Effects of partial frequency redistribution functions RII,RIII and RV on source functions

The effects of partial frequency redistribution on the formation of spectral lines have been studied. We considered the angle-averaged R_II, R_III andR _v types of redistribution with isotropic phase function, Transfer equation with plane-parallel geometry is solved in isothermal atmospheres. For an atmosphere with constant thermal sources, the frequency-dependent source function S_L (R _v) lies below S_L (R_III) but above S_L(R _III) in the line wings.     

The transfer of polarized radiation in spectral lines: Solar-type stellar atmospheres

The polarization structure in several spectral lines in solar type stars is computed using the method described by McKenna (1981, 1984a). The frequency redistribution function used for these calculations is a linear combination ofR _II andR _III. The line profiles and polarization structures have been computed for several weak solar resonance lines includingKi 7664 Å, Sri 4607 Å, Baii 4554 Å, for various polar angles along the stellar disk. Both the line profiles and polarization structures as well as the center to limb behavior of the line center polarization agree well with observations.The somewhat stronger resonance line Cai 4227 Å shows a different polarization structure when compared to the weaker solar resonance lines. It is found that for strong resonance lines the proper redistribution function to be used is a linear combination ofR _III andR _v (see McKenna, 1981, 1984b; Heinzel, 1981). The major reason for this is that for strong resonance lines both the upper and lower levels are broadened by collisions. This violates the assumptions upon which the redistribution functionsR _II andR _III are based.     

Astrophysical spectroscopy and neutron reactions: Integral transforms and Voigt functions

The Voigt functionsK(x, y) andL(x, y) which play an essential role in astrophysical spectroscopy and neutron physics are investigated and generalized from the viewpoint of integral operators. Unified representations and series expansions involving classical functions of mathematical physics and multivariable hypergeometric functions are established. From the delicate asymptotic analysis of Laplace and Hankel integral transforms we extract complete and rigorous asymptotic expansions of the generalized Voigt functions for large values of the variablesx andy which are of great value in the theory of spectral line profiles.     

An electron temperature distribution derived from optical and radio measurements of HII regions

Radio measurements of the electron temperature ofHii regions are obtained from the ratio of the brightness temperature of a hydrogen recombination line to that of the adjacent continuum, while optical measurements are obtained from the ratio of [Oiii] forbidden-line intensities. The radio and optical measurements made under the assumption of an isothermalHii region,T _R andT _opt respectively, are combined to derive a temperature distribution for an entire nebula. A sphericalHii region in local thermodynamic equilibrium with constant density which is optically thin in both the line and the continuum is used as a model. Assuming linear temperature gradients withT _R=6000K andT _opt=10000K, it is found thatT=12000K (1–0.74r/R), wherer is the distance from the center andR is the radius of the nebula.     

A model of the Algol type close binary TT hydrae

UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and. a model of this important Algol system. While the photometric ratios of radii inV andB are in agreement givingk = 0.3812 for a limb darkening coefficient ofx = 0.6, application of Irwin’s (1947) method givesx = 0.4 forU. The primary is found to be a main sequence Al V star of mass 2.61M _⊙ and radius 2.01 R_⊙, and the secondary is classified as a Kl III star of mass 0.70M _⊙ and radius 5.33R _⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed.     

A unified presentation of the Voigt functions

This paper aims at presenting a unified study of the Voigt functionsK(x,y) andL(x,y) which play a rather important role in several diverse fields of physics such as astrophysical spectroscopy and the theory of neutron reactions. Explicit expressions for these functions are given in terms of relatively more familiar special functions of one and two variables; indeed, each of these representations will naturally lead to various other needed properties of the Voigt functions.     

Ar XIII line ratios in solar flares

Theoretical ArXIII electron-density-sensitive emission line ratios, derived using electron impact excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(242.22 )/I(236.27 ),R ₂ =I(210.46 )/I(236.27 ), andR ₃ =I(248.68 )/I(236.27 ). Electron densities deduced from the observed values ofR ₁,R ₂, andR ₃ for solar flares obtained with the NRL S082A slitless spectrograph on boardSkylab are in excellent agreement, and furthermore compare favorably with those determined from line ratios in CaXV, which is formed at a similar electron temperature to that of ArXIII. These results provide experimental support for the accuracy of the atomic data adopted in the analysis, as well as for the techniques used to calculate the line ratios.     

High-resolution Martian atmosphere modeling

A multilayer radiative transfer, high-spectral-resolution infrared model of the lower atmosphere of Mars has been constructed to assess the effect of scattering on line profiles. The model takes into account aerosol scattering and absorption and includes a line-by-line treatment of scattering and absorption by CO₂ and H₂O. The aerosol complex indices of refraction used were those measured on montmorillonite and basalt chosen on the basis of Mars ir data from the NASA Lear Airborne Observatory. The particle sizes and distribution were estimated using Viking data. The molecular line treatment employs the AFGL line parameters and Voigt profiles. The modling results indicate that the line profiles are only slightly affected by normal aerosol scattering and absorption, but the effect could be appreciable for heavy loading. The technique described permits a quantitative approach to assessing and correcting for the effect of aerosols on lineshapes in planetary atmospheres.     

Some unified presentations of the Voigt functions

The principal object of this note is to provide a natural further step toward the unified presentations of the Voigh functionsK(x, y) andL(x, y) which play a rather important role in such diverse fields of physics as astrophysical spectroscopy and the theory of neutron reactions. Explicit representations for these functions, given in terms of some relatively more familiar special functions of one and two variables, are potentially useful in finding many other needed (numerical or analytical) properties of the Voigt functions. Several erroneous recent contributions to the theory of Voigt functions, including (for example) the main result of A. Siddiqui (1990), are also corrected here.     

A comparison of theoretical Sv emission line strengths with extreme ultraviolet observations of a sunspot

Electron impact excitation rates for transitions in the S v ion, calculated with theR-matrix code, are used to derive the electron temperature sensitive emission line ratiosR ₁ =I(854.8 Å)/I(786.9 Å),R ₂ =I(852.2 Å)/I(786.9 Å),R ₃ =I(849.2 Å)/I(786.9 Å), andR ₄ =I(1199.1 Å)/I(786.9 Å), which are found to be significantly different from previous estimates. A comparison of the present results with observational data for a sunspot obtained with the Harvard S-055 spectrometer on boardSkylab reveals generally good agreement between theory and experiment, except in the case ofR ₁, which is probably due to blending in the 854.8 Å feature. The possible effects of Lyman continuum absorption on the observed line ratios is briefly discussed.     

Isotropization in bianchi type-I vacuum cosmology

We have found the most general solution for the Bianchi type-I equations in the Brans-Dicke theory (BDT) for the vacuum case. It is shown that forw > 500 the Universe will become isotropic for any amount of initial anisotropy, secondly it is shown that in the extended inflation scenario, the BDT-scalar field can avoid the inflation in one direction,R ₃. In the other scale factorsR ₁ andR ₂ there is inflationary expansion.     

A unified presentation of the Voigt functions

In the present paper, we have given a generalization of a unified study of the Voigt functionsK(x, y) andL(x, y) obtained by Srivastava and Miller (1987; Vol. 135, pp. 111–118) which play an important role in several diverse fields of physics-such as astrophysical spectroscopy and the theory of neutron reactions. Explicit expressions for these functions are given in terms of relatively more familiar special functions of one and two variables; indeed, each of these representations will naturally lead to various other needed properties of the Voigt functions.     

The solution of radiation transfer problem for a slab with space-dependent albedo and anisotropic scattering

The transport of thermal radiation has been considered within a finite slab which absorb and scatter anisotropically. The problem involves the space-dependent single-scattering albedow(x). Two approximations are taken forw(x). In the first it is represented in exponential form asw(x)=w ₀ exp(–x/s), wherew ₀ ands are given constants andx is the optical variable. The second approximation assumes the formw(x) = _r=0 ^R d _r ^* p _r (x/a), whered _r ^* are known expansion coefficients anda is the half optical thickness of the slab. Analytic expressions for the forward, backward radiation intensities and fluxes are given in each approximation. The solution of the linear transport equation is performed on the basis of integral Fourier transforms.     

Small perturbations in flat galaxies

The aim of this series of papers is to develop straightforward methods of computing the response of flat galaxies to small perturbations. This Paper I considers steady state problems; Paper II considers time varying perturbations and the effects of resonances; and Paper III applies the methods developed in Papers I and II to a numerical study of the stability of flat galaxies.The general approach is to study the dynamics of each individual orbit. The orbits are described by their apocentric and pericentric radii,r _a andr _p , and the distribution function of an equilibrium model is a function ofr _a andr _p . The mass density and potential corresponding to a distribution function is found by means of an expansion in Hankel-Laguerre functions; the coefficients of the expansion being found by taking moments of the mass density of the individual orbits. This leads to a simple method of constructing equilibrium models.The response to a small perturbation is found by seeking the response of each orbit. When the perturbations are axisymmetric and slowly varying, the response can be easily found using adiabatic invariants. The potential is expanded in a series of Hankel-Laguerre functions, and the response operator becomes a discrete matrix. The condition that the model is stable against adiabatic radial perturbations is that the largest eigenvalue of the response matrix should be less than one.An analytic approximation to the response matrix is derived, and applied to estimate the eccentricity needed for stability against local perturbations.     

Effect of parallel electric fields on whistler mode waves in an anisotropic Jovian magnetospheric plasma

The effect of parallel electrostatic field on the amplification of whistler mode waves in an anisotropic bi-Maxwellian weakly ionized plasma for Jovian magnetospheric conditions has been carried out. The growth rate for different Jovian magnetospheric plasma parameters forL = 5.6R _j has been computed with the help of general dispersion relation for the whistler mode electromagnetic wave of a drifted bi-Maxwellian distribution function. It is observed that the growth or damping of whistler mode waves in Jovian magnetosphere is possible when the wave vector is parallel or antiparallel to the static magnetic field and the effect of this field is more pronounced at low frequency wave spectrum.     

Line formation in spherical media with partial frequency redistribution

The effects of partial redistribution of frequency on the formation of spectral lines in a static and spherically symmetric media have been investigated. The partial redistribution functionsR _I andR _II (Hummer, 1962) have been employed to calculate the lines for a two-level atom in non-LTE in a spherically symmetric medium with homogenous physical characteristics whose ratiosB/A (of outer to inner radii) are equal to 2 and 10. These results are compared with those formed in a plane-parallel medium withB/A=1. Two types of atmosphere are treated: (1) a pure scattering medium with =0 and =0, and (2) an atmosphere with a constant source of emission =10^–4 and =0, where is the probability per scatter that a photon will be destroyed by collisional de-excitation and is the ratioK _c/K _l of opacity due to continuous absorption per unit interval of frequency to that in the line. Lines formed in complete redistribution also have been calculated for the sake of comparison, and the total optical depth in all cases has been taken to be 10³ at the line centre.Vast differences have been found between the lines formed by complete and partial redistribution functions (which, for the sake of simplicity, we shall hereafter refer to as CRD and PRD, respectively). In the case of a purely scattering medium, a small amount of emission is observed in the wings for all cases of scattering functions in the spherical medium as a result of the combined effects of curvature and physical scattering. In the scattering medium, more photons are scattered into the cores of the lines by PRD than in the case of CRD. The lines formed in the medium with internal sources show emission in all cases with small absorption in the cores, except those lines formed by the angle-dependent PRD functions which again depend on the geometrical extension of the medium.     

Ca X line ratios in solar flares

Theoretical Ca X electron temperature sensitive emission line ratios, derived using electron excitation rates interpolated from accurateR-matrix calculations, are presented forR ₁ =I(419.74 )/I(574.02 ,),R ₂ =I(411.65 )/I(574.02 ),R ₃ =I(419.74 )/I(557.75 ), andR ₄ =I(411.65 )/I(557.75 ). A comparison of these with observational data for three solar flares, obtained by the Naval Research Laboratory's S082A slitless spectrograph on boardSkylab, reveals good agreement between theory and observation forR ₁ andR ₃ in one event, which provides limited support for the accuracy of the atomic data adopted in the analysis. However, in the other flares the observed values ofR ₁ –R ₄ are much larger than the theoretical high-temperature limits, which is probably due to blending of the 419.74 line with Civ 419.71 , and 411.65 with possibly Ciii 411.70 .     

Line formation in moving media: Asymptotic expansions of some special functions

Line formation in the spectrum of a moving medium with a spherical geometry is considered. In the Sobolev approximation there are some special functions that determine the source function and the force of radiation pressure in the line. The most important case is that of a small dimensionless velocity gradient (i.e., a large dimensionless Sobolev length τ) and a small ratio β of the opacity in the continuum to the opacity in the line. Until now there has been no detailed analytical information about the asymptotic behavior of these functions. For the case of a Doppler profile of the absorption coefficient, we clarify the nontrivial structure of their total asymptotic expansions for τ » 1, β « 1, and arbitrary Βτ. We give an algorithm for obtaining all the coefficients of these expansions and give explicit expressions for the first few coefficients. We also compare the asymptotic expansions with the numerical calculations of these functions available in the literature. We also briefly consider the case of a power-law decrease in the absorption coefficient in the line wing (and, in more detail, the case of Lorentz wings of the Voigt profile).     

Constraining the cosmological time variation of the fine - structure constant

The variation of the fine-structure constant α = e ² / ħc can be probed by comparing the wavelength of atomic transitions from the redshift of quasars in the Universe and laboratory over cosmological time scales t ~ 10¹⁰ yr. After a careful selection of pairs of lines, the Thong method with a derived analytical expression for the error analysis was applied to compute the α variation. We report a new constraint on the variation of the fine-structure constant based on the analysis of the C_IV, N_V, Mg_II, Al_III, and Si_IV doublet absorption lines. The weighted mean value of the variation in α derived from our analysis over the redshift range 0.4939 ≤ z ≤ 3.7 is = ( 0.09 ± 0.07)×10⁻⁵. This result is three orders of magnitude better than the results obtained by earlier analysis of the same data on the constraint on Δα/α .     

Comments on ‘the angle-dependent redistribution functionsR III andR IV’ by S. J. McKenna

It is shown that the complicated form of the line absorption probability function for scattering in subordinate lines, derived by McKenna (1984), is an artifact of adopting a mathematically inconvenient expression for the corresponding redistribution function. It is demonstrated that the absorption probability must be given by the Voigt function.