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Aims. We investigate the relationship between the photospheric magnetic field and the emission of the mid chromosphere of the Sun. Methods. We simultaneously observed the Stokes parameters of the photospheric iron line pair at 630.2 nm and the intensity profile of the chromospheric Ca  H line at 396.8 nm in a quiet Sun region at a heliocentric angle of 53• . Various line parameters have been deduced from the Ca  H line profile. The photospheric magnetic field vector has been reconstructed from an inversion of the measured Stokes profiles. After alignment of the Ca and Fe maps, a common mask has been created to define network and inter-network regions. We perform a statistical analysis of network and inter-network properties. The H-index is the integrated emission in a 0.1 nm band around the Ca core. We separate a non-magnetically, H non , and a magnetically, H mag , heated component from a non-heated component, H co in the H-index. Results. The average network and inter-network H-indices are equal to 12 and 10 pm, respectively. The emission in the network is correlated with the magnetic flux density, approaching a value of H ≈ 10 pm for vanishing flux. The inter-network magnetic field is dominated by weak field strengths with values down to 200 G and has a mean absolute flux density of about 11 Mx cm −2 . Conclusions. We find that a dominant fraction of the calcium emission caused by the heated atmosphere in the magnetic network has non-magnetic origin (H mag ≈ 2 pm, H non ≈ 3 pm). Considering the effect of straylight, the contribution from an atmosphere with no temperature rise to the H-index (H co ≈ 6 pm) is about half of the observed H-index in the inter-network. The H-index in the inter-network is not correlated to any property of the photospheric magnetic field, suggesting that magnetic flux concentrations have a negligible role in the chromospheric heating in this region. The height range of the thermal coupling between the photosphere and low/mid chromosphere increases in presence of magnetic field. In addition, we demonstrate that a poor signal-to-noise level in the Stokes profiles leads to a significant over-estimation of the magnetic field strength.

Abstract. Realistic simulations of solar (magneto-)convection require an accurate treatment of the non-grey character of the radiative energy transport. Owing to the large number of spectral lines in the solar atmosphere, statistical representations of the line opacities have to be used in order to keep the problem numerically tractable. We consider two statistical approaches, the opacity distribution function (ODF) concept and the multigroup (or opacity binning) method and provide a quantitative assessment of the errors that arise from the application of these methods in the context of 2D/3D simulations. In a first step, the ODF-and multigroup methods are applied to a 1D model-atmosphere and the resulting radiative heating rates are compared. A number of 4−6 frequency bins is found to warrant a satisfactory modeling of the radiative energy exchange. Further tests in 2D model-atmospheres show the applicability of the multigroup method in realistic situations and underline the importance of a non-grey treatment. Furthermore, we address the question of an appropriate opacity average in multigroup calculations and discuss the significance of velocity gradients for the radiative heating rates.

Abstract. Photospheric magnetic elements are most conspicuously visible in high-resolution G-band filtergrams. We show that their enhanced contrast in the G-band is due to a reduction of the CH abundance by dissociation in the deep photospheric layers of the flux tube, where it is hotter than in the surrounding atmosphere. As a consequence, the CH-lines weaken, allowing more of the continuum to "shine" through the forest of G-band CH-lines. We suggest that other molecular bands or atomic lines may exhibit a similar behaviour.

Aims. We study chromospheric emission to understand the temperature stratification in the solar chromosphere.Methods. We observed the intensity profile of the Ca ii H line in a quiet Sun region close to the disk center at the German Vacuum Tower Telescope. We analyze over 10 5 line profiles from inter-network regions. For comparison with the observed profiles, we synthesize spectra for a variety of model atmospheres with a non local thermodynamic equilibrium (NLTE) radiative transfer code.Results. A fraction of about 25% of the observed Ca ii H line profiles do not show a measurable emission peak in H 2v and H 2r wavelength bands (reversal-free). All of the chosen model atmospheres with a temperature rise fail to reproduce such profiles. On the other hand, the synthetic calcium profile of a model atmosphere that has a monotonic decline of the temperature with height shows a reversal-free profile that has much lower intensities than any observed line profile. Conclusions. The observed reversal-free profiles indicate the existence of cool patches in the interior of chromospheric network cells, at least for short time intervals. Our finding is not only in conflict with a full-time hot chromosphere, but also with a very cool chromosphere as found in some dynamic simulations.