Abstract. This paper presents the results of an investigation of the quiet Sun's magnetic field based on high-resolution infrared spectropolarimetric observations obtained with the Tenerife Infrared Polarimeter (TIP) at the German VTT of the Observatorio del Teide. We observed two very quiet regions at disc centre. The seeing was exceptionally good during both observing runs, being excellent during one of them. In both cases the network was intentionally avoided to the extent possible, to focus the analysis on the characteristics of the weak polarization signals of the inter-network regions. We find that the Stokes V profile of Fe  15648 Å line in almost 50% of the pixels and Stokes Q and/or U in 20% of the pixels have a signal above 10 −3 (in units of continuum intensity I c ), which is significantly above the noise level of 2−3 × 10 −4 . This implies that we detect fluxes as low as 2 × 10 15 Mx/px. We find evidence that we have detected most of the net flux that is in principle detectable at 1 resolution with the Zeeman effect. The observed linear polarization resulting from the transverse Zeeman effect indicates that the magnetic fields have a broad range of inclinations, although most of the pixels show polarization signatures which imply an inclination of about 20• . Nearly 30% of the selected V-profiles have irregular shapes with 3 or more lobes, suggesting mixed polarities with different LOS velocity within the resolution element. The profiles are classified using a single value decomposition approach. The spatial distribution of the magnetic signal shows that profiles of different classes (having different velocities, splitting, asymmetries) are clustered together and form patches, close to the spatial resolution in size. Most of the field is found to be located in intergranular lanes. The statistical properties of the mainly inter-network field sampled by these observations are presented, showing that most of the observed fields are weak with relatively few kG features. The field strength distribution peaks at 350 G and has a FWHM of 300 G. Other parameters, such as profile asymmetries, filling factors and line-of-sight velocities are also determined and discussed.

Velocity oscillations in sunspot umbrae have been measured simultaneously in two spectral lines: the photospheric Silicon i 10827Å line and the chromospheric Helium i 10830Å multiplet. From the full Stokes inversion of temporal series of spectropolarimetric observations we retrieved, among other parameters, the line of sight velocity temporal variations at photospheric and chromospheric heights. Chromospheric velocity oscillations show a three minute period with a clear sawtooth shape typical of propagating shock wave fronts. Photospheric velocity oscillations have basically a five minute period, although the power spectrum also shows a secondary peak in the three minute band which has proven to be predecessor for its chromospheric counterpart. The derived phase spectra yield a value of the atmospheric cut-off frequency around 4 mHz and give evidence for the upward propagation of higher frequency oscillation modes. The phase spectrum has been reproduced with a simple model of linear vertical propagation of slow magneto-acoustic waves in a stratified magnetized atmosphere that accounts for radiative losses through Newton's cooling law. The model explains the main features in the phase spectrum, and allows us to compute the theoretical time delay between the photospheric and chromospheric signals, which happens to have a strong dependence on frequency. We find a very good agreement between this and the time delay obtained directly from the cross-correlation of photospheric and chromospheric velocity maps filtered around the 6 mHz band. This allows us to infer that the 3-minute power observed at chromospheric heights comes directly from the photosphere by means of linear wave propagation, rather than from non-linear interaction of 5-minute (and/or higher frequency) modes.

Flares and X-ray jets on the Sun arise in active regions where magnetic flux emerges from the solar interior amd interacts with the ambient magnetic field. The interactions are believed to occur in electric current sheets separating regions of opposite magnetic polarity. The current sheets located in the corona or upper chromosphere have long been thought to act as an important source of coronal heating, requiring their location in the corona or upper chromosphere. The dynamics and energetics of these sheets are governed by a complex magnetic field structure that, until now, has been difficult to measure. Here we report the determination of the full magnetic vector in an interaction region near the base of the solar corona. The observations reveal two magnetic features that characterize young active regions on the Sun: a set of rising magnetic loops and a tangential discontinuity of the magnetic field direction, the latter being the observational signature of an electric current sheet. This provides strong support for coronal heating models based on the dissipation of magnetic energy at current sheets.

In this paper, we study the heating of the magnetized solar chromosphere induced by the large fraction of neutral atoms present in this layer. The presence of neutrals, together with the decrease with height of the collisional coupling, leads to deviations from the classical MHD behavior of the chromospheric plasma. A relative net motion appears between the neutral and ionized components, usually referred to as ambipolar diffusion. The dissipation of currents in the chromosphere is enhanced orders of magnitude due to the action of ambipolar diffusion, as compared to the standard ohmic diffusion. We propose that a significant amount of magnetic energy can be released to the chromosphere just by existing force-free 10-40 G magnetic fields there. As a consequence, we conclude that ambipolar diffusion is an important process that should be included in chromospheric heating models, as it has the potential to rapidly heat the chromosphere. We perform analytical estimations and numerical simulations to prove this idea.Subject headings: Sun: chromosphere -Sun: magnetic field -Sun: numerical simulations 1 Although the term "ambipolar diffusion" is widely used in the literature, we consider more appropriate the term "diffusion by neutrals", or "neutral diffusion". In the rest of the paper we will use both terminologies interchangeably.

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We derive self-consistent formalism for the description of multi-component partially ionized solar plasma, by means of the coupled equations for the charged and neutral components for an arbitrary number of chemical species, and the radiation field. All approximations and assumptions are carefully considered. Generalized Ohm's law is derived for the single-fluid and two-fluid formalism. Our approach is analytical with some orderof-magnitude support calculations. After general equations are developed we particularize to some frequently considered cases as for the interaction of matter and radiation.

Waves observed in the photosphere and chromosphere of sunspots show complex dynamics and spatial patterns. The interpretation of high-resolution sunspot wave observations requires modeling of three-dimensional non-linear wave propagation and mode transformation in the sunspot upper layers in realistic spot model atmospheres. Here we present the first results of such modeling. We have developed a 3D non-linear numerical code specially designed to calculate the response of magnetic structures in equilibrium to an arbitrary perturbation. The code solves the 3D nonlinear MHD equations for perturbations; it is stabilized by hyper-diffusivity terms and is fully parallelized. The robustness of the code is demonstrated by a number of standard tests. We analyze several simulations of a sunspot perturbed by pulses of different periods at subphotospheric level, from short periods, introduced for academic purposes, to longer and realistic periods of three and five minutes. We present a detailed description of the three-dimensional mode transformation in a non-trivial sunspotlike magnetic field configuration, including the conversion between fast and slow magneto-acoustic waves and the Alfvén wave, by calculation of the wave energy fluxes. Our main findings are the following: (1) the conversion from acoustic to the Alfvén mode is only observed if the the driving pulse is located out of the sunspot axis, but this conversion is energetically inefficient; (2) as a consequence of the cut-off effects and refraction of the fast magneto-acoustic mode, the energy of the evanescent waves with periods around 5 minutes remains almost completely below the level β = 1; (3) waves with frequencies above the cut-off propagate field-aligned to the chromosphere and their power becomes dominating over that of evanescent 5-minute oscillations, in agreement with observations.

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