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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.

This paper presents the results of a detailed theoretical investigation of the iron line formation NLTE problem in a three-dimensional model of the solar photosphere, which we have obtained from a very recent radiation hydrodynamics simulation of solar surface convection. In this Ðrst paper we have neglected the e †ects of horizontal radiative transfer on the atomic level populations, but we have considered a realistic atomic model for iron that contains hundreds of radiative transitions from the UV to the IR. The self-consistent solutions of the kinetic and transfer equations have been obtained with a new NLTE code, which is based on very efficient iterative methods. We Ðnd that overionization due to the near-UV radiation Ðeld does take place but mainly in the granular atmospheric regions. This wellknown NLTE mechanism tends to produce underpopulation of all the Fe I levels and a very small overexcitation of the Fe II levels. All over the three-dimensional photospheric model Fe II is the dominant ionization stage. We Ðnd signiÐcant LTE versus NLTE discrepancies mainly for the low-excitation Fe I lines. This applies to both the vertically emergent proÐles from the granular regions and also to the spatially averaged proÐles. These discrepancies are due to the line opacity deÐcits that result from the aforementioned underpopulation of the Fe I levels. The emergent proÐles of the low-excitation lines of Fe I are thus weaker in NLTE than in LTE. In particular, the largest errors in the equivalent widths (due to the LTE assumption) are found for the weakest low-excitation lines of Fe I. We also give quantitative estimates of the errors in the temperature structure of semiempirical solar granulation models obtained via the application of LTE inversion techniques to several groups of Fe I lines. For instance, the widely used Fe I 6301 and 6302 lines tend to lead to an overestimation of about 100È200 K in the Ó granular regions but to a similar underestimation in the intergranular plasma.The present paper considers also the case of the Sun observed with low spatial resolution, with particular emphasis on the long-standing iron abundance problem. We show that it is possible to obtain a very good Ðt to the observed spectral line shapes by slightly changing the iron abundance (for both the LTE and NLTE cases). In general, the iron abundance we need for reaching the best NLTE Ðt to observed equivalent widths is 0.074^0.03 dex larger than that needed to obtain the best LTE Ðt. Our most relevant conclusion with regard to the solar iron abundance issue is the following : if NLTE e †ects are fully taken into account in the three-dimensional model of the solar photosphere, we obtain the meteoritic iron abundance value However, if the abundance analysis is done assuming LTE, (A Fe \ 7.50). we Ðnd in close agreement with the recent LTE analysis of Asplund and collaborators. A Fe \ 7.43, Our results do indicate that NLTE e †ects are signiÐcant but not above the 0.1 dex level in the Sun. We consider our NLTE result for the i...