Numerical methods in polarized radiative transfer

This paper looks at three aspects of numerical methods for solving polarized radiative transfer problems associated with spectral line formation in the presence of a magnetic field. First we prove Murphy's law for Stokes evolution operators which is the basis of the efficient algorithm used in the SPSR software package to compute the Stokes line depression contribution functions. Then we use a two-stream model to explain the efficacy of the field-free method in which the non-LTE line source function in a uniform magnetic field is approximated by the source function neglecting the magnetic field. Finally we introduce a totally new and computationally efficient approach to solving non-LTE problems based on a method of sparsely representing integral operators using wavelets. As an illustration, the wavelet method is used to solve the source function integral equation for a two-level atomic model in a finite atmosphere with coherent scattering, ignoring polarization.     

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.     

Stokes Diagnostics of 2D MHD-Simulated Solar Magnetogranulation

The properties of solar magnetic fields on scales less than the spatial resolution of solar telescopes are studied. A synthetic infrared spectropolarimetric diagnostic based on a 2D MHD simulation of magnetoconvection is used for this. Analyzed are two time sequences of snapshots that likely represent two regions of the network fields with their immediate surroundings on the solar surface with unsigned magnetic flux densities of 300 and 140 G. In the first region from the probability density functions of the magnetic field strength it is found that the most probable field strength at log τ ₅=0 is equal to 250 G. Weak fields (B<500 G) occupy about 70% of the surface, whereas stronger fields (B>1000 G) occupy only 9.7% of the surface. The magnetic flux is −28 G and its imbalance is −0.04. In the second region, these parameters are correspondingly equal to 150 G, 93.3%, 0.3%, −40 G, and −0.10. The distribution of line-of-sight velocities on the surface of log τ ₅=−1 is estimated. The mean velocity is equal to 0.4 km s⁻¹ in the first simulated region. The average velocity in the granules is −1.2 km s⁻¹ and in the intergranules it is 2.5 km s⁻¹. In the second region, the corresponding values of the mean velocities are equal to 0, −1.8, and 1.5 km s⁻¹. In addition the asymmetry of synthetic Stokes V profiles of the Fe i 1564.8 nm line is analyzed. The mean values of the amplitude and area asymmetry do not exceed 1%. The spatially smoothed amplitude asymmetry is increased to 10% whereas the area asymmetry is only slightly varied.     

Zeeman-Doppler imaging of solar-type stars: Multi line technique

In this work, a multi-line spectropolarimetric detection using an Echelle spectrograph is described. The polarization of Zeeman effect is detected by the use of more than 200 lines observed in the solar type star, HR1099. Using the statistics analysis in a sample of 200 lines, we found on the average a polarization signal of about 3 × 10^–4.     

Non-LTE polarized radiative transfer in intermediate magnetic fields: Numerical problems and results

This paper presents some numerical results relative to a solution, based on the density matrix formalism, of the non-LTE, polarized radiative transfer problem for a two-level atom. The results concern the atomic upper level population and alignment, and the emergent radiation Stokes profiles, for a plane-parallel, static, isothermal atmosphere embedded in a magnetic field of intermediate strength, such that the Zeeman splitting has to be taken into account in the line profile. Zeeman coherences are neglected, whereas magneto-optical effects are taken into account, resulting in a full 4×4 absorption matrix. Induced emission is neglected and complete frequency redistribution, in the rest and laboratory frames, is assumed. Pure Doppler absorption profile (gaussian shape) has also been assumed. The presentation of the results is preceded by a brief discussion of their accuracy and of the numerical difficulties that were met in the solution of the problem.On leave from the Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 5, I-50125 Firenze, Italia     

The first and second order moments of the polarization profiles of hydrogen lines

The main properties of the first- and second-order moments of polarized hydrogen lines, forming in the presence of stationary electric and magnetic fields, are reviewed. The analytical results presented here apply directly to the case of optically-thin emission lines in the LTE regime. Some applications of such results to electric- and magnetic-field diagnostics in (solar) plasmas are then briefly considered.On leave from the Dipartimento di Astronomia e Scienza dello Spazio, Università di Firenze, Largo E. Fermi 5, I-50125 Firenze, Italy     

The importance of continuum radiation for the stellar wind hydrodynamics of hot stars

The contribution of bound-free and free-free processes to the outward acceleration of Pup is studied and is found to be negligible.     

Atomic coherences and level-crossings physics

A synthesis work about the interaction of matter with polarized radiation, applied to solar magnetic field diagnostics, has recently been done by Stenflo (1994). This synthesis uses the classical theory of matter-radiation interaction - supplemented by the theory of partial redistribution of Omont, Smith, and Cooper (1972), on the one hand, and full quantum matter-radiation interaction theory, unable to take into account the partial frequency redistribution effects, on the other hand. The need of a full quantum approach taking into account the partial frequency redistribution effects appears as a unifying purpose; the present work, using the density matrix formalism, is a first attempt in this direction.     

Testing the Hapke photometric model: Improved inversion and the porosity correction

In conjunction with a companion paper (Shepard, M.K., Helfenstein, P. [2011]. Icarus, submitted for publication), we derive, test, and apply a detailed approach for visualizing the phase angle dependence of light scattering in particulate soils from both whole-disk and disk-resolved observations. To reduce the number of model parameters and provide stronger constraints on model fits, we combine Hapke’s (Hapke, B. [2008]. Icarus 195, 918-926) recent correction for effects of porosity with his (Hapke, B. [1986]. Icarus 67, 264-280) model of the shadow hiding opposition effect. We further develop our method as a tool for least-squares fitting of Hapke’s model to photometric data. Finally, we present an improved method for estimating uncertainties in retrieved values of Hapke model parameters. We perform a preliminary test of the model on spectrogoniometric measurements from three selected laboratory samples from Shepard and Helfenstein (Shepard, M.K., Helfenstein, P. [2007]. J. Geophys. Res. 112 (E03001), 17). Our preliminary suite of test samples is too small and selective to permit the drawing of general conclusions. However, our results suggest that Hapke’s porosity correction improves the fidelity of fits to samples composed of low- and moderate-albedo particles and may allow for more reliable retrieval of porosity estimates in these materials. However, we find preliminary evidence that in high-albedo surfaces, the effects of porosity may be difficult to detect.     

Center to limb variation of penumbral Stokes V profiles

We investigated the horizontal and the vertical component of the Evershed flow (EF). To this end, we computed average Stokes V profiles for various velocity classes in penumbrae at different heliocentric angles. Our results show that for blueshifted profiles an additional lobe with the same polarity as the spot is present in the blue side of the average Stokes V profile. The amplitude of the additional lobe grows with increasing blueshift and with increasing heliocentric angle. For small redshifts, the profiles show an additional lobe with the opposite polarity as the spot on the red side of the average Stokes V profile. Even at disk center, the original polarity of the average Stokes V profile is reversed for strong redshifts. The transition between the different types of Stokes V profiles is continuous and indicates that not only the vertical, but also the horizontal EF is a magnetized stream of plasma in a magnetic background field (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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。     

Measurement of the full Stokes vector of He I 10830 Å

First observations of the full Stokes vector in the upper chromosphere are presented. The He I 10830 Å line, which has been shown to give reliable measurements of the line-of-sight component of the magnetic field vector, has been used for this purpose. It is shown that the difference between the appearance of chromospheric and photospheric magnetic structures observed close to the solar limb is largely due to the difference in height to which they refer and projection effects. The observations do suggest, however, that the magnetic field above sunspot penumbrae is somewhat more vertical in the chromosphere than in the photosphere.The National Optical Astronomy Obervatories are operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under cooperative agreement with the National Science Foundation     

黑子磁场的Stokes光谱反演技术

对太阳大气磁场的可靠测量有助于人们更好地理解太阳活动区内外的许多活动现象,如耀斑的触发和能量释放过程、黑子的形态和黑子大气的平衡、日珥的形成等.由于原子在磁场中的一些能级会产生分裂(Zeeman效应),使对应这些能级的谱线分裂成若干个具有不同偏振特性的分量,因此目前对黑子磁场的测量主要是通过偏振光,即Stokes参量I、Q、U、V的观测来实现的.该文主要介绍近30年来太阳黑子光谱反演的方法以及所取得的成就;同时也对光谱反演和滤光器型的望远镜矢量磁场的测量进行了简单的比较.     

Stokes polarimetry at the Kodaikanal tower tunnel telescope

A Stokes Polarimeter has been developed using a masked CCD arrangement for the measurement of the vector magnetic field of sunspots. Charge shifting within the CCD is used to record near simultaneous orthogonal polarisation. The testing of the Stokes Polarimeter and the behavior of the integrated system combined with the Kodaikanal tower tunnel telescope will be discussed.     

Solar Stokes Spectrum Observation at Yunnan Astronomical Observatory

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耀斑与磁环拓扑界面附近的色球视向速度

在一些活动区中，耀斑与光球层磁对消的密切关系，已被观测确认，磁对消先于耀斑几小时到一天，此时，色球视向速度场呈现特定的式样，即在磁环拓扑界面上，出现紫移窄带，而耀斑亮块均落在拓扑界面两边的红移区，这一观测事实支持磁对消为低层大气的磁重联，并证实这种重联与日冕中的能量快速释放有密切关系。     

Evidence of Magnetic Helicity in Emerging Flux and Associated Flare

The aim of this paper is to look at the magnetic helicity structure of an emerging active region and show that both emergence and flaring signatures are consistent with a same sign for magnetic helicity. We present a multiwavelength analysis of an M1.6 flare occurring in the NOAA active region 10365 on 27 May 2003, in which a large new bipole emerges in a decaying active region. The diverging flow pattern and the “tongue” shape of the magnetic field in the photosphere with elongated polarities are highly suggestive of the emergence of a twisted flux tube. The orientation of these tongues indicates the emergence of a flux tube with a right-hand twist (i.e., positive magnetic helicity). The flare signatures in the chromosphere are ribbons observed in Hα by the MSDP spectrograph in the Meudon solar tower and in 1600 Å by TRACE. These ribbons have a J shape and are shifted along the inversion line. The pattern of these ribbons suggests that the flare was triggered by magnetic reconnection at coronal heights below a twisted flux tube of positive helicity, corresponding to that of the observed emergence. It is the first time that such a consistency between the signatures of the emerging flux through the photosphere and flare ribbons has been clearly identified in observations. Another type of ribbons observed during the flare at the periphery of the active region by the MSDP and SOHO/EIT is related to the existence of a null point, which is found high in the corona in a potential field extrapolation. We discuss the interpretation of these secondary brightenings in terms of the “breakout” model and in terms of plasma compression/heating within large-scale separatrices.     

Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Evolution of neutron star magnetic fields

This paper reviews the current status of the theoretical models of the evolution of the magnetic fields of neutron stars other than magnetars. It appears that the magnetic fields of neutron stars decay significantly only if they are in binary systems. Three major physical models for this, namely spindown-induced flux expulsion, ohmic evolution of crustal field and diamagnetic screening of the field by accreted plasma, are reviewed.