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1.
A moment method with three stream division of the radiation field was suggested by Wilson, Wan and Sen (1980) for solving radiative transfer problems in stationary, non-grey extended shells surrounding a central star. Use was made of the generalised Eddington relations as the closure conditions of the moment equations. In the present paper the same method has been utilised to study the radiative transfer problems in a non-grey, expanding gaseous spherical shells surrounding a central star. The transfer equation has been set in comoving frame in spherical geometry. The radiation and material quantities, angles and frequencies have been expressed in comoving frame. The mean intensity, flux and K-integrals have been calculated for extensive atmospheres in the presence of different velocity fields.  相似文献   

2.
H. Frisch 《Solar physics》1996,164(1-2):49-66
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.  相似文献   

3.
Given a relativistically expanding source, the transformation of the emission spectrum from the comoving frame of the source to the observer's frame is calculated. In particular, we deal with two special cases, that of a uniformly expanding sphere and that of a cylinder. In each case we consider a power-law spectrum with two distinct regions — the optically thick and thin parts — and transform those regions separately. The results are discussed, and a generalized procedure for transforming a spectrum of unspecified form is outlined. This procedure takes into account any bulk motion by the source as well as expansion. Finally, applications of this procedure to astrophysical sources are briefly discussed.  相似文献   

4.
A general expression for the gravity darkening of the tidally and non-uniformly rotating Roche components of close binary systems is used to calculate the uniform rotational effects on line profiles in an expanding atmosphere. We consider a non-local thermodynamic equilibrium (non-LTE) two-level atom approximation in an extended atmosphere, and use Von Zeipel's theorem for the incident radiation at the maximum optical depth  (τ=τmax)  in the atmosphere. These calculations are performed with uniform rotational velocities of 1, 4 and 8 mtu (mean thermal units). It is found that rotation dilutes the radiation field which is similar to the expansion velocity.
We also study rotational aspects, which make the outer layers of the star distorted. The equation of line transfer is solved in the comoving frame of the expanding atmosphere of the primary using complete redistribution in the line. We use a linear law for the velocity of expansion such that the density varies as r −3, where r is the radius of the star, satisfying the law of conservation of mass. It is found that rotation broadens the line profile, and P-Cygni-type line profiles are obtained.  相似文献   

5.
The problem of polarization of the resonance lines formed in extended spherical atmospheres is studied in detail. In this paper, the atmosphere is assumed to be at rest. The basic problem of resonance line polarization in spherical atmospheres as compared to the conventionally used plane-parallel atmospheres, is studied in Nagendra (1988). Our main interest in this paper is to understand the behaviour of polarized radiation fields in extended model spherical atmospheres so that some constraints can be placed on the model parameters in the modelling work conected with observations of polarization across resonance lines. A comparison of polarized lines formed under three kinds of line-scattering mechanisms is also made. They are CS=coherent scatteirng, CRD=complete redistribution, and PRD=partial frequency redistribution which, in the increasing order of generality, provide a good approximation in the two-level atom approach, to the resonance line polarization. The dependence of polarization on the opacity laws, extendedness and on optical depth is studied in detail. The distribution of line intensity and polarization across the visible disk of an extended model stellar atmosphere is studied, in view of the possible disk-resolved observations in future, of the extended atmospheres of the stars.  相似文献   

6.
Equations of fully general relativistic radiation hydrodynamics in Kerr space–time are derived. While the interactions between matter and radiation are introduced in the comoving frame, the derivatives used when describing the global evolutions of both the matter and the radiation are given in the Boyer–Lindquist frame (BLF) which is a frame fixed to the coordinate describing the central black hole. Around a rotating black hole, both the matter and the radiation are influenced by the frame-dragging effects due to the black hole's rotation. As a fixed frame, we use the locally non-rotating reference frame (LNRF) which is one of the orthonormal frame. While the special relativistic effects such as beaming effects are introduced by the Lorentz transformation connecting the comoving frame and the LNRF, the general relativistic effects such as frame dragging and gravitational redshift are introduced by the tetrads connecting the LNRF and the BLF.  相似文献   

7.
The theory of polarized scattering in a stellar atmosphere is formulated, first within the framework of classical physics, then in terms of quantum mechanics. The expression for the redistribution matrix that describes partial redistribution in polarization and frequency is derived for the general case when the magnetic field is of arbitrary strength. The special cases of weak fields (the Hanle limit) and zero fields (non-magnetic scattering) are discussed. Observational examples of spectral signatures in linear polarization are presented, which show effects of hyperfine structure, interference between fine structure components, and molecular scattering.  相似文献   

8.
A direct iteration has been performed to obtain a simultaneous solution of the equations of line transfer in an expanding spherically symmetric atmosphere in the comoving frame with statistical equilibrium for a non-LTE, two-level atom. The solution converges in three or four iterations to an accuracy of 1 per cent of the ratio of the population densities of the two levels. As initial values, the upper level population was set equal to zero or to the LTE densities. The final solution on convergence indicates enhanced population of these levels over the initial values assumed, Large velocity gradients enhance this effect whereas large geometrical sizes of the atmospheres tend to reduce it.  相似文献   

9.
The non-LTE equations for the transfer of polarized radiation are solved for a two-level model of the Ca ii K ion in the atmospheric models of Gingerich et al. (1971) and Vernazza et al. (1981). The line formation model treats partial redistribution effects, including collisions. The effects of magnetic fields and of quantum mechanical interference are neglected. The response of the intensity, percentage polarization and Q Stokes parameter to changes in the calcium abundance, van der Waals damping parameter and atmospheric models is discussed.  相似文献   

10.
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.  相似文献   

11.
We present multifrequency observations of a sample of 15 radio-emitting broad absorption-line quasars (BAL QSOs), covering a spectral range between 74 MHz and 43 GHz. They mostly display convex radio spectra which typically peak at about 1–5 GHz (in the observer's rest frame), flatten at MHz frequencies, probably due to synchrotron self-absorption, and become steeper at high frequencies, i.e. ν≳ 20 GHz. Very Large Array (VLA) 22-GHz maps (HPBW ∼80 mas) show unresolved or very compact sources, with linear projected sizes of ≤1 kpc. About two-thirds of the sample looks unpolarized or weakly polarized at 8.4 GHz, frequency in which reasonable upper limits could be obtained for polarized intensity. Statistical comparisons have been made between the spectral index distributions of samples of BAL and non-BAL QSOs, both in the observed and in the rest frame, finding steeper spectra among non-BAL QSOs. However, constraining this comparison to compact sources results in no significant differences between both distributions. This comparison is consistent with BAL QSOs not being oriented along a particular line of sight. In addition, our analysis of the spectral shape, variability and polarization properties shows that radio BAL QSOs share several properties common to young radio sources like compact steep spectrum or gigahertz peaked spectrum sources.  相似文献   

12.
Conclusions Besides the problems considered here, one can find comparatively easily asymptotic solutions in a problem with a spherically symmetric exponential distribution of the primary sources, and also in the case when the primary sources are distributed uniformly within a sphere of finite radius. However, we do not give these solutions because they are cumbersome. Note that some of these problems may have direct astrophysical applications. For example, the problem of a point source can arise in the determination of the source function in the problem of the emission of a planetary nebula.The results of the present work, and also of the majority of the other investigations have been obtained under the assumption of complete frequency redistribution for scattering in the comoving coordinate system. In reality, this assumption is not strictly satisfied. However, calculations made recently for moving media [13, 14] have shown that the results found for true and complete redistribution differ little from one another, these differences being less than in the case of a medium which is not in motion.A. A. Zhdanov Leningrad State University. Translated from Astrofizika, Vol. 14, No. 1, pp. 111–121, January–March, 1978.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
A new method is proposed to determine all components of the solar magnetic fields using the cumulants of the profile of a magnetic sensitive line. The method is based on polarization measurements in a number of points of the line profile and subsequent calculation of the amplitudes and phases of its two first Fourier-harmonics.  相似文献   

16.
The causality of superluminal signal transfer in the galaxy background is scrutinized. The cosmic time of the comoving galaxy frame determines a distinguished time order for events connected by superluminal signals. Every observer can relate his rest frame to the galaxy frame, and compare so the time order of events in his proper time to the cosmic time order. In this way all observers arrive at identical conclusions on the causality of events connected by superluminal signals. The energy of tachyons (superluminal particles) is defined in the comoving galaxy frame analogous to the energy of subluminal particles. It is positive in the galaxy frame and bounded from below in the rest frames of geodesically moving observers, so that particle-tachyon interactions can be based on energy-momentum conservation. We study tachyons in a Robertson-Walker cosmology with linear expansion factor and open, negatively curved 3-space (Milne universe). This cosmology admits globally geodesic rest frames for uniformly moving observers, synchronized by Lorentz boosts. In this context we show that no signals can be sent into the past of observers. If an observer emits a tachyonic signal, then the response of a second observer can never reach him prior to the emission, i.e., no predetermination can occur. The proof is based on the positivity of tachyonic energy. This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

17.
The partial frequency redistribution function for zero natural line width with dipole scattering (RI) has been considered in obtaining the simultaneous solution of the statistical equilibrium and line transfer equations in the comoving frame of the expanding gas. We have considered a non-LTE two level atom in an expanding spherical medium whose outer radii are 3, 10 and 20 times the stellar radius with a total optical depthT ≃ 2 × 103. In all the cases, we have calculated the population ratio of the two levels N2/N1 and compared these results with those obtained by using different expansion velocities and geometrical extensions. Initially, the upper level population (N2) is set equal to zero. The converged simultaneous solution shows that the upper level population is enhanced considerably from the initial value. Variation in velocity gradients seem to have little effect on the ratio N2/N1 when the geometrical thickness of the medium is 3 or 10 times the stellar radius. However, when the thickness is increased to 20 times the central radius, the velocity gradients change the ratio N2/N1 considerably in the region where log T ≤ 2. The effect of variation of geometrical thickness is to reduce the N2/N1 ratio atτ = 0.  相似文献   

18.
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.  相似文献   

19.
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20.
This paper presents a brief history of the development of devices and techniques for high-precision measurements of stellar magnetic fields. Two main approaches for the processing of spectral-polarimetric observations are described: the method of least-squares deconvolution (LSD), which is used to find a mean-weighted average of the normalized polarization profile using a set of spectral lines, and a method in which each individual spectral line is used to determine the magnetic field, viz., the single line method (SL). The advantages and disadvantages of the LSD and SL methods are discussed.  相似文献   

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