Small-scale internetwork (IN) features are thought to be the major source of fresh magnetic flux in the quiet Sun. During its first science flight in 2009, the balloon-borne observatory Sunrise captured images of the magnetic fields in the quiet Sun at a high spatial resolution. Using these data we measure the rate at which the IN features bring magnetic flux to the solar surface. In a previous paper it was found that the lowest magnetic flux in small-scale features detected using the Sunrise observations is 9 × 10 14 Mx. This is nearly an order of magnitude smaller than the smallest fluxes of features detected in observations from Hinode satellite. In this paper, we compute the flux emergence rate (FER) by accounting for such small fluxes, which was not possible before Sunrise. By tracking the features with fluxes in the range 10 15 − 10 18 Mx, we measure an FER of 1100 Mx cm −2 day −1 . The smaller features with fluxes ≤ 10 16 Mx are found to be the dominant contributors to the solar magnetic flux. The FER found here is an order of magnitude higher than the rate from the Hinode, obtained with a similar feature tracking technique. A wider comparison with the literature shows, however, that the exact technique of determining the rate of the appearance of new flux can lead to results that differ by up to two orders of magnitude, even when applied to similar data. The causes of this discrepancy are discussed and first qualitative explanations proposed.

The scattering polarization in the solar spectrum is traditionally modeled with each spectral line treated separately, but this is generally inadequate for multiplets where J-state interference plays a significant role. Through simultaneous observations of all the 3 lines of a Cr i triplet, combined with realistic radiative transfer modeling of the data, we show that it is necessary to include J-state interference consistently when modeling lines with partially interacting fine structure components. Polarized line formation theory that includes J-state interference effects together with partial frequency redistribution for a two-term atom is used to model the observations. Collisional frequency redistribution is also accounted for. We show that the resonance polarization in the Cr i triplet is strongly affected by the partial frequency redistribution effects in the line core and near wing peaks. The Cr i triplet is quite sensitive to the temperature structure of the photospheric layers. Our complete frequency redistribution calculations in semi-empirical models of the solar atmosphere cannot reproduce the observed near wing polarization or the cross-over of the Stokes Q/I line polarization about the continuum polarization level that is due to the J-state interference. When however partial frequency redistribution is included, a good fit to these features can be achieved. Further, to obtain a good fit to the far wings, a small temperature enhancement of the FALF model in the photospheric layers is necessary.

Context. Stellar spectral synthesis is essential for various applications, ranging from determining stellar parameters to comprehensive stellar variability calculations. New observational resources as well as advanced stellar atmosphere modelling, taking three dimensional effects from radiative magnetohydrodynamics calculations into account, require a more efficient radiative transfer. Aims. For accurate, fast and flexible calculations of opacity distribution functions (ODFs), stellar atmospheres, and stellar spectra, we developed an efficient code building on the well-established ATLAS9 code. The new code also paves the way for easy and fast access to different elemental compositions in stellar calculations. Methods. For the generation of ODF tables, we further developed the well-established DFSYNTHE code by implementing additional functionality and a speed-up by employing a parallel computation scheme. In addition, the line lists used can be changed from Kurucz's recent lists. In particular, we implemented the 3 line list. Results. A new code, the Merged Parallelised Simplified ATLAS, is presented. It combines the efficient generation of ODF, atmosphere modelling, and spectral synthesis in local thermodynamic equilibrium, therefore being an all-in-one code. This all-in-one code provides more numerical functionality and is substantially faster compared to other available codes. The fully portable MPS-ATLAS code is validated against previous ATLAS9 calculations, the PHOENIX code calculations, and high-quality observations.

Context. The Hanle effect is used to determine weak turbulent magnetic fields in the solar atmosphere, usually assuming that the angular distribution is isotropic, the magnetic field strength constant, and that micro-turbulence holds, i.e. that the magnetic field correlation length is much less than a photon mean free path. Aims. To examine the sensitivity of turbulent magnetic field measurements to these assumptions, we study the dependence of Hanle effect on the magnetic field correlation length, its angular, and strength distributions. Methods. We introduce a fairly general random magnetic field model characterized by a correlation length and a magnetic field vector distribution. Micro-turbulence is recovered when the correlation length goes to zero and macro-turbulence when it goes to infinity. Radiative transfer equations are established for the calculation of the mean Stokes parameters and they are solved numerically by a polarized approximate lambda iteration method. Results. We show that optically thin spectral lines and optically very thick ones are insensitive to the correlation length of the magnetic field, while spectral lines with intermediate optical depths (around 10-100) show some sensitivity to this parameter. The result is interpreted in terms of the mean number of scattering events needed to create the surface polarization. It is shown that the single-scattering approximation holds good for thin and thick lines but may fail for lines with intermediate thickness. The dependence of the polarization on the magnetic field vector probability density function (PDF) is examined in the micro-turbulent limit. A few PDFs with different angular and strength distributions, but equal mean value of the magnetic field, are considered. It is found that the polarization is in general quite sensitive to the shape of the magnetic field strength PDF and somewhat to the angular distribution. Conclusions. The mean field derived from Hanle effect analysis of polarimetric data strongly depends on the choice of the field strength distribution used in the analysis. It is shown that micro-turbulence is in general a safe approximation.

Coherent scattering of limb-darkened radiation is responsible for the generation of the linearly polarized spectrum of the Sun (the Second Solar Spectrum). This Second Solar Spectrum is usually observed near the limb of the Sun, where the polarization amplitudes are largest. At the center of the solar disk the linear polarization is zero for an axially symmetric atmosphere. Any mechanism that breaks the axial symmetry (like the presence of an oriented magnetic field, or resolved inhomogeneities in the atmosphere) can generate a non-zero linear polarization. In the present paper we study the linear polarization near the disk center in a weakly magnetized region, where the axisymmetry is broken. We present polarimetric (I, Q/I , U/I , and V /I) observations of the Ca i 4227 Å line recorded around μ = cos θ = 0.9 (where θ is the heliocentric angle) and a modeling of these observations. The high sensitivity of the instrument (ZIMPOL-3) makes it possible to measure the weak polarimetric signals with great accuracy. The modeling of these high-quality observations requires the solution of the polarized radiative transfer equation in the presence of a magnetic field. For this we use standard one-dimensional model atmospheres. We show that the linear polarization is mainly produced by the Hanle effect (rather than by the transverse Zeeman effect), while the circular polarization is due to the longitudinal Zeeman effect. A unique determination of the full B vector may be achieved when both effects are accounted for. The field strengths required for the simultaneous fitting of Q/I, U/I, and V /I are in the range 10-50 G. The shapes and signs of the Q/I and U/I profiles are highly sensitive to the orientation of the magnetic field.