We investigate the linear correlation coefficient between the intensities at different wavelengths in photospheric and chromospheric spectral lines. Waves that propagate vertically through the stratified solar atmosphere affect different wavelengths at different times. This leads to a characteristic pattern of (non-)coherence of the intensity at various wavelengths. We derived the correlation matrices for several photospheric and chromospheric spectral lines from observations. For comparison with the observations, we calculate correlation matrices for spectra from LTE modeling approaches, 1-D NLTE simulations, and a 3-D MHD simulation run. We apply the correlation method also to temperature maps at different optical depth layers. 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. All chromospheric spectral lines show a more complex pattern. In the case of Ca II H, the 1-D NLTE simulations of monochromatic waves produce a correlation matrix that qualitatively matches to the observations. The photospheric signature is well reproduced in the matrix derived from the 3-D MHD simulation. 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.
In the present work we expand the study of time-dependent ionization previously identified to be of pivotal importance for acoustic waves in solar magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known to be an important heating agent of solar magnetic regions. Our models also consider new results of wave energy generation as well as an updated determination of the mixing length of convection now identified as 1.8 scale heights in the upper solar convective layers. We present 1D wave simulations for the solar chromosphere by studying tubes of different spreading as a function of height aimed at representing tubes in environments of different magnetic filling factors. Multilevel radiative transfer has been applied to correctly represent the total chromospheric emission function. The effects of time-dependent ionization are significant in all models studied. They are most pronounced behind strong shocks and in low-density regions, i.e. the middle and high chromosphere. Concerning our models of different tube spreading, we attained pronounced differences between the various types of models, which were largely initiated by different degrees of dilution of the wave energy flux as well as the density structure partially shaped by strong shocks, if existing. Models showing a quasi-steady rise of temperature with height are obtained via monochromatic waves akin to previous acoustic simulations. However, longitudinal flux tube waves are identified as insufficient to heat the solar transition region and corona in agreement with previous studies.
A fast and reasonably accurate method for calculating the total radiative losses by Ca ii and Mg ii ions for time-dependent chromospheric wave calculations has been developed.The method is based on a two-level atom procedure with pseudo-partial frequency redistribution ( pseudo-PRD).The speed of the method is due to scaling of the total losses from single-line results.Acceleration of computation speeds by factors of roughly 10 2 -10 3 can be achieved.The method is tested against the results from a modified version of the multilevel atom code MULTI.
It is widely believed that the heating of the chromosphere in quiet-Sun internetwork regions is provided by dissipation of acoustic waves that are excited by the convective motions close to the top of the convection zone and in the photospheric overshoot layer. This view lately became challenged by observations suggesting that the acoustic energy flux into the chromosphere is too low, by a factor of at least ten. Based on a comparison of TRACE data with synthetic image sequences for a three-dimensional simulation extending from the top layers of the convection zone to the middle chromosphere, we come to the contradicting conclusion that the acoustic flux in the model provides sufficient energy for heating the solar chromosphere of internetwork regions. The role of a weak magnetic field and associated electric current sheets is also discussed.
It is widely believed that the heating of the chromosphere in quiet-Sun internetwork regions is provided by dissipation of acoustic waves that are excited by the convective motions close to the top of the convection zone and in the photospheric overshoot layer. This view lately became challenged by observations suggesting that the acoustic energy flux into the chromosphere is too low, by a factor of at least ten. Based on a comparison of TRACE data with synthetic image sequences for a three-dimensional simulation extending from the top layers of the convection zone to the middle chromosphere, we come to the contradicting conclusion that the acoustic flux in the model provides sufficient energy for heating the solar chromosphere of internetwork regions. The role of a weak magnetic field and associated electric current sheets is also discussed.