Magnetic Field Diagnostics Research Articles

Internal Gravity Waves in the Magnetized Solar Atmosphere. II. Energy Transport

Abstract In this second paper of the series on internal gravity waves (IGWs), we present a study of the generation and propagation of IGWs in a model solar atmosphere with diverse magnetic conditions. A magnetic field-free and three magnetic models that start with an initial, vertical, homogeneous field of 10, 50, and 100 G magnetic flux density, are simulated using the CO5BOLD code. We find that the IGWs are generated in similar manner in all four models in spite of the differences in the magnetic environment. The mechanical energy carried by IGWs is significantly larger than that of the acoustic waves in the lower part of the atmosphere, making them an important component of the total wave energy budget. The mechanical energy flux (106–103 W m−2) is a few orders of magnitude larger than the Poynting flux (103–101 W m−2). The Poynting fluxes show a downward component in the frequency range corresponding to the IGWs, which confirm that these waves do not propagate upward in the atmosphere when the fields are predominantly vertical and strong. We conclude that, in the upper photosphere, the propagation properties of IGWs depend on the average magnetic field strength and therefore these waves can be potential candidates for magnetic field diagnostics of these layers. However, their subsequent coupling to Alfvénic waves is unlikely in a magnetic environment permeated with predominantly vertical fields, and therefore they may not directly or indirectly contribute to the heating of layers above plasma-β less than 1.

Magnetic Field Diffusion in Medium-Walled Conductors

The diffusion of transient magnetic fields through the walls of a hollow conductive shell is an important phenomenon of interest throughout a variety of pulsed power applications. Basic solutions do exist for cylindrical geometries in the limiting case that the skin depth is much larger than the wall thickness; however, in many pulsed applications, the transient skin depth is often similar to the conductor thickness. As the underlying thin-wall assumption begins to breakdown, the production of complex eddy current distributions in the conductor walls results in deviation from these simplified analytical solutions of the diffused field. Precise calculation of these current distributions is essential for many applications including inductive shielding and magnetic field diagnostics near conductors. Electromagnetic simulations using the finite-element method provide a more accurate picture of the diffusion process in this regime. A high magnetic field testbed facilitates measurement of the diffused fields in order to verify simulation accuracy. The effect of material conductivity, wall thickness, and conductor geometry on the diffusion process is examined.

Non-damping oscillations at flaring loops

Context. Quasi-periodic oscillations are usually detected as spatial displacements of coronal loops in imaging observations or as periodic shifts of line properties (i.e., Doppler velocity, line width and intensity) in spectroscopic observations. They are often applied for remote diagnostics of magnetic fields and plasma properties on the Sun. Aims. We combine the imaging and spectroscopic measurements of available space missions, and investigate the properties of non-damping oscillations at flaring loops. Methods. We used the Interface Region Imaging Spectrograph (IRIS) to measure the spectrum over a narrow slit. The double-component Gaussian fitting method was used to extract the line profile of Fe XXI 1354.08 Å at the “O I” spectral window. The quasi-periodicity of loop oscillations were identified in the Fourier and wavelet spectra. Results. A periodicity at about 40 s is detected in the line properties of Fe XXI 1354.08 Å, hard X-ray emissions in GOES 1−8 Å derivative, and Fermi 26−50 keV. The Doppler velocity and line width oscillate in phase, while a phase shift of about π/2 is detected between the Doppler velocity and peak intensity. The amplitudes of Doppler velocity and line width oscillation are about 2.2 km s−1 and 1.9 km s−1, respectively, while peak intensity oscillates with amplitude at about 3.6% of the background emission. Meanwhile, a quasi-period of about 155 s is identified in the Doppler velocity and peak intensity of the Fe XXI 1354.08 Å line emission, and AIA 131 Å intensity. Conclusions. The oscillations at about 40 s are not damped significantly during the observation; this might be linked to the global kink modes of flaring loops. The periodicity at about 155 s is most likely a signature of recurring downflows after chromospheric evaporation along flaring loops. The magnetic field strengths of the flaring loops are estimated to be about 120−170 G using the magnetohydrodynamic seismology diagnostics, which are consistent with the magnetic field modeling results using the flux rope insertion method.

Spatial measurement in rotating magnetic field plasma acceleration method by using two-dimensional scanning instrument and thrust stand.

A two-dimensional scanning probe instrument has been developed to survey spatial plasma characteristics in our electrodeless plasma acceleration schemes. In particular, diagnostics of plasma parameters, e.g., plasma density, temperature, velocity, and excited magnetic field, are essential for elucidating physical phenomena since we have been concentrating on next generation plasma propulsion methods, e.g., Rotating Magnetic Field plasma acceleration method, by characterizing the plasma performance. Moreover, in order to estimate the thrust performance in our experimental scheme, we have also mounted a thrust stand, which has a target type, on this movable instrument, and scanned the axial profile of the thrust performance in the presence of the external magnetic field generated by using permanent magnets, so as to investigate the plasma captured in a stand area, considering the divergent field lines in the downstream region of a generation antenna. In this paper, we will introduce the novel measurement instrument and describe how to measure these parameters.

Assessing the Capabilities of Dynamic Coronal Seismology of Alfvénic Waves through Forward Modeling

Abstract Coronal seismology is a diagnostic tool used in solar physics for measuring parameters that are otherwise hard to measure; of these parameters, magnetic field values are arguably the most important. The parameters are inferred by combining observations of waves with magnetohydrodynamic (MHD) wave theory. To date, coronal seismology has successfully been applied to various single-oscillation events. Such events are relatively rare, resulting in rare occasions to use diagnostics. Ubiquitous waves in the solar atmosphere might, however, allow for the possibility of dynamic coronal seismology, which involves the continuous inversions of coronal parameters and would constitute a huge leap forward in many areas of solar physics. In this paper, we investigate the robustness and accuracy of magnetic field diagnostics applied to forward-modeled 3D MHD simulations of propagating Alfvénic waves. We find that the seismologically measured magnetic field values are reassuringly close to the input value (within ≈20%) for a range of setups studied, providing encouragement and confidence for the further development of dynamic coronal seismology.

The Antiderivative of the Stokes V Polarization Profile. I. A Simple Procedure for Magnetic Field Characterization

Abstract Derived here is a more conceptually intuitive means of interpreting magnetic-field diagnostics from circularly polarized lines in a wide array of astrophysical applications. The method applies to individual “Stokes V” profile snapshots and complements standard Zeeman Doppler imaging techniques by providing the explicit form of the averaging kernel for the magnetic field that the polarization diagnostic is sensitive to. This new perspective centers on the antiderivative, or cumulative integral with respect to frequency, of the Stokes V profile. The new approach would not yield different answers for magnetic field determinations, but rather presents a more directly conceptual means of understanding the connection between what is observed and what types of fields produce it. In particular, it elucidates how lateral and line-of-sight field gradients affect the Zeeman profile. This approach is especially useful when the Zeeman shift varies in a way that correlates with the Doppler shift, as then spectral resolution serves as a proxy for spatial imaging in each polarization snapshot. Hence, the perspective is particularly useful for rapidly rotating stars, hypersonic winds, galactic rotation, and large-amplitude turbulence, when the longitudinal field varies across the source or with depth. The approach also generates an improved unsigned mean-field diagnostic that suffers less polarity cancellation than the commonly used center-of-gravity diagnostic. Reduced cancellation produces a better estimate of the field magnitude in toroidal, spotty, or dipolar fields, and a complementary comparison with the current unsigned diagnostic can help characterize the degree of field polarity reversal concealed within integrated diagnostics.

Millimeter radiation from a 3D model of the solar atmosphere

We use state-of-the-art, three-dimensional non-local thermodynamic equilibrium (non-LTE) radiative magnetohydrodynamic simulations of the quiet solar atmosphere to carry out detailed tests of chromospheric magnetic field diagnostics from free-free radiation at millimeter and submillimeter wavelengths (mm/submm). The vertical component of the magnetic field was deduced from the mm/submm brightness spectra and the degree of circular polarization synthesized at millimeter frequencies. We used the frequency bands observed by the Atacama Large Millimeter/Submillimeter Array (ALMA) as a convenient reference. The magnetic field maps obtained describe the longitudinal magnetic field at the effective formation heights of the relevant wavelengths in the solar chromosphere. The comparison of the deduced and model chromospheric magnetic fields at the spatial resolution of both the model and current observations demonstrates a good correlation, but has a tendency to underestimate the model field. The systematic discrepancy of about 10 percent is probably due to averaging of the restored field over the heights contributing to the radiation, weighted by the strength of the contribution. On the whole, the method of probing the longitudinal component of the magnetic field with free-free emission at mm/submm wavelengths is found to be applicable to measurements of the weak quiet-Sun magnetic fields. However, successful exploitation of this technique requires very accurate measurements of the polarization properties (primary beam and receiver polarization response) of the antennas, which will be the principal factor that determines the level to which chromospheric magnetic fields can be measured. Consequently, high-resolution and high-precision observations of circularly polarized radiation at millimeter wavelengths can be a powerful tool for producing chromospheric longitudinal magnetograms.

Inversion of Zeeman polarization for solar magnetic field diagnostics

The topic of magnetic field diagnostics with the Zeeman effect is currently vividly discussed. There are some testable inversion codes available to the spectropolarimetry community and their application allowed for a better understanding of the magnetism of the solar atmosphere. In this context, we propose an inversion technique associated with a new numerical code. The inversion procedure is promising and particularly successful for interpreting the Stokes profiles in quick and sufficiently precise way. In our inversion, we fit a part of each Stokes profile around a target wavelength, and then determine the magnetic field as a function of the wavelength which is equivalent to get the magnetic field as a function of the height of line formation.To test the performance of the new numerical code, we employed “hare and hound” approach by comparing an exact solution (called input) with the solution obtained by the code (called output). The precision of the code is also checked by comparing our results to the ones obtained with the HAO MERLIN code. The inversion code has been applied to synthetic Stokes profiles of the Na D1 line available in the literature. We investigated the limitations in recovering the input field in case of noisy data. As an application, we applied our inversion code to the polarization profiles of the Fe iλ 6302.5 Å observed at IRSOL in Locarno.

Near-Sun and 1 AU magnetic field of coronal mass ejections: a parametric study

Aims. The magnetic field of coronal mass ejections (CMEs) determines their structure, evolution, and energetics, as well as their geoeffectiveness. However, we currently lack routine diagnostics of the near-Sun CME magnetic field, which is crucial for determining the subsequent evolution of CMEs. Methods. We recently presented a method to infer the near-Sun magnetic field magnitude of CMEs and then extrapolate it to 1 AU. This method uses relatively easy to deduce observational estimates of the magnetic helicity in CME-source regions along with geometrical CME fits enabled by coronagraph observations. We hereby perform a parametric study of this method aiming to assess its robustness. We use statistics of active region (AR) helicities and CME geometrical parameters to determine a matrix of plausible near-Sun CME magnetic field magnitudes. In addition, we extrapolate this matrix to 1 AU and determine the anticipated range of CME magnetic fields at 1 AU representing the radial falloff of the magnetic field in the CME out to interplanetary (IP) space by a power law with index aB. Results. The resulting distribution of the near-Sun (at 10 Rs ) CME magnetic fields varies in the range [0.004, 0.02] G, comparable to, or higher than, a few existing observational inferences of the magnetic field in the quiescent corona at the same distance. We also find that a theoretically and observationally motivated range exists around aB = -1.6 +-0.2, thereby leading to a ballpark agreement between our estimates and observationally inferred field magnitudes of magnetic clouds (MCs) at L1. Conclusions. In a statistical sense, our method provides results that are consistent with observations.

Scientific objectives and capabilities of the Coronal Solar Magnetism Observatory

AbstractMagnetic influences increase in importance in the solar atmosphere from the photosphere out into the corona, yet our ability to routinely measure magnetic fields in the outer solar atmosphere is lacking. We describe the scientific objectives and capabilities of the COronal Solar Magnetism Observatory (COSMO), a proposed synoptic facility designed to measure magnetic fields and plasma properties in the large‐scale solar atmosphere. COSMO comprises a suite of three instruments chosen to enable the study of the solar atmosphere as a coupled system: (1) a coronagraph with a 1.5 m aperture to measure the magnetic field, temperature, density, and dynamics of the corona; (2) an instrument for diagnostics of chromospheric and prominence magnetic fields and plasma properties; and (3) a white light K‐coronagraph to measure the density structure and dynamics of the corona and coronal mass ejections. COSMO will provide a unique combination of magnetic field, density, temperature, and velocity observations in the corona and chromosphere that have the potential to transform our understanding of fundamental physical processes in the solar atmosphere and their role in the origins of solar variability and space weather.

Diagnostics of Coronal Magnetic Fields through the Hanle Effect in UV and IR Lines

The plasma thermodynamics in the solar upper atmosphere, particularly in the corona, are dominated by the magnetic field, which controls the flow and dissipation of energy. The relative lack of knowledge of the coronal vector magnetic field is a major handicap for progress in coronal physics. This makes the development of measurement methods of coronal magnetic fields a high priority in solar physics. The Hanle effect in the UV and IR spectral lines is a largely unexplored diagnostic. We use magnetohydrodynamic (MHD) simulations to study the magnitude of the signal to be expected for typical coronal magnetic fields for selected spectral lines in the UV and IR wavelength ranges, namely the H I Ly-$\alpha$ and the He I 10830 {\AA} lines. We show that the selected lines are useful for reliable diagnosis of coronal magnetic fields. The results show that the combination of polarization measurements of spectral lines with different sensitivities to the Hanle effect may be most appropriate for deducing coronal magnetic properties from future observations.

Theory of Thomson scattering in inhomogeneous media.

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.

Blind Stereoscopy of the Coronal Magnetic Field

We test the feasibility of 3D coronal-loop tracing in stereoscopic EUV image pairs, with the ultimate goal of enabling efficient 3D reconstruction of the coronal magnetic field that drives flares and coronal mass ejections (CMEs). We developed an automated code designed to perform triangulation of coronal loops in pairs (or triplets) of EUV images recorded from different perspectives. The automated (or blind) stereoscopy code includes three major tasks: (i) automated pattern recognition of coronal loops in EUV images, (ii) automated pairing of corresponding loop patterns from two different aspect angles, and (iii) stereoscopic triangulation of 3D loop coordinates. We perform tests with simulated stereoscopic EUV images and quantify the accuracy of all three procedures. In addition we test the performance of the blind stereoscopy code as a function of the spacecraft-separation angle and as a function of the spatial resolution. We also test the sensitivity to magnetic non-potentiality. The automated code developed here can be used for analysis of existing {\sl Solar TErrestrial RElationship Observatory (STEREO)} data, but primarily serves for a design study of a future mission with dedicated diagnostics of non-potential magnetic fields. For a pixel size of 0.6\arcsec (corresponding to the {\sl Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA)} spatial resolution of 1.4\arcsec), we find an optimum spacecraft-separation angle of $\alpha_s \approx 5^\circ$.

Indications of 8-kilogauss magnetic field existence in the sunspot umbra

We present magnetic field diagnostics in two big sunspot of different magnetic polarity observed on 18 May 2002 and 29 October 2003. In these sunspots, according to visual measurements, magnetic field strength in Fe I 5250.2Ǻ line was about 3500 gauss. The existence of stronger fields follows from the detailed study of fine spectral effects in I±V and V profiles of Fe I 6301.5 and 6302.5Ǻ lines, such as: (a) non-parallelism of bisectors in Fe I 6301.5 line related to distance about ±250mǺ from the line center, and (b) weak secondary Stokes V peaks on distance, on the average, ±375mǺ from the Fe I 6302.5Ǻ center. Consequently, we argue that these peculiarities indicate to the fact that spatially unresolved magnetic fields exist in the sunspot umbra, their strength being about 8kG. In small structures with such very strong fields magnetic polarity was the same as in the background field of the sunspot umbra, and Doppler velocity is about −1.9km/s (lifting of plasma).

The Influence of Atomic Model on the Theoretical Profile of Scattering Polarization

The diagnosis of solar magnetic field is a very important part in the studies of solar physics. The Stokes parameters I, Q, U, and V can give a complete description of the state of polarized light. By an inversion of the observed Stokes parameters, the information of solar magnetic field can be diagnosed. In the recent decades, the diagnosis of magnetic field is mainly based on the Zeeman effect, by which the produced line splitting is used for the diagnosis of a strong magnetic field up to several hundred Gauss. But in the solar quiet regions, there exist a large amount of weak magnetic fields with a strength less than 100 Gauss, which can be diagnosed by the Hanle effect, thus the diagnosis of weak magnetic field by the Hanle effect is one of the main topics in the diagnostics of magnetic field, and a more completely understanding for the polarization mechanism is needed. This paper focuses on the influences of atomic model on the scattering-caused line profile, and the Hanle effect when there is magnetic field existed. We adopt the neutral magnesium as a target in the study, the seven-, four-, and two-level atomic models are selected to investigate respectively the influences of these atomic models on the scattering polarization and the Hanle effect. It is found that there is a great difference between the polarization degrees produced by the two-level atomic model and multi-level ones (the seven- and four-levels). For the two-level atomic model, the b4 line is not affected by the Hanle effect of low levels, but for the multi-level atomic models, it does. Comparing the seven- and four-level atomic models, the polarization degree of spectral lines only has a small variation, and the behavior of Hanle effect is basically the same. The main conclusion of this paper is that when the linear polarization Q/I profiles of the 3 neutral magnesium b lines are used for the inversion of magnetic field, at least the four-level atomic model should be adopted. This mainly depends on the atomic level distribution in the forming region of the spectral line, the atomic levels with a greater occupation number must be considered in the study.

Scattering polarization of Mg I b triplet in solar chromosphere

Aims. The magnetic field in the chromosphere of the quiet sun is too weak to be diagnosed via the general Zeeman effect. To obtain the hidden magnetic field vector, a complete comprehension of the linear polarization produced by scattering and modified by magnetic field is needed. We report a systematic and quantitative investigation of the sensitivity of the fractional linear polarization of the magnesium triplet to a weak magnetic field in the chromosphere, which can be a guide for the diagnostics of a weak magnetic field in the solar chromosphere. Methods. We focus on the fractional linear polarization of the magnesium triplet induced by scattering. We use the quantum theory under the flat-spectrum approximation developed by Landi Degl'Innocenti for the investigation. A seven-level atomic model of magnesium is adopted, while we do not take the radiative transfer or partial frequency redistribution (PRD) into account. Results. Polarization is directly related to the anisotropy factor, and modified by the continuum, collision, and magnetic field as well as dichroism effect. In our calculation, the elastic collision rates found are not large enough to destroy the population imbalances of the lower levels of the b(2) and b(1) lines. This is the prerequisite for the lower level Hanle effect and dichroism effect. When considering the dichroism effect, the magnetic field can influence the polarization not only in the line cores but also in the line wings. However, the magnetic field cannot obviously influence the polarization degree in the line wings once the continuum becomes significant. The polarization of the triplet is sensitive to the magnetic field between 0.001 and 0.1 Gauss due to the lower level Hanle effect and between 1 and 10 Gauss due to the upper level Hanle effect. In the lower level Hanle effect dominated region, the Q/I amplitude of the b(4) line increases with magnetic field strength because of the coupling among atomic alignments of the involved levels as described in the statistical equilibrium equations, while the amplitudes of the b2 and b1 lines decrease. In the upper level Hanle effect dominated region, the most sensitive line is the b(4). Conclusions. The polarized lower levels and the contribution of dichroism have to be considered to fit the observed profiles of Mg I b triplet in the line cores. Therefore the b(2) and b(1) lines can be potential candidates for probing sub-Gauss range magnetic field, because their Q/I amplitudes are sensitive to the magnetic field strength between 0.001 and 0.1 Gauss due to the lower level Hanle effect. The b(4) line is suitable for diagnostics of magnetic field between 1 Gauss and 10 Gauss.

Paschen-Back effect involving atomic fine and hyperfine structure states

AbstractThe linear polarization in spectral lines produced by coherent scattering is significantly modified by the quantum interference between the atomic states in the presence of a magnetic field. When magnetic fields produce a splitting which is of the order of or greater than the fine or hyperfine structure splittings, we enter the Paschen-Back effect (PBE) regime, in which the magnetic field dependence of the Zeeman splittings and transition amplitudes becomes non-linear. In general, PBE occurs for sufficiently strong fields when the fine structure states are involved and for weak fields in the case of hyperfine structure states. In this work, we apply the recently developed theory of PBE in the atomic fine and hyperfine structure states including the effects of partial frequency redistribution to the case of Li i 6708 Å doublet. We explore the signatures of PBE in a single scattering event and their applicability to the solar magnetic field diagnostics.

Spatial variations of Stokes profiles of magnetoactive lines Fe I

Solutions of the polarized radiative transfer problem were obtained within the 3D MHD model of the quiet solar atmosphere. Spatial variations of the Stokes profile parameters caused by the granulation structure and small-scale magnetic fields in the quiet solar photosphere for neutral iron magnetoactive lines are studied. The modulation effect of Stokes V profile parameters (amplitude and area) by the granulation structure of the solar photosphere is revealed. This effect is significant mainly in intergranules, in which the modulation depth reaches 50%. The correlation of Stokes profile parameters with small-scale solar granulation magnetic fields is investigated. It is shown that it is possible to construct calibration relationships that provide the correlation coefficient of 0.98 in diagnostics of small-scale magnetic fields using Stokes profile parameters of Fe I lines λ 525.02 and λ 524.71 nm.

Small-scale magnetic field diagnostics in solar flares using bisectors of I ± V profiles

In the present study, spatially unresolved magnetic fields in solar flares are investigated by analyzing the fine structure of Zeeman splitting in two FeI lines. Namely, we consider bisector splitting of I±V Stokes profiles in 5123.7 and 5233Ǻ lines. The analysis of bisector splitting functions (BSF) of the 5233Ǻ line averaged over 12 solar flares of different classes, from C5 to X1.4, reveals two distinct peaks, around Δλ=80–110mǺ and 170–200mǺ. Such peculiarities indicate the unacceptability of weak field approximation for FeI 5233 line and need interpretation in the framework of inhomogeneous models with strong magnetic field components. Consequently, we argue that the named two peaks can reflect the existence of two discrete modes of subtelescopic magnetic fields with strengths about 6 and 12kG in photospheric layers.

On the diagnostics of solar small scale magnetic fields

The model of small scale magnetic fields was proposed. The fields are described by two distribution functions: for unsigned magnetic field and for field vectors directions. The distribution functions were used to derive expressions for elements of the line absorption matrix and to deduce function that characterizes mutual cancellation of magnetic fields. We received the solutions for polarized radiative transfer problem within 3D MHD model of the solar photosphere and determined Stokes profiles parameters for two magnetosensitive lines Fe I λ525.0nm and λ524.7nm. The Stokes profiles parameters of the lines were used for further test diagnostics of small scale magnetic fields. A regression approach to diagnostics of the magnetic fields was proposed. The correlation between theoretical and reproduced parameters of small scale magnetic fields is greater than 0.95.