Time-dependent hydrogen ionisation in the solar chromosphere. I: Methods and first results

An approximate method for solving the rate equations for the hydrogen populations was extended and implemented in the three-dimensional radiation (magneto-)hydrodynamics code CO5BOLD. The method is based on a model atom with six energy levels and fixed radiative rates. It has been tested extensively in one-dimensional simulations. The extended method has been used to create a three-dimensional model that extends from the upper convection zone to the chromosphere. The ionisation degree of hydrogen in our time-dependent simulation is comparable to the corresponding equilibrium value up to 500 km above optical depth unity. Above this height, the non-equilibrium ionisation degree is fairly constant over time and space, and tends to be at a value set by hot propagating shock waves. The hydrogen level populations and electron density are much more constant than the corresponding values for statistical equilibrium, too. In contrast, the equilibrium ionisation degree varies by more than 20 orders of magnitude between hot, shocked regions and cool, non-shocked regions. The simulation shows for the first time in 3D that the chromospheric hydrogen ionisation degree and electron density cannot be calculated in equilibrium. Our simulation can provide realistic values of those quantities for detailed radiative transfer computations.Comment: 8 pages, 7 figure

Small-scale structure and dynamics of the lower solar atmosphere

The chromosphere of the quiet Sun is a highly intermittent and dynamic phenomenon. Three-dimensional radiation (magneto-)hydrodynamic simulations exhibit a mesh-like pattern of hot shock fronts and cool expanding post-shock regions in the sub-canopy part of the inter-network. This domain might be called "fluctosphere". The pattern is produced by propagating shock waves, which are excited at the top of the convection zone and in the photospheric overshoot layer. New high-resolution observations reveal a ubiquitous small-scale pattern of bright structures and dark regions in-between. Although it qualitatively resembles the picture seen in models, more observations - e.g. with the future ALMA - are needed for thorough comparisons with present and future models. Quantitative comparisons demand for synthetic intensity maps and spectra for the three-dimensional (magneto-)hydrodynamic simulations. The necessary radiative transfer calculations, which have to take into account deviations from local thermodynamic equilibrium, are computationally very involved so that no reliable results have been produced so far. Until this task becomes feasible, we have to rely on careful qualitative comparisons of simulations and observations. Here we discuss what effects have to be considered for such a comparison. Nevertheless we are now on the verge of assembling a comprehensive picture of the solar chromosphere in inter-network regions as dynamic interplay of shock waves and structuring and guiding magnetic fields.Comment: 8 pages, 2 figures, to appear in the proceedings of the IAU Symposium No. 247, Waves & Oscillations in the Solar Atmosphere: Heating and Magneto-Seismology (Venezuela 2007

Vortex Flows in the Solar Chromosphere -- I. Automatic detection method

Solar "magnetic tornadoes" are produced by rotating magnetic field structures that extend from the upper convection zone and the photosphere to the corona of the Sun. Recent studies show that such rotating features are an integral part of atmospheric dynamics and occur on a large range of spatial scales. A systematic statistical study of magnetic tornadoes is a necessary next step towards understanding their formation and their role for the mass and energy transport in the solar atmosphere. For this purpose, we have developed a new automatic detection method for chromospheric swirls, i.e. the observable signature of solar tornadoes or, more generally, chromospheric vortex flows and rotating motions. Unlike the previous studies that relied on visual inspections, our new method combines a line integral convolution (LIC) imaging technique and a scalar quantity which represents a vortex flow on a two-dimensional plane. We have tested two detection algorithms, based on the enhanced vorticity and vorticity strength quantities, by applying them to 3D numerical simulations of the solar atmosphere with CO5BOLD. We conclude that the vorticity strength method is superior compared to the enhanced vorticity method in all aspects. Applying the method to a numerical simulation of the solar atmosphere revealed very abundant small-scale, short-lived chromospheric vortex flows that had not been found by visual inspection before.Comment: 12 pages, 9 figures, accepted for publication in A&

Inter-network regions of the Sun at millimetre wavelengths

The continuum intensity at wavelengths around 1 mm provides an excellent way to probe the solar chromosphere. Future high-resolution millimetre arrays, such as the Atacama Large Millimeter Array (ALMA), will thus produce valuable input for the ongoing controversy on the thermal structure and the dynamics of this layer. Synthetic brightness temperature maps are calculated on basis of three-dimensional radiation (magneto-)hydrodynamic (MHD) simulations. While the millimetre continuum at 0.3mm originates mainly from the upper photosphere, the longer wavelengths considered here map the low and middle chromosphere. The effective formation height increases generally with wavelength and also from disk-centre towards the solar limb. The average intensity contribution functions are usually rather broad and in some cases they are even double-peaked as there are contributions from hot shock waves and cool post-shock regions in the model chromosphere. Taking into account the deviations from ionisation equilibrium for hydrogen gives a less strong variation of the electron density and with it of the optical depth. The result is a narrower formation height range. The average brightness temperature increases with wavelength and towards the limb. The relative contrast depends on wavelength in the same way as the average intensity but decreases towards the limb. The dependence of the brightness temperature distribution on wavelength and disk-position can be explained with the differences in formation height and the variation of temperature fluctuations with height in the model atmospheres.Comment: 15 pages, 10 figures, accepted for publication in A&A (15.05.07

Three-dimensional hydrodynamical CO5BOLD model atmospheres of red giant stars VI. First chromosphere model of a late-type giant

Although observational data unequivocally point out to the presence of chromospheres in red giant stars, no attempts have been made so far to model them using 3D hydrodynamical model atmospheres. We therefore compute an exploratory 3D hydrodynamical model atmosphere for a cool red giant in order to study the dynamical and thermodynamic properties of its chromosphere, as well as the influence of the chromosphere on its observable properties. 3D radiation hydrodynamics simulations are carried out with the CO5BOLD model atmosphere code for a star with the atmospheric parameters (Teff=4010 K, log g=1.5, [M/H]=0.0), which are similar to those of the K-type giant star Aldebaran (alpha Tau). ... we compute the emergent continuum intensity maps at different wavelengths, spectral line profiles of Ca II K, the Ca II infrared triplet line at 854.2nm, and H alpha, as well as the spectral energy distribution (SED) of the emergent radiative flux. The initial model quickly develops a dynamical chromosphere characterised by propagating and interacting shock waves. The peak temperatures in the chromospheric shock fronts reach values on the order of up to 5000 K although the shock fronts remain quite narrow. Like for the Sun, the gas temperature distribution in the upper layers is composed of a cool component due to adiabatic cooling in the expanding post-shock regions and a hot component due to shock waves. For this red giant model, the hot component is a rather flat high-temperature tail, which nevertheless affects the resulting average temperatures significantly. The simulations show that the atmospheres of red giant stars are dynamic and intermittent. Consequently, many observable properties cannot be reproduced with one-dimensional static models but demand for advanced 3D HD modelling. Furthermore, including a chromosphere in the models might produce significant contributions to the emergent UV flux.Comment: 14 pages, 8 figures, A&A (2017, accepted