Context. Acoustic waves are one of the primary suspects besides magnetic fields for the chromospheric heating process to temperatures above radiative equilibrium (RE). Aims. We derived the mechanical wave energy as seen in line-core velocities on disc centre to obtain a measure of mechanical energy flux with height for a comparison with the energy requirements in a semi-empirical atmosphere model, the Harvard-Smithsonian reference atmosphere (HSRA). Methods. We analyzed a 1-hour time series and a large-area map of Ca II H spectra on the traces of propagating waves. We analyzed the velocity statistics of several spectral lines in the wing of Ca II H, and the line-core velocity of Ca II H. We converted the velocity amplitudes into volume (∝ρv 2 ) and mass energy densities (∝v 2 ). For comparison, we used the increase of internal energy (∝RρΔT ) necessary to lift a RE atmosphere to the HSRA temperature stratification. Results. We find that the velocity amplitude grows in agreement with linear wave theory and thus slower with height than predicted from energy conservation. The mechanical energy of the waves above around z ∼ 500 km is insufficient to maintain on a longterm average the chromospheric temperature rise in the semi-empirical HSRA model. The intensity variations of the Ca line core (z ∼ 1000 km) can, however, be traced back to the velocity variations of the lowermost forming spectral line considered (z ∼ 250 km). Conclusions. The chromospheric intensity, and hence, (radiation) temperature variations are seen to be induced by passing waves originating in the photosphere. The wave energy is found to be insufficient to maintain the temperature stratification of the semiempirical HSRA model above 500 km. We will in a following paper of this series investigate the energy contained in the intensity variations to see if the semi-empirical model is appropriate for the spectra.

Context. Ground-based imaging and imaging spectropolarimetric data are often subjected to post-facto reconstruction techniques to improve the spatial resolution. Aims. We test the effects of reconstruction techniques on two-dimensional data to determine the best approach to improve our data. Methods. We obtained an 1-h time-series of spectropolarimetric data in the Fe i line at 630.25 nm with the Göttingen Fabry-Pérot Interferometer (FPI) that are accompanied by imaging data in the blue continuum at 431.3 nm and Ca ii H at 396.85 nm. We apply both speckle and (multi-object) multi-frame blind deconvolution ((MO)MFBD) techniques. We use the "Göttingen" speckle and speckle deconvolution codes and the MOMFBD code in the implementation of Van Noort et al. (2005). We compare the resulting spatial resolution and investigate the impact of the image reconstruction on spectral characteristics of the Göttingen FPI data. Results. The speckle reconstruction and MFBD perform similar for our imaging data with nearly identical intensity contrasts. MFBD provides a better and more homogeneous spatial resolution at the shortest wavelength when applied to a series of image bursts. The MOMFBD and speckle deconvolution of the intensity spectra lead to similar results, but our choice of settings for the MOMFBD yields an intensity contrast smaller by about 2% at a comparable spatial resolution. None of the reconstruction techniques introduces significant artifacts in the intensity spectra. The speckle deconvolution (MOMFBD) has a rms noise in Stokes V/I of 0.32% (0.20%). The deconvolved spectra thus require a high significance threshold of about 1.0% to separate noise peaks from true signal. A comparison to spectra with a significantly higher signal-to-noise (S/N) ratio and to spectra from a magneto-hydrodynamical simulation reveals that the Göttingen FPI can only detect about 30% of the polarization signal present in quiet Sun areas. The distribution of NCP values for the speckle-deconvolved data matches that of observations with higher S/N better than MOMFBD, but shows seemingly artificially sharp boundaries and unexpected changes of the sign. Conclusions. For our imaging data, both MFBD and speckle reconstruction are equivalent, with a slightly better and more stable performance of MFBD. For the spectropolarimetric data, the higher intensity contrast of the speckle deconvolution is balanced by the smaller amplification of the noise level in the MOMFBD at a comparable spatial resolution. The noise level prevents the detection of weak and diffuse magnetic fields. Future efforts should be directed to improve the S/N of the Göttingen FPI spectra for spectropolarimetric observations to lower the final significance thresholds.

Context. The energy source powering the solar chromosphere is still undetermined, but leaves its traces in observed intensities. Aims. We investigate the statistics of the intensity distributions as a function of the wavelength for Ca ii H and the Ca ii IR line at 854.2 nm to estimate the energy content in the observed intensity fluctuations. Methods. We derived the intensity variations at different heights of the solar atmosphere, as traced by the line wings and line cores of the two spectral lines. We converted the observed intensities to absolute energy units employing reference profiles calculated in non-local thermal equilibrium (NLTE). We also converted the intensity fluctuations to corresponding brightness temperatures assuming LTE. Results. The root-mean-square (rms) fluctuations of the emitted intensity are about 0.6 (1.2) W m −2 ster −1 pm −1 near the core of the Ca ii IR line at 854.2 nm (Ca ii H), corresponding to relative intensity fluctuations of about 20% (30%). For the line wing, we find rms values of about 0.3 W m −2 ster −1 pm −1 for both lines, corresponding to relative fluctuations below 5%. The relative rms values show a local minimum for wavelengths forming at a height of about 130 km, but otherwise increase smoothly from the wing to the core, i.e., from photosphere to chromosphere. The corresponding rms brightness temperature fluctuations are below 100 K for the photosphere and up to 500 K in the chromosphere. The skewness of the intensity distributions is close to zero in the outer line wing and positive throughout the rest of the line spectrum, owing to the frequent occurrence of high-intensity events. The skewness shows a pronounced local maximum at locations with photospheric magnetic fields for wavelengths in-between those of the line wing and the line core (z ≈ 150−300 km), and a global maximum at the very core (z ≈ 1000 km) for both magnetic and field-free locations. Conclusions. The energy content of the intensity fluctuations is insufficient to create a chromospheric temperature rise that would be similar to the one in most reference models of the solar atmosphere. The increase in the rms fluctuations with height indicates the presence of upwardly propagating acoustic waves of increasing oscillation amplitude. The intensity and temperature variations indicate that there is a clear increase in dynamical activity from photosphere towards the chromosphere, but the variations fall short of the magnitude predicted by fully dynamical chromospheric models by a factor of about five. The enhanced skewness between the photosphere and lower solar chromosphere at magnetic locations is indicative of a mechanism that acts solely on magnetized plasma.

Context. The penumbra of sunspots has a complex magnetic field topology whose three-dimensional organization remains unclear after more than a century of investigation. Aims. I derive a geometrical model of the penumbral magnetic field topology from an uncombed inversion setup designed to reproduce the net circular polarization (NCP) of simultaneous spectra in near-infrared (IR; 1.56 μm) and visible (VIS; 630 nm) spectral lines. Methods. I inverted the co-spatial spectra of five photospheric lines with a model that mimicked vertically interlaced magnetic fields with two distinct components, labeled background field and flow channels because of their characteristic properties (flow velocity, field inclination). The flow channels were modeled as a perturbation of the constant background field with a Gaussian shape using the SIRGAUS code. The location and extension of the Gaussian perturbation in the optical depth scale retrieved by the inversion code were then converted to a geometrical height scale. By estimating the geometrical size of the flow channels, I investigated the relative amount of magnetic flux in the flow channels and the background field atmosphere.Results. The uncombed model is able to reproduce the NCP well on the limb side of the spot and less successfully on the center side; the VIS lines are better reproduced than the near-IR lines. I find that the Evershed flow happens along nearly horizontal field lines close to the solar surface given by optical depth unity. The magnetic flux that is related to the flow channels constitutes about 20−50% of the total magnetic flux in the penumbra. Conclusions. The gradients that can be produced by a Gaussian perturbation are too small for a perfect reproduction of the NCP in the IR lines with their small formation height range, where a step function seems to be required. Two peculiarities of the observed NCP, a sign change in the NCP of the VIS lines on the center side and a ring structure around the umbra with opposite signs of the NCP in the Ti i line at 630.37 nm and the Fe i line at 1565.2 nm, deserve closer attention in future modeling attempts. The large fraction of magnetic flux related to the flow channel component could suffice to replenish the penumbral radiative losses in the flux tube picture.

Aims. We present constraints on the thermodynamical structure of the chromosphere from ground-based observations of the Ca ii H line profile near and off the solar limb. Methods. We obtained a slit-spectrograph data set of the Ca ii H line with a high signal-to-noise ratio in a field of view extending 20 across the limb. We analyzed the spectra for the characteristic properties of average and individual off-limb spectra. We used various tracers of the Doppler shifts, such as the location of the absorption core, the ratio of the two emission peaks H 2V and H 2R , and intensity images at a fixed wavelength. Results. The average off-limb profiles show a smooth variation with increasing limb distance. The line width increases up to a height of about 2 Mm above the limb. The profile shape is fairly symmetric with nearly identical H 2V and H 2R intensities; at a height of 5 Mm, it changes into a single Gaussian without emission peaks. We find that all off-limb spectra show large Doppler shifts that fluctuate on the smallest resolved spatial scales. The variation is more prominent in cuts parallel to the solar limb than on those perpendicular to it. As far as individual structures can be unequivocally identified at our spatial resolution, we find a specific relation between intensity enhancements and Doppler shifts: elongated brightenings are often flanked all along their extension by velocities in opposite directions. Conclusions. The average off-limb spectra of Ca ii H present a good opportunity to test static chromospheric atmosphere models because they lack the photospheric contribution that is present in disk-center spectra. We suggest that the observed relation between intensity enhancements and Doppler shifts could be caused by waves propagating along the surfaces of flux tubes: an intrinsic twist of the flux tubes or a wave propagation inclined to the tube axis would cause a helical shape of the Doppler excursions, visible as opposite velocity at the sides of the flux tube. Spectroscopic data allow one to distinguish this from a sausage-mode oscillation where the maximum Doppler shift and the tube axis would coincide.

Context. The process that heats the solar chromosphere is a difficult target for observational studies because the assumption of local thermal equilibrium (LTE) is not valid in the upper solar atmosphere, which complicates the analysis of spectra. Aims. We investigate the linear correlation coefficient between the intensities at different wavelengths in photospheric and chromospheric spectral lines because the correlation can be determined directly for any spectra from observations or modeling. Waves which propagate vertically through the stratified solar atmosphere affect different wavelengths at different times when the contribution functions for each wavelength peak in different layers. This leads to a characteristic pattern of (non-)coherence of the intensity at various wavelengths with respect to each other which carries information on the physical processes. Methods. We derived the correlation matrices for several photospheric and chromospheric spectral lines from observations. We separated locations with a significant photospheric polarization signal and thus magnetic fields from those without a polarization signal. For comparison with the observations, we calculated correlation matrices for spectra from simplified LTE modeling approaches, 1-D NLTE simulations, and a 3-D MHD simulation run. We applied the correlation method also to temperature maps at different optical depth layers derived from a LTE inversion of Ca ii H spectra.Results. We find that all photospheric spectral lines show a similar pattern: a pronounced asymmetry of the correlation between line core and red or blue wing. The pattern cannot be reproduced with a simulation of the granulation pattern, but with waves that travel upwards through the formation heights of the lines. The correct asymmetry between red and blue wing only appears when a temperature enhancement occurs simultaneously with a downflow velocity in the wave simulation. All chromospheric spectral lines show a more complex pattern. The 1-D NLTE simulations of monochromatic waves produce a correlation matrix that qualitatively matches the observations near the very core of the Ca ii H line. The photospheric signature is well reproduced in the correlation matrix derived from the 3-D MHD simulation. Conclusions. The correlation matrices of observed photospheric and chromospheric spectral lines are highly structured with characteristic and different patterns in every spectral line. The comparison with matrices derived from simulations and simple modeling suggests that the main driver of the detected patterns are upwards propagating waves. Application of the correlation method to 3-D temperature cubes seems to be a promising tool for a detailed comparison of simulation results and observations in future studies.

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