Frequency Redistribution Research Articles

Lyman radiative transfer in a multiphase medium

Hydrogen Lyman a (Lya) is our primary emission-line window into high-redshift galaxies. Despite an extensive literature, Lya radiative transfer in the most realistic case of a dusty, multiphase medium has received surprisingly little detailed theoretical attention. We investigate Lya resonant scattering through an ensemble of dusty, moving, optically thick gas clumps. We treat each clump as a scattering particle and use Monte Carlo simulations of surface scattering to quantify continuum and Lya surface scattering angles, absorption probabilities, and frequency redistribution, as a function of the gas dust content. This atomistic approach speeds up the simulations by many orders of magnitude, making possible calculations which are otherwise intractable. Our fitting formulae can be readily adapted for fast radiative transfer in numerical simulations. With these surface scattering results, we develop an analytic framework for estimating escape fractions and line widths as a function of gas geometry, motion, and dust content. Our simple analytic model shows good agreement with full Monte Carlo simulations. We show that the key geometric parameter is the average number of surface scatters for escape in the absence of absorption, N 0 , and we provide fitting formulae for several geometries of astrophysical interest. We consider the following two interesting applications. (i) Equivalent widths (EWs). Lya can preferentially escape from a dusty multiphase interstellar medium if most of the dust lies in cold neutral clouds, which Lya photons cannot penetrate. This might explain the anomalously high EWs sometimes seen in high-redshift/submillimetre sources. (ii) Multiphase galactic outflows. We show the characteristic profile is asymmetric with a broad red tail, and relate the profile features to the outflow speed and gas geometry. Many future applications are envisaged.

Wolf‐Rayet Mass‐Loss Limits Due to Frequency Redistribution

The hypothesis that CAK-type line driving is responsible for the large observed Wolf-Rayet (W-R) mass-loss rates has been called into question in recent theoretical studies. The purpose of this paper is to reconsider the plausibility of line driving of W-R winds within the standard approach using the Sobolev approximation while advancing the conceptual understanding of this topic. Due to the multiple scattering required in this context, of particular importance is the role of photon frequency redistribution into spectral gaps, which in the extreme limit yields the statistical Sobolev-Rosseland (SSR) mean approximation. Interesting limits to constrain are the extremes of no frequency redistribution, wherein the small radii and corresponding high W-R surface temperature induces up to twice the mass-loss rate relative to cooler stars, and the SSR limit, whereby the reduced efficiency of the driving drops the mass flux by as much as an order of magnitude whenever there exist significant gaps in the spectral line distribution. To see how this efficiency drop might be sufficiently avoided to permit high W-R mass loss, we explore the suggestion that ionization stratification may serve to fill the gaps globally over the wind. We find that global ionization changes can only fill the gaps sufficiently to cause about a 25% increase in the mass-loss rate over the local SSR limit. Higher temperatures and more ionization states (especially of iron) may be needed to achieve optically thick W-R winds, unless strong clumping corrections eliminate the need for such winds.

Radiation trapping in a cold atomic gas

We experimentally study radiation trapping of near-resonant light in a cloud of laser-cooled rubidium atoms. Unlike in most previous studies, dealing with hot vapors, collisional broadening is here negligible and Doppler broadening due to the residual atomic velocity is narrower than the homogeneous broadening. This is an interesting new regime, at the boundary between coherent and incoherent radiation transport. We analyze in detail our low-temperature data (quasi-elastic regime) and then provide some experimental evidence for Doppler-based frequency redistribution. The data are compared with an analytical model valid for coherent transport and a Monte Carlo simulation including the Doppler effect.

Multi-wavelength Diagnostics of Bombardment by Non-thermal Particles in Solar Flares

Chromospheric lines, including H alpha, Ly alpha, Ly beta and CaII K, CaII 8542, are systemically and quantitatively investigated with respect to the non-thermal excitation and ionization due to particle beam bombardment for a series of solar semi-empirical atmospheric models. As a result we propose to use the contrast in the integrated intensity of hydrogen lines to estimate the total energy flux of the bombarding beam during the solar flare impulsive phase. Partial frequency redistribution is considered in the Ly alpha line calculation and a smaller intensity enhancement in the H alpha line-centers is found than in the previous results of Fang et al.

Fast Method for Calculating Chromospheric Caiiand MgiiRadiative Losses

A fast and reasonably accurate method for calculating the total radiative losses by Ca II and Mg II ions for time-dependent chromospheric wave calculations has been developed. The method is based on a two-level atom procedure with pseudo-partial frequency redistribution (pseudo-PRD). The speed of the method is due to scaling of the total losses from single-line results. Acceleration of computation speeds by factors of roughly 102-103 can be achieved. The method is tested against the results from a modified version of the multilevel atom code MULTI.

Resonance scattering formalism for the hydrogen lines in the presence of magnetic and electric fields

We derive a formalism for the computation of resonance-scattering polarization of hydrogen lines in the presence of simultaneous magnetic and electric fields, within a framework of the quantum theory of polarized line formation in the limit of complete frequency redistribution and of collisionless regime. Quantum interferences between fine-structure levels are included in this formalism. In the presence of a magnetic field, these interferences affect, together with the magnetic Hanle effect, the polarization of the atomic levels. In the presence of an electric field, interferences between distinct orbital configurations are also induced, further affecting the polarization of the hydrogen levels. In turn, the electric field is expected to affect the polarization of the atomic levels (electric Hanle effect), in a way analogous to the magnetic Hanle effect. We find that the simultaneous action of electric and magnetic fields give rise to complicated patterns of polarization and depolarization regimes, for varying geometries and field strengths.

Line Formation Theory for the Multiterm Atom with Hyperfine Structure in a Magnetic Field

Within the framework of the quantum theory of polarized line formation, in the limit of complete frequency redistribution and of the collisionless regime, we derive explicit formulae describing the statistical equilibrium and the radiative emission of a multiterm atom with hyperfine structure, in the presence of an external magnetic field. The formulae we obtained for the radiative rates of the statistical equilibrium equations and for the radiative coefficients of the transfer equation for polarized radiation can be applied to investigate the formation of spectral lines for which both fine-structure and hyperfine-structure effects are important (e.g., the D1 and D2 lines of Na I in the solar atmosphere).

Radiative transfer in cylindrical threads with incident radiation

A method is proposed for the solution of NLTE radiative transfer equations in long cylinders with an external incident radiation that varies with direction. This method is designed principally for the modelling of elongated structures imbedded in the solar corona (loops, prominence threads). The radiative transfer problem under consideration is a 2D one, since the source functions and absorption coefficients vary with both distance to axis and azimuth. The method is based on the general principles of finite-differences and accelerated Λ -iteration. A Fourier series is used for interpolation in azimuth. The method is applied to a line emitted by a two-level atom with complete frequency redistribution. Convergence properties of the method and influence of the inclination angle on the source function are discussed.

Scattering polarization in strong chromospheric lines

Although the triplet polarization structure of the Na  D2 and Ca  4227 A lines in the second solar spectrum has been known for more than two decades, a clear and consistent explanation has been lacking. Here we show that the qualitative profile shape may be explained in terms of the anisotropy of the radiation field and partial frequency redistribution (PRD) effects. The complicated frequency and depth dependence of the anisotropy can be understood in terms of simple arguments that involve the source function gradient and boundary effects. We show in particular that the triplet peak structure of the polarization profile of Na  D2 has basically the same origin as for the Ca  4227 A line. Hyperfine structure and lower-level atomic polarization only modify the core polarization without altering the overall qualitative features. For our calculations we adopt a numerical method that combines the advantages of both the classical formalism with integral source function and the density-matrix formalism. In a first step, a multi-level, PRD-capable MALI code, which solves the statistical equilibrium and the radiative transfer equation self-consistently, computes intensity, opacities and collision rates. Keeping these quantities fixed, we obtain the scattering polarization in a second step by solving the radiative transfer equation for the transitions of interest with the classical formalism, which assumes a two-level atomic model with unpolarized lower level. Quantum interferences and lower-level atomic polarization are included in terms of a wavelength dependent polarizability W2, which is independently obtained with the density-matrix formalism.

Non-local radiation transport via coupling constants for the radially inhomogeneous Hg–Ar positive column

A model is presented for the radially inhomogeneous Hg–Ar positive column discharge with properties similar to the standard fluorescent lamp. The model combines the electron excitation reactions and radiation trapping to self-consistently solve the spatially dependent species rate equations. Collision rates are evaluated from the electron distribution function determined from the inhomogeneous Boltzmann equation with the gradient term. Radiation processes are evaluated through frequency dependent cell-to-cell coupling constants. This general radiation transport method accounts for non-local photo-pumping, line overlap within the isotopic structure of the Hg resonance lines, and an emission line profile subject to partial frequency redistribution. The coupling constants agree with a more computationally intensive Monte Carlo code. The emission line profile provides an effective decay rate for the 185 nm line, which follows trends in measurements. In contrast, the use of a uniform constant escape factor for radiation trapping leads to centrally constricted profiles for the Hg excited states. Model results for the mean electron energy, distribution function and density distribution of Hg triplet levels are found to agree with existing spatially resolved data. Predicted and measured broad profiles for the Hg triplet levels are attributed to photo-pumping of the outer plasma regions by inner ones.

Photon trajectories in incoherent atomic radiation trapping as Lévy flights.

Photon trajectories in incoherent radiation trapping for Doppler, Lorentz, and Voigt line shapes under complete frequency redistribution are shown to be Lévy flights. The jump length (r) distributions display characteristic long tails. For the Lorentz line shape, the asymptotic form is a strict power law r(-3/2), while for Doppler the asymptotic is r(-2)(ln(r)(-1/2). For the Voigt profile, the asymptotic form always has a Lorentz character, but the trajectory is a self-affine fractal with two characteristic Hausdorff scaling exponents.

Mass-loss rates for hot luminous stars: the influence of line branching

The effect of photon frequency redistribution by line branching on mass-loss rates for hot luminous stars is investigated. Monte Carlo simulations are carried out for a range of OB-star models which show that previous mass-loss calculations which neglect non-resonance line scattering overestimate mass-loss rates for luminous O stars by ~20 per cent. For luminous B stars the effect is somewhat larger, typically ~50 per cent. A Wolf-Rayet star model is used to investigate line branching in the strong wind limit. In this case the effect of line branching is much greater, giving mass-loss rates that are smaller by a factor ~3 from computations which neglect branching.

Time-dependent radiative transfer in magneto-optical traps

We investigate radiation-imprisonment (RI) phenomena in a system of cold atoms trapped in magneto-optical traps (MOTs) when cooling lasers are switched off for a short period. The problem is formulated within the framework of the Streater-Cooper-Sandle equation that belongs to the Markov class and accounts for photon frequency redistribution in multiple scattering processes. On the basis of a semiclassical approach, we derive explicit analytical solutions for the spectral problem of the RI equation neglecting Doppler effects. The analysis reveals peculiarities in emission profiles under initial partial saturation of the resonance transition by the probe laser pulse. Comparison between theoretical and experimental data on effective radiative lifetimes obtained in Cs and Rb MOTs confirms the validity of the discussed nonstationary model of RI in cold samples. For small detunings, the Streater-Cooper-Sandle equation agrees with the experimental data, while in the case of large detunings, the theory does not agree, probably due to non-Markovian effects.

Effect of frequency redistribution in X-ray laser modeling

Calculations are presented of the spectral emissivity corrected for higher-order processes such as photon scattering. Usually, photon scattering is taken into account by postulating a complete frequency redistribution approximation, i.e., same absorption and emission spectra. However, cases exist in hot and dense plasmas for which partial frequency redistribution and angular redistribution play an important role for the radiative transfer mechanisms. Examples of X-ray lasers based on neon-like germanium ion emitters and hydrogen-like carbon ion emitters are considered.

Mechanism of radial redistribution of energetic trapped ions due to m=2/n=1 kink instability in plasmas with an internal transport barrier in the Joint European Torus

Internal radial redistribution of MeV energy ion cyclotron resonance frequency driven hydrogen minority ions was inferred from neutral particle analyzer measurements during large amplitude magnetohydrodynamic activity in plasmas with an internal transport barrier in the Joint European Torus. A theory is developed for energetic ion redistribution during a m=2/n=1 kink mode instability. Plasma motion during the instability or during subsequent magnetic reconnection generates an electric field which can change the energy and radial position of the energetic ions. The magnitude of ion energy change depends on the value of the safety factor at the plasma core, q(0) from which the energetic ions are redistributed. A relation is found for the corresponding change in canonical momentum Pφ, which leads to radial displacement of the ions. The model yields distinctive new features of energetic ion redistribution such as more vertical particle displacement as q(0) increases from 1 to 2. Predicted characteristics of ion redistribution are compared with the measurements, and good correlation is found. Sometimes the energetic ions were further transported to the plasma edge due to interaction with a long-lived magnetic fluctuation (often in the form of a magnetic island) with chirping frequency in the laboratory frame which developed after the m=2/n=1 kink instability. Convection of resonant ions trapped in a radially moving phase-space island is modeled to understand the physics of such events.

Modeling the Lyα radiation of high-redshift galaxies

The Lyα line emission of high-redshift galaxies depends on the density and temperature distribution of the gas, the kinematics and the dust content. We use a finite element method to model theLyα radiation of different 3D configurations considering complete frequency redistribution and the influence of velocity fields. Our results show that the central absorption feature of the double-peaked Lyα line profile observed in many radio galaxies with z=2-4 is probably the consequence of frequency redistribution rather than foreground absorption. The blue peak of the profile is enhanced for models with in fall motion and the red peak for models with outflow motion. In particular, we attempt to model the extendedLyα emission of high-redshift radio galaxies, where we consider results of corresponding hydrodynamical simulations to select possible model configurations. We find that Lyα photons scattered outside a jet-influenced low-density region are able to produce an extended Lyα halo.

Polarization of Cosmic Microwave Backgdound Scattered by Moving Flat Protoobjects

The work is devoted to the investigations of possible observational manifestations of protoobjects related to the “dark ages” epoch (10 < z < 1000), before formation of self-luminous galaxies and stars. These objects can distort the cosmic microwave background. Formation of these objects is described in the “pancake theory” and in the model of “hierarchic clustering.” According to these theories we may consider these protoobjects as flat layers. We consider both Thomson (with Rayleigh phase matrix) and resonance (for complete frequency redistribution) scattering of cosmic microwave background radiation by a moving flat layer. The resulting anisotropy and polarization of cosmic microwave radiation are calculated for a wide range of layer optical thickness (from an optically thin layer to an optically thick one). Analytical solutions are also obtained for the case of an optically thin layer and are compared with the numerical ones.

LYα LINE FORMATION IN HUBBLE-TYPE SPHERICAL OUTFLOWS IN STARBURST GALAXIES

Almost half of primeval galaxies show P-Cygni type profiles in the Ly emission line. The main underlying mechanism for the profile formation in these systems is thought to be the frequency re-distribution of the line photons in expanding scattering media surrounding the emission source. A Monte Carlo code is developed to investigate the Ly line transfer in an optically thick and moving medium with a careful consideration of the scattering in the damping wings. Typical column densities and expansion velocities of neutral hydrogen investigated in this study are and . We investigate the dependence of the emergent profiles on the kinematics and on the column density. Our numerical results are applied to show that the damped Ly absorbers may possess an expanding H I supershell with bulk flow of and H I column density . We briefly discuss the observational implications.

Effects of the heliospheric interface on the interplanetary Lyman α glow seen at 1 AU from the Sun

This work presents multiple scattering computations of interplanetary background line profiles using Angle Dependent Partial Frequency Redistribution to model the scattering process as explained by Quémerais ([CITE]). The density and velocity distribution of hydrogen atoms in the heliosphere was computed using a self-consistent model of the solar wind interaction with the two-component (H atoms and plasma) interstellar plasma (Izmodenov et al. [CITE]). We show that the main difference of the heliospheric interface model as compared to the classical hot model lies in the existence of three populations of H atoms in the heliosphere. These populations are primary interstellar atoms, secondary interstellar atoms created by charge exchange in the outer heliosheath and a hot component (around 150 000 K) created in the inner heliosheath. The two interstellar components provide additional asymmetry in the backscattered Lyα profile at 1 AU, which is not expected from the classical hot model. At the Earth orbit in the upwind direction, the hot component of the backscattered intensity represents less than 5% of the total intensity. It reaches 15% in the downwind direction. Although the heliospheric interface has some effect on the upwind to downwind ratio of total backscattered Lyα intensity, on the apparent velocity and apparent temperature of interplanetary line profiles, they are difficult to discriminate from the results of the variations of the solar parameters. Therefore our following models should include time-dependence effects on the interplanetary hydrogen distribution. Finally, it is concluded that measurements of interplanetary Lyα profiles in the inner heliosphere may serve as a good diagnostic of the heliospheric interface. The existence of a faint hot component in the Lyman α backscattered profiles would serve as a new tool to study the heliospheric interface.

Hanle effect with angle-dependent partial redistribution

The polarized line transfer equation for the Hanle effect is solved in the framework of an exact partial frequency redistribution (PRD) theory developed by Bommier (1997a,b). In that theory the effect of collisions on the Hanle effect is considered self-consistently. We follow that approach in the line transfer computations presented here. The theory formulated by Bommier clearly recognizes two levels of approximations for exact PRD, in order to facilitate the solution of the line transfer equation. The second level employs angle-dependent redistribution functions, and numerically represents a more difficult problem compared to the third level, which involves only the use of angle-averaged frequency redistribution functions. We present a method which can solve the problem in both the levels of approximation. The method is based on a perturbative approach to line polarization. Although computationally expensive, it offers the only practical means of solving the angle-dependent Hanle PRD problem. We discuss the numerical aspects of assembling the so called “frequency domain dependent redistribution matrices”, and also an efficient way of computing the scattering integral. Some examples are presented to illustrate the interesting aspects of the Hanle-PRD problem with angle-dependent frequency redistribution. A comparison of the emergent profiles computed under angle-averaged and angle-dependent redistribution is carried out, and the effect of collisions is investigated. We show that it is necessary to incorporate an angle-dependent redistribution mechanism especially in the computation of the Stokes U parameter. We demonstrate that the use of simple frequency domains is good enough in practical applications of the Hanle PRD theory.