arXiv subjects

Jiri Stepan

Publications and source records attributed to Jiri Stepan.

At least 19 recordsLinked to original sources

arXiv2025

The uncertainty of magnetic fields in 3D non-local thermodynamic equilibrium inversions

We describe our approach to solve the problem of ensuring the solenoidality of the magnetic field vector in three-dimensional (3D) inversions, as well as the estimation of the uncertainty in the inferred magnetic field. The solenoidality of the magnetic field vector is often disregarded in the inversion of spectropolarimetric data due to limitations in the traditional one-dimensional inversion techniques. We propose a method to ensure the solenoidal condition in 3D inversions based on our meshfree approach. The increase in dimensionality with respect to the 1D inversion techniques is such that some of the traditional methods to determine the uncertainties become unfeasible. We propose a method based on a Monte Carlo approach to determine the uncertainty of the magnetic field inference. Due to the physics of the problem, we can compute the uncertainty increasing the total required computational time by just a factor of about two. We also propose a metric to quantify the uncertainty to describe the degree of confidence of the magnetic field inference. Finally, we perform a numerical experiment to demonstrate the feasibility of both the method and the metric proposed to quantify the uncertainty.

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arXiv2023

The He I 10830 A line: Radiative transfer and differential illumination effects

We study the formation of the Stokes profiles of the He I multiplet at 10830 A when relaxing two of the approximations that are often considered in the modeling of this multiplet, namely the lack of self-consistent radiation transfer and the assumption of equal illumination of the individual multiplet components. This He I multiplet is among the most important ones for the diagnostic of the outer solar atmosphere from spectropolarimetric observations, especially in prominences, filaments, and spicules. However, the goodness of these approximations is yet to be assessed, especially in situations where the optical thickness is of the order or larger than one, and radiation transfer has a significant impact in the local anisotropy and the ensuing spectral line polarization. This issue becomes particularly relevant in the ongoing development of new inversion tools which take into account multi-dimensional radiation transfer effects. To relax these approximations we generalize the multi-term equations for the atomic statistical equilibrium to allow for differential illumination of the multiplet components and implement them in a one-dimensional radiative transfer code. We find that, even for this simple geometry and relatively small optical thickness, both radiation transfer and differential illumination effects have a significant impact on the emergent polarization profiles. This should be taken into account in order to avoid potentially significant errors in the inference of the magnetic field vector.

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arXiv2022

Novel framework for the three-dimensional NLTE inverse problem

The inversion of spectropolarimetric observations of the solar upper atmosphere is one of the most challenging goals in solar physics. If we account for all relevant ingredients of the spectral line formation process, such as the three-dimensional (3D) radiative transfer out of local thermodynamic equilibrium (NLTE), the task becomes extremely computationally expensive. Instead of generalizing 1D methods to 3D, we have developed a new approach to the inverse problem. In our meshfree method, we do not consider the requirement of 3D\,NLTE consistency as an obstacle, but as a natural regularization with respect to the traditional pixel-by-pixel methods. This leads to more robust and less ambiguous solutions. We solve the 3D\,NLTE inverse problem as an unconstrained global minimization problem that avoids repetitive evaluations of the $\Lambda$ operator. Apart from the 3D\,NLTE consistency, the method allows us to easily include additional conditions of physical consistency such as the zero divergence of the magnetic field. Stochastic ingredients make the method less prone to ending up within the local minima of the loss function. Our method is capable of solving the inverse problem faster by several orders of magnitude than by using grid-based methods. The method can provide accurate and physically consistent results if sufficient computing time is available, along with approximate solutions in the case of very complex plasma structures or limited computing time.

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arXiv2021

Mapping Solar Magnetic Fields from the Photosphere to the Base of the Corona

Routine ultraviolet imaging of the Sun's upper atmosphere shows the spectacular manifestation of solar activity; yet we remain blind to its main driver, the magnetic field. Here we report unprecedented spectropolarimetric observations of an active region plage and its surrounding enhanced network, showing circular polarization in ultraviolet (Mg II $h$ & $k$ and Mn I) and visible (Fe I) lines. We infer the longitudinal magnetic field from the photosphere to the very upper chromosphere. At the top of the plage chromosphere the field strengths reach more than 300 gauss, strongly correlated with the Mg II $k$ line core intensity and the electron pressure. This unique mapping shows how the magnetic field couples the different atmospheric layers and reveals the magnetic origin of the heating in the plage chromosphere.

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arXiv2021

Evaluating the reliability of a simple method to map the magnetic field azimuth in the solar chromosphere

The Zeeman effect is of limited utility for probing the magnetism of the quiet solar chromosphere. The Hanle effect in some spectral lines is sensitive to such magnetism, but the interpretation of the scattering polarization signals requires taking into account that the chromospheric plasma is highly inhomogeneous and dynamic (i.e., that the magnetic field is not the only cause of symmetry breaking). Here we investigate the reliability of a well-known formula for mapping the azimuth of chromospheric magnetic fields directly from the scattering polarization observed in the \ion{Ca}{2}~8542~\AA\, line, which is typically in the saturation regime of the Hanle effect. To this end, we use the Stokes profiles of the \ion{Ca}{2}~8542~\AA\, line computed with the PORTA radiative transfer code in a three-dimensional (3D) model of the solar chromosphere, degrading them to mimic spectropolarimetric observations for a range of telescope apertures and noise levels. The simulated observations are used to obtain the magnetic field azimuth at each point of the field of view, which we compare with the actual values within the 3D model. We show that, apart from intrinsic ambiguities, the method provides solid results. Their accuracy depends more on the noise level than on the telescope diameter. Large-aperture solar telescopes, like DKIST and EST, are needed to achieve the required noise-to-signal ratios using reasonable exposure times.

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arXiv2020

Near optimal angular quadratures for polarised radiative transfer

In three-dimensional (3D) radiative transfer (RT) problems, the tensor product quadratures are generally not optimal in terms of the number of discrete ray directions needed for a given accuracy of the angular integration of the radiation field. In this paper, we derive a new set of angular quadrature rules that are more suitable for solving 3D RT problems with the short- and long-characteristics formal solvers. These quadratures are more suitable than the currently used ones for the numerical calculation of the radiation field tensors that are relevant in the problem of the generation and transfer of polarised radiation without assuming local thermodynamical equilibrium (non-LTE). We show that our new quadratures can save up to about 30\,\% of computing time with respect to the Gaussian-trapezoidal product quadratures with the same accuracy.

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arXiv2019

IRIS Mg II Observations and Non-LTE Modeling of Off-limb Spicules in a Solar Polar Coronal Hole

We investigated the off-limb spicules observed in the Mg II h and k lines by IRIS in a solar polar coronal hole. We analyzed the large dataset of obtained spectra to extract quantitative information about the line intensities, shifts, and widths. The observed Mg II line profiles are broad and double-peaked at lower altitudes, broad but flat-topped at middle altitudes, and narrow and single-peaked with the largest Doppler shifts at higher altitudes. We use 1D non-LTE vertical slab models (i.e. models which consider departures from Local Thermodynamic Equilibrium) in single-slab and multi-slab configurations to interpret the observations and to investigate how a superposition of spicules along the line of sight (LOS) affects the synthetic Mg II line profiles. The used multi-slab models are either static, i.e. without any LOS velocities, or assume randomly assigned LOS velocities of individual slabs, representing the spicule dynamics. We conducted such single-slab and multi-slab modeling for a broad set of model input parameters and showed the dependence of the Mg II line profiles on these parameters. We demonstrated that the observed line widths of the h and k line profiles are strongly affected by the presence of multiple spicules along the LOS. We later showed that the profiles obtained at higher altitudes can be reproduced by single-slab models representing individual spicules. We found that the multi-slab model with a random distribution of the LOS velocities ranging from -25 to 25 km s$^{-1}$ can well reproduce the width and the shape of Mg II profiles observed at middle altitudes.

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arXiv2018

Comparison of theoretical and observed Ca~{\sc ii}~8542 Stokes profiles in quiet regions at the centre of the solar disc

Interpreting the Stokes profiles observed in quiet regions of the solar chromosphere is a challenging task. The Stokes Q and U profiles are dominated by the scattering polarisation and the Hanle effect, and these processes can only be correctly quantified if 3D radiative transfer effects are taken into account. Forward-modelling of the intensity and polarisation of spectral lines using a 3D model atmosphere is a suitable approach in order to statistically compare the theoretical and observed line profiles. Our aim is to present novel observations of the Ca 8542 line profiles in a quiet region at the centre of the solar disc and to quantitatively compare them with the theoretical Stokes profiles. We aim at estimating the reliability of the 3D model atmosphere using not only the line intensity but the full vector of Stokes parameters. We used data obtained with the ZIMPOL instrument at the IRSOL and compared the observations with the theoretical profiles computed with the PORTA radiative transfer code, using as solar model atmosphere a 3D snapshot taken from a radiation-magnetohydrodynamics simulation. The synthetic profiles were degraded to match the instrument and observing conditions. The degraded theoretical profiles of the Ca 8542 line are qualitatively similar to the observed ones. We confirm that there is a fundamental difference in the widths of all Stokes profiles: the observed lines are wider than the theoretical lines. We find that the amplitudes of the observed profiles are larger than those of the theoretical ones, which suggests that the symmetry breaking effects in the solar chromosphere are stronger than in the model atmosphere. This means that the isosurfaces of temperature, velocity, and magnetic field strength and orientation are more corrugated in the solar chromosphere than in the currently available 3D radiation-magnetohydrodynamics simulation.

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arXiv2015

Three-dimensional radiative transfer simulations of the scattering polarization of the hydrogen Ly$\alpha$ line in a MHD model of the chromosphere-corona transition region

Probing the magnetism of the upper solar chromosphere requires measuring and modeling the scattering polarization produced by anisotropic radiation pumping in UV spectral lines. Here we apply PORTA (a novel radiative transfer code) to investigate the hydrogen Ly$\alpha$ line in a 3D model of the solar atmosphere resulting from a state of the art MHD simulation. At full spatial resolution the linear polarization signals are very significant all over the solar disk, with a large fraction of the field of view showing line-center amplitudes well above the 1% level. Via the Hanle effect the line-center polarization signals are sensitive to the magnetic field of the model's transition region, even when its mean field strength is only 15 G. The breaking of the axial symmetry of the radiation field produces significant forward-scattering polarization in Ly$\alpha$, without the need of an inclined magnetic field. Interestingly, the Hanle effect tends to decrease such forward-scattering polarization signals in most of the points of the field of view. When the spatial resolution is degraded, the line-center polarization of Ly$\alpha$ drops below the 1% level, reaching values similar to those previously found in 1D semi-empirical models (i.e., up to about 0.5%). The center to limb variation of the spatially-averaged polarization signals is qualitatively similar to that found in 1D models, with the largest line-center amplitudes at $\mu=\cos\theta\approx 0.4$ ($\theta$ being the heliocentric angle). These results are important, both for designing the needed space-based instrumentation and for a reliable interpretation of future observations of the Ly$\alpha$ polarization.

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arXiv2013

Scattering polarization in solar flares

There is an ongoing debate about the origin and even the very existence of a high degree of linear polarization of some chromospheric spectral lines observed in solar flares. The standard explanation of these measurements is in terms of the impact polarization caused by non-thermal proton and/or electron beams. In this work, we study the possible role of resonance line polarization due to radiation anisotropy in the inhomogeneous medium of the flare ribbons. We consider a simple two-dimensional model of the flaring chromosphere and we solve self-consistently the non-LTE problem taking into account the role of resonant scattering polarization and of the Hanle effect. Our calculations show that the horizontal plasma inhomogeneities at the boundary of the flare ribbons can lead to a significant radiation anisotropy in the line formation region and, consequently, to a fractional linear polarization of the emergent radiation of the order of several percent. Neglecting the effects of impact polarization, our model can provide a clue for resolving some of the common observational findings, namely: (1) why a high degree of polarization appears mainly at the edges of the flare ribbons; (2) why polarization can also be observed during the gradual phase of a flare; (3) why polarization is mostly radial or tangential. We conclude that the radiation transfer in the realistic multi-dimensional models of solar flares needs to be considered as an essential ingredient for understanding the observed spectral line polarization.

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arXiv2013

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.

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arXiv2012

The Hanle effect of Ly$\alpha$ in an MHD model of the Solar Transition Region

In order to understand the heating of the solar corona it is crucial to obtain empirical information on the magnetic field in its lower boundary (the transition region). To this end, we need to measure and model the linear polarization produced by scattering processes in strong UV lines, such as the hydrogen Ly$\alpha$ line. The interpretation of the observed Stokes profiles will require taking into account that the outer solar atmosphere is highly structured and dynamic, and that the height of the transition region may well vary from one place in the atmosphere to another. Here we report on the Ly$\alpha$ scattering polarization signals we have calculated in a realistic model of an enhanced network region, resulting from a state-of-the-art radiation MHD simulation. This model is characterized by spatially complex variations of the physical quantities at transition region heights. The results of our investigation lead us to emphasize that scattering processes in the upper solar chromosphere should indeed produce measurable linear polarization in Ly$\alpha$. More importantly, we show that via the Hanle effect the model's magnetic field produces significant changes in the emergent $Q/I$ and $U/I$ profiles. Therefore, we argue that by measuring the polarization signals produced by scattering processes and the Hanle effect in Ly$\alpha$ and contrasting them with those computed in increasingly realistic atmospheric models, we should be able to decipher the magnetic, thermal and dynamic structure of the upper chromosphere and transition region of the Sun.

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arXiv2012

The scattering polarization of the Ly-alpha lines of H I and He II taking into account PRD and J-state interference effects

Recent theoretical investigations have pointed out that the cores of the Ly-alpha lines of H I and He II should show measurable scattering polarization signals when observing the solar disk, and that the magnetic sensitivity, through the Hanle effect, of such linear polarization signals is suitable for exploring the magnetism of the solar transition region. Such investigations were carried out in the limit of complete frequency redistribution (CRD) and neglecting quantum interference between the two upper J-levels of each line. Here we relax both approximations and show that the joint action of partial frequency redistribution (PRD) and J-state interference produces much more complex fractional linear polarization (Q/I) profiles, with large amplitudes in their wings. Such wing polarization signals turn out to be very sensitive to the temperature structure of the atmospheric model, so that they can be exploited for constraining the thermal properties of the solar chromosphere. Finally, we show that the approximation of CRD without J-state interference is however suitable for estimating the amplitude of the linear polarization signals in the core of the lines, where the Hanle effect operates.

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arXiv2012

A 3D Radiative Transfer Code for Modeling the Hanle Effect in the Lyman-alpha line

In order to obtain empirical information on the magnetism of the solar transition region we need to measure and interpret the linear polarization produced by scattering processes in FUV and EUV spectral lines. Via the Hanle effect such linear polarization signals are sensitive to the magnetic fields expected for the quiet and active regions of the outer solar atmosphere. For example, the Ly$α$ line of H\,{\sc i} at 1216\,Å is mainly sensitive to magnetic strengths between 10 and 100 G. The interpretation of the observed spectral line polarization requires the development of suitable modeling tools. To this end, we have developed a three-dimensional (3D), non-LTE multilevel radiative transfer code for modeling the intensity and linear polarization produced by scattering processes in spectral lines and its modification by the Hanle effect.

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arXiv2011

The Ly-alpha Lines of H I and He II: A Differential Hanle Effect for Exploring the Magnetism of the Solar Transition Region

The Ly-alpha line of He II at 304 Å is one of the spectral lines of choice for EUV channels of narrow-band imagers on board space telescopes, which provide spectacular intensity images of the outer solar atmosphere. Since the magnetic field information is encoded in the polarization of the spectral line radiation, it is important to investigate whether the He II line radiation from the solar disk can be polarized, along with its magnetic sensitivity. Here we report some theoretical predictions concerning the linear polarization signals produced by scattering processes in this strong emission line of the solar transition region, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. We find that the fractional polarization amplitudes are significant (${\sim}1%$), even when considering the wavelength-integrated signals. Interestingly, the scattering polarization of the Ly-alpha line of He II starts to be sensitive to the Hanle effect for magnetic strengths B>100 G (i.e., for magnetic strengths of the order of and larger than the Hanle saturation field of the hydrogen Ly-alpha line at 1216 Å). We therefore propose simultaneous observations of the scattering polarization in both Ly-alpha lines to facilitate magnetic field measurements in the upper solar chromosphere. Even the development of a narrow-band imaging polarimeter for the He II 304 Å line alone would be already of great diagnostic value for probing the solar transition region.

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arXiv2011

The Hanle Effect of the Hydrogen Ly-alpha Line for Probing the Magnetism of the Solar Transition Region

We present some theoretical predictions concerning the amplitude and magnetic sensitivity of the linear polarization signals produced by scattering processes in the hydrogen Ly-alpha line of the solar transition region. To this end, we have calculated the atomic level polarization (population imbalances and quantum coherences) induced by anisotropic radiation pumping in semi-empirical and hydrodynamical models of the solar atmosphere, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. The line-center amplitudes of the emergent linear polarization signals are found to vary typically between 0.1% and 1%, depending on the scattering geometry and the strength and orientation of the magnetic field. The results shown here encourage the development of UV polarimeters for sounding rockets and space telescopes with the aim of opening up a diagnostic window for magnetic field measurements in the upper chromosphere and transition region of the Sun.

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arXiv2011

Scattering polarization and the Hanle effect in H-alpha as a probe of chromospheric magnetism: Modeling vs. Observations

The Hanle effect in strong spectral lines is the physical mechanism that should be increasingly exploited for quantitative explorations of the magnetism of the quiet solar chromospheric plasma. Here we show, by means of multilevel radiative transfer calculations and new spectropolarimetric observations, that the amplitude and shape of the scattering polarization profiles of the H-alpha line is very sensitive to the strength and structure of the chromospheric magnetic field. The interpretation of the observations in terms of one-dimensional radiative transfer modeling suggests that there is an abrupt magnetization in the upper chromosphere of the quiet Sun.

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arXiv2011

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.

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