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IPRT Polarized Radiative Transfer Model Intercomparison Project-Phase A

The polarization state of electromagnetic radiation scattered by atmospheric particles such as aerosols, cloud droplets, or ice crystals contains much more information about the optical and microphysical properties than the total intensity alone. For this reason an increasing number of polarimetric observations are performed from space, from the ground and from aircraft. Polarized radiative transfer models are required to interpret and analyse these measurements and to develop retrieval algorithms exploiting polarimetric observations. In the last years a large number of new codes have been developed, mostly for specific applications. Benchmark results are available for specific cases, but not for more sophisticated scenarios including polarized surface reflection and multi-layer atmospheres. The International Polarized Radiative Transfer (IPRT) working group of the International Radiation Commission (IRC) has initiated a model intercomparison project in order to fill this gap. This paper presents the results of the first phase A of the IPRT project which includes ten test cases, from simple setups with only one layer and Rayleigh scattering to rather sophisticated setups with a cloud embedded in a standard atmosphere above an ocean surface. All scenarios in the first phase A of the intercomparison project are for a one-dimensional plane-parallel model geometry. The commonly established benchmark results are available at the IPRT website

radiative transfer

Effect of polarized radiative transfer on the Hanle magnetic field determination in prominences: Analysis of hydrogen H alpha line observations at Pic-du-Midi

The linear polarization of the Hydrogen H alpha line of prominences has been computed, taking into account the effect of a magnetic field (Hanle effect), of the radiative transfer in the prominence, and of the depolarization due to collisions with the surrounding electrons and protons. The corresponding formalisms are developed in a forthcoming series of papers. In this paper, the main features of the computation method are summarized. The results of computation have been used for interpretation in terms of magnetic field vector measurements from H alpha polarimetric observations in prominences performed at Pic-du-Midi coronagraph-polarimeter. Simultaneous observations in one optically thin line (He I D(3)) and one optically thick line (H alpha) give an opportunity for solving the ambiguity on the field vector determination.

Bommier, V.

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarization

Monte Carlo Simulations of Polarized Radiative Transfer in Neutron Star Atmospheres

Soft X-ray emission from neutron stars affords powerful diagnostic tools for uncovering their surface and interior properties, as well as their geometric configurations. In the atmospheres of neutron stars, the presence of magnetic fields alters the photon-electron scattering cross sections, resulting in nontrivial angular dependence of intensity and polarization of the emergent signals. This paper presents recent developments of our Monte Carlo simulation, MAGTHOMSCATT, which tracks the complex electric field vector for each photon during its transport. Our analysis encompasses the anisotropy and polarization characteristics of X-ray emission for field strengths ranging from nonmagnetic to extremely magnetized regimes that are germane to magnetars. In the very low field domain, we reproduced the numerical solution to the radiative transfer equation for nonmagnetic Thomson scattering, and provided analytical fits for the angular dependence of the intensity and the polarization degree. These fits can be useful for studies of millisecond pulsars and magnetic white dwarfs. By implementing a refined injection protocol, we show that, in the magnetar regime, the simulated intensity and polarization pulse profiles of emission from extended surface regions becomes invariant with respect to the ratio of photon (ω) and electron cyclotron (ω B ) frequencies once ω/ω B ≲ 0.01. This circumvents the need for simulations pertinent to really high magnetic field strengths, which are inherently slower. Our approach will be employed elsewhere to model observational data to constrain neutron star geometric parameters and properties of emitting hot spots on their surfaces.

79 ASTRONOMY AND ASTROPHYSICS

Transfer of polarized radiation in self-absorbed synchrotron sources. II - Treatment of inhomogeneous media and calculation of emergent polarization

As an extension of previous treatments of polarized radiation transfer in homogeneous synchrotron sources, a transfer procedure is derived, based on the coupled-wave formulation, which allows consideration of inhomogeneous sources. It is shown that plasma characteristic wave eccentricities in a source must be fairly large unless Faraday rotation per absorption depth is very large, and that coupling between characteristic waves can be strong in inhomogeneous self-absorbed sources. Calculations are made of the polarized radiation emergent from a source with a boundary of finite thickness. It is found that neglect of propagation effects in the source boundary introduces no significant errors at optically thin frequencies, but that below the self-absorption turnover the emergent polarization may depend significantly upon such effects. In particular, the sign of the circular polarization and the linear polarization position angle depend upon the absorption depth in the boundary region.

Jones, T. W.

A new polarized atmospheric radiative transfer model

A plane-parallel polarized radiative transfer model is described. The model is used to compute the radiance exiting a vertically inhomogeneous atmosphere containing randomly-oriented particles. Both solar and thermal sources of radiation are considered. A direct method of incorporating the polarized scattering information is combined with the doubling and adding method to produce a relatively simple formulation. Several numerical results are presented for verification and comparison.

Evans, K. F.

Transfer of polarized radiation in self-absorbed synchrotron sources. I - Results for a homogeneous source

The solution to the equation of transfer of polarized radiation in a steady-state homogeneous rarefied medium is applied to self-absorbed synchrotron sources. Relativistic electrons (independent of the presence of any cold plasma) can quite easily produce in such sources significant Faraday rotation and/or conversion of linear to circular polarization. Structural inhomogeneities do not obviate the importance of these phenomena in compact nonthermal sources. Contrary to the calculation of Pacholczyk and Swihart (1975), the circular polarization for a homogeneous source changes sign just below the self-absorption turnover as the source becomes opaque, even when polarization conversion dominates; however, for a physically realistic source, structural inhomogeneity may alter this behavior. The observational evidence bearing upon these effects is reviewed.

Jones, T. W.

Generation and transfer of polarized radiation in the solar atmosphere: Physical mechanisms and magnetic-field diagnostics

The main physical mechanisms responsible for the generation and transfer of polarized radiation in the solar atmosphere can be classified in a suitable bidimensional diagram with an indicator of the magnetic field strength on its vertical axis and an indicator of the radiation field anisotropy on its horizontal axis. The various polarimetric observations performed on solar spectral lines are interpreted with different theoretical schemes according to their classification in the diagram and to the optical depths involved. These theoretical schemes, and the associated diagnostic tools for inferring the magnetic field vector from observations are reviewed. In particular, the role of magneto-optical effects in determining the direction of the observed linear polarization in active regions is discussed in some detail.

Deglinnocenti, E. L.

APC: A New Code for Atmospheric Polarization Computations

A new polarized radiative transfer code Atmospheric Polarization Computations (APC) is described. The code is based on separation of the diffuse light field into anisotropic and smooth (regular) parts. The anisotropic part is computed analytically. The smooth regular part is computed numerically using the discrete ordinates method. Vertical stratification of the atmosphere, common types of bidirectional surface reflection and scattering by spherical particles or spheroids are included. A particular consideration is given to computation of the bidirectional polarization distribution function (BPDF) of the waved ocean surface.

surface reflection

Vector Radiative Transfer Code SORD: Performance Analysis and Quick Start Guide

We present a new open source polarized radiative transfer code SORD written in Fortran 9095. SORD numerically simulates propagation of monochromatic solar radiation in a plane-parallel atmosphere over a reflecting surface using the method of successive orders of scattering (hence the name). Thermal emission is ignored. We did not improve the method in any way, but report the accuracy and runtime in 52 benchmark scenarios. This paper also serves as a quick start users guide for the code available from ftp:maiac.gsfc.nasa.govpubskorkin, from the JQSRT website, or from the corresponding (first) author.

polarized radiative transfer

Solar system applications of Mie theory and of radiative transfer of polarized light

A theory of the multiple scattering of polarized light is discussed using the doubling method of van de Hulst. The concept of the Stokes parameters is derived and used to develop the form of the scattering phase matrix of a single particle. The diffuse reflection and transmission matrices of a single scattering plane parallel atmosphere are expressed as a function of the phase matrix, and the symmetry properties of these matrices are examined. Four matrices are required to describe scattering and transmission. The scattering matrix that results from the addition of two identical layers is derived. Using the doubling method, the scattering and transmission matrices of layers of arbitrary optical thickness can be derived. The doubling equations are then rewritten in terms of their Fourier components. Computation time is reduced since each Fourier component doubles independently. Computation time is also reduced through the use of symmetry properties.

Whitehill, L. P.

Broad-band polarization in molecular spectra

The rotational lines of the CN(0,0) red system have been observed to show a strongly asymmetric Zeeman profile. Certain molecules are very susceptible to magnetic perturbation because of the weakness of their spin-rotation coupling; a fairly weak magnetic field can cause a complete Paschen-Back effect. The calculation of transition probabilities incorporating this effect into the Hamiltonian is discussed, and the detailed calculation is then given. The resulting transition probabilities are transformed into synthetic line profiles by using the Unno (1956) model of polarized radiation transfer. The dependence of the net polarized flux on magnetic field and equivalent width is investigated. It is shown that entire band systems may be significantly polarized. Broad-band circular polarization of sunspots may be due, in part, to molecular bands. Analysis of the CH G band indicates a magnetic field of 0.25-0.50 x 10 to the 6th gauss in the white dwarf G99-37, an order of magnitude lower than previous estimates.

Illing, R. M. E.

Polarization radiation in the planetary atmosphere delimited by a heterogeneous diffusely reflecting surface

Spatial frequency characteristics (SFC) and the scattering functions were studied in the two cases of a uniform horizontal layer with absolutely black bottom, and an isolated layer. The mathematical model for these examples describes the horizontal heterogeneities in a light field with regard to radiation polarization in a three dimensional planar atmosphere, delimited by a heterogeneous surface with diffuse reflection. The perturbation method was used to obtain vector transfer equations which correspond to the linear and nonlinear systems of polarization radiation transfer. The boundary value tasks for the vector transfer equation that is a parametric set and one dimensional are satisfied by the SFC of the nonlinear system, and are expressed through the SFC of linear approximation. As a consequence of the developed theory, formulas were obtained for analytical calculation of albedo in solving the task of dissemination of polarization radiation in the planetary atmosphere with uniform Lambert bottom.

Strelkov, S. A.