The influence of sunspot canopies on magnetic inclination measurements in solar plages

Sunspots are known to have large, low-lying magnetic canopies, i.e. horizontal magnetic fields overlying a field-free medium, that cover substantial fractions of active region plage. In this paper we consider the influence of such canopies on the inclination of plage magnetic fields. We find that for observations in spectral lines like 5250.2Å the neglect of a sunspot canopy when determining magnetic inclination angles of plage fields can introduce errors exceeding 5–10°. This is particularly true if the observations do not have high spatial resolution. Thus this effect may explain some of the measurements of substantially inclined fields in solar plages. Furthermore we find that the Fe I 15648 Å line is far superior in giving correct flux-tube inclinations in the presence of a sunspot magnetic canopy. Finally, the inversion of full Stokes profiles is shown to produce more reliable results than results obtained by considering only ratios of individual Stokes profile parameters.     

Measurements of solar magnetic fields by Fourier transform techniques

The Fourier techniques of Paper I have been exhaustively calibrated using Unno's results for the absorption profile of a simple Zeeman triplet. If a simple transformation is applied to the normalized line depths, then magnetic field strengths and inclination angles can be measured very accurately from noisy, saturated line profiles. Systematic errors caused by saturation effects can be estimated and reduced by varying one parameter. When a significant fraction of the line profile is unsplit and unpolarized, large errors may be made in measurements of low fields, unless the line is sufficiently weak. For a weak line, a vertical field of 1600 gauss can be measured to 10% accuracy even when 70% of the line profile is stray light. These stray light errors are troublesome in measuring fields of gaps and pores but not sunspots. Numerical results of our error analysis are presented graphically.     

The line-ratio method applied to vectormagnetographic measurements

Since solar magnetic fields are inhomogeneous, the averaging of Stokes parameter I within the entrance slit of the magnetograph is different from averaging Stokes Q₀ and V, because the former contains also light from non-magnetic, while the latter only contain light from magnetic regions. If the magnetographic calibration functions are calculated for homogeneous magnetic fields, errors arise, when they are used to reduce measurements of inhomogeneous fields. Therefore, we propose to use the line-ratio method to transform magnetographic measurements into the parameters of the magnetic vector field. The Q ratios and the V ratios of two carefully selected lines are free from errors of this kind. This is also the case for the Q ratios in line core and line wings in single-line magnetographs. An iterative method is presented to calculate the magnetic field parameters using the corresponding new calibration functions. An important advantage is, that the influence of scattered light in sunspots is also eliminated in a good approximation and the filling factor in plages can be estimated. This method is now used to determine magnetic vector fields in plages and sunspots of active regions with a new double-vector magnetograph.     

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。     

The determination of vector magnetic fields in prominences from the observations of the Stokes profiles in the D3 line of helium

A method is presented to measure the magnetic field vector in prominences by means of the polarimetric observations in the D₃ line of He obtained with the High Altitude Observatory Stokes polarimeter. The characteristics of the observed Stokes profiles are discussed. The theory of the Hanle effect is reformulated in the representation of the irreducible tensors of the density matrix, and is generalized to derive the circular polarization profiles across the spectral line in terms of the intensity and direction of the prominence magnetic field. The circular polarization profile so deduced can be employed to obtain useful information which adds to that carried by the linear polarization observations. A non-linear least-squares algorithm is proposed to derive the measurement of the magnetic field from the observations, and a consistency check is suggested to test the adequacy of the theoretical model to describe the physics of the He I atomic excitation in prominences.On leave from: Astrophysical Observatory of Arcetri, Largo E. Fermi, 5, 50125 Firenze, Italy.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

The derivation of vector magnetic fields from stokes profiles: Integral versus least squares fitting techniques

We compare the results of two distinct methods for deriving photospheric vector magnetic fields from the Zeeman effect as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA.). One method ignores magneto-optical effects but allows for an absolute determination of B from the integral properties of the Stokes profiles, under the assumption of weak field strength. The other method is an iterative least-squares fitting technique developed by Lites and Skumanich which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. We find empirically that for sunspot fields above 1500 gauss the two methods agree in derived azimuthal and inclination angles to within ± 20 degs., Furthermore, for such fields, the estimate of the line of sight field and the transverse field derived using the two methods agree to within ± 500 gauss. In weak field strength regions the integral method can be used with little error and computational load in the estimation of the line of sight field, the transverse field and the inclination angle but the disagreement in derived azimuthal angle is considerable ( ± 90 degs.).     

Vector magnetic fields in prominences

The Stokes components of He i D₃ emission in two quiescent prominences, using full spectral profile measurements, are analyzed to derive vector magnetic fields. Two independently developed schemes, based on the Hanle effect, are used for interpretation. They involve solutions of the statistical equilibrium equations for the He i D₃ multiplet, including the effect of coherency and full level crossing, which predict the magnetic field dependence of the observed polarization. Derived magnetic field vector solutions for each pair of linear polarization Stokes profiles corresponding to an observational point in the prominence are, intrinsically, not uniquely determined, and a set of possible solutions is usually obtained. However, mutual consistency of these solutions with those independently predicted by the form of the circular polarized component, allow, in almost all cases, rejection of all solutions of a set except one symmetrical pair. Of such a pair, a unique solution can be determined with a high confidence level by reference to independent potential field information. Field vectors are found usually to be close to horizontal and normal to the prominence surface, but extreme exceptions are found. Field values range from 6 G to 60 G. The derived vectorfield configurations and their magnitudes are briefly discussed relative to these prominences and to different quiescent prominence models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.     

Changes in measured vector magnetic fields when transformed into heliographic coordinates

In this paper we investigate the changes that occur in measured magnetic fields when they are transformed into a heliographic coordinate system. To carry out this investigation we took measurements of the vector magnetic field of an active region that was observed at 1/3 the solar radius from disk center and transformed the observed field into heliographic coordinates. We also examined differences in the calculated potential field that occur when the heliographic normal component of the field is used as the boundary condition rather than the observed line-of-sight component. The results of this analysis show (1) that the observed fields of sunspots more closely resemble the generally accepted picture of the distribution of umbral fields if they are displayed in heliographic coordinates, (2) that the differences in the potential calculations are less than 200 G in field strength and 20° in field azimuth outside sunspots, and (3) that differences in the two potential calculations in the sunspot areas are no more than 400 G in field strength but range from 60 to 80° in field azimuth in localized umbral areas.     

Rotation of the large-scale solar magnetic fields in the equatorial region

A study is made of the rotation of large-scale magnetic fields using the synoptic maps from the Kitt Peak National Observatory for the time interval 1976–1985. The auto-correlation method and the mass-centers method of magnetic structures was applied to infer mean differential rotation profiles and rotation profiles separately for each magnetic field polarity. It has been found that in both hemispheres the leading polarity rotates faster than the following polarity at all latitudes by about 0.04° day^–1. The maximum rotation rate of the leading polarity is reached at about 6° latitude. In the mean profile for both polarities, this brings about two angular velocity maxima at 6° latitudes in both hemispheres. Such a profile appears as to have a dimple on the equator.     

Continuous monitoring of nightside upper thermospheric mass densities in the martian southern hemisphere over 4 martian years using electron reflectometry

Details are presented of an improved technique to use atmospheric absorption of magnetically reflecting solar wind electrons to constrain neutral mass densities in the nightside martian upper thermosphere. The helical motion of electrons on converging magnetic field lines, through an extended neutral atmosphere, is modeled to enable prediction of loss cone pitch angle distributions measured by the Magnetometer/Electron Reflectometer (MAG/ER) experiment on Mars Global Surveyor at 400 km altitude. Over the small fraction of Mars' southern hemisphere (∼2.5%) where the permanent crustal magnetic fields are both open to the solar wind and sufficiently strong as to dominate the variable induced martian magnetotail field, spherical harmonic expansions of the crustal fields are used to prescribe the magnetic field along the electron's path, allowing least-squares fitting of measured loss cones, in order to solve for parameters describing the vertical neutral atmospheric mass density profile from 160 to 230 km. Results are presented of mass densities in the southern hemisphere at 2 a.m. LST at the mean altitude of greatest sensitivity, 180 km, continuously over four martian years. Seasonal variability in densities is largely explained by orbital and latitudinal changes in dayside insolation that impacts the nightside through the resulting thermospheric circulation. However, the physical processes behind repeatable rapid, late autumnal cooling at mid-latitudes and near-aphelion warming at equatorial latitudes is not fully clear. Southern winter polar warming is generally weak or nonexistent over several Mars years, in basic agreement with MGS and MRO accelerometer observations. The puzzling response of mid-latitude densities from 160° to 200° E to the 2001 global dust storm suggests unanticipated localized nightside upper thermospheric lateral and vertical circulation patterns may accompany such storms. The downturn of the 11-year cycle of solar EUV flux is likely responsible for lower aphelion densities in 2004 and 2006 (Mars years 27 and 28).     

Calibration of Vector Magnetograms with the Chromospheric Mg b2 Line

Stokes polarization profiles of the Mg?b₂ 5172.68 Å spectral line on two simple sunspots are obtained with the Multi-Channel Solar Telescope (MCST) at the Huairou Solar Observing Station (HSOS). This is done by means of scanning this line over the wavelength interval from 200 mÅ redward of the line center to 200 mÅ blueward, in steps of 10 mÅ. A generalized analytic solution to the transfer equation for polarized radiation is presented. With a nonlinear least-square fitting technique, the linear calibration coefficients for the low-chromospheric longitudinal magnetic field is obtained in the weak-field case. We also discuss the problems in calibrating the transverse field with this line. It is shown that the weak-field approximation is not applicable to the chromospheric Mg?b₂ line for the transverse component of the magnetic field.     

Axial tilt angles of sunspot groups

Digitized Mount Wilson sunspot data from 1917 to 1985 are analyzed to examine tilt angles determined from the area-weighted positions of leading and following sunspots. These spot group tilt angles are examined in relation to other group characteristics to give information which may relate to the formation and evolution of sunspot groups and the magnetic connection of groups to subsurface magnetic flux tubes. The average tilt angle of all 24816 (multiple-spot) group observations in this study is found to be + 4.2 ± 0.2 deg, where the positive sign signifies that the leading spots lie equatorward of the following spots. Sunspot group areas are significantly larger on average for groups nearer the average tilt angle, which is similar to a result found earlier for active region plages. Average tilt angles are found to be larger at higher latitudes, confirming earlier results. There is a strong negative correlation between average daily latitudinal motion (plus to poles) and group tilt angle. That is, for groups within about 40 deg of the average tilt angle, smaller tilt angles are associated with more positive (poleward) daily drift. Groups nearest the average tilt angle rotate the fastest, on average, the amplitude differences being between about +0.1 and – 0.1 deg day^–1 for groups near and far from the average tilt angle, respectively. Groups with tilt angles near the average show a negative daily separation change between leading and following spots of close to 4 Mm day^–1 on average. Groups on either side of the average tilt angle show spot separations that are on average more positive. A similar effect is not seen for the daily variations of group areas. These results are discussed in relation to analogous recent results for active region magnetic fields. More evidence is found for a qualitative difference between the magnetic fields of sunspots and of plages, relating, perhaps, to a difference in subsurface connection of the field lines or to different physical mechanisms that may play a role for fields of different field strengths.Operated by the Association of Universities for Research in Astronomy, Inc., under Cooperative Agreement with the National Science Foundation.     

Stray-light correction in magnetograph observations using the maximum entropy method

We have developed a method of stray-light correction which is applicable to filter-based magnetograph observations. Stray-light-corrected Stokes images are obtained by performing the deconvolution of observed Stokes images by the point spread function which is determined from the Stokes I image. For image deconvolution, the maximum entropy principle is used to guarantee that intensity should be positive and polarization degrees should be less than unity. We present an iterative algorithm for the maximum entropy method, which seeks the solution in Fourier space and thus accomplishes fast convergence. We find that our method is effective in correcting stray light which has a spread angle greater than the full width at half maximum of the point spread function. We also discuss the effect of stray light on magnetograph calibration.     

太阳大气中矢量磁场信息的推导

一种能从观测到的斯托克斯轮廓中提取太阳表面矢量磁场信息的方法在本文中提出，它利用斯托克斯轮廓非线心的极值点处相应参量对波长的导数为零这一数学事实，假设表面附近磁场矢量及热力学参量的变化梯度足够小以致所考虑的极值点的波长位置不随深度改变或此变化呆忽则使得偏振辐射围方程组得到极大的简化；再应用数值方法从此简化方程组中解出辐射表面附近的磁场矢量参数。通过拟合理论轮廓表明该法确实可以得到表面近似的磁场矢量     

A Monte Carlo Code to Compute Energy Fluxes in Cometary Nuclei

A Monte Carlo model designed to compute both the input and output radiation fields from spherical-shell cometary atmospheres has been developed. The code is an improved version of that by H. Salo (1988, Icarus76, 253-269); it includes the computation of the full Stokes vector and can compute both the input fluxes impinging on the nucleus surface and the output radiation. This will have specific applications for the near-nucleus photometry, polarimetry, and imaging data collection planned in the near future from space probes. After carrying out some validation tests of the code, we consider here the effects of including the full 4×4 scattering matrix in the calculations of the radiative flux impinging on cometary nuclei. As input to the code we used realistic phase matrices derived by fitting the observed behavior of the linear polarization as a function of phase angle. The observed single scattering linear polarization phase curves of comets are fairly well represented by a mixture of magnesium-rich olivine particles and small carbonaceous particles. The input matrix of the code is thus given by the phase matrix for olivine as obtained in the laboratory plus a variable scattering fraction phase matrix for absorbing carbonaceous particles. These fractions are 3.5% for Comet Halley and 6% for Comet Hale-Bopp, the comet with the highest percentage of all those observed.The errors in the total input flux impinging on the nucleus surface caused by neglecting polarization are found to be within 10% for the full range of solar zenith angles. Additional tests on the resulting linear polarization of the light emerging from cometary nuclei in near-nucleus observation conditions at a variety of coma optical thicknesses show that the polarization phase curves do not experience any significant changes for optical thicknesses τ?0.25 and Halley-like surface albedo, except near 90° phase angle.     

Magnetograph measurements with temperature-sensitive lines

Certain discrepancies between theoretical and empirical calibrations of magnetograph response are resolved by recognizing the existence of line profile changes in magnetic regions. Many of the photospheric lines commonly used for magnetic field measurements weaken greatly in magnetic regions outside of sunspots. Unless due account is made of the line profile change, the magnetograph measurements underestimate magnetic flux and field strengths.The 5250.2 Å line is especially sensitive to weakening in magnetic regions. Measurements made with this line underestimate the true field by a factor ranging from about two on the linear portion of the profile to five near the line core.Kitt Peak National Observatory Contribution No. 500.Operated by the Association of Universities for Research in Astronomy Inc., under contract with the National Science Foundation.     

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.     

Observational Study of Sunspot Oscillations in Stokes I,Q, U,and V

Time series of 2-dimensional spectro-polarmetric data were obtained with the intent of studying the temporal behavior of velocity, magnetic flux, and characteristics of the Stokes V profile in a small region of a larger sunspot. Full Stokes profiles in I, Q, U, and V were obtained. Velocity oscillations were found at frequencies of 3.3 mHz in each of the profiles. Acoustic power maps indicate that locations of highest power correspond to areas in which the polarization signal was greatest, therefore no conclusion about the type of wave mode participating in the oscillations can be made. Velocity amplitudes were I: 71 m s^–1, Q: 47 m s^–1, U: 65 m s^–1 and V: 86 m s^–1. Oscillatory behavior was also detected in longitudinal field strength, with an r.m.s. amplitude of 22 G, at 2.6 and 3.3 mHz. The power was localized at the umbral/penumbral boundary. A phase analysis indicates a –130° phase difference with Stokes V velocity oscillations at 3.3 mHz and a 75° difference at 2.6 mHz. Results are consistent with magnetic field lines swaying in response to a p-mode driver. No oscillatory behavior was seen in Stokes V asymmetry or amplitude splitting.     

Monochromatic images of sunspots in linearly polarized radiation and the structure of their magnetic fields

When unipolar sunspots are observed in the linearly polarized radiation represented by the Stokes parametersQ andU of magneto-sensitive spectral lines, their images display a complicated and interesting configuration. This is caused by the magneto-optical effect and also is connected with the 3-D structure of spot magnetic fields. In the process of numerical simulation it is possible to infer the regularity of variation of the angle of inclination of magnetic lines of force with distance from the spot center.     

Evolution of solar magnetic fields over an 11-year period

Digitized data on solar magnetic fields recorded at the Mount Wilson Observatory during the period August 1959–May 1970 have been used to study the large-scale evolution of the photospheric magnetic fields. The latitude distribution (butterfly diagram) of the magnetic field is compared with the distribution of sunspots, faculae, prominences and the intensity of the green-line corona. The evolution of the sector structure of the field is calculated. 36 synoptic charts, each representing an average of four solar rotations, illustrate the evolution of the magnetic field over the 11-year period.On leave from the Lund Observatory, Lund, Sweden.The National Center for Atmospheric Research is sponsored by the National Science Foundation.