Asymmetric Shapes of Radio Recombination Lines from Ionized Stellar Winds

Recombination line profile shapes are derived for ionized spherical stellar winds at radio wavelengths. It is assumed that the wind is optically thick owing to free-free opacity. Emission lines of arbitrary optical depth are obtained assuming that the free-free photosphere forms in the outer, constant expansion portion of the wind. Previous works have derived analytic results for isothermal winds when the line and continuum source functions are equal. Here, semi-analytic results are derived for when the source functions are not equal to reveal that line shapes can be asymmetric about line center. A parameter study is presented and applications discussed.Comment: accepted to Revista Mexicana de Astronom\'ia y Astrof\'isic

Analytical computation of impedance integrals with power-law Green's functions

In this contribution, a method is presented for reducing the number of subsequent integrations that occur in impedance integrals with Green's functions of the form R., with R the distance between source and observation point. The method allows the number of integrations to be reduced to 1 in the two dimensional case and 2 in the three dimensional case, irrespective of the number of subsequent integrations that were originally present. These last integrations can be done analytically using well-known results if nu is an element of Z, resulting in a computation that is free of numerical integrations. The dynamic Green's function can be treated in a semi-analytical way, by expanding it into a Taylor series in the wavenumber. The method can be applied if both the basis and test functions are polynomial functions with polygonal support and if certain non-parallelity conditions are satisfied

The Hanle Effect as a Diagnostic of Magnetic Fields in Stellar Envelopes. V. Thin Lines from Keplerian Disks

This paper focuses on the polarized profiles of resonance scattering lines that form in magnetized disks. Optically thin lines from Keplerian planar disks are considered. Model line profiles are calculated for simple field topologies of axial fields (i.e., vertical to the disk plane) and toroidal fields (i.e., purely azimuthal). A scheme for discerning field strengths and geometries in disks is developed based on Stokes Q-U diagrams for the run of polarization across line profiles that are Doppler broadened by the disk rotation. A discussion of the Hanle effect for magnetized disks in which the magnetorotational instability (MRI) is operating is also presented. Given that the MRI has a tendency to mix the vector field orientation, it may be difficult to detect the disk fields with the longitudinal Zeeman effect, since the amplitude of the circularly polarized signal scales with the net magnetic flux in the direction of the observer. The Hanle effect does not suffer from this impediment, and so a multi-line analysis could be used to constrain field strengths in disks dominated by the MRI.Comment: to appear in Astrophysical Journa

An iterative algorithm for sparse and constrained recovery with applications to divergence-free current reconstructions in magneto-encephalography

We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices present in the problem (in the linear constraint, in the data misfit part and in penalty term of the functional). None of the three matrices must be invertible. Convergence is proven in a finite-dimensional setting. We apply the algorithm to a synthetic problem in magneto-encephalography where it is used for the reconstruction of divergence-free current densities subject to a sparsity promoting penalty on the wavelet coefficients of the current densities. We discuss the effects of imposing zero divergence and of imposing joint sparsity (of the vector components of the current density) on the current density reconstruction.Comment: 21 pages, 3 figure

Procedural Rights and Issues in the Enforcement of Articles 81 and 82 of the EC Treaty

A discussion of evidentiary and procedural standards regarding Articles 81(1) and 82 of the EC Treaty, which deal with infringements of anti-competitive collusion

A broadband stable addition theorem for the two dimensional MLFMA

Integral equations arising from the time-harmonic Maxwell equations contain the Green function of the Helmholtz equation as the integration kernel. The structure of this Green function has allowed the development of so-called fast multipole methods (FMMs), i.e. methods for accelerating the matrix-vector products that are required for the iterative solution of integral equations. Arguably the most widely used FMM is the multilevel fast multipole algorithm (MLFMA). It allows the simulation of electrically large structures that are intractable with direct or iterative solvers without acceleration. The practical importance of the MLFMA is made all the more clear by its implementation in various commercial EM software packages such as FEKO and CST Microwave studio

Long-Wavelength, Free-Free Spectral Energy Distributions from Porous Stellar Winds

The influence of macroclumps for free-free spectral energy distributions (SEDs) of ionized winds is considered. The goal is to emphasize distinctions between microclumping and macroclumping effects. Microclumping can alter SED slopes and flux levels if the volume filling factor of the clumps varies with radius; however, the modifications are independent of the clump geometry. To what extent does macroclumping alter SED slopes and flux levels? In addressing the question, two specific types of macroclump geometries are explored: shell fragments ("pancake"-shaped) and spherical clumps. Analytic and semi-analytic results are derived in the limiting case that clumps never obscure one another. Numerical calculations based on a porosity formalism is used when clumps do overlap. Under the assumptions of a constant expansion, isothermal, and fixed ionization wind, the fragment model leads to results that are essentially identical to the microclumping result. Mass-loss rate determinations are not affected by porosity effects for shell fragments. By contrast, spherical clumps can lead to a reduction in long-wavelength fluxes, but the reductions are only significant for extreme volume filling factors.Comment: to appear in MNRA

Accurate computation and tabulation of the scalar Green function for bi-anisotropic media and its derivatives

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