Relation between photospheric magnetic field and chromospheric emission

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 II H line at 396.8 nm in a quiet Sun region at a heliocentric angle of 53 degrees. Various line parameters have been deduced from the Ca II 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 approximate to 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 approximate to 2 pm, H-non approximate to 3 pm). Considering the effect of straylight, the contribution from an atmosphere with no temperature rise to the H-index ( H-co approximate to 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.