On the Collective Magnetic Field Strength and Vector Structure of Dark Umbral Cores Measured by the Hinode Spectropolarimeter

We study 7530 sunspot umbrae and pores measured by the Hinode Spectropolarimeter (SP) between November 2006 and November 2012. We primarily seek confirmation of the long term secular decrease in the mean magnetic field strength of sunspot umbrae found by Penn and Livingston (IAU Symp. 273, 126, 2011) between 1998 and 2011. The excellent SP photometric properties and full vector magnetic field determinations from full-Stokes Milne–Eddington inversions are used to address the interrelated properties of the magnetic field strength and brightness temperature for all umbral cores. We find non-linear relationships between magnetic field strength and umbral temperature (and continuum contrast), as well as between umbral radius and magnetic field strength. Using disambiguated vector data, we find that the azimuths measured in the umbral cores reflect an organization weakly influenced by Joy’s law. The large selection of umbrae displays a log-normal size spectrum similar to earlier solar cycles. Influenced by the amplitude of the solar cycle and the non-linear relationship between umbral size and core magnetic field strength, the distribution of core magnetic field strengths, fit most effectively with a skew-normal distribution, shows a weak solar cycle dependence. Yet, the mean magnetic field strength does not show a significant long term trend.     

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Overview and Performance

The Helioseismic and Magnetic Imager (HMI) began near-continuous full-disk solar measurements on 1 May 2010 from the Solar Dynamics Observatory (SDO). An automated processing pipeline keeps pace with observations to produce observable quantities, including the photospheric vector magnetic field, from sequences of filtergrams. The basic vector-field frame list cadence is 135 seconds, but to reduce noise the filtergrams are combined to derive data products every 720 seconds. The primary 720 s observables were released in mid-2010, including Stokes polarization parameters measured at six wavelengths, as well as intensity, Doppler velocity, and the line-of-sight magnetic field. More advanced products, including the full vector magnetic field, are now available. Automatically identified HMI Active Region Patches (HARPs) track the location and shape of magnetic regions throughout their lifetime. The vector field is computed using the Very Fast Inversion of the Stokes Vector (VFISV) code optimized for the HMI pipeline; the remaining 180^° azimuth ambiguity is resolved with the Minimum Energy (ME0) code. The Milne–Eddington inversion is performed on all full-disk HMI observations. The disambiguation, until recently run only on HARP regions, is now implemented for the full disk. Vector and scalar quantities in the patches are used to derive active region indices potentially useful for forecasting; the data maps and indices are collected in the SHARP data series, hmi.sharp_720s. Definitive SHARP processing is completed only after the region rotates off the visible disk; quick-look products are produced in near real time. Patches are provided in both CCD and heliographic coordinates. HMI provides continuous coverage of the vector field, but has modest spatial, spectral, and temporal resolution. Coupled with limitations of the analysis and interpretation techniques, effects of the orbital velocity, and instrument performance, the resulting measurements have a certain dynamic range and sensitivity and are subject to systematic errors and uncertainties that are characterized in this report.     

Imaging Spectroscopy of a White-Light Solar Flare

We report observations of a white-light solar flare (SOL2010-06-12T00:57, M2.0) observed by the Helioseismic Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO) and the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The HMI data give us the first space-based high-resolution imaging spectroscopy of a white-light flare, including continuum, Doppler, and magnetic signatures for the photospheric Fe i line at 6173.34 Å and its neighboring continuum. In the impulsive phase of the flare, a bright white-light kernel appears in each of the two magnetic footpoints. When the flare occurred, the spectral coverage of the HMI filtergrams (six equidistant samples spanning ±172 mÅ around nominal line center) encompassed the line core and the blue continuum sufficiently far from the core to eliminate significant Doppler crosstalk in the latter, which is otherwise a possibility for the extreme conditions in a white-light flare. RHESSI obtained complete hard X-ray and γ-ray spectra (this was the first γ-ray flare of Cycle 24). The Fe i line appears to be shifted to the blue during the flare but does not go into emission; the contrast is nearly constant across the line profile. We did not detect a seismic wave from this event. The HMI data suggest stepwise changes of the line-of-sight magnetic field in the white-light footpoints.     

On the Formation Height of the SDO/HMI Fe 6173 ? Doppler Signal

The Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO) is designed to study oscillations and the magnetic field in the solar photosphere. It observes the full solar disk in the Fe?i absorption line at 6173 Å. We use the output of a high-resolution, 3D, time-dependent, radiation-hydrodynamic simulation based on the CO ⁵ BOLD code to calculate profiles F(??,x,y,t) for the Fe?i 6173 Å line. The emerging profiles F(??,x,y,t) are multiplied by a representative set of HMI filter-transmission profiles R _i (??, 1??i??6) and filtergrams I _i (x,y,t; 1??i??6) are constructed for six wavelengths. Doppler velocities V _HMI(x,y,t) are determined from these filtergrams using a simplified version of the HMI pipeline. The Doppler velocities are correlated with the original velocities in the simulated atmosphere. The cross-correlation peaks near 100 km, suggesting that the HMI Doppler velocity signal is formed rather low in the solar atmosphere. The same analysis is performed for the SOHO/MDI Ni?i line at 6768 Å. The MDI Doppler signal is formed slightly higher at around 125 km. Taking into account the limited spatial resolution of the instruments, the apparent formation height of both the HMI and MDI Doppler signal increases by 40 to 50 km. We also study how uncertainties in the HMI filter-transmission profiles affect the calculated velocities.     

Physical properties of solar chromospheric plages

We propose chromospheric models of plages to explain profiles of the Ca ii H, K, λl8498, λ8542, and λ8662 lines described in Paper I. These models are consistent with boundary conditions imposed by the photosphere and the Lyman continuum. We find that increasing emission in these lines is consistent with a picture of increasing temperature gradient in the low chromosphere and the resulting increase in pressure and electron density at similar line optical depths. With this picture we suggest how to empirically determine the distribution of chromospheric parameters across the solar disk directly from Ca ii filtergrams. We also propose that the high density aspects of solar activity are produced by steep temperature gradients in the low chromosphere and thus by the enhanced heating mechanisms that steepen these gradients.     

Bidimensional analysis of solar active regions and flares

We describe a method of solar bidimensional spectroscopy exploiting the performances of a Universal Birefringent Filter (UBF) like that of the Sacramento Peak Observatory, which enable an estimate of the profile of some chromospheric lines with moderate spectral resolution ( \((\lambda /\Delta \lambda = 2.5 x 10^4 )\) ). The numerical inversion technique of Backus and Gilbert has been used to retrieve the estimated line profiles; the capabilities of the proposed method is fully analyzed with some numerical tests and examples. Correction procedures for errors in the positions of the UBF passband, random fluctuations of the exposure times and non-uniform brightness distribution on the filtergrams are also presented. The whole method has been tested on the recovery of quiet atmosphere line profiles and the results derived for the Na D₂ line show that the proposed method is completely suitable for many investigations in solar physics.     

Observations of Unresolved Photospheric Magnetic Fields in Solar Flares Using Fe i and Cr i Lines

The structure of the photospheric magnetic field during solar flares is examined using echelle spectropolarimetric observations. The study is based on several Fe i and Cr i lines observed at locations corresponding to brightest Hα emission during thermal phase of flares. The analysis is performed by comparing magnetic-field values deduced from lines with different magnetic sensitivities, as well as by examining the fine structure of I±V Stokes-profiles’ splitting. It is shown that the field has at least two components, with stronger unresolved flux tubes embedded in weaker ambient field. Based on a two-component magnetic-field model, we compare observed and synthetic line profiles and show that the field strength in small-scale flux tubes is about 2?–?3 kG. Furthermore, we find that the small-scale flux tubes are associated with flare emission, which may have implications for flare phenomenology.     

Spectropolarimetric investigation of an Ellerman bomb: 2. Photospheric models

Semiempirical models of the photosphere of an Ellerman bomb in the NOAA 11024 active region were obtained using profiles of Stokes parameters I, Q, U, and V of photospheric lines. Spectropolarimetric observations were conducted using the French–Italian THEMIS telescope (Tenerife, Spain). The SIR inversion code [28] was used in the modeling. The models have two components: a magnetic flux tube and nonmagnetic surroundings. The dependences of temperature, magnetic field strength, inclination of the magnetic field vector, and line-of-sight velocity in the tube on the optical depth were obtained. The models demonstrate that the thermodynamic parameters of the Ellerman bomb photosphere differ considerably from those of the quiet photosphere. The temperature in the tube model varied nonmonotonically with height and deviated by up to 700–900 K from its values for the quiet photosphere. Downflows were observed in the lower and the upper photospheric layers. The line-of-sight velocity in the upper layers of the photosphere was as high as 17 km/s. The magnetic field strength in the models varied from 0.1–0.13 T in the lower photospheric layers to 0.04–0.07 T in the upper ones. The physical state of the photosphere did change in the course of observations.     

Doppler-Zeeman mapping of the rapidly rotating magnetic CP star HD 37776

We present the results of our analysis of magnetic-field configuration and abundance anomalies on the surface of the rapidly rotating, chemically peculiar helium-strong variable B2 V star HD 37776 with unresolved Zeeman components of spectral lines. Simultaneous inversion of the observed Stokes I and V profiles, which realizes the method of Doppler-Zeeman mapping [1], has been applied for the first time. Spectroscopic observations were carried out with the Main stellar spectrograph of the 6-m Special Astrophysical Observatory telescope equipped with a Zeeman analyzer and a CCD array, which allowed spectra in right-and left-hand circularly polarized light to be taken simultaneously at a signal-to-noise ratio S/N≥200 [2]. The profile width of winged spectral lines (reaching 5 Å) is determined by Zeeman line splitting; however, the observed Zeeman components are blurred and unresolved because of the rapid stellar rotation. When solving the inverse problem, we sought for the magnetic-field configuration in the form of a combination of arbitrarily oriented dipole, quadrupole, and octupole placed at the stellar center. The observed Stokes I and V profiles for eight spectral lines of He, O II, Al III, Si III, and Fe III averaged over the visible stellar surface were used as input data. We constructed a model of the magnetic field from the condition of coincidence of magnetic maps obtained from different lines of different chemical elements and from the condition of a minimum profile residual. This model is a combination of centered coaxial dipole and quadrupole with the dominant quadrupole component at 30°<i<50°, β=40°, and a maximum surface field strength H _s=60 kG. A comparison of our abundance maps with the field configuration shows that the He concentration is at a maximum in the regions of maximum radial field, while the maximum concentrations of O, Al, Si, and Fe coincide with the regions of maximum tangential field.     

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.     

Asymmetries in stokes profiles of magnetic lines: A linear analysis in terms of velocity gradients

A linear analysis of the asymmetries in Stokes profiles of magnetic lines is performed. The asymmetries in the linear and circular polarization profiles are characterized by suitable quantities, \(\delta \tilde Q\) and \(\delta \tilde V\) , strictly related to observed profiles. The response functions of \(\delta \tilde Q\) and \(\delta \tilde V\) to velocity fields are introduced and computed for various configurations of the magnetic field vector in a Milne-Eddington atmosphere. Some conclusions are drawn as to the importance of the asymmetries in Stokes profiles for recovering the velocity gradients from observations.     

Comments on solar linear force-free field and application of FFT analysis

We begin with some comments on the methods of computation of the magnetic fields of solar active regions in terms of force-free field, and point out some mistakes in the solutions. Then we propose a method of quasi-linear force-free field, and probe the application of fast Fourier transform (FFT) in its computation. The magnetic field of the active region NOAA 9165 on 2000-09-15 is taken as an example, and three different methods are used in the determination of the configuration of magnetic lines. The results are then compared with the fine Hα filtergrams of Ganyu Station of Purple Mountain Observatory.     

Interpreting the Helioseismic and Magnetic Imager (HMI) Multi-Height Velocity Measurements

The Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) filtergrams, taken at six wavelengths around the Fe i 6173.3 Å line, contain information about the line-of-sight velocity over a range of heights in the solar atmosphere. Multi-height velocity inferences from these observations can be exploited to study wave motions and energy transport in the atmosphere. Using realistic convection-simulation datasets provided by the STAGGER and MURaM codes, we generate synthetic filtergrams and explore several methods for estimating Dopplergrams. We investigate at which height each synthetic Dopplergram correlates most strongly with the vertical velocity in the model atmospheres. On the basis of the investigation, we propose two Dopplergrams other than the standard HMI-algorithm Dopplergram produced from HMI filtergrams: a line-center Dopplergram and an average-wing Dopplergram. These two Dopplergrams correlate most strongly with vertical velocities at the heights of 30?–?40 km above (line center) and 30?–?40 km below (average wing) the effective height of the HMI-algorithm Dopplergram. Therefore, we can obtain velocity information from two layers separated by about a half of a scale height in the atmosphere, at best. The phase shifts between these multi-height Dopplergrams from observational data as well as those from the simulated data are also consistent with the height-difference estimates in the frequency range above the photospheric acoustic-cutoff frequency.     

The Temperature – Magnetic Field Relation in Observed and Simulated Sunspots

Observations of the relation between continuum intensity and magnetic field strength in sunspots have been made for nearly five decades. This work presents full-Stokes measurements of the full-split (\(g = 3\)) line Fe i 1564.85 nm with a spatial resolution of \(0.5^{\prime\prime}\) obtained with the GREGOR Infrared Spectrograph in three large sunspots. The continuum intensity is corrected for instrumental scattered light, and the brightness temperature is calculated. Magnetic field strength and inclination are derived directly from the line split and the ratio of Stokes components. The continuum intensity (temperature) relations to the field strength are studied separately in the umbra, light bridges, and penumbra. The results are consistent with previous studies, and it was found that the scatter of values in the relations increases with increasing spatial resolution thanks to resolved fine structures. The observed relations show trends common for the umbra, light bridges, and the inner penumbra, while the outer penumbra has a weaker magnetic field than the inner penumbra at equal continuum intensities. This fact can be interpreted in terms of the interlocking comb magnetic structure of the penumbra. A comparison with data obtained from numerical simulations was made. The simulated data generally have a stronger magnetic field and a weaker continuum intensity than the observations, which may be explained by stray light and limited spatial resolution of the observations, and also by photometric inaccuracies of the simulations.     

The 3D Geometry of Active Region Upflows Deduced from Their Limb-to-Limb Evolution

We analyze the evolution of coronal plasma upflows from the edges of AR 10978, which has the best limb-to-limb data coverage with Hinode’s EUV Imaging Spectrometer (EIS). We find that the observed evolution is largely due to the solar rotation progressively changing the viewpoint of nearly stationary flows. From the systematic changes in the upflow regions as a function of distance from disc center, we deduce their 3D geometrical properties as inclination and angular spread in three coronal lines (Si vii, Fe xii, and Fe xv). In agreement with magnetic extrapolations, we find that the flows are thin, fan-like structures rooted in quasi separatrix layers (QSLs). The fans are tilted away from the AR center. The highest plasma velocities in these three spectral lines have similar magnitudes and their heights increase with temperature. The spatial location and extent of the upflow regions in the Si vii, Fe xii, and Fe xv lines are different owing to i) temperature stratification and ii) line of sight integration of the spectral profiles with significantly different backgrounds. We conclude that we sample the same flows at different temperatures. Further, we find that the evolution of line widths during the disc passage is compatible with a broad range of velocities in the flows. Everything considered, our results are compatible with the AR upflows originating from reconnections along QSLs between over-pressure AR loops and neighboring under-pressure loops. The flows are driven along magnetic field lines by a pressure gradient in a stratified atmosphere. Our interpretation of the above results is that, at any given time, we observe the superposition of flows created by successive reconnections, leading to a broad velocity distribution.     

On the mass motions and the atmospheric states of moustaches

Analyses of broad moustache profiles of Balmer lines and Ca ii H and K lines are performed based upon our spectroscopic observation under good seeing conditions. Hα emission profiles are found to consist of three components, i.e., a central absorption, a Gaussian core and a power-law wing. Each of them has a different Doppler shift from others. From the data of Doppler shifts, mass motions with velocity of about 6 km s^?1 are found to be present in chromospheric levels of moustache atmospheres. Computations of Hα emission profiles radiated from a variety of model atmospheres are made. Comparison of computed profiles with the observed ones leads us to the conclusion that a broad Hα profile is due to a formation of heated (ΔT = 1500 K) and condensed (?/? ₀ = 5) chromospheric layers relative to the normal.     

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 i λ 6302.5 Å observed at IRSOL in Locarno.     

The chromospheric magnetograph

By comparison of photoelectric magnetograms with high resolution Hα pictures it is possible to formulate a set of rules by which the magnetic field may be derived directly from the filtergrams. This is possible because of the regularities of magnetic field configurations on the sun and because chromospheric morphology is determined by the magnetic field. Off-band pictures (preferably 0.5 Å red) show a well-defined enhanced chromospheric network, the boundaries of which coincide with the 5 G contour of longitudinal field on the Mt. Wilson magnetograms. The actual fields are presumably more concentrated along the dark structure of the network. Higher fields are marked by filled-in cells. Regions of predominantly transverse fields may be inferred from the absence of normal network structure and the presence of chromospheric fibrils. The quiet chromosphere is recognized by the presence of oscillatory motion and the absence of fibrils or strong network structure. Thus, the chromosphere may be divided into three types of regions: enhanced network, horizontal field, and quiet network. The polarity of the magnetic field may be recognized by plage-antiplage asymmetry; that is, the fact that only following magnetic fields show bright plage in the center of Hα.     

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.     

Active Region Photospheric Magnetic Properties Derived from Line-of-Sight and Radial Fields

The effect of using two representations of the normal-to-surface magnetic field to calculate photospheric measures that are related to the active region (AR) potential for flaring is presented. Several AR properties were computed using line-of-sight (\(B_{\mathrm{los}}\)) and spherical-radial (\(B_{r}\)) magnetograms from the Space-weather HMI Active Region Patch (SHARP) products of the Solar Dynamics Observatory, characterizing the presence and features of magnetic polarity inversion lines, fractality, and magnetic connectivity of the AR photospheric field. The data analyzed correspond to \({\approx\,}4{,}000\) AR observations, achieved by randomly selecting 25% of days between September 2012 and May 2016 for analysis at 6-hr cadence. Results from this statistical study include: i) the \(B_{r}\) component results in a slight upwards shift of property values in a manner consistent with a field-strength underestimation by the \(B_{\mathrm{los}}\) component; ii) using the \(B_{r}\) component results in significantly lower inter-property correlation in one-third of the cases, implying more independent information as regards the state of the AR photospheric magnetic field; iii) flaring rates for each property vary between the field components in a manner consistent with the differences in property-value ranges resulting from the components; iv) flaring rates generally increase for higher values of properties, except the Fourier spectral power index that has flare rates peaking around a value of \(5/3\). These findings indicate that there may be advantages in using \(B_{r}\) rather than \(B_{\mathrm{los}}\) in calculating flare-related AR magnetic properties, especially for regions located far from central meridian.