Observation of Hα line impact polarization in solar flares

We present the results of studying the impact linear polarization of 32 solar flares of X-ray classes C, M, and X (two flares) observed with the Large Solar Vacuum Telescope. It has turned out that there is evidence for impact polarization only in 13 of them. The newly obtained data have confirmed that the linear Stokes parameters are predominantly 2–7%, while the spatial sizes of flaring points with nonzero Stokes parameters are small (1″-2″). Two features of the manifestation of impact polarization in flares revealed by these studies are of greatest interest: (1) at the two foot points of a single flare loop or an arcade of loops, both the Hα intensity profiles and the Stokes profiles differ in behavior; (2) based on the Hα line, we have found for the first time that the sign of the Stokes parameters changes not only across the flare ribbon but also with depth of the chromosphere.     

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.     

A metric and optimization scheme for microlens planet searches

OGLE III and MOA-II are discovering 600–1000 Galactic bulge microlens events each year. This stretches the resources available for intensive follow-up monitoring of the light curves in search of anomalies caused by planets near the lens stars. We advocate optimizing microlens planet searches by using an automatic prioritization algorithm based on the planet detection zone area probed by each new data point. This optimization scheme takes account of the telescope and detector characteristics, observing overheads, sky conditions and the time available for observing on each night. The predicted brightness and magnification of each microlens target are estimated by fitting to available data points. The optimization scheme then yields a decision on which targets to observe and which to skip, and a recommended exposure time for each target, designed to maximize the planet detection capability of the observations. The optimal strategy maximizes detection of planet anomalies, and this must be coupled with rapid data reduction to trigger continuous follow-up of anomalies that are thereby found. A web interface makes the scheme available for use by human or robotic observers at any telescope. We also outline a possible self-organizing scheme that may be suitable for coordination of microlens observations by a heterogeneous telescope network.     

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.     

Polarization in spectral lines

A unifying theoretical approach is presented to derive from the general principles of Quantum Electrodynamics both the radiative transfer equations for polarized radiation and the statistical equilibrium equations for an atomic system interacting with a polarized radiation field. The radiation field is described by means of Stokes parameters while the atomic system is described in terms of its density-matrix operator. The non-diagonal terms of the density matrix are fully accounted for so that this formalism can be suitably employed to describe a wide variety of physical phenomena like resonance scattering, the Hanle effect and the Zeeman effect, either in optically thin or optically thick atmospheres, together with all the possible intermediate situations.The general formulae derived in the first sections of the paper are subsequently particularized introducing the dipole approximation in the relevant matrix elements describing the interaction between the atomic system and the radiation field. The final equations assume a quite compact expression by the introduction of suitable spherical tensors connected with the components of the polarization unit vectors associated with each direction of the radiation field. The general expressions and the main properties of these tensors are discussed in the Appendix.     

Stokes parameters for Thomson scattering in a strong magnetic field

The effect of a strong magnetic field on neutron stars or white dwarfs is calculated for Thomson scattering. The Stokes parameters for the scattered radiation are computed explicitly in terms of the state of polarization of the incident wave, the electron-cyclotron frequency, the angle of incidence, and the angle of scattering. The effect of the magnetic field on these parameters is considered in detail for incoming radiation propagating along or across the external magnetic field. The criterion for the magnetic field to substantially affect the Stokes parameters is that the photon frequency be less than the electron-cyclotron frequency.     

磁光效应与太阳黑子磁场结构

本文在考虑磁光效应条件下,根据对斯托克斯参数转移方程组求得的数值解,计算了单极太阳黑子的线偏振讯号的单色像,并与美国马歇尔空间飞行中心的观测资料进行了对比,结果表明,径向黑子磁场模型给出与观测相似的单色像,而旋涡形模型导致与观测有显著差异的图像。因此可以认为径向模型更接近于实际情况。     

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.     

On the efficiency of polarization measurements while studying aerosols in the terrestrial atmosphere

It has been shown that the orbital polarization measurements of the Earth in the spectral range λ > 300 nm do not allow the sets of the Stokes parameters satisfying the homogeneity requirement for the optical properties of the “atmosphere + surface” system to be retrieved. Due to this, the atmospheric and surface contributions cannot be correctly separated and the physical properties of the atmospheric aerosol cannot be determined. This is caused by the optical heterogeneity of the system, the different nature of aerosol above different relief features, and the poorly predictable temporal changes of the optical properties of the “atmosphere + surface” system. Observations at λ < 300 nm are more acceptable, since not only the surface but also the tropospheric layer of the atmosphere, which are both mostly subjected to the effects of horizontal inhomogeneity and temporal variations, become practically invisible due to a high absorption by the ozone layer. Because of this, from the scans along specified latitude zones, one may obtain the quasi-homogeneous dependences of the second Stokes parameter Q(α) (U(α) = 0) suitable for estimating the physical characteristics of the stratospheric aerosol and revealing their horizontal and temporal variations.     

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)     

Difference imaging photometry of blended gravitational microlensing events with a numerical kernel

The numerical kernel approach to difference imaging has been implemented and applied to gravitational microlensing events observed by the PLANET collaboration. The effect of an error in the source-star coordinates is explored and a new algorithm is presented for determining the precise coordinates of the microlens in blended events, essential for accurate photometry of difference images. It is shown how the photometric reference flux need not be measured directly from the reference image but can be obtained from measurements of the difference images combined with the knowledge of the statistical flux uncertainties. The improved performance of the new algorithm, relative to isis2 , is demonstrated.     

Magneto-optical effect and structure of sunspot magnetic field

On the basis of a numerical soluton of the equations of transfer of Stokes parameters including the magneto-optical effect, we calculated monochromatic images of unipolar sunspots in the linear polarization signal and compared them with the observed data obtained at Marshall Space Flight Center, U.S.A. The results show that our radial fan-shaped model of sunspot magnetic field give images that are similar to the observed ones while a spiral model gives rather different pictures. We can therefore regard the former model as being the more realistic.     

Mangeto-optical effects in sunspots and their vector magnetic field

The system of transfer equations of the four Stokes parameters I, Q, U, V under the action of the magneto-optical effect (i.e. the Unno-Beckers equations) are numerically solved in this paper for the magneto-sensitive lines FeI λλ 6302.499 and 5324.191 using an appropriate sunspot model. The errors in the expressions for the coefficients _r and _W in Beckers' paper [2] have been corrected for. From the results of calculations, features of the profiles of the Stokes parameters dependent on the magnetic vector have been isolated. Our computations also show that the magneto-optical effect should be taken into consideration in the measurement of the vector magnetic fields.

In the fourth section of this paper we have established a simple and convenient method for obtaining-information on the magnetic vector (including the field strength B, its inclination to the line of sight γ and its azimuth χ) from the profiles of the Stokes parameters. It consists of three steps: (1) The value of B is determined from the distance of the highest point in the V-profile from the central line. (2) γ is then found from V_max, i.e maximum value of V. (3) Lastly, the angle χ is found from Q₀, i.e. the value of Q at line centre.     

The main sequence location as function of chemical composition

Available data for computed zero-age lines are analyzed, and empirical formulae giving the luminosity as function of the chemical composition are derived. Mass-luminosity relations are also presented for a very wide range of the chemical composition parameters (X, Y, Z). Comparison with the observed zero-age lines are discussed.     

A small source in Q2237+0305?

Microlensing in Q2237+0305 between 1985 and 1995 has been interpreted in two different ways. First, the observed variations can be explained through microlensing by stellar mass objects of a continuum source with dimensions significantly smaller than the microlens Einstein Radius ( ₀), but consistent with that expected for thermal accretion discs . However, other studies have shown that models having sources as large as 5 ₀ can reproduce the observed variation . In this paper we present evidence in favour of a small source. Our approach uses the distribution of microlensed light-curve derivatives to place statistical limits (as a function of source size) on the number of microlens Einstein radii crossed by the source during the monitoring period. In contrast with previous analyses, our results are therefore not dependent on an assumed time-scale. Limits on the source size are obtained from two separate light-curve features. First, recently published monitoring data show large variations (0.81.5 mag) between image brightnesses over a period of 700 d or 15 per cent of the monitoring period. Secondly, the 1988 peak in the image A light curve had a duration that is a small fraction (0.02) of the monitoring period. Such rapid microlensing rises and short microlensing peaks only occur for small sources. We find that the observed large, rapid variation limits the source size to be <0.2 ₀ (95 per cent confidence). The width of the light-curve peak provides a stronger constraint of <0.025 ₀ (99 per cent confidence). The Einstein radius (projected into the source plane) of the average microlens mass m in Q2237+0305 is The interpretation that stars are responsible for microlensing in Q2237+0305 therefore results in limits on the continuum source size that are consistent with current accretion disc theory.     

Radiative transfer for polarized light: Equivalence between Stokes parameters and coherency matrix formalisms

Two formal solutions of the radiative transfer equation for polarized light have been proposed. One uses the Stokes parameters to describe the polarization, while the other uses the coherency matrix. It is shown in the present work that they are equivalent. Both can be used to compute response and contribution functions for the Stokes parameters and both require the solution of systems of differential equations with similar numbers of independent variables. New equations to solve the radiative transfer problem using the Stokes parameters formalism are presented. In addition, a computer code which synthesizes the Stokes profiles by means of these equations is described.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Polarimetry of solar pores

We address the magnetic field structure of solar pores. The data were obtained at the Gregory Coudè telescope at Izaña using the AT1 CCD camera system to observe pores with three spectral lines: one magnetically sensitive line, recording all 4 Stokes profiles, and two g = 0 lines where only the intensity profiles were measured. The data reduction included the standard procedure (removing dark current and flatfielding) as well as destretching of the polarimetric spectra and removing the non-magnetic straylight by means of a 2-d deconvolution of the observed intensity variation using a Lucy-Richardson restoration algorithm. In the following analysis we first determined the temperature- and pressure stratification of the pore using the g = 0 lines and then applied an inversion of the Stokes profiles to get the parameters of the magnetic field. Across the pore we find a strong variation of the resulting field strength as well as of the inclination and the azimuth, consistent with the assumption of a canopy forming in the higher atmosphere.     

A quantitative comparison of vector magnetic field measurement and analysis techniques

We make a quantitative comparison between spectral vs filter measurement and analysis techniques for extraction of solar vector magnetic fields from polarimetric data using as a basis the accurately calibrated, high angular resolution Stokes profile data from the Advanced Stokes Polarimeter. It is shown that filter-based measurements deliver qualitative images of the field alignment for sunspots that are visually similar to images derived from the more detailed analysis of the Stokes profiles. However, quantitative comparison with least-squares fits to the full Stokes profiles show that both the strength of the field predicted by the filter-based analysis and its orientation contain substantial errors. These errors are largest for plage regions outside of sunspots, where the field strengths are inferred to be only a fraction of their true values, and errors in the orientation of 40–50° are common. Within sunspots, errors of 20° are commonplace. The greatest source of these errors is the inability of the filter-based measurements to account for the small fill fraction of magnetic fields or, equivalently, scattered light in the instrument, which reduce the degree of polarization. The uncertainties of the full profile fitting methods are also discussed, along with the errors introduced by coarser wavelength sampling of the observed Stokes profiles. The least-squares fitting procedure operates best when the profiles are sampled at least as frequently as one Doppler width of the line.On leave from the Instituto de Astrofísica de Canarias, La Laguna, Tenerife, Spain.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.