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Most static 1D atmosphere models in the quiet Sun predict a rise of the gastemperature at chromospheric layers, but numerical simulations only yield anincrease in the brightness temperature. We investigate the thermal structure inthe solar chromosphere as derived from an LTE inversion of Ca II H spectra inQS and active regions. We investigate the temperature stratifications ondifferences between magnetic and field-free regions in the QS, and between QSand ARs. We determine the energy content of individual calcium bright grains(BGs). The rms temperature fluctuations are below 100 K in the photosphere and200-300 K in the chromosphere. The average temperature stratification in the QSdoes not exhibit a clear chromospheric temperature rise, opposite to the ARcase. We find an energy content of about 7*10E18 J for BGs that repeat with acadence of about 160 secs. The precursors of BGs have a vertical extent ofabout 200 km and a horizontal extent of about 1 Mm. The comparison of observedwith synthetic NLTE profiles confirms that the solar chromosphere in the QSoscillates between an atmosphere in radiative equilibrium and one with amoderate chromospheric temperature rise. Two-dimensional x-z temperature mapsexhibit nearly horizontal canopy-like structures with a few Mm extent aroundphotospheric magnetic field concentrations at a height of about 600 km. Thelarge difference between QS regions and ARs, and the better match of AR andnon-LTE reference spectra suggest that magnetic heating processes are moreimportant than commonly assumed. The temperature fluctuations in QS derived bythe LTE inversion do not suffice on average to maintain a stationarychromospheric temperature rise. The spatially and vertically resolvedinformation on the temperature structure allows one to investigate in detailthe topology and evolution of the thermal structure in the lower solaratmosphere.

The energy of waves in the photosphere and lower chromosphere: IV. Inversion results of Ca II H spectra