Multilevel Radiative Transfer Research Articles

The diagnostic potential of the weak field approximation for investigating the quiet Sun magnetism: the Si I 10 827 Å line

Aims. We aim to investigate the validity of the weak field approximation (WFA) for determining magnetic fields in quiet regions of the solar photosphere using the polarization caused by the Zeeman effect in the Si I10 827 Å line.Methods. We solved the NLTE line formation problem by means of multilevel radiative transfer calculations in a three-dimensional (3D) snapshot model taken from a state-of-the-art magneto-convection simulation of the small-scale magnetic activity in the quiet solar photosphere. The 3D model used is characterized by a surface mean magnetic field strength of about 170 G. The calculated Stokes profiles were degraded because of the atmospheric turbulence of Earth and light diffraction by the telescope aperture. We apply the WFA to the StokesI,Q,U,Vprofiles calculated for different seeing conditions and for the apertures of the VTT, GREGOR, EST and DKIST telescopes. We compare the inferred longitudinal and transverse components of the magnetic field with the original vertical and horizontal fields of the 3D model.Results. We find that with a spatial resolution significantly better than 0.5″ the surface maps of the magnetic field inferred from the Stokes profiles of the Si I10 827 Å line applying the WFA are close to the magnetic field of the model on the corrugated surface, corresponding to line optical depth unity at Δλ ≈ 0.1 Å for a disk-center line of sight. The correlation between them is relatively high, except that the inferred longitudinal and transverse components of the magnetic field turn out to be lower than in the 3D model.Conclusions. The use of the WFA for interpreting high-spatial-resolution spectropolarimetric observations of the Si I10 827 Å line obtained with telescopes like GREGOR, EST, and DKIST allows the longitudinal and transverse components of the magnetic field to be retrieved with reasonable precision over the whole quiet solar photosphere, the result being worse for telescopes of lower aperture.

FBILI method for multi-level line transfer

Efficient non-LTE multilevel radiative transfer calculations are needed for a proper interpretation of astrophysical spectra. In particular, realistic simulations of time-dependent processes or multi-dimensional phenomena require that the iterative method used to solve such non-linear and non-local problem is as fast as possible. There are several multilevel codes based on efficient iterative schemes that provide a very high convergence rate, especially when combined with mathematical acceleration techniques. The Forth-and-Back Implicit Lambda Iteration (FBILI) developed by Atanacković-Vukmanović et al. [1] is a Gauss-Seidel-type iterative scheme that is characterized by a very high convergence rate without the need of complementing it with additional acceleration techniques. In this paper we make the implementation of the FBILI method to the multilevel atom line transfer in 1D more explicit. We also consider some of its variants and investigate their convergence properties by solving the benchmark problem of CaII line formation in the solar atmosphere. Finally, we compare our solutions with results obtained with the well known code MULTI.

The Physical Origin and Magnetic Sensitivity of the Scattering Polarization Observed in the O i IR Triplet at 777 nm

Abstract The linearly polarized solar limb spectrum caused by the absorption and scattering of anisotropic radiation has a very rich diagnostic potential, given its sensitivity to the thermal, dynamic, and magnetic structure of the solar atmosphere. A crucial first step toward its scientific exploitation is understanding the physical origin of the observed spectral line polarization and its magnetic sensitivity via the Hanle and Zeeman effects. Here, we study the linear polarization signals observed in the IR triplet of O i at 777 nm, describing in detail the multilevel radiative transfer calculations that allowed us to decipher their physical origin. We investigate the sensitivity of the calculated scattering polarization signals to various modeling parameters, finding that the observed fractional linear polarization pattern originates mainly in the solar chromosphere, although the intensity profiles of the O i IR triplet come mainly from the lower photosphere. We find that the three lines are sensitive, via the Hanle effect, to magnetic fields with strengths between 0.01 and 30 G, in a extended region of the solar atmosphere. We show this through calculations of the response function to magnetic field perturbations in a semi-empirical model of the quiet Sun atmosphere. The dominant response of the linear polarization signals occurs at heights km above the visible model’s surface, which demonstrates that the scattering linear polarization signals of the oxygen IR triplet encode information on the magnetism of the solar chromosphere.

Herschel/HIFI observations of the circumstellar ammonia lines in IRC+10216.

A discrepancy exists between the abundance of ammonia (NH3) derived previously for the circumstellar envelope (CSE) of IRC+10216 from far-IR submillimeter rotational lines and that inferred from radio inversion or mid-infrared (MIR) absorption transitions. To address the discrepancy described above, new high-resolution far-infrared (FIR) observations of both ortho- and para-NH3 transitions toward IRC+10216 were obtained with Herschel, with the goal of determining the ammonia abundance and constraining the distribution of NH3 in the envelope of IRC+10216. We used the Heterodyne Instrument for the Far Infrared (HIFI) on board Herschel to observe all rotational transitions up to the J = 3 level (three ortho- and six para-NH3 lines). We conducted non-LTE multilevel radiative transfer modelling, including the effects of near-infrared (NIR) radiative pumping through vibrational transitions. The computed emission line profiles are compared with the new HIFI data, the radio inversion transitions, and the MIR absorption lines in the ν2 band taken from the literature. We found that NIR pumping is of key importance for understanding the excitation of rotational levels of NH3. The derived NH3 abundances relative to molecular hydrogen were (2.8 ± 0.5) × 10-8 for ortho-NH3 and [Formula: see text] for para-NH3, consistent with an ortho/para ratio of 1. These values are in a rough agreement with abundances derived from the inversion transitions, as well as with the total abundance of NH3 inferred from the MIR absorption lines. To explain the observed rotational transitions, ammonia must be formed near to the central star at a radius close to the end of the wind acceleration region, but no larger than about 20 stellar radii (1σ confidence level).

THE HANLE AND ZEEMAN POLARIZATION SIGNALS OF THE SOLAR Ca II 8542 Å LINE

ABSTRACT We highlight the main results of a three-dimensional (3D) multilevel radiative transfer investigation about the solar disk-center polarization of the Ca ii 8542 Å line. First, through the use of a 3D model of the solar atmosphere, we investigate the linear polarization that occurs due to the atomic level polarization produced by the absorption and scattering of anisotropic radiation, taking into account the symmetry-breaking effects caused by its thermal, dynamic, and magnetic structure. Second, we study the contribution of the Zeeman effect to the linear and circular polarization. Finally, we show examples of the Stokes profiles produced by the joint action of the atomic level polarization and the Hanle and Zeeman effects. We find that the Zeeman effect tends to dominate the linear polarization signals only in the localized patches of opposite magnetic polarity, where the magnetic field is relatively strong and slightly inclined; outside such very localized patches, the linear polarization is often dominated by the contribution of atomic level polarization. We demonstrate that a correct modeling of this last contribution requires taking into account the symmetry-breaking effects caused by the thermal, dynamic, and magnetic structure of the solar atmosphere, and that in the 3D model used the Hanle effect in forward-scattering geometry (disk-center observation) mainly reduces the polarization corresponding to the zero-field case. We emphasize that, in general, a reliable modeling of the linear polarization in the Ca ii 8542 Å line requires taking into account the joint action of atomic level polarization and the Hanle and Zeeman effects.

CHROMOSPHERIC POLARIZATION IN THE PHOTOSPHERIC SOLAR OXYGEN INFRARED TRIPLET

We present multilevel radiative transfer modeling of the scattering polarization observed in the solar O I infrared triplet around 777 nm. We demonstrate that the scattering polarization pattern observed on the solar disk forms in the chromosphere, far above the photospheric region where the bulk of the emergent intensity profiles originates. We study the sensitivity of the polarization pattern to the thermal structure of the solar atmosphere and to the presence of weak magnetic fields (0.01 - 100 G) through the Hanle effect, showing that the scattering polarization signals of the oxygen infrared triplet encode information on the magnetism of the solar chromosphere.

RH 1.5D: a massively parallel code for multi-level radiative transfer with partial frequency redistribution and Zeeman polarisation

The emergence of three-dimensional magneto-hydrodynamic (MHD) simulations of stellar atmospheres has sparked a need for efficient radiative transfer codes to calculate detailed synthetic spectra. We present RH 1.5D, a massively parallel code based on the RH code and capable of performing Zeeman polarised multi-level non-local thermodynamical equilibrium (NLTE) calculations with partial frequency redistribution for an arbitrary amount of chemical species. The code calculates spectra from 3D, 2D or 1D atmospheric models on a column-by-column basis (or 1.5D). While the 1.5D approximation breaks down in the cores of very strong lines in an inhomogeneous environment, it is nevertheless suitable for a large range of scenarios and allows for faster convergence with finer control over the iteration of each simulation column. The code scales well to at least tens of thousands of CPU cores, and is publicly available. In the present work we briefly describe its inner workings, strategies for convergence optimisation, its parallelism, and some possible applications.

PORTA: A three-dimensional multilevel radiative transfer code for modeling the intensity and polarization of spectral lines with massively parallel computers

The interpretation of the intensity and polarization of the spectral line radiation produced in the atmosphere of the Sun and of other stars requires solving a radiative transfer problem that can be very complex, especially when the main interest lies in modeling the spectral line polarization produced by scattering processes and the Hanle and Zeeman effects. One of the difficulties is that the plasma of a stellar atmosphere can be highly inhomogeneous and dynamic, which implies the need to solve the non-equilibrium problem of the generation and transfer of polarized radiation in realistic three-dimensional (3D) stellar atmospheric models. Here we present PORTA, an efficient multilevel radiative transfer code we have developed for the simulation of the spectral line polarization caused by scattering processes and the Hanle and Zeeman effects in 3D models of stellar atmospheres. The numerical method of solution is based on the non-linear multigrid iterative method and on a novel short-characteristics formal solver of the Stokes-vector transfer equation which uses monotonic B\'ezier interpolation. Therefore, with PORTA the computing time needed to obtain at each spatial grid point the self-consistent values of the atomic density matrix (which quantifies the excitation state of the atomic system) scales linearly with the total number of grid points. Another crucial feature of PORTA is its parallelization strategy, which allows us to speed up the numerical solution of complicated 3D problems by several orders of magnitude with respect to sequential radiative transfer approaches, given its excellent linear scaling with the number of available processors. The PORTA code can also be conveniently applied to solve the simpler 3D radiative transfer problem of unpolarized radiation in multilevel systems.

The excitation of circumstellar C2in carbon-rich post-AGB object IRAS 22272+5435

Context. Observations of the circumstellar envelopes of post-asymptotic giant branch (post-AGB) stars provide information about their mass-loss history during the AGB phase and about the chemistry inside envelopes after that phase. Aims. We analyze visual observations of C2 molecule in absorption and millimeter and sub-millimeter observations of CO molecule in emission with the aim of determining the physical and chemical conditions in the circumstellar shell of the carbon-rich post-AGB star IRAS 22272+5435. Methods. We determined the column densities and excitation structure of C2 from equivalent width analysis of the molecular absorptions. The thermal and density structure of post-AGB shell (AGB remnant) is constrained by multilevel radiative transfer modeling of CO emission lines. The chemical structure of the envelope was computed and then used in the multilevel radiative transfer in C2 for comparison with observed column densities. Results. We estimate the column density of C2 to be 3.2 × 1015 cm−2. From the chemical model we estimate peak abundance of C2 as 6.8 × 10−6 relative to nucleon density. The absorption of molecular lines originate in the ring between 5 and 10 × 1016 cm. The excitation temperature of the lowest levels of 58 K is consistent with the gas kinetic temperature derived from the CO modeling. The initial abundance of the parent molecule C2H2 inferred from the analysis is found to be 1.27 × 10−5 relative to nucleon density. Conclusions. C2 molecule is a promising tool for probing the temperature structure of the envelopes of post-AGB objects and indirectly for determining the chemical abundance of acetylene.

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.

SCATTERING POLARIZATION OF HYDROGEN LINES IN WEAKLY MAGNETIZED STELLAR ATMOSPHERES. I. FORMULATION AND APPLICATION TO ISOTHERMAL MODELS

Although the spectral lines of hydrogen contain valuable information on the physical properties of a variety of astrophysical plasmas, including the upper solar chromosphere, relatively little is known about their scattering polarization signals whose modification via the Hanle effect may be exploited for magnetic field diagnostics. Here we report on a basic theoretical investigation of the linear polarization produced by scattering processes and the Hanle effect in Ly-a, Ly-b and H-a taking into account multilevel radiative transfer effects in an isothermal stellar atmosphere model, the fine-structure of the hydrogen levels, as well as the impact of collisions with electrons and protons. The main aim of this first paper is to elucidate the physical mechanisms that control the linear polarization in the three lines, as well as its sensitivity to the perturbers density and to the strength and structure of micro-structured and deterministic magnetic fields. To this end, we apply an efficient radiative transfer code we have developed for performing numerical simulations of the Hanle effect in multilevel systems with overlapping line transitions. For low density plasmas such as that of the upper solar chromosphere collisional depolarization is caused mainly by collisional transitions between the fine-structure levels of n=3, so that it is virtually insignificant for Ly-a but important for Ly-b and H-a. We show the impact of the Hanle effect on the three lines taking into account the radiative transfer coupling between the different hydrogen line transitions. For example, we demonstrate that the linear polarization profile of the H-a line is sensitive to the presence of magnetic field gradients in the line core formation region and that in solar-like chromospheres selective absorption of polarization components does not play any significant role on the emergent scattering polarization.

Physics of Solar Prominences: I—Spectral Diagnostics and Non-LTE Modelling

This review paper outlines background information and covers recent advances made via the analysis of spectra and images of prominence plasma and the increased sophistication of non-LTE (i.e. when there is a departure from Local Thermodynamic Equilibrium) radiative transfer models. We first describe the spectral inversion techniques that have been used to infer the plasma parameters important for the general properties of the prominence plasma in both its cool core and the hotter prominence-corona transition region. We also review studies devoted to the observation of bulk motions of the prominence plasma and to the determination of prominence mass. However, a simple inversion of spectroscopic data usually fails when the lines become optically thick at certain wavelengths. Therefore, complex non-LTE models become necessary. We thus present the basics of non-LTE radiative transfer theory and the associated multi-level radiative transfer problems. The main results of one- and two-dimensional models of the prominences and their fine-structures are presented. We then discuss the energy balance in various prominence models. Finally, we outline the outstanding observational and theoretical questions, and the directions for future progress in our understanding of solar prominences.

Properties of prominence fine-structure threads derived from SOHO/SUMER hydrogen Lyman lines

Context. The SOHO/SUMER observations provide us for the first time with the prominence spec tra in the Lyman-� line outside the attenuator together with the higher members of the hydrogen Lyman series. Aims. We derive the prominence fine-structure thread properties by compar ing the SOHO/SUMER hydrogen Lyman series observations with the synthetic Lyman lines. Methods. To obtain the synthetic profiles of the Lyman lines, we use 2D prominence fin e-structure thread models with a PCTR and consistently solved the 2D non-LTE multilevel radiative transfer. The trial-and-erro r method was applied to find the model with the best agreement between the synthetic Lyman line profiles and the observed ones. Results. The properties of the resulting model with the best match of the synthetic and observed line profiles are central (minimum) temperature T0 = 7000 K, maximum column mass in the centre of the thread M0 = 1.1× 10 −4 g cm −2 , horizontal field strength in the middle of the thread Bx(0) = 6 Gauss and the boundary pressure p0 = 0.015 dyn cm −2 . Conclusions. The Lyman line profiles observed by SOHO/SUMER can be better reproduced by using multi-thread models consisting of a set of the 2D prominence fine-structure threads placed perpendicularly to th e line-of-sight, rather than with the single-thread model.

Fast multilevel radiative transfer

The vast majority of recent advances in the field of numerical radiative transfer relies on approximate operator methods better known in astrophysics as Accelerated Lambda-Iteration (ALI). A superior class of iterative schemes, in term of rates of convergence, such as Gauss–Seidel and successive overrelaxation methods were therefore quite naturally introduced in the field of radiative transfer by Trujillo Bueno and Fabiani Bendicho [A novel iterative scheme for the very fast and accurate solution of non-LTE radiative transfer problems. Astrophys J 1995;455:646]; it was thoroughly described for the non-LTE two-level atom case. We describe hereafter in details how such methods can be generalized when dealing with non-LTE unpolarised radiation transfer with multilevel atomic models, in monodimensional geometry.

Very Efficient Methods for Multilevel Radiative Transfer in Atomic and Molecular Lines

The development of fast numerical methods for multilevel radiative transfer (RT) applications often leads to important break- throughs in astrophysics, because they allow the investigation of prob- lems that could not be properly tackled using the methods previously available. Probably, the most familiar example is the so-called Multi- level Accelerated -Iteration (MALI) technique of Rybicki & Hummer for the case of a local approximate operator, which is based on Ja- cobi iteration. However, there are superior operator-splitting methods, based on Gauss-Seidel (GS) and Successive Overrelaxation (SOR) it- eration, which provide a dramatic increase in the speed with which non-LTE multilevel transfer problems can be solved in one, two and three-dimensional geometries. Such RT methods, which were intro- duced by Trujillo Bueno & Fabiani Bendicho ten years ago, are the main subject of the rst part of this paper. We show in some detail how they can be applied for solving multilevel RT problems in spherical geometry, for both atomic and molecular line transitions. The second part of the article addresses the issue of the calculation of the molecu- lar number densities when the approximation of instantaneous chemical equilibrium turns out to be inadequate, which happens to be the case whenever the dynamical time scales of the astrophysical plasma under consideration are much shorter than the time needed by the molecules to form.

Line Polarization of Molecular Lines at Radio Frequencies: The Case of DR 21(OH)

We present polarization observations in DR 21(OH) from thermal dust emission at 3 mm and from CO J = 1 → 0 line emission. The observations were obtained using the Berkeley-Illinois-Maryland Association (BIMA) array. Lai et al. observed this region at 1.3 mm for the polarized continuum emission and also measured the CO J = 2 → 1 polarization. Our continuum polarization results are consistent with those of Lai et al. However, the direction of the linear polarization for the J = 1 → 0 is perpendicular to that of the CO J = 2 → 1 polarization. This unexpected result was explored by obtaining numerical solutions to the multilevel radiative transfer equations for a gas with anisotropic optical depths. We find that in addition to the anisotropic optical depths, anisotropic excitation due to a source of radiation that is external to the CO is needed to understand the orthogonality in the directions of polarization. The continuum emission by dust grains at the core of DR 21(OH) is sufficient to provide this external radiation. The CO polarization must arise in relatively low density (n ~ 100 cm-3 ) envelope gas. We infer B ~ 10 μG in this gas, which implies that the envelope is subcritical.

Improving the Numerical Modeling of the OiResonance Triplet in the Solar Spectrum

We present a slight modification to an existing multilevel radiative transfer code that allows us to include the effects of frequency cross redistribution (XRD) between lines sharing the same upper level. With this improved code, we calculate theoretical profiles of the O I resonance triplet lines at 130 nm through a hydrostatic model of the average quiet Sun. The width of the calculated XRD profiles show good agreement with an observed, spatially averaged disk-center spectrum obtained with the high-resolution telescope spectrometer (HRTS) spectrograph. This is in stark contrast to profiles calculated with complete frequency redistribution (CRD) and ordinary partial frequency redistribution (PRD), which have Lorentzian wings that are too broad. We find deep central reversals, contrary to most observed profiles, but we note that this discrepancy is to a large degree the result of limited instrumental spectral resolution.

Prominence fine structures in a magnetic equilibrium: Two-dimensional models with multilevel radiative transfer

In this paper we construct theoretical models for vertical prominence threads which are in magnetohydrostatic (MHS) equilibrium. These models are fully two-dimensional (2D) and take the form of vertically infinite threads hanging in a horizontal magnetic field. A typical example of such a 2D magnetic-dip structure is shown for the case when the central cool parts are surrounded by the prominence-corona transition region (PCTR). We display 2D variations of the pressure, density and temperature. While the pressure variations follow from the MHS equilibrium, the kinetic temperature was specified empirically. As a next step, we have solved the 2D multilevel non-LTE transfer problem in such thread-like structures, in order to predict the spatial variations of the emergent hydrogen spectrum. It is demonstrated that the hydrogen Lyman lines (treated with partial redistribution) show significant spatial variations of the intensity and that an important difference exists between the line profiles emergent along and across the magnetic field lines. We also discuss how these intensity variations compare to recent SOHO/SUMER prominence observations, namely we show the effects of line-profile averaging over the fine-structure threads which are below the instrumental resolution. Finally we make some suggestions for future modelling and observations.

Multilevel Radiative Transfer with Partial Frequency Redistribution

A multilevel accelerated lambda iteration (MALI) method for radiative transfer calculations with partial frequency redistribution (PRD) is presented. The method, which is based on Rybicki & Hummer's complete frequency redistribution (CRD) formalism with full preconditioning, consistently accounts for overlapping radiative transitions. Its extension to PRD is implemented in a very natural way through the use of the Ψ operator operating on the emissivity rather than the commonly used Λ operator, which operates on the source function. Apart from requiring an additional inner computational loop to evaluate the PRD emission-line profiles with fixed population numbers, implementation of the presented method requires only a trivial addition of computer code. Since the presented method employs a diagonal operator, it is easily extended to different geometries. Currently, it has been implemented for one-, two-, and three-dimensional Cartesian grids and spherical symmetry. In all cases, the speed of convergence with PRD is very similar to that in CRD, with the former sometimes even surpassing the latter. Sample calculations exhibiting the favorable convergence behavior of the PRD code are presented in the case of the Ca II H and K lines, the Mg II h and k lines, and the hydrogen Lyα and Lyβ lines in a one-dimensional solar model and the Ca II resonance lines in a two-dimensional flux-sheet model.

Non-LTE model chromospheres of ζ Aurigae stars

Plane-parallel, one-component, non-local thermodynamic equilibrium (LTE), semi­ empirical model chromospheres have been constructed for the primary stars in the , Aurigae systems HR 6902 and 22 Vul. This has been accomplished by means of radiative transfer calculations undertaken with a non-LTE multilevel radiative transfer code, MULTI, and curves of growth applied to chromospheric eclipse spectra. The former are the subject of this paper, which is divided into two parts. The first briefly describes the observations and derivation of basic stellar parameters, while the second concerns the radiative transfer calculations and conclusions which follow from them. In particular, the calculated model photospheres plus chromospheres are used to investigate the relative contribution of primary and secondary stars to the overall radiation field. The radiation field of the hot secondary is approximated by use of an appropriate Kurucz model atmosphere. Although the hot companion is wholly responsible for the ionization of the metals, this is not the case as far as excitation is concerned. Use of a 47-level Fe atomic model demonstrates the intimate convolution between atomic and atmospheric physics. The chromospheres calculated by radiative transfer methods are compared with th9se derived empirically by curves of growth and are found· to be comparable in the line-forming region of Ca II H & K, Mg II h & k and the many Fe II lines. Finally, owing to the effects of radiative transitions from high-lying levels-which are enhanced by the radiation field of the hot companion, it is found that lines resulting from transitions from the a 4F, a 4D and a 4p levels of Fe II may not be used to derive an inner wind temperature for 22 Vul. This is the first time that, Aurigae chromospheres have been the subject of such intensive radiative transfer calculations.