scholarly journals Boundary conditions for polarized radiative transfer with incident radiation

2013 ◽  
Vol 559 ◽  
pp. A68
Author(s):  
M. Faurobert ◽  
I. Milić ◽  
O. Atanacković
Keyword(s):  
Radiative Transfer ◽  
Boundary Conditions ◽  
Incident Radiation

Differential Approximation to Radiative Transfer in Semitransparent Media

1985 ◽  
Vol 107 (2) ◽  
pp. 478-481 ◽  
Author(s):  
F. H. Azad
Keyword(s):  
Integral Equation ◽  
Radiative Transfer ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Exact Formulation ◽  
Differential Approximation ◽  
Reflection And Refraction ◽  
Integrated Intensity ◽  
Dielectric Interfaces ◽  
Semitransparent Medium

Radiative transfer in a semitransparent medium is treated using the differential approximation. Boundary conditions are formulated to accommodate direction-dependent reflection and refraction at a dielectric interfaces. The approximate results are compared to numerical solution of the exact integral equation. Also, a modification based on the exact formulation of the integrated intensity at the interface is presented that significantly improves the accuracy of the differential approximation in the optically thin regimes.

The Solution of Transient Radiative Transfer With Collimated Incident Serial Pulse in a Plane-Parallel Medium by the DRESOR Method

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Qiang Cheng ◽  
Huai-Chun Zhou ◽  
Zhi-Feng Huang ◽  
Yong-Lin Yu ◽  
De-Xiu Huang
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Radiative Transfer ◽  
Incident Radiation ◽  
Anisotropic Scattering ◽  
Time Dependent ◽  
Temporal Response ◽  
One Dimensional ◽  
Unit Energy ◽  
The Monte Carlo Method

A time-dependent distribution of ratios of energy scattered by the medium or reflected by the boundary surfaces (DRESOR) method was proposed to solve the transient radiative transfer in a one-dimensional slab. This slab is filled with an absorbing, scattering, and nonemitting medium and exposed to a collimated, incident serial pulse with different pulse shapes and pulse widths. The time-dependent DRESOR values, representing the temporal response of an instantaneous, incident pulse with unit energy and the same incident direction as that for the serial pulse, were proposed and calculated by the Monte Carlo method. The temporal radiative intensity inside the medium with high directional resolution can be obtained from the time-dependent DRESOR values. The transient incident radiation results obtained by the DRESOR method were compared to those obtained with the Monte Carlo method, and good agreements were achieved. Influences of the pulse shape and width, reflectivity of the boundary, scattering albedo, optical thickness, and anisotropic scattering on the transient radiative transfer, especially the temporal response along different directions, were investigated.

scholarly journals Quiet-Sun hydrogen Lyman-α line profile derived from SOHO/SUMER solar-disk observations

2020 ◽  
Vol 644 ◽  
pp. A109
Author(s):  
S. Gunár ◽  
P. Schwartz ◽  
J. Koza ◽  
P. Heinzel
Keyword(s):  
Solar Cycle ◽  
Radiative Transfer ◽  
Solar Disk ◽  
Incident Radiation ◽  
Radiation Boundary Condition ◽  
Quiet Sun ◽  
Synthetic Spectra ◽  
Raster Scans ◽  
Radiation Boundary ◽  
Coronal Structures

Context. The solar radiation in the Lyman-α spectral line of hydrogen plays a significant role in the illumination of chromospheric and coronal structures, such as prominences, spicules, chromospheric fibrils, cores of coronal mass ejections, and solar wind. Moreover, it is important for the investigation of the heliosphere, Earth’s ionosphere, and the atmospheres of planets, moons, and comets. Aims. We derive a reference quiet-Sun Lyman-α spectral profile that is representative of the Lyman-α radiation from the solar disk during a minimum of solar activity. This profile can serve as an incident radiation boundary condition for the radiative transfer modelling of chromospheric and coronal structures. Because the solar radiation in the Lyman lines is not constant over time but varies significantly with the solar cycle, we provide a method for the adaptation of the incident radiation Lyman line profiles (Lyman-α and higher lines) to a specific date. Moreover, we analyse how the change in the incident radiation influences the synthetic spectra produced by the radiative transfer modelling. Methods. We used SOHO/SUMER Lyman-α raster scans obtained without the use of the attenuator in various quiet-Sun regions on the solar disk. The observations were performed on three consecutive days (June 24, 25, and 26, 2008) during a period of minimum solar activity. The reference Lyman-α profile was obtained as a spatial average over eight available raster scans. To take into account the Lyman-α variation with the solar cycle, we used the LISIRD composite Lyman-α index. To estimate the influence of the change in the incident radiation in the Lyman lines on the results of radiative transfer models, we used a 2D prominence fine structure model. Results. We present the reference quiet-Sun Lyman-α profile and a table of coefficients describing the variation of the Lyman lines with the solar cycle throughout the lifetime of SOHO. The analysis of the influence of the change in the incident radiation shows that the synthetic spectra are strongly affected by the modification of the incident radiation boundary condition. The most pronounced impact is on the central and integrated intensities of the Lyman lines. There, the change in the synthetic spectra can often have the same amplitude as the change in the incident radiation itself. The impact on the specific intensities in the peaks of reversed Lyman-line profiles is smaller but still significant. The hydrogen Hα line can also be considerably affected, despite the fact that the Hα radiation from the solar disk does not vary with the solar cycle.

scholarly journals Combining magnetohydrostatic constraints with Stokes profiles inversions

2019 ◽  
Vol 632 ◽  
pp. A111 ◽  
Author(s):  
J. M. Borrero ◽  
A. Pastor Yabar ◽  
M. Rempel ◽  
B. Ruiz Cobo
Keyword(s):  
Magnetic Field ◽  
Radiative Transfer ◽  
Boundary Conditions ◽  
Optical Depth ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Gas Pressure ◽  
Order Of Magnitude

Context. Inversion codes for the polarized radiative transfer equation, when applied to spectropolarimetric observations (i.e., Stokes vector) in spectral lines, can be used to infer the temperature T, line-of-sight velocity vlos, and magnetic field B as a function of the continuum optical-depth τc. However, they do not directly provide the gas pressure Pg or density ρ. In order to obtain these latter parameters, inversion codes rely instead on the assumption of hydrostatic equilibrium (HE) in addition to the equation of state (EOS). Unfortunately, the assumption of HE is rather unrealistic across magnetic field lines, causing estimations of Pg and ρ to be unreliable. This is because the role of the Lorentz force, among other factors, is neglected. Unreliable gas pressure and density also translate into an inaccurate conversion from optical depth τc to geometrical height z. Aims. We aim at improving the determination of the gas pressure and density via the application of magnetohydrostatic (MHS) equilibrium instead of HE. Methods. We develop a method to solve the momentum equation under MHS equilibrium (i.e., taking the Lorentz force into account) in three dimensions. The method is based on the iterative solution of a Poisson-like equation. Considering the gas pressure Pg and density ρ from three-dimensional magnetohydrodynamic (MHD) simulations of sunspots as a benchmark, we compare the results from the application of HE and MHS equilibrium using boundary conditions with different degrees of realism. Employing boundary conditions that can be applied to actual observations, we find that HE retrieves the gas pressure and density with an error smaller than one order of magnitude (compared to the MHD values) in only about 47% of the grid points in the three-dimensional domain. Moreover, the inferred values are within a factor of two of the MHD values in only about 23% of the domain. This translates into an error of about 160 − 200 km in the determination of the z − τc conversion (i.e., Wilson depression). On the other hand, the application of MHS equilibrium with similar boundary conditions allows determination of Pg and ρ with an error smaller than an order of magnitude in 84% of the domain. The inferred values are within a factor of two in more than 55% of the domain. In this latter case, the z − τc conversion is obtained with an accuracy of 30 − 70 km. Inaccuracies are due in equal part to deviations from MHS equilibrium and to inaccuracies in the boundary conditions. Results. Compared to HE, our new method, based on MHS equilibrium, significantly improves the reliability in the determination of the density, gas pressure, and conversion between geometrical height z and continuum optical depth τc. This method could be used in conjunction with the inversion of the radiative transfer equation for polarized light in order to determine the thermodynamic, kinematic, and magnetic parameters of the solar atmosphere.

Sign in / Sign up

Export Citation Format

Share Document