Structure of a simple sunspot from the inversion of IR spectral data

Analysis of spectral data of two neighboring infrared lines, Fe I 15648.5 Å (g = 3) and FeI 15652.9 Å (g_eff = 1.53) are carried out for a simple sunspot when it was near the solar disk center (μ = 0.92), to understand the basic structure of sunspot magnetic field. Inversions of Stokes profiles are carried out to derive different atmospheric parameters both as a function of location within the sunspot and height in the atmosphere. As a result of the inversion we have obtained maps of magnetic field strength, temperature, line‐of‐sight velocity, field inclination and azimuth for different optical depth layers between log(τ₅) = 0 and log(τ₅) = –2.0. In this paper we present few results from our inversion for a layer averaged between log(τ5) from 0.0 to –0.5.     

Oscillations in a solar pore

Temporal variations of a solar pore were observed at the ground based Vacuum Tower Telescope (VTT) on Tenerife and with the satellite TRACE. At the VTT Stokes I and V of the iron line at 1.56μm originating in the deep photosphere, was measured. TRACE delivered UV images at 170 nm which show chromospheric continuum. In a part of the pore we find oscillations of the magnetic field in the 5 minute range. Velocities derived from shifts of the Stokes V profiles show 5 minutes everywhere in the pore, but the coherence of magnetic field and velocities is low. The intensity at 170 nm varies with 3 minutes, and for a part of the whole time series additionally with 4 minutes.     

Imaging Spectropolarimetry of Ti I 2231 nm in a Sunspot

Spectro-polarimetric observations at 2231 nm were made of NOAA 10008 near the west solar limb on 29 June 2002 using the National Solar Observatory McMath–Pierce Telescope at Kitt Peak and the California State University Northridge – National Solar Observatory infrared camera. Scans of spectra in both Stokes I and Stokes V were collected; the intensity spectra were processed to remove strong telluric absorption lines, and the Stokes V umbral spectra were corrected for instrumental polarization. The sunspot temperature is computed using the continuum contrast and umbral temperatures down to about 3700 K are observed. A strong Tii line at 2231.0 nm is used to probe the magnetic and velocity fields in the spot umbra and penumbra. Measurements of the Tii equivalent width versus plasma temperature in the sunspot agree with model predictions. Zeeman splitting measurements of the Stokes I and Stokes V profiles show magnetic fields up to 3300 G in the umbra, and a dependence of the magnetic field on the plasma temperature similar to that which was seen using Fei 1565 nm observations of the same spot two days earlier. The umbral Doppler velocity measurements are averaged in 16 azimuthal bins, and no radial flows are revealed to a limit of ±200 m s^–1. A Stokes V magnetogram shows a reversal of the line-of-sight magnetic component between the limb and disk center sides of the penumbra. Because the Tii line is weak in the penumbra, individual spectra are averaged in azimuthal bins over the entire penumbral radial extent. The averaged Stokes V spectra show a magnetic reversal as a function of sunspot azimuthal angle. The mean penumbral magnetic field as measured with the Stokes V Zeeman component splitting is 1400 G. Several weak spectral lines are observed in the sunspot and the variation of the equivalent width versus temperature for four lines is examined. If these lines are from molecules, it is possible that lines at 2230.67, 2230.77, and 2231.70 nm originate from OH, while the line at 2232.21 nm may originate from CN.     

Observational evidences for multi-component magnetic field structure in solar flares

Two solar flares of 25 July 1981 and 5 November 2004 of importance 2N and M4.1/1B, respectively, were investigated using observational data obtained with the Echelle spectrograph of the Kyiv University Astronomical Observatory. Stokes I and V profiles of the FeI lines 5233, 5247.1, 5250.2, 5250.6, 5576.1 and of CrI 5247.6 Å have been analyzed. We found several evidences for the existence of spatially unresolved magnetic field structures with kG strengths. In particular, the values of the measured average longitudinal field B _∥ depend on the Lande factors g of the lines: in general, B _∥ increases with increasing factor g. Analogously, the observed line ratio B _∥(5250.2)/B _∥(5247.1) is increasing with increasing distance Δλ from the line center. The observed Stokes V profiles show some deviations from that of an assumed homogeneous field, presented by the Stokes I gradient, dI/dλ. A comparison with the non-split line FeI 5576.1 Å shows that some of these deviations are real and indicate the presence of subtelescopic magnetic elements with discrete field strengths of several kG. The lines with large Lande factors have considerable broadenings of the Stokes I profiles, indicating a strong background magnetic field of mixed polarity. On the basis of all these data we conclude that a four-component magnetic field structure is a possible explanation. The field strengths are about ±1.05 kG in the background field, and 1.3?1.5, 3.9?4.0, and 7.4?7.8 kG at level of middle photosphere (h ≈ 300 km) in the spatially unresolved, small-scale magnetic elements.     

The formation of asymmetric Stokes V profiles in the presence of a magnetopause

A magnetopause that separates two regimes of different flow, additional to the separation of a magnetic field from a field-free plasma, gives rise to the formation of asymmetric Stokes profiles. Using a simple two-layer model atmosphere, where one layer comprises a magnetic field, the other being field-free, it is shown by analytical derivation that a wide variety of Stokes V profiles can be produced, having amplitude asymmetries a in the range –a. These include two-humped V profiles, which have two lobes of equal sign. For the most simple models, the asymmetry depends on the ratio of continuum intensity to the Planck radiation intensity of the magnetic layer at the wavelength of the spectral line under consideration, and on the line depth. Two-humped profiles (|a|>1) require the temperature of the magnetic layer to surpass the temperature of the line-core forming region, implying a temperature inversion, so that the V profile is partially in emission. The confrontation of this formation scenario with properties of observed one-lobe profiles of quiet-Sun network regions is inconclusive due to insufficient spatial resolution and lack of a sufficient sample of simultaneously recorded Stokes spectral lines of varying line depths. It seems, however, to be in good agreement with the observed frequent occurrence of abnormal V profiles of the very strong Nai D ₂ and D ₂ spectral line. A possible observational verification for the present formation scenario of abnormal Stokes V profiles and a novel method of Stokes inversion are discussed.     

The determination of the solar vector magnetic field at the surface from Stokes profiles

A simple method is proposed to infer the vector magnetic field at the surface of the Sun from Stokes profiles. This is based on the assumption that the variations of thermodynamical and magnetic field parameters with depth near the surface are so small that the displacements of the wavelengths at which the Stokes profiles reach their extrema can be ignored. And hence the polarized radiative transfer equations are greatly reduced to a set of non-linear equations with vector magnetic field parameters (, , ) which can be solved by a numerical iteration method. By fitting the synthetic profiles, it is shown that this proposed method can produce information on the vector field at the surface. It is also used to revise the observed profiles and it is found that the observed sunspot has the magnetic field structure of the fan model with the lines of magnetic field twisted.     

Abnormal Stokes Profiles of the Photospheric Lines in the Region of Chromospheric Dual Flows in the Surroundings of a Solar Pore: 1. Observations

The results of the analysis of the full Stokes profiles of the photospheric lines Fe I λ 630.15 nm and Fe I λ 630.25 nm in a region of chromospheric dual flows appearance in the vicinity of a small pore are presented. The analysis is based on the spectropolarimetric observations of the active region NOAA 11024 with the THEMIS French–Italian telescope (Tenerife Island, Spain). The temporal variations in the high-resolution Stokes parameters I, Q, U, and V were considered for each pixel. It was found that the dual chromospheric flows appeared in the region of the abnormal Stokes profiles of the photospheric lines. Most of the Stokes profiles Q, U, and V have a complex shape and vary greatly from pixel to pixel, which indicates strong inhomogeneities in the structure of the magnetic field in that region. The amplitude and shape of the Stokes profiles were rapidly changing during the observations. A change in the polarity of the photospheric magnetic field took place during the observations in the region of a bright chromospheric point. The evidence of the emergence of a new small-scale magnetic flux of the opposite polarity is obtained; this could lead to magnetic reconnections, appearance of dual chromospheric flows, and occurrence of a microflare.     

A relation between magnetic field strength and temperature in sunspots

We present Stokes I Zeeman splitting measurements of sunspots using the highly sensitive (g = 3) Fe i line at = 1.5649 m. The splittings are compared with simultaneous intensity measurements in the adjacent continuum. The relation between magnetic field strength and temperature has a characteristic, nonlinear shape in all the spots studied. In the umbra, there is an approximately linear relation between B ² and T _b, consistent with magnetohydrostatic equilibrium in a nearly vertical field. A distinct flattening of the B ² vs T _brelationship in the inner penumbra may be due to changes in the lateral pressure balance as the magnetic field becomes more horizontal; spatially unresolved intensity inhomogeneities may also influence the observed relation.Operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation.     

Heights of formation of non-magnetic solar lines suitable for velocity studies

Heights of formation of lines that do not exhibit Zeeman splitting are calculated using an LTE, partial non-LTE, and full non-LTE approach. Non-magnetic (g=0) lines are valuable for velocity investigations in quiet-Sun magnetic field regions, and a knowledge of their formation heights is useful for obtaining three dimensional velocity profiles in these regions. Presently at Sacramento Peak Observatory. Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

On the diagnostic of magnetic fields in sunspots through the interpretation of stokes parameters profiles

The inversion routine proposed by Aueret al. (1977), for the determination of vector magnetic fields from Stokes profiles, has been generalized to include magneto-optical and damping effects. Synthetic profiles have then been generated from a sunspot model atmosphere accounting for the depth variation of the relevant physical parameters such as the magnetic field amplitude, inclination angle, etc...., each variation being considered one at a time. Alfvén waves and magnetic inhomogeneities over the field of view have also been considered. These synthetic profiles have been presented to the inversion routine. The results of the fits show that the magnetic field amplitude and direction are always recovered with good accuracy when these quantities are constant in the model atmosphere, and, in those cases where te magnetic field vector is supposed to vary monotonically with optical depth, the values recovered are always intermediate between the values corresponding to the top and bottom of the atmosphere. Moreover, we found that the differences between synthetic and best-fit profiles are able to characterize, in many cases, the particular physical situation considered.     

High-precision magnetic field measurements of Ap and Bp stars

In this paper we describe a new approach for measuring the mean longitudinal magnetic field and net linear polarization of Ap and Bp stars. As was demonstrated by Wade et al., least-squares deconvolution (LSD; Donati et al.) provides a powerful technique for detecting weak Stokes V , Q and U Zeeman signatures in stellar spectral lines. These signatures have the potential to apply strong new constraints to models of stellar magnetic field structure. Here we point out two important uses of LSD Stokes profiles. First, they can provide very precise determinations of the mean longitudinal magnetic field. In particular, this method allows one frequently to obtain 1 σ error bars better than 50 G, and smaller than 20 G in some cases. This method is applicable to both broad- and sharp-lined stars, with both weak and strong magnetic fields, and effectively redefines the quality standard of longitudinal field determinations. Secondly, LSD profiles can in some cases provide a measure of the net linear polarization, a quantity analogous to the broad-band linear polarization recently used to derive detailed magnetic field models for a few stars (e.g. Leroy et al.). In this paper we report new high-precision measurements of the longitudinal fields of 14 magnetic Ap/Bp stars, as well as net linear polarization measurements for four of these stars, derived from LSD profiles.     

High resolution observations of small-scale magnetic elements and interpretation

This contribution deals with the properties of small-scale magnetic elements in plages. Spectro-polarimetric observations, obtained with the highest possible spatial resolution with the German solar telescopes at the Observatorio del Teide on Tenerife, were analysed. We conclude from the spread of line parameters measured in the Stokes I and V profiles of Fe I and Fe II lines that a wide range of magnetic properties is realised in the solar atmosphere. The flow velocities in small-scale magnetic flux tubes, deduced from the zero-crossing of the V profiles at high spatial resolution, show a fluctuation of v _Doppler = 580 m s^-1. This is substantially smaller than the turbulent broadening velocities of v _Doppler = 2 – 3 km s^–1 commonly derived by fitting V profiles from flux tube models to low spatial resolution data, e.g. from a Fourier Transform Spectrometer. Attempts to explain the high resolution I and V profiles by models of hydrostatic flux tubes are discussed. It appears impossible to accomplish agreement between the modeled and observed radiation of lines with strong and weak magnetic sensitivity at the same time. We suggest a scenario in which small-scale magnetic elements possess substructure and are dynamic, with gas flows and magnetic field strengths varying in space and time.     

Measuring Magnetic Oscillations in the Solar Photosphere: Coordinated Observations with MDI,ASP and MWO

A comprehensive observing effort was undertaken to simultaneously obtain full Stokes profiles as well as longitudinal magnetogram maps of a positive plage region on 8 December, 1998 with the Michelson Doppler Imager, the Advanced Stokes Polarimeter and Mt. Wilson Observatory magnetograph. We compare 1.2 spatially-averaged signals of velocities as well as filter magnetograph longitudinal flux signals with Stokes determined fluctuations in filling factor, field inclination, magnetic flux and field strength. The velocity signals are in excellent agreement. Michelson Doppler Imager magnetic flux correlates best with fluctuations in the Advanced Stokes Polarimeter filling factor, not inclination angle or field strength. A correlated flux and filling factor change in the absence of a field strength fluctuation can be understood in terms of internally unperturbed flux tubes being buffeted by external pressure fluctuations. The 12.5 square aperture spatially averaged Mt. Wilson magnetograph signals are compared with Michelson Doppler Imager signals from the corresponding observing area. Velocity signals are in superb agreement. Magnetic signals exhibit similar oscillatory behavior. Lack of Advanced Stokes Polarimeter data for this time excludes interpretation of magnetic fluctuations as due to filling factor or field inclination angle. Mt. Wilson Observatory simultaneous sampling of the nickel and sodium spectral line profiles with several wing pairs allowed inter-comparison of signals from different heights of formation. Slight phase shifts and large propagation speeds for the velocity signals are indicative of modified standing waves. Phase speeds associated with magnetic signals are characteristic of photospheric Alfvén speeds for plage fields. The phase speed increase with height agrees with the altitude dependence of the Alfvén speed. The observed fluctuations and phases are interpreted as a superposition of signatures from the horizontal component of the driving mechanism sweeping the field lines in/out of the resolution area and the magnetic response of the flux tube to this buffeting.     

Modified methods of stellar magnetic field measurements

The standard methods of the magnetic field measurement, based on an analysis of the relation between the Stokes V‐parameter and the first derivative of the total line profile intensity, were modified by applying a linear integral operator L to both sides of this relation. As the operator L, the operator of the wavelet transform with DOG‐wavelets is used. The key advantage of the proposed method is an effective suppression of the noise contribution to the line profile and the Stokes parameter V. The efficiency of the method has been studied using model line profiles with various noise contributions. To test the proposed method, the spectropolarimetric observations of the A0 star α² CVn, the Of?p star HD 148937, and the A0 supergiant HD 92207 were used. The longitudinal magnetic field strengths calculated by our method appeared tobe in good agreement with those determined by other methods. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Inversion of Stokes vector profiles in terms of a 3-component model

Various spectropolarimetric observations show peculiar Stokes profiles that reveal the coexistence of at least two magnetic components in the same resolution element. An example is given by observations of the full Stokes vector in a complex active region performed with the ZIMPOL I Stokes polarimeter. In order to deduce the physical parameters of the observed regions from such measured profiles, we have extended an existing inversion code, so that it can now fit the data with models composed of up to three different atmospheric components. Two of these components are magnetic and may possess different field strengths, field geometries, temperature stratifications, and velocity fields. The third component describes the field free atmosphere surrounding the magnetic features.The so extended inversion code has then been applied to the ZIMPOL I data. In this paper we present and discuss sample fits. The code is able to reproduce the observed complex Stokes profiles with good accuracy and provides physical parameters for both of the coexisting magnetic atmospheres. Inversion tests with a 2-component model (with one magnetic and one non-magnetic component) applied to the same profiles do not reproduce the measurements sufficiently well.     

太阳Stokes光谱望远镜的结构及其数据处理方法

云南天文台的太阳Stokes光谱望远镜是一台通过测量磁敏谱线的Stokes参数I,Q,U和V的轮廓来研究太阳磁场精细结构的光谱型矢量磁场测量仪。它利用4个完整的Stokes轮廓所蕴含的丰富信息,完全确定辐射的偏振状态,从而精确地测定太阳黑子区的矢量磁场。文章首先介绍了该望远镜的结构,进而详细地介绍了该望远镜所测量的偏振光谱资料的处理方法。     

Photospheric Stratification of a Central Umbral Dot Using Stokes Profiles Recorded by Hinode: A Different Single-Case Study

We aim to study the physical nature of a central umbral dot (UD) close to disk center by analyzing full-Stokes spectra of the two Fe?i lines at 630 nm recorded by the spectropolarimeter on Hinode. Thermal and magnetic properties of the UD were directly inferred from Stokes profiles. Then, we applied the inversion code SIR to retrieve a single-component magnetic model atmosphere that recovers the observed full-Stokes profiles. The inversion results and direct inferences from the iron line pair are consistent. The studied UD does not show any signatures of upflows, but tends to show downflows. At the deeper-half of the photosphere (logτ>?1.0), the UD exhibits rapid changes in temperature with respect to its surroundings. The UD has a large magnetic field strength of about 3000 G without significant reduction at its center. Magnetic field lines are more vertical and twisted in the UD area than in the magnetic field of its surroundings. To explain the observational findings, we propose that the UD perturbs the funnel magnetic field of the umbra, making a tilt-ankle-knee configuration. A new interesting inference, deduced from the blending spectral lines in the observed wavelength interval, is that the shape and surface span of the UD in normalized intensity filtergrams computed at the core of the blending lines differ from the UD area seen in continuum intensity and in the filtergrams computed at the core of the iron line pair.     

Simultaneous Stokes-V diagnostic of a Sunspot using Mg b and Fe I lines

Simultaneous observations of Stokes profiles in photospheric Fei (630.15 nm and 630.25 nm) and chromospheric Mgi b ₁ and b ₂ (518.4 nm and 517.3 nm) lines over a sunspot are presented. Observations were carried out using the Advanced Stokes Polarimeter of HAO/NSO, VTT, SacPeak, U.S.A. The Stokes-V amplitude asymmetries for these lines are analyzed. The values of amplitude asymmetry in Mgb lines are negative in disk-center-side penumbra while they are positive in limb-side penumbra. This trend is similar in nature to photospheric Fei line observations. Further, the spatial distribution of Stokes-V asymmetry is analyzed using Net Circular Polarization (NCP) maps. The chromospheric and photospheric NCP maps are different in many aspects. These observations with longitudinal magnetic field, estimated using weak field approximation, are discussed in this paper.     

The polarization-free approximation applied to multi-level non-LTE radiative transfer

The polarization-free (POF) approximation (Trujillo Bueno and Landi Degl'Innocenti, 1996) is capable of accounting for the approximate influence of the magnetic field on the statistical equilibrium, without actually solving the full Stokes vector radiative transfer equation. The method introduces the Zeeman splitting or broadening of the line absorption profile I in the scalar radiative transfer equation, but the coupling between Stokes I and the other Stokes parameters is neglected. The expected influence of the magnetic field is largest for strongly-split strong lines and the effect is greatly enhanced by gradients in the magnetic field strength. Formally the interaction with the other Stokes parameters may not be neglected for strongly-split strong lines, but it turns out that the error in Stokes I obtained through the POF approximation to a large extent cancels the neglect of interaction with the other Stokes parameters, so that the resulting line source functions and line opacities are more accurate than those obtained with the field-free approach. Although its merits have so far only been tested for a two-level atom, we apply the POF approximation to multi-level non-LTE radiative transfer problems on the premise that there is no essential difference between these two cases. Final verification of its validity in multi-level cases still awaits the completion of a non-LTE Stokes vector transfer code.For two realistic multi-level cases (CaII and MgI in the solar atmosphere) it is demonstrated that the POF method leads to small changes, with respect to the field-free method, in the line source functions and emergent Stokes vector profiles (much smaller than for a two-level atom). Real atoms are dominated by strong ultraviolet lines (only weakly split) and continua, and most lines with large magnetic splitting (in the red and the infrared) are at higher excitation energies, i.e. they are relatively weak and unable to produce significant changes in the statistical equilibrium. We find that it is generally unpredictable by how much the POF results will differ from the field-free results, so that it is nearly always necessary to confirm predictions by actual computations.The POF approximation provides more reliable results than the field-free approximation without significantly complicating the radiative transfer problem, i.e. without solving any extra equations and without excessive computational resource requirements, so that it is to be preferred over the field-free approximation.     

High-resolution spectroscopy of active regions

This paper discusses the analysis of spectrograms of solar magnetic structures obtained with high spatial resolution in both directions of circular polarization, with application to observations of flux emergence. We assume each spatial resolution element to contain two atmospheric components: mean non-magnetic photosphere and unresolved magnetic structure. We first define observable spectral-line parameters, and then calibrate the derivation of magnetic-structure parameters by computer simulations in which we vary the fractional contribution of the magnetic component, its field strength and its field inclination, and the line-of-sight velocity difference between the components. This grid of synthesized profiles then serves to define the uniqueness and margins of trial-and-error fits to the observed parameters.We present results for an emerging flux region. Magnetic flux is present over most of its area. The magnetic field strength outside pores is between 100 and 1700 G, and in one magnetic knot it is about 1150 G. The field inclination and the fractional area cannot be determined separately, but the mean magnetic flux density is well determined: it ranges between 80 and 120 G, and in some patches and the knot between 120 and 210 G.There is a strong downflow just outside a fast-growing pore.