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Register a new userRadiative transfer in cylindrical threads with incident radiation VII. Multi-thread models
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We solved the radiative transfer and statistical equilibrium equations in a two-dimensional cross-section of a cylindrical structure oriented horizontally and lying above the solar surface. The cylinder is filled with a mixture of hydrogen and helium and is illuminated at a given altitude from the solar disc. We constructed simple models made from a single thread or from an ensemble of several threads along the line of sight. This first use of two-dimensional, multi-thread fine structure modelling combining hydrogen and helium radiative transfer allowed us to compute synthetic emergent spectra from cylindrical structures and to study the effect of line-of-sight integration of an ensemble of threads under a range of physical conditions. We analysed the effects of variations in temperature distribution and in gas pressure. We considered the effect of multi-thread structures within a given field of view and the effect of peculiar velocities between the structures in a multi-thread model. We compared these new models to the single thread model and tested them with varying parameters. These new computations show, for the first time, the effect of integrating the radiation emitted in H and He lines by several cylindrical threads that are static or moving along the line of sight. They can be used to interpret high-spatial and spectral resolutions of cylindrical structures found in the solar atmosphere, such as cool coronal loops or prominence threads.
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Spectral lines of helium are commonly observed on the Sun. These observations contain important informations about physical conditions and He/H abundance variations within solar outer structures. The modeling of chromospheric and coronal loop-like structures visible in hydrogen and helium lines requires the use of appropriate diagnostic tools based on NLTE radiative tranfer in cylindrical geometry. We use iterative numerical methods to solve the equations of NLTE radiative transfer and statistical equilibrium of atomic level populations. These equations are solved alternatively for the hydrogen and helium atoms, using cylindrical coordinates and prescribed solar incident radiation. Electron density is determined by the ionization equilibria of both atoms. Two-dimension effects are included. The mechanisms of formation of the principal helium lines are analyzed and the sources of emission inside the cylinder are located. The variations of spectral line intensities with temperature, pressure, and helium abundance, are studied. The simultaneous computation of hydrogen and helium lines, performed by the new numerical code, allows the construction of loop models including an extended range of temperatures.
We compare maps of scattering polarization signals obtained from three-dimensional (3D) radiation transfer calculations in a magneto-convection model of the solar atmosphere using formal solvers based on the short characteristics (SC) and the long characteristics (LC) methods. The SC method requires less computational work, but it is known to introduce spatial blurring in the emergent radiation for inclined lines of sight. For polarized radiation this effect is generally more severe due to it being a signed quantity and to the sensitivity of the scattering polarization to the models inhomogeneities. We study the differences in the polarization signals of the emergent spectral line radiation calculated with such formal solvers. We take as a case study already published results of the scattering polarization in the Sr I $4607~unicode{xC5}$ line obtained with the SC method, demonstrating that in high-resolution grids it is accurate enough for that type of study. In general, the LC method is the preferred one for accurate calculations of the emergent radiation, reason why it is now one of the options in the public version of the 3D radiative transfer code PORTA.
The new version of TLUSTY allows for the calculation of restricted NLTE in cool stars using pre-calculated opacity tables. We demonstrate that TLUSTY gives consistent results with MULTI, a well-tested code for NLTE in cool stars. We use TLUSTY to perform LTE and a series of NLTE calculations of Na, Mg, K and Ca using all combinations of 1, 2, 3 and the 4 elements mentioned above simultaneously in NLTE. In this work we take into account how departures from LTE in one element can affect others through changes in the opacities due to NLTE. We find that atomic Mg, which provides strong UV opacity, and shows departures from LTE in the low-energy states, can impact the NLTE populations of Ca, leading to abundance corrections as large as 0.07 dex. The differences in the derived abundances between the single-element and the multi-element cases can exceed those between the single-element NLTE and an LTE analysis, warning that this is not always a second-order effect. By means of detailed tests for three stars with reliable atmospheric parameters (Arcturus, Procyon and the Sun) we conclude that our NLTE calculations provide abundance corrections in the optical up to 0.1, 0.2 and 0.7 dex for Ca, Na and K, but LTE is a good approximation for Mg. In the H-band, NLTE corrections are much smaller, under 0.1 dex. The derived NLTE abundances in the optical and in the IR are consistent. For all four elements, in all three stars, NLTE line profiles fit better the observations than the LTE counterparts. For elements where over-ionisation is an important NLTE mechanism are likely affected by departures from LTE in Mg . Special care must be taken with the collisions adopted for high-lying levels when calculating NLTE profiles of lines in the H-band. The derived NLTE corrections in the optical and in the H-band differ, but the derived NLTE abundances are consistent between the two spectral regions.
Resonance spectral lines such as H I Ly {alpha}, Mg II h&k, and Ca II H&K that form in the solar chromosphere are influenced by the effects of 3D radiative transfer as well as partial redistribution (PRD). So far no one has modeled these lines including both effects simultaneously owing to the high computing demands of existing algorithms. Such modeling is however indispensable for accurate diagnostics of the chromosphere. We present a computationally tractable method to treat PRD scattering in 3D model atmospheres using a 3D non-LTE radiative transfer code. To make the method memory-friendly, we use the hybrid approximation of Leenaarts et al. (2012) for the redistribution integral. To make it fast, we use linear interpolation on equidistant frequency grids. We verify our algorithm against computations with the RH code and analyze it for stability, convergence, and usefulness of acceleration using model atoms of Mg II with the h&k lines and H I with the Ly {alpha} line treated in PRD. A typical 3D PRD solution can be obtained in a model atmosphere with $252 times 252 times 496$ coordinate points in 50 000--200 000 CPU hours, which is a factor ten slower than computations assuming complete redistribution. We illustrate the importance of the joint action of PRD and 3D effects for the Mg II h&k lines for disk-center intensities as well as the center-to-limb variation. The proposed method allows simulating PRD lines in time series of radiation-MHD models in order to interpret observations of chromospheric lines at high spatial resolution.
Threads are the building blocks of solar prominences and very often show longitudinal oscillatory motions that are strongly attenuated with time. The damping mechanism responsible for the reported oscillations is not fully understood yet. To understand the oscillations and damping of prominence threads it is mandatory to investigate first the nature of the equilibrium solutions that arise under static conditions and under the presence of radiative losses, thermal conduction and background heating. This provides the basis to calculate the eigenmodes of the thread models. The nonlinear ordinary differential equations for hydrostatic and thermal equilibrium under the presence of gravity are solved using standard numerical techniques and simple analytical expressions are derived under certain approximations. The solutions to the equations represent a prominence thread, i.e., a dense and cold plasma region of a certain length that connects with the corona through a prominence corona transition region (PCTR). The solutions can also match with a chromospheric-like layer if a spatially dependent heating function localised around the footpoints is considered. We have obtained static solutions representing prominence threads and have investigated in detail the dependence of these solutions on the different parameters of the model. Among other results, we have shown that multiple condensations along a magnetic field line are possible, and that the effect of partial ionisation in the model can significantly modify the thermal balance in the thread and therefore their length. This last parameter is also shown to be comparable to that reported in the observations when the radiative losses are reduced for typical thread temperatures.
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