Solar Magnetic Flux Tube Simulations with Time-Dependent Ionization

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 1-D wave simulations for the solar chromosphere by studying tubes of different spreading as function of height aimed at representing tubes in environments of different magnetic filling factors. Multi-level 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.Comment: 13 pages, 9 figures, 4 tables; Mon. Not. R. Astron. Soc.; in pres

Reversal-free CaIIH profiles: a challenge for solar chromosphere modeling in quiet inter-network

We study chromospheric emission to understand the temperature stratification in the solar chromosphere. We observed the intensity profile of the CaIIH line in a quiet Sun region close to the disk center at the German Vacuum Tower Telescope. We analyze over 10^5 line profiles from inter-network regions. For comparison with the observed profiles, we synthesize spectra for a variety of model atmospheres with a non local thermodynamic equilibrium (NLTE) radiative transfer code. A fraction of about 25% of the observed CaIIH line profiles do not show a measurable emission peak in H_{2v} and H_{2r} wavelength bands (reversal-free). All of the chosen model atmospheres with a temperature rise fail to reproduce such profiles. On the other hand, the synthetic calcium profile of a model atmosphere that has a monotonic decline of the temperature with height shows a reversal-free profile that has much lower intensities than any observed line profile. The observed reversal-free profiles indicate the existence of cool patches in the interior of chromospheric network cells, at least for short time intervals. Our finding is not only in conflict with a full-time hot chromosphere, but also with a very cool chromosphere as found in some dynamic simulations.Comment: 8 pages, accepted in A&

Multiwavelength studies of MHD waves in the solar chromosphere: An overview of recent results

The chromosphere is a thin layer of the solar atmosphere that bridges the relatively cool photosphere and the intensely heated transition region and corona. Compressible and incompressible waves propagating through the chromosphere can supply significant amounts of energy to the interface region and corona. In recent years an abundance of high-resolution observations from state-of-the-art facilities have provided new and exciting ways of disentangling the characteristics of oscillatory phenomena propagating through the dynamic chromosphere. Coupled with rapid advancements in magnetohydrodynamic wave theory, we are now in an ideal position to thoroughly investigate the role waves play in supplying energy to sustain chromospheric and coronal heating. Here, we review the recent progress made in characterising, categorising and interpreting oscillations manifesting in the solar chromosphere, with an impetus placed on their intrinsic energetics.Comment: 48 pages, 25 figures, accepted into Space Science Review

Definition and significance of average temperatures in time-dependent solar chromosphere models

We assess different types of average temperatures in time-dependent solar chromosphere models. They include the conventional definition of mean and median temperature, and a formal definition related to the model-dependent hydrogen ionization degree, referred to as ionization temperature. It is found that the latter is always higher than the mean and median temperatures, except in the photosphere, and that the mean temperatures are always higher than the median temperatures, especially in models with frequency spectra. The most dramatic differences are attained in the topmost portion of one of our models with the ionization temperatures up to a factor 150 higher than the mean and median temperatures. The differences between the mean, median, and ionization temperatures are a direct consequence of nonlinearities (“spikyness”) of the temperatures in the models mostly due to strong shocks. The main results hold for both acoustic and magnetic models despite significant differences in the initial wave energy fluxes, densities, and geometrical settings

Linear wavelength correlation matrices of photospheric and chromospheric spectral lines

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 \ion{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 \ion{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 signature of chromospheric heating in Ca II H spectra

Context.The heating process that balances the solar chromospheric energy losses has not yet been determined. Conflicting views exist on the source of the energy and the influence of photospheric magnetic fields on chromospheric heating. Aims.We analyze a 1-h time series of cospatial \ion{Ca}{ii} H intensity spectra and photospheric polarimetric spectra around 630 nm to derive the signature of the chromospheric heating process in the spectra and to investigate its relation to photospheric magnetic fields. The data were taken in a quiet Sun area on disc center without strong magnetic activity. Methods.We have derived several characteristic quantities of \ion{Ca}{ii} H to define the chromospheric atmosphere properties. We study the power of the Fourier transform at different wavelengths and the phase relations between them. We perform local thermodynamic equilibrium (LTE) inversions of the spectropolarimetric data to obtain the photospheric magnetic field, once including the Ca intensity spectra. Results.We find that the emission in the \ion{Ca}{ii} H line core at locations without detectable photospheric polarization signal is due to waves that propagate in around 100 s from low forming continuum layers in the line wing up to the line core. The phase differences of intensity oscillations at different wavelengths indicate standing waves for $\nu <$ 2 mHz and propagating waves for higher frequencies. The waves steepen into shocks in the chromosphere. On average, shocks are both preceded and followed by intensity reductions. In field-free regions, the profiles show emission about half of the time. The correlation between wavelengths and the decorrelation time is significantly higher in the presence of magnetic fields than for field-free areas. The average \ion{Ca}{ii} H profile in the presence of magnetic fields contains emission features symmetric to the line core and an asymmetric contribution, where mainly the blue H2V emission peak is increased (shock signature). Conclusions.We find that acoustic waves steepening into shocks are responsible for the emission in the \ion{Ca}{ii} H line core for locations without photospheric magnetic fields. We suggest using wavelengths in the line wing of \ion{Ca}{ii} H, where LTE still applies, to compare theoretical heating models with observations