Polarimetry in the Mg ii h and k lines

The Ultraviolet Spectrometer and Polarimeter (UVSP) on the SMM satellite has been used to record the linear polarization profile across the Mgii h and k lines, including its center-to-limb variation. Linear polarization with an orientation of the electric vector parallel to the solar limb is detected in the line wings on the short wavelength side of the k line and on the long wavelength side of the h line, in agreement with theoretical predictions of Auer et al. (1980). The predicted negative polarization (electric vector perpendicular to the limb) between the h and k lines is however not confirmed by the observations. Instead values close to zero are indicated there, although the statistical significance of the results is marginal.We have examined possible explanations of such a discrepancy between theory and observations. After having rejected other alternatives (e.g., opacity effects, different continuum polarization, or deviations from a plane-parallel stratification), it is suggested that the solution may be found in a treatment of partial redistribution of the polarized radiation with the quantum-mechanical interference between the two scattering transitions being included as an integral part of the redistribution problem.     

The effect of angle-dependent non-coherent electron scattering and partial redistribution on the polarization of resonance lines

The polarized radiative transfer equation is solved when angle-dependent partial redistribution and non-coherent electron scattering are included as line-scattering mechanisms. A static atmosphere with plane parallel symmetry is assumed. Test calculations are used to illustrate the effects of the electron-scattering coefficient, the thermalization parameter and the continuous absorption coefficient on the line polarization. Results of angle-averaged and angle-dependent redistribution functions are compared and it is shown that angle-dependent functions should be used to model the wing polarization of optically thin lines. The lower the continuous absorption compared with the electron scattering, the higher the wing polarization.     

Multidimensional radiative transfer: Applications to planetary coronae

A numerical solution to the integral equation for radiative transfer by resonance reradiation in an isothermal spherical atmosphere is described. The method presented is 100 times more efficient than earlier spherical radiative transfer models. The new model can accommodate density variations in the full three dimensional space and includes effects due to the presence of pure absorbers. Complete frequency redistribution is assumed for photon scattering. Applications of this model to the problem of solar photons scattered by atomic hydrogen in the atmospheres of Venus, Earth and Mars are described, and limb and disk profiles, as well as equivalent mean disk intensities for Venus, Earth and Mars, are presented.     

The transfer of polarized radiation in spectral lines: Formalism and solutions in simple cases

A general treatment of the transfer of polarized radiation in spectral lines assuming a Rayleigh phase function and a general law of frequency redistribution is derived. It is shown how nine families of coupled integral equations for the moments of the radiation field arise which are necessary to fully describe the state of polarization of the emergent radiation from a plane-parallel, semi-infinite atmosphere. The special case of angle independent redistribution functions is derived from the general formalism, and it is shown how the nine families of integral equations reduce to the six linearly independent integral equations derived by Collins (1972). To serve as a test of the formulation, solutions for isothermal atmospheres are given.     

Partial frequency redistribution of polarized radiation

Resonance polarization, which is created by the scattering of an anisotropic radiation field in regions of zero or weak magnetic fields, is strongly dependent on the frequency redistribution taking place during the scatterings. Here we discuss the frequency redistribution matrix relevant to resonance lines, concentrating on linear polarization. First we analyze in detail the redistribution matrix in a zero magnetic field given by the theory of Omont, Smith and Cooper (1972), revisited by Domke and Hubeny (1988). We explain that the linear polarization maxima which may appear in the wings of the Stokes Q profiles of strong resonances lines such as the Ca I 4227 Å line are coherent frequency redistribution effects. Various approximate forms of the frequency redistribution matrix are also examined. For resonance polarization in a weak magnetic field, we suggest a new expression for the redistribution matrix which can be used at all line frequencies, and is consistent with the condition that the Hanle effect acts only in the line core.     

MSX mid-infrared imaging of massive star birth environments – I. Ultracompact H ii regions

In solar extreme ultraviolet spectra the He  i and He  ii resonance lines show unusual behaviour and have anomalously high intensities compared with other transition region lines. The formation of the helium resonance lines is investigated through extensive non-local thermal equilibrium radiative transfer calculations. The model atmospheres of Vernazza, Avrett & Loeser are found to provide reasonable matches to the helium resonance line intensities but significantly overestimate the intensities of other transition region lines. New model atmospheres have been developed from emission measure distributions derived by Macpherson & Jordan, which are consistent with SOHO observations of transition region lines other than those of helium. These models fail to reproduce the observed helium resonance line intensities by significant factors. The possibility that non-Maxwellian electron distributions in the transition region might lead to increased collisional excitation rates in the helium lines is studied. Collisional excitation and ionization rates are recomputed for distribution functions with power-law suprathermal tails that may form by the transport of fast electrons from high-temperature regions. Enhancements of the helium resonance line intensities are found, but many of the predictions of the models regarding line ratios are inconsistent with observations. These results suggest that any such departures from Maxwellian electron distributions are not responsible for the helium resonance line intensities.     

Polarization of emerging resonance radiation: model profiles

The limiting polarization of a resonance line is examined for standard radiative transfer of polarized radiation in a semi-infinite scattering atmosphere with complete frequency redistribution. Two families of profiles of the line absorption coefficient, which are generalizations of Lorentz and Doppler profiles, are examined. It is shown that for both families this parameter approaches the Sobolev-Chandrasekhar limit when the fraction of absorption within the frequency interval (expressed in appropriate units) from −1 to 1 relative to the total absorption in the line approaches unity.     

Partial redistribution effects on line polarization in the presence of velocity fields

Velocity fields in line formation regions strongly affect the line polarization. The conventionally used observer's frame method of solving the polarized transfer equation becomes expensive and inaccurate for partial redistribution problems, when large amplitude velocity fields have to be considered in the observer's frame. An alternative method of solution is the comoving frame method. Partial redistribution problems are solved using comoving frame formalism for line polarization caused by resonance scattering.     

Inhomogeneities of the stellar winds of hot supergiants

The causes of variability of line profiles in the spectra of O supergiants are analyzed. It is suggested that the main cause of the variability is the motion in the atmosphere of dense clumps of matter (inhomogeneities or clouds) along the Une of sight between star and observer. The profiles of C IV and Si IV UV resonance lines in the spectra of bright OB supergiants are calculated for spherically symmetric atmospheres and for atmospheres with inhomogeneity along the line of sight. The dependence of the line profiles on the distance of the inhomogeneity from the center of the star is investigated. It is shown that the formation and evolution with time of discrete absorption components (DACs) in the profiles of C IV and Si IV UV resonance lines can be explained within the framework of the proposed model of variability of line profiles. The parameters of the inhomogeneities moving in the atmosphere to produce DACs are estimated. Translated from Astrofizika, Vol. 41, No. 3, pp. 423–441, July–September, 1998.     

Circular polarization of sunlight reflected by planetary atmospheres

Multiple scattering calculations are performed in order to investigate the nature of the circular polarization of sunlight reflected by planetary atmospheres. Contour diagrams as a function of size parameter and phase angle are made for the integrated light from a spherical but locally plane-parallel atmosphere of spherical particles. To investigate the origin of the circular polarization, results are also computed for second-order scattering and for a simpler semiquantitative model of scattering by two particles. Observations of the circular polarization of the planets are presently too meager for accurate deduction of cloud particle properties. However, certain very broad constraints can be placed on the properties of the dominant cloud particles on Jupiter and Saturn. The cloud particle size and refractive index deduced for the Jupiter clouds by Loskutov, Morozhenko, and Yanovitskii from analyses of the linear polarization are not consistent with the circular polarization. The few available circular polarization observations of Venus are also examined.     

Formation depths of lithium resonance absorption lines in the atmospheres of late-type stars and brown dwarfs

A numerical technique for determining absorption line formation depths in the atmospheres of late-type stars and substellar-mass subdwarfs is proposed. The technique is based on estimating individual absorptions contributed by certain layers of the stellar model atmosphere to the resulting equivalent width of a spectral line. In particular, the proposed technique can be used when considering lithium absorption lines formed at the background of molecular bands. The technique is applied to the formation of lithium lines in stellar atmospheres, specifically, in the atmosphere of the Sun (spectral type G2V) and those of the red giant star in the binary system RS Oph (M2III), the giant carbon star WZ Cas (C6), and the brown dwarf LP944-20 (M9V).     

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.     

Theoretical study of partial frequency redistribution function in irradiated, moving atmospheres of close binary components

We have studied the effects of partial frequency redistribution function with angle-averaged   R _II-A  in irradiated and moving atmospheres of close binary components. We have considered the atmospheric extension of the primary component to be twice the radius of the primary component in a close binary system. We have considered two cases: (i) when the atmosphere is at rest and (ii) when the atmosphere is moving. In both the cases, we have computed the line profiles along the line of sight for a given optical depth. The irradiation from the secondary component is assumed to be one, five and 10 times the self-radiation. The line fluxes in the line of sight are calculated by using the total source functions due to self-radiation of the primary component and due to the irradiation from the secondary component. We have noted double-peaked emission lines in the case of a static medium and a reduction of emission peaks in the case of velocity field.     

Ionization structure of the atmospheres and line profiles in the spectra of Wolf-Rayet stars

The ionization structure of the atmospheres of Wolf-Rayet (WR) and WC stars is studied. The stellar atmospheres were assumed to consist of helium, hydrogen, and carbon. Profiles of the C III l 5696 line are calculated, both for a spherically symmetric atmosphere with a density that decreases monotonically outward and for an atmosphere containing a dense condensation (inhomogeneity). The dependence of line profiles on the parameters of the inhomogeneity is investigated. It is shown that profiles of the C III λ 5696 line calculated assuming no inhomogeneities in the atmosphere are too weak, whereas assuming the existence of inhomogeneities enables one to reconcile the observed and calculated profiles. An equation is obtained relating the mass of an inhomogeneity to the flux in the detail of the total profile of the CIII λ 5696 line formed by that inhomogeneity. This equation is used to construct a stochastic cloud model of the atmosphere of a WR star, consisting of a large number of inhomogeneities in a homogeneous, spherically symmetric stellar wind. In the proposed model, the formation of inhomogeneities was treated as a random process. It is shown that in this model it is possible both to obtain an average line profile corresponding to the observed one and to reproduce the amplitude and overall pattern of variability of profiles in the spectra of Wolf-Rayet stars. Translated from Astrofizika, Vol. 42, No. 3, pp. 373–398, July–September, 1999.     

The profiles of polarized broad Hα lines in radio galaxies

We present spectropolarimetric observations of seven broad-line radio galaxies. We find significantly polarized broad Hα emission in four objects including two, Arp 102B and 3C 390.3, which have double-peaked line profiles. In these objects the prominent redshifted and blueshifted peaks of the broad Hα line have no clear counterparts in polarized flux. This conflicts with theoretical predictions for a relativistic line-emitting disc with an electron scattering atmosphere, one of the leading models advanced to account for the double-peaked lines. The shapes and widths of the polarized line profiles can be explained if, as expected in unified schemes, the scattering occurs near the poles of an obscuring torus. However, the observed polarization position angles favour geometries in which the scattering plane is perpendicular to the radio jet. A configuration in which Hα photons emitted by a biconical flow are scattered off the inner wall of the torus has this property, and would also produce a single-peaked scattered line profile. With the exception of 3C 227, the sample as a whole conforms to the general trend in powerful radio galaxies for the optical polarization to be aligned with the radio source axis, favouring toroidal rather than polar scattering.     

Polarized line formation by resonance scattering: Lorentz profile

Multiple resonance scattering of spectral line radiation is examined in atmospheres with uniformly distributed sources of unpolarized radiation. It is assumed that the profile of the absorption coefficient is lorentzian and that scattering involves complete frequency redistribution. The polarization characteristics of the emerging radiation are determined by iterative solution of a nonlinear Ambartsumyan-Chandrasekhar matrix integral equation. In particular, it is found that for pure scattering the maximum polarization at the limb of the disk is 5.421%. The polarization characteristics of the emerging radiation are compared for three different absorption profiles: Lorentz, Doppler, and rectangular (monochromatic radiation). __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 199–217 (May 2007).     

Mode identification from time-resolved spectroscopy of the pulsating white dwarf G29‐38

We have used time-resolved spectroscopy to measure the colour dependence of pulsation amplitudes in the DAV white dwarf G29-38. Model atmospheres predict that mode amplitudes should change with wavelength in a manner that depends on the spherical harmonic degree ℓ of the mode. This dependence arises from the convolution of mode geometry with wavelength-dependent limb darkening. Our analysis of the six largest normal modes detected in Keck observations of G29-38 reveals one mode with a colour dependence different from the other five, permitting us to identify the ℓ-value of all six modes and to test the model predictions. The Keck observations also show pulsation amplitudes that are unexpectedly asymmetric within absorption lines. We show that these asymmetries arise from surface motions associated with the non-radial pulsations (which are discussed in detail in a companion paper). By incorporating surface velocity fields into line profile calculations, we are able to produce models that more closely resemble the observations.     

Line formation in microturbulent magnetic fields

The formation of Zeeman lines in Gaussian microturbulent magnetic fields is considered assuming LTE. General formulae are derived for the local mean values of the transfer matrix elements. The cases of one-dimensional (longitudinal), isotropic, and two-dimensional (transversal) magnetic microturbulence are studied in some detail. Asymptotic formulae are given for small mean as well as for small microturbulent magnetic fields. Characteristic effects of magnetic microturbulence on the transfer coefficients are: (i) the broadening of the frequency contours, although only for the case of longitudinal Zeeman effect and longitudinal magnetic microturbulence this effect can be described analogous to Doppler broadening, (ii) the appearance of a pseudo-Zeeman structure for nonlongitudinal magnetic microturbulence, (iii) the reduction of maximal values of circular polarization, and (iv) the appearance of characteristic linear polarization effects due to the anisotropy of the magnetic microturbulence.Line contours and polarization of Zeeman triplets are computed for Milne-Edddington atmospheres. It is shown that magnetic intensification due to microturbulent magnetic fields may be much more efficient than that due to regular fields. The gravity center of a Zeeman line observed in circularly polarized light remains a reasonable measure of the line of sight component of the mean magnetic field for a line strength47-1. For saturated lines, the gravity center distance depends significantly on the magnetic microturbulence and its anisotropy. The influence of magnetic microturbulence on the ratio of longitudinal field magnetographic signals shows that unique conclusions about the magnetic microstructure can be drawn from the line ratio measurement only in combination with further spectroscopic data or physical reasoning.