different magnetic structures. We find t…
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 …
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…
Sunspots, faculae and the magnetic network contribute to solar irradiance variations. The contribution due to faculae and the network is of basic importance, but suffers from considerable uncertainty. We determine the contrasts of active region faculae and the network, both as a function of heliocentric angle and magnetogram signal. To achieve this, we analyze near-simultaneous full disk images of photospheric continuum intensity and line-of-sight magnetic field provided by the Michelson Doppler Interferometer (MDI) on board the SOHO spacecraft. Starting from the surface distribution of the so…
We present a series of models for the plasma properties along open magnetic flux tubes rooted in solar coronal holes, streamers, and active regions. These models represent the first self-consistent solutions that combine: (1) chromospheric heating driven by an empirically guided acoustic wave spectrum, (2) coronal heating from Alfven waves that have been partially reflected, then damped by anisotropic turbulent cascade, and (3) solar wind acceleration from gradients of gas pressure, acoustic wave pressure, and Alfven wave pressure. The only input parameters are the photospheric lower boundary …
Previous studies have found that coronal loops have a nearly uniform thickness, which seems to disagree with the characteristic expansion of active region magnetic fields. This is one of the most intriguing enigmas in solar physics. We here report on the first comprehensive one-to-one comparison of observed loops with corresponding magnetic flux tubes obtained from cotemporal magnetic field extrapolation models. We use EUV images from TRACE, magnetograms from the MDI instrument on SOHO, and linear force-free field extrapolations. For each loop, we find the particular value of the force-free pa…
We present results from numerical modeling of emerging flux regions on the solar surface. The modeling was carried out by means of 3D radiative MHD simulations of the rise of buoyant magnetic flux tubes through the convection zone and into the photosphere. Due to the strong stratification of the convection zone, the rise results in a lateral expansion of the tube into a magnetic sheet, which acts as a reservoir for small-scale flux emergence events at the scale of granulation. The interaction of the convective downflows and the rising magnetic flux undulates it to form serpentine field lines e…
We examine the excitation of oscillations in the magnetic network of the Sun through the footpoint motion of photospheric magnetic flux tubes located in intergranular lanes. The motion is derived from a time series of high-resolution G band and continuum filtergrams using an object-tracking technique. We model the response of the flux tube to the footpoint motion in terms of the Klein-Gordon equation, which is solved analytically as an initial value problem for transverse (kink) waves. We compute the wave energy flux in upward propagating transverse waves. In general we find that the injection…
Comprehending the manner in which magnetic fields affect propagating waves is a first step toward constructing accurate helioseismic models of active region sub-surface structure and dynamics. Here, we present a numerical method to compute the linear interaction of waves with magnetic fields embedded in a solar-like stratified background. The ideal Magneto-Hydrodynamic (MHD) equations are solved in a 3-dimensional box that straddles the solar photosphere, extending from 35 Mm within to 1.2 Mm into the atmosphere. One of the challenges in performing these simulations involves generating a Magne…
We aim to identify the physical processes which occur in the magnetic network of the chromosphere and which contribute to its dynamics and heating. Specifically, we study the propagation of transverse (kink) MHD waves which are impulsively excited in flux tubes through footpoint motions. When these waves travel upwards, they get partially converted to longitudinal waves through nonlinear effects (mode coupling). By solving the nonlinear, time-dependent MHD equations we find that significant longitudinal wave generation occurs in the photosphere typically for Mach numbers as low as 0.2 and that…
We present the magnetic landscape of the polar region of the Sun that is unprecedented in terms of high spatial resolution, large field of view, and polarimetric precision. These observations were carried out with the Solar Optical Telescope aboard \emph{Hinode}. Using a Milne-Eddington inversion, we found many vertically-oriented magnetic flux tubes with field strength as strong as 1 kG that are scattered in latitude between 70-90 degree. They all have the same polarity, consistent with the global polarity of the polar region. The field vectors were observed to diverge from the center of the …
We have simulated the 3D emergence and interaction of two twisted flux tubes, which rise from the interior into the outer atmosphere of the Sun. We present evidence for the multiple formation and eruption of flux ropes inside the emerging flux systems and hot arcade-like structures in between them. Their formation is due to internal reconnection, occurring between oppositely directed, highly stretched and sheared fieldlines at photospheric heights. Most of the eruptions escape into the corona, but some are confined and fade away without leaving the low atmosphere. As these flux ropes erupt, ne…
The sharp magnetic discontinuities which naturally appear in solar magnetic flux tubes driven by turbulent photospheric motions are associated with intense currents. \citet{Par83} proposed that these currents can become unstable to a variety of microscopic processes, with the net result of dramatically enhanced resistivity and heating (nanoflares). The electric fields associated with such ``hot spots'' are also expected to enhance particle acceleration. We test this hypothesis by exact relativistic orbit simulations in strong random phase magnetohydrodynamic (MHD) turbulence which is forming l…
A simple model of the coronal magnetic field prior to the CME eruption on May 12 1997 is developed. First, the magnetic field is constructed by superimposing a large-scale background field and a localized bipolar field to model the active region (AR) in the current-free approximation. Second, this potential configuration is quasi-statically sheared by photospheric vortex motions applied to two flux concentrations of the AR. Third, the resulting force-free field is then evolved by canceling the photospheric magnetic flux with the help of an appropriate tangential electric field applied to the c…
In recent years, our knowledge of photospheric magnetic fields went through a thorough transformation--nearly unnoticed by dynamo theorists. It is now practically certain that the overwhelming majority of the unsigned magnetic flux crossing the solar surface is in turbulent form (intranetwork and hidden fields). Furthermore, there are now observational indications (supported by theoretical arguments discussed in this paper) that the net polarity imbalance of the turbulent field may give a significant or even dominant contribution to the weak large-scale background magnetic fields outside unipo…
The study of magnetic connectivity in the solar corona reveals a need to generalize the field line mapping technique to arbitrary geometry of the boundaries and systems of coordinates. Indeed, the global description of the connectivity in the corona requires the use of the photospheric and solar wind boundaries. Both are closed surfaces and therefore do not admit a global regular system of coordinates. At least two overlapping regular systems of coordinates for each of the boundaries are necessary in this case to avoid spherical-pole-like singularities in the coordinates of the footpoints. Thi…
(abridged) We investigate how the properties of the corona and solar wind in the open coronal holes depend on the properties of the magnetic fields and their footpoint motions at the surface, by perfoming 1D MHD simulations from the photosphere to 0.3 or 0.1AU. We impose low-frequency (<0.05Hz) transverse fluctuations of the field lines at the photosphere with various amplitude, spectrum, and polarization in the open flux tubes with different photospheric field strength, B, and super-radial expansion of the cross section, f_max. We find that a transonic solar wind is the universal consequence.…
We show that the coronal heating and the fast solar wind acceleration in the coronal holes are natural consequence of the footpoint fluctuations of the magnetic fields at the photosphere, by performing one-dimensional magnetohydrodynamical simulation with radiative cooling and thermal conduction. We initially set up a static open flux tube with temperature 10^4K rooted at the photosphere. We impose transverse photospheric motions corresponding to the granulations with velocity <dv> = 0.7km/s and period between 20 seconds and 30 minutes, which generate outgoing Alfven waves. We self-consistentl…
We investigate the thermal and kinematic configuration of a sunspot penumbra using very high spectral and spatial resolution intensity profiles of the non-magnetic Fe I 557.6 nm line. The dataset was acquired with the 2D solar spectrometer TESOS. The profiles are inverted using a one-component model atmosphere with gradients of the physical quantities. From this inversion we obtain the stratification with depth of temperature, line-of-sight velocity, and microturbulence across the penumbra. Our results suggest that the physical mechanism(s) responsible for the penumbral filaments operate prefe…
Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field $B_e$, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field $B_p$ that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the conv…
