SPIN: An Inversion Code for the Photospheric Spectral Line

Inversion codes are the most useful tools to infer the physical properties of the solar atmosphere from the interpretation of Stokes profiles. In this paper, we present the details of a new Stokes Profile INversion code (SPIN) developed specifically to invert the spectro-polarimetric data of the Multi-Application Solar Telescope (MAST) at Udaipur Solar Observatory. The SPIN code has adopted Milne–Eddington approximations to solve the polarized radiative transfer equation (RTE) and for the purpose of fitting a modified Levenberg–Marquardt algorithm has been employed. We describe the details and utilization of the SPIN code to invert the spectro-polarimetric data. We also present the details of tests performed to validate the inversion code by comparing the results from the other widely used inversion codes (VFISV and SIR). The inverted results of the SPIN code after its application to Hinode/SP data have been compared with the inverted results from other inversion codes.     

The Helioseismic and Magnetic Imager (HMI) Vector Magnetic Field Pipeline: Optimization of the Spectral Line Inversion Code

The Very Fast Inversion of the Stokes Vector (VFISV) is a Milne–Eddington spectral line inversion code used to determine the magnetic and thermodynamic parameters of the solar photosphere from observations of the Stokes vector in the 6173 Å Fe i line by the Helioseismic and Magnetic Imager (HMI) onboard the Solar Dynamics Observatory (SDO). We report on the modifications made to the original VFISV inversion code in order to optimize its operation within the HMI data pipeline and provide the smoothest solution in active regions. The changes either sped up the computation or reduced the frequency with which the algorithm failed to converge to a satisfactory solution. Additionally, coding bugs which were detected and fixed in the original VFISV release are reported here.     

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.     

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.     

VFISV: Very Fast Inversion of the Stokes Vector for the Helioseismic and Magnetic Imager

In this paper we describe in detail the implementation and main properties of a new inversion code for the polarized radiative transfer equation (VFISV: Very Fast Inversion of the Stokes Vector). VFISV will routinely analyze pipeline data from the Helioseismic and Magnetic Imager (HMI) on-board of the Solar Dynamics Observatory (SDO). It will provide full-disk maps (4096×4096 pixels) of the magnetic field vector on the Solar Photosphere every ten minutes. For this reason VFISV is optimized to achieve an inversion speed that will allow it to invert sixteen million pixels every ten minutes with a modest number (approx. 50) of CPUs. Here we focus on describing a number of important details, simplifications and tweaks that have allowed us to significantly speed up the inversion process. We also give details on tests performed with data from the spectropolarimeter on-board of the Hinode spacecraft.     

Sensitivity Kernels for Time-Distance Inversion

Inversion of local-area helioseismic time-distance data has so far only been done in the ray approximation (Kosovichev, 1996). Since this is a high-frequency approximation its applicability can be questioned for the solar case. Bogdan (1997) showed that for a simple solar model the localized wave packets do follow, but are not confined to, the ray path. We use an approximation based on the first Fresnel zone that has been developed in geophysics by Snieder and Lomax (1996) to go beyond the ray approximation in the inversions. We have calculated sensitivity kernels using both approximations. To test them we use a finite-difference forward modeling of the whole wave field in an acoustic medium reminiscent of the Sun. We use the finite-difference modeling to calculate sensitivity kernels for the full wave field and compare this with the other kernels. The results show that the Fresnel-zone-based kernels are in good agreement with the sensitivity obtained from the modeling. Thus these new kernels represent a significant step forward in the inversion of time-distance data.     

Testing Helioseismic-Holography Inversions for Supergranular Flows Using Synthetic Data

Supergranulation is one of the most visible length scales of solar convection and has been studied extensively by local helioseismology. We use synthetic data computed with the Seismic Propagation through Active Regions and Convection (SPARC) code to test regularized-least squares (RLS) inversions of helioseismic-holography measurements for a supergranulation-like flow. The code simulates the acoustic wavefield by solving the linearized three-dimensional Euler equations in Cartesian geometry. We model a single supergranulation cell with a simple, axisymmetric, mass-conserving flow. The use of simulated data provides an opportunity for direct evaluation of the accuracy of measurement and inversion techniques. The RLS technique applied to helioseismic-holography measurements is generally successful in reproducing the structure of the horizontal-flow field of the model supergranule cell. The errors are significant in horizontal-flow inversions near the top and bottom of the computational domain as well as in vertical-flow inversions throughout the domain. We show that the errors in the vertical velocity are due largely to cross talk from the horizontal velocity.     

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.     

Physical State of the Photosphere at the Onset Phase of a Two-Ribbon Solar Flare

We study the physical state of the photosphere at about 30 minutes before and at the onset of a 2N/M2 two-ribbon solar flare. Semiempirical photospheric models are obtained for two Hα-kernels with the help of the SIR inversion code described by Ruiz Cobo and del Toro Iniesta (Astrophys. J. 398, 375, 1992). The models derived from the inversion reproduce spectral observations in seven Fraunhofer lines. The inferred models show variations in all photospheric parameters both before and at the onset of the flare relative to the quiet-Sun model. The temperature enhancement in the upper photospheric layers is found in the atmospheres in both kernels. The dynamical structure in the models reveals the variations at the onset of the flare relative to the preflaring ones. The inferred atmospheres show some difference in the thermodynamical parameters of two kernels.     

Validation of Spherically Symmetric Inversion by Use of a Tomographically Reconstructed Three-Dimensional Electron Density of the Solar Corona

Determining the coronal electron density by the inversion of white-light polarized brightness (pB) measurements by coronagraphs is a classic problem in solar physics. An inversion technique based on the spherically symmetric geometry (spherically symmetric inversion, SSI) was developed in the 1950s and has been widely applied to interpret various observations. However, to date there is no study of the uncertainty estimation of this method. We here present the detailed assessment of this method using a three-dimensional (3D) electron density in the corona from 1.5 to 4 R _⊙ as a model, which is reconstructed by a tomography method from STEREO/COR1 observations during the solar minimum in February 2008 (Carrington Rotation, CR 2066). We first show in theory and observation that the spherically symmetric polynomial approximation (SSPA) method and the Van de Hulst inversion technique are equivalent. Then we assess the SSPA method using synthesized pB images from the 3D density model, and find that the SSPA density values are close to the model inputs for the streamer core near the plane of the sky (POS) with differences generally smaller than about a factor of two; the former has the lower peak but extends more in both longitudinal and latitudinal directions than the latter. We estimate that the SSPA method may resolve the coronal density structure near the POS with angular resolution in longitude of about 50°. Our results confirm the suggestion that the SSI method is applicable to the solar minimum streamer (belt), as stated in some previous studies. In addition, we demonstrate that the SSPA method can be used to reconstruct the 3D coronal density, roughly in agreement with the reconstruction by tomography for a period of low solar activity (CR 2066). We suggest that the SSI method is complementary to the 3D tomographic technique in some cases, given that the development of the latter is still an ongoing research effort.     

基于支持向量机的太阳磁场活动区极性反转线位置的探测

太阳磁场的极性反转线(Polarity Inversion Line, PIL)是研究太阳活动、分析太阳磁场结构演变和预测太阳耀斑最重要的日面特征之一.磁场极性反转的位置是太阳耀斑和暗条可能出现的位置."先进天基太阳天文台(ASO-S)"是中国首颗空间太阳专用观测卫星,其搭载的"全日面矢量磁像仪(Full-Disk Vector Magnetograph, FMG)"主要任务是探测高空间、高时间分辨率的全日面矢量磁场.为了提高观测数据使用效率、快速监测太阳活动水平、提高太阳耀斑与日冕物质抛射的预报水平以及更好地服务于FMG数据处理与分析系统,采用了图像自动识别与处理技术,更加精确有效地检测极性反转线.从支持向量机(Support Vector Machine, SVM)的模型出发,将极性反转线位置的探测问题转化为一个模式识别中的二分类问题,提出了一种基于支持向量机的极性反转线检测算法,自动探测与识别太阳动力学天文台(Solar Dynamics Observatory, SDO)日震和磁成像仪(Helioseismic and Magnetic Imager, HMI)磁图的极性反转线位置.与现有算法的对比结果表明,此算法可以精确直观地检测太阳活动区的极性反转线.     

What are solar faculae?

Results are presented of observations of the facula area near the solar disc center. Observations were performed at the German Vacuum Tower Telescope of the Observatorio del Teide (Tenerife) with the simultaneous use of two instruments, i.e., TESOS in the Ba IIλ 455.4 nm line to measure intensity variations in the photosphere and, at the same time, TIP in the Fe I (λλ 1564.3–1565.8 nm) line to measure Stokes parameters. Using the Fourier filtering technique, we separated the convective and wave components of the intensity field. Stokes parameters Fe I λ 1564.8 nm and λ 1565.2 nm were inverted by the SIR inversion code to estimate the magnetic field strength. We found that the contrast of intergranular lines of the facula in the continuum is almost independent of the magnetic field strengh (in the range from 30 to 160 mT). This result casts doubt on the assertion that solar faculae are a cluster of magnetic flux tubes. Most likely, due to the decrease of transparency of the matter in a strong (approximately 1 kilogauss) magnetic field, we can see the hot walls of granules.     

Interpretation of observations by inversion

The most recent developments in inversion techniques of the radiative transfer equation are critically reviewed and some of their findings are summarized to illustrating their achievements. Two significantly different approaches are currently being used that deserve consideration, each characterized by whether or not the model solar atmospheres are changed iteratively by the algorithm. The comparison between the two may help in finding future inversion techniques that can solve many challenging problems of solar physics that still need to be properly settled. These problems themselves suggest strategies that look more suitable than others.     

Stokes profiles inversion techniques

Inversion techniques of the radiative transfer equation for polarized light are presented as one of the best current procedures to infer the vector magnetic field, as well as other quantities governing the physical state of the atmospheric layers that photons are coming from. Several characteristics of the various available inversion procedures are pointed out. They are mostly based on the diagnostic contents of the spectral lines as well as on the main hypotheses assumed in these procedures. In particular, the role of gradients in the atmospheric quantities is emphasized as of paramount importance in any diagnostic analysis and, hence, in any interpretation of inversion results.     

Response of the radial stratification at the base of the convection zone to the activity cycle

We have analyzed the differences in the oscillation eigenfrequencies measured over more than two years of GONG observations (December 1995–April 1998) and SOI/MDI observations (May 1996–July 1998). We have inverted these data to look for signatures of the solar activity cycle on the stratification. A one-dimensional (radial) structure inversion code was used to study temporal variations of the sound speed distribution at the boundary between the radiative and convective zones. Such variations could be an indication of the presence of a toroidal magnetic field anchored in this region.     

WIMPs and solar evolution code

The Saclay solar evolution code is used to check the effect of WIMPs on solar evolution. In this paper we study the effects of various types of Cosmion-matter interactions, give constraints on the crosssections compatible with the measured neutrino rate of 2 SNU on chlorine, and relate these constraints to ongoing dark matter detection experiments.Unité associée au CNRS UA 280, F-75251 Paris Cedex 05, France.On leave from LPC, Collège de France.     

The Calculation of Solar Gamma-Rays by TALYS

Solar gamma-ray lines, produced from nuclear reactions of accelerated particles interacting with the solar atmospheric medium, are the most direct diagnosis for the acceleration and transportation of energetic electrons and ions in solar flares. Much information about composition, spectrum, and angular distribution of the accelerated ions, as well as the elemental abundances of the ambient solar atmosphere can be derived from solar gamma-ray line spectra. A new gamma-ray calculation program has been developed by using an efficient nuclear code − TALYS. The theory of gamma-ray production in solar flares is treated in detail. The characteristics of gamma-ray spectrum are also presented.     

Investigation on numerical accuracy of ZAMS models of one solar mass

Helioseismology requires solar models computed with great accuracy. Results of investigations about the incidence in ZAMS models of one solar mass of the numerical errors arising from the interpolation of opacity tables and from the integration of the atmosphere are reported.Though the numerical accuracy reached by some actual codes is of the order of 10^–4 (Christensen-Dalsgaard, 1989), it looks optimistic to expect a numerical accuracy better than few percent for models without mesh refinements in opacity tables and more consistency between atmospheric and internal structure models.Since most of the calculations were made with a new code based on spline/collocation, the numerical method used is outlined in an Appendix.