Linear wavelength correlation matrices of photospheric and chromospheric spectral lines

Abstract

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.

The energy of waves in the photosphere and lower chromosphere

“…Overview maps of these observations can be found in Fig. 16 in Beck & Rammacher (2010). One of the AR maps is described in detail in Bethge et al (2012).…”

“…For the analysis of Ca ii H spectra, one therefore has to rely on methods that are (hopefully) insensitive to NLTE effects, using observed quantities that are as direct as possible to derive solar atmospheric properties (e.g., Beck & Rammacher 2010). In the first two papers of this series (Beck et al 2009, 2012, BE09 andBE12 in the following), we investigated the statistics of velocity and intensity oscillations in Ca ii spectra, using only Ca ii H for the first study, and then added Ca ii IR at 854 nm for the latter thanks to new observations covering both lines simultaneously.…”

The energy of waves in the photosphere and lower chromosphere

“…The other three data sets are large-area maps of the active region NOAA 10978 (cf. Beck & Rammacher 2010;Bethge et al 2012). The parameters most relevant in the present context are the slit width of 0.…”

“…Beck & Rammacher 2010) between intensity vs. wavelength and temperature vs. log τ. Figure 4 shows the result for the large-area scan on the disc centre.…”

Application of speckle and (multi-object) multi-frame blind deconvolution techniques on imaging and imaging spectropolarimetric data

“…The MHD simulation was performed with the CO 5 BOLD code (Freytag et al 2002) and is described in more detail in Schaffenberger et al (2005Schaffenberger et al ( , 2006. For one simulation snap shot, spectra of the two Fe i lines at 630 nm were synthesized with a spectral sampling of 2 pm per pixel (for more details see Steiner et al 2008;Beck & Rammacher 2010). Figure 12 later on shows maps of the continuum intensity I c for the three additional data sets.…”