Time‐dependent Ionization in Dynamic Solar and Stellar Atmospheres. I. Methods

Rammacher, W.; Ulmschneider, P.

doi:10.1086/374661

Cited by 34 publications

(47 citation statements)

References 31 publications

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“…The solar chromospheric models based on acoustic waves or longitudinal flux-tube waves are calculated using the numerical code by Rammacher & Ulmschneider (2003) and . This code allows one to compute one-dimensional time-dependent wave propagation in solar and stellar atmospheres, while incorporating the treatment of hydrogen ionization through solving the time-dependent statistical rate equations (see also Carlsson & Stein 1992, 1995 for another version of that method).…”

Section: (Magneto-)hydrodynamic Computer Codementioning

confidence: 99%

“…These models take into account the generation, propagation, and dissipation of the waves, as well as the description of emergent emission. Recent models for the Sun have been given by Rammacher & Ulmschneider (2003), Bogdan et al (2003), and Wedemeyer et al (2004). Simulations of chromospheric heating for stars other than the Sun by our group include models by Cuntz et al (1999), Fawzy et al (2002), and Rammacher & Cuntz (2003).…”

Section: Introductionmentioning

confidence: 99%

“…These fluctuations are due to shock heating and are particularly pronounced if the ionization of hydrogen is described in a self-consistent, time-dependent manner (e.g., Carlsson & Stein 1994, 1995Rammacher & Ulmschneider 2003;, as in this case very high temperature jumps occur immediately behind strong shocks. Other types of models used to derive time-averaged temperatures in the solar chromosphere are semi-empirical models, which interpret spectral information ranging from UV to the optical and infrared regimes.…”

Section: Introductionmentioning

confidence: 99%

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

Rammacher¹,

Cuntz

2005

A&A

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Abstract.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.

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Section: (Magneto-)hydrodynamic Computer Codementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Rammacher¹,

Cuntz

2005

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“…For magnesium and calcium it is more important to include PRD and have a large temperature range than to include effects of non-equilibrium ionization and we choose the Bifrost 2D simulations. Non-equilibrium ionization is not important for calcium (Wedemeyer-Böhm & Carlsson 2011) while Rammacher & Ulmschneider (2003) and test-calculations with RADYN indicate that ionization/recombination times are as long as 100−500 s for magnesium and therefore of importance for the ionization balance. However, we will see that magnesium is almost exclusively in the form of Mg ii in the temperature range where magnesium is important for the cooling/heating of the chromosphere and the neglect of non-equilibrium ionization is therefore not important for the results.…”

Section: Introductionmentioning

confidence: 98%

Approximations for radiative cooling and heating in the solar chromosphere

Carlsson

Leenaarts

2012

A&A

185

163

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Context. The radiative energy balance in the solar chromosphere is dominated by strong spectral lines that are formed out of LTE. It is computationally prohibitive to solve the full equations of radiative transfer and statistical equilibrium in 3D time dependent MHD simulations. Aims. We look for simple recipes to compute the radiative energy balance in the dominant lines under solar chromospheric conditions. Methods. We use detailed calculations in time-dependent and 2D MHD snapshots to derive empirical formulae for the radiative cooling and heating. Results. The radiative cooling in neutral hydrogen lines and the Lyman continuum, the H and K and intrared triplet lines of singly ionized calcium and the h and k lines of singly ionized magnesium can be written as a product of an optically thin emission (dependent on temperature), an escape probability (dependent on column mass) and an ionization fraction (dependent on temperature). In the cool pockets of the chromosphere the same transitions contribute to the heating of the gas and similar formulae can be derived for these processes. We finally derive a simple recipe for the radiative heating of the chromosphere from incoming coronal radiation. We compare our recipes with the detailed results and comment on the accuracy and applicability of the recipes.

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“…As a third numerical experiment, we used spectra generated from 1-D NLTE simulations done with the WAVE code (Rammacher & Ulmschneider 2003). The simulations were performed similar to Carlsson & Stein (1997) with a photospheric piston that excites acoustic waves of various types.…”

Section: Nlte 1-d Simulationsmentioning

confidence: 99%

Linear wavelength correlation matrices of photospheric and chromospheric spectral lines

Beck¹,

Rammacher²

2010

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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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Time‐dependent Ionization in Dynamic Solar and Stellar Atmospheres. I. Methods

Cited by 34 publications

References 31 publications

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

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

Approximations for radiative cooling and heating in the solar chromosphere

Linear wavelength correlation matrices of photospheric and chromospheric spectral lines

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