Numerical simulations of the quiet chromosphere

Numerical simulations of the solar chromosphere have become increasingly realistic over the past 5 years. However, many observed chromospheric structures and behavior are not reproduced. Current models do not show fibrils in Ca II 8542, and neither reproduce the Ca II 8542 bisector. The emergent H-alpha line core intensity computed from the models show granulation instead of chromospheric shocks or fibrils. I discuss these deficiencies and speculate about what physics should be included to alleviate these shortcomings.Comment: 6 pages, 2 Figures. To appear in Proceedings of the 25th NSO Workshop: Chromospheric Structure and Dynamic

Numerical non-LTE 3D radiative transfer using a multigrid method

3D non-LTE radiative transfer problems are computationally demanding, and this sets limits on the size of the problems that can be solved. So far Multilevel Accelerated Lambda Iteration (MALI) has been to the method of choice to perform high-resolution computations in multidimensional problems. The disadvantage of MALI is that its computing time scales as $\mathcal{O}(n^2)$, with $n$ the number of grid points. When the grid gets finer, the computational cost increases quadratically. We aim to develop a 3D non-LTE radiative transfer code that is more efficient than MALI. We implement a non-linear multigrid, fast approximation storage scheme, into the existing Multi3D radiative transfer code. We verify our multigrid implementation by comparing with MALI computations. We show that multigrid can be employed in realistic problems with snapshots from 3D radiative-MHD simulations as input atmospheres. With multigrid, we obtain a factor 3.3-4.5 speedup compared to MALI. With full-multigrid the speed-up increases to a factor 6. The speedup is expected to increase for input atmospheres with more grid points and finer grid spacing. Solving 3D non-LTE radiative transfer problems using non-linear multigrid methods can be applied to realistic atmospheres with a substantial speed-up.Comment: Accepted for publication by A&

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

Solar off-limb emission of the OI 7772 \AA\ line

The aim of this paper is to understand the formation of the OI line at 7772 \AA\ in the solar chromosphere. We used SST/CRISP observations to observe OI 7772 \AA\ in several places around the solar limb. We compared the observations with synthetic spectra calculated with the RH code in the one-dimension spherical geometry mode. New accurate hydrogen collisional rates were included for the RH calculations. The observations reveal a dark gap in the lower chromosphere, which is caused by variations in the line opacity as shown by our models. The lower level of the 7772 \AA\ transition is populated by a downward cascade from the continuum. We study the effect of Lyman-$\beta$ pumping and hydrogen collisions between the triplet and quintet system in OI. Both have a small but non-negligible influence on the line intensity.Comment: 9 pages, 12 figures, Accepted for publication in A&

Detailed and simplified non-equilibrium helium ionization in the solar atmosphere

Helium ionization plays an important role in the energy balance of the upper chromosphere and transition region. Helium spectral lines are also often used as diagnostics of these regions. We carry out 1D radiation-hydrodynamics simulations of the solar atmosphere and find that the helium ionization is mostly set by photoionization and direct collisional ionization, counteracted by radiative recombination cascades. By introducing an additional recombination rate mimicking the recombination cascades, we construct a simplified 3 level helium model atom consisting of only the ground states. This model atom is suitable for modeling non-equilibrium helium ionization in 3D numerical models. We perform a brief investigation of the formation of the He I 10830 and He II 304 spectral lines. Both lines show non-equilibrium features that are not recovered with statistical equilibrium models, and caution should therefore be exercised when such models are used as a basis in the interpretation of observations.Comment: 11 pages, 9 figures. Accepted for publication in Ap

What do iris observations of Mg II k tell us about the solar plage chromosphere?

We analyze observations from the Interface Region Imaging Spectrograph of the Mg II k line, the Mg II UV subordinate lines, and the O I 135.6 nm line to better understand the solar plage chromosphere. We also make comparisons with observations from the Swedish 1 m Solar Telescope of the H{\alpha} line, the Ca II 8542 line, and Solar Dynamics Observatory/Atmospheric Imaging Assembly observations of the coronal 19.3 nm line. To understand the observed Mg II profiles, we compare these observations to the results of numerical experiments. The single-peaked or flat-topped Mg II k profiles found in plage imply a transition region at a high column mass and a hot and dense chromosphere of about 6500 K. This scenario is supported by the observed large-scale correlation between moss brightness and filled-in profiles with very little or absent self-reversal. The large wing width found in plage also implies a hot and dense chromosphere with a steep chromospheric temperature rise. The absence of emission in the Mg II subordinate lines constrain the chromospheric temperature and the height of the temperature rise while the width of the O I 135.6 nm line sets a limit to the non-thermal velocities to around 7 km/s

The Formation of IRIS Diagnostics. IX. The Formation of the C I 135.58 Line in the Solar Atmosphere

The C I 135.58 line is located in the wavelength range of NASA's Interface Region Imagin Spectrograph (IRIS) small explorer mission. We here study the formation and diagnostic potential of this line by means of non local-thermodynamic-equilibrium modeling, employing both 1D and 3D radiation-magnetohydrodynamic models. The C I/C II ionization balance is strongly influenced by photoionization by Ly-alpha emission. The emission in the C I 135.58 line is dominated by a recombination cascade and the line forming region is optically thick. The Doppler shift of the line correlates strongly with the vertical velocity in its line forming region, which is typically located at 1.5 Mm height. With IRIS the C I 135.58 line is usually observed together with the O I 135.56 line, and from the Doppler shift of both lines, we obtain the velocity difference between the line forming regions of the two lines. From the ratio of the C I/O I line core intensity, we can determine the distance between the C I and the O I forming layers. Combined with the velocity difference, the velocity gradient at mid-chromospheric heights can be derived. The C I/O I total intensity line ratio is correlated with the inverse of the electron density in the mid-chromosphere. We conclude that the C I 135.58 line is an excellent probe of the middle chromosphere by itself, and together with the O I 135.56 line the two lines provide even more information, which complements other powerful chromospheric diagnostics of IRIS such as the Mg II h and k lines and the C II lines around 133.5 nm

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

Non-equilibrium hydrogen ionization in 2D simulations of the solar atmosphere

The ionization of hydrogen in the solar chromosphere and transition region does not obey LTE or instantaneous statistical equilibrium because the timescale is long compared with important hydrodynamical timescales, especially of magneto-acoustic shocks. We implement an algorithm to compute non-equilibrium hydrogen ionization and its coupling into the MHD equations within an existing radiation MHD code, and perform a two-dimensional simulation of the solar atmosphere from the convection zone to the corona. Analysis of the simulation results and comparison to a companion simulation assuming LTE shows that: a) Non-equilibrium computation delivers much smaller variations of the chromospheric hydrogen ionization than for LTE. The ionization is smaller within shocks but subsequently remains high in the cool intershock phases. As a result, the chromospheric temperature variations are much larger than for LTE because in non-equilibrium, hydrogen ionization is a less effective internal energy buffer. The actual shock temperatures are therefore higher and the intershock temperatures lower. b) The chromospheric populations of the hydrogen n = 2 level, which governs the opacity of Halpha, are coupled to the ion populations. They are set by the high temperature in shocks and subsequently remain high in the cool intershock phases. c) The temperature structure and the hydrogen level populations differ much between the chromosphere above photospheric magnetic elements and above quiet internetwork. d) The hydrogen n = 2 population and column density are persistently high in dynamic fibrils, suggesting that these obtain their visibility from being optically thick in Halpha also at low temperature.Comment: 10 pages, 4 figure