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1.
S. I. Grachev 《Astrophysics》2001,44(4):505-517
A new method is proposed for the numerical solution of nonsteady problems in the theory of radiative transfer. In this method, if the solution at some time t (such as the initial time) is known, then by representing the radiation intensity and all time-dependent quantities (level populations, kinetic temperature, etc.) in the form of Taylor series expansions in the vicinity of t, one can, from the transfer equation and the equations accompanying it (population equations, energy-balance equation, etc.), find all derivatives of that solution at the given time from certain recursive equations. From the Taylor series one can then calculate the solution at some later time t + t, and so forth. The method enables one to analyze nonsteady tradiative transfer both in stationary media and in media with characteristics that vary with time in a given way. This method can also be used to solve nonlinear problems, i.e., those in which the radiation field significantly affects the characteristics of the medium. No iterations are used for this: everything comes down to calculations based on recursive equations. Several problems, both linear and nonlinear, are solved as examples.  相似文献   

2.
We have calculated prominence thread models for different values of the center temperature and pressure. We have simultaneously solved the radiative transfer, statistical equilibrium and ionization equilibrium equations assuming a three-level atom plus continuum. We have also computed the energy balance equation including the hydrogen radiative losses from our calculations, plus other radiative losses and heat conduction. Some models have been calculated assuming possible variations in thermal conductivity and heating terms. We computed the lines and continua emitted by a number of threads, in order to compare with the observations and evaluate how the different values of the parameters affect the profiles and absolute intensities of L, L, H, and Ly continuum.Member of the Carrera del Investigador, CONICET, Argentina.c.c.67 Suc. 28 Buenos Aires 1428, Argentina.  相似文献   

3.
Magnan  C.  De Laverny  P. 《Astrophysics》1994,37(2):167-181
We consider the problem of determining the radiation fields reflected and transmitted by a slab containing multilevel hydrogen atoms and illuminated on one side by a given radiation field. We treat the extreme non-LTE situation in which the populations of the different levels are determined by the radiative processes. We take into account the population and the transfer effects in a self-consistent way by solving the transfer equations in all the lines and continua together with the equations of statistical equilibrium for all levels. We limit ourselves to the idealistic case of rectangular profiles in the lines and continua and to a model of atoms with 4 levels and a continuum. Under conditions close to thermodynamic equilibrium we empirically derive a Schuster-like law for the continua with transmitted radiation fields varying as the inverse of the optical thickness. Turning to out-of-equilibrium conditions we emphasize the crucial role of the loss probability of the Ly photons. Owing to the rapid decrease of the excitation/ionization degree in the medium and contrary to the conservative case the optical thicknesses of the subordinate transitions now remain finite even when the population of the fundamental level along the line-of-sight becomes infinite. As a result of this relative transparency the strong emission lines formed by recombination mechanisms can escape from the medium. Although the present problem remains largely academic because of the number of simplifications introduced we suggest some possible applications and developments.Published in Astrofizika, Vol. 37, No. 2, pp. 313–338, April–June, 1994.  相似文献   

4.
The polarization-free (POF) approximation (Trujillo Bueno and Landi Degl'Innocenti, 1996) is capable of accounting for the approximate influence of the magnetic field on the statistical equilibrium, without actually solving the full Stokes vector radiative transfer equation. The method introduces the Zeeman splitting or broadening of the line absorption profile I in the scalar radiative transfer equation, but the coupling between Stokes I and the other Stokes parameters is neglected. The expected influence of the magnetic field is largest for strongly-split strong lines and the effect is greatly enhanced by gradients in the magnetic field strength. Formally the interaction with the other Stokes parameters may not be neglected for strongly-split strong lines, but it turns out that the error in Stokes I obtained through the POF approximation to a large extent cancels the neglect of interaction with the other Stokes parameters, so that the resulting line source functions and line opacities are more accurate than those obtained with the field-free approach. Although its merits have so far only been tested for a two-level atom, we apply the POF approximation to multi-level non-LTE radiative transfer problems on the premise that there is no essential difference between these two cases. Final verification of its validity in multi-level cases still awaits the completion of a non-LTE Stokes vector transfer code.For two realistic multi-level cases (CaII and MgI in the solar atmosphere) it is demonstrated that the POF method leads to small changes, with respect to the field-free method, in the line source functions and emergent Stokes vector profiles (much smaller than for a two-level atom). Real atoms are dominated by strong ultraviolet lines (only weakly split) and continua, and most lines with large magnetic splitting (in the red and the infrared) are at higher excitation energies, i.e. they are relatively weak and unable to produce significant changes in the statistical equilibrium. We find that it is generally unpredictable by how much the POF results will differ from the field-free results, so that it is nearly always necessary to confirm predictions by actual computations.The POF approximation provides more reliable results than the field-free approximation without significantly complicating the radiative transfer problem, i.e. without solving any extra equations and without excessive computational resource requirements, so that it is to be preferred over the field-free approximation.  相似文献   

5.
Gontikakis  C.  Vial  J.-C.  Gouttebroze  P. 《Solar physics》1997,172(1-2):189-197
The diagnostic of eruptive prominences needs the development of new tools. Here we propose the Lyman and Balmer lines of hydrogen, which are important in the radiative budget. In the NLTE radiative transfer calculations, we include the effect of the outward motion of the structure associated with the eruption of the prominence. The treatment of the resonance scattering of L and L with partial redistribution gives higher intensities, and a higher ionization than the complete redistribution, but the two approaches converge to the same solution as the velocity increases. As a first step in the diagnostic, we present new results concerning the variation of the integrated intensities of hydrogen lines with respect to the radial velocity.  相似文献   

6.
Stokes inversion calculation is a key process in resolving polarization information on radiation from the Sun and obtaining the associated vector magnetic fields. Even in the cases of simple local thermodynamic equilibrium(LTE) and where the Milne-Eddington approximation is valid, the inversion problem may not be easy to solve. The initial values for the iterations are important in handling the case with multiple minima. In this paper, we develop a fast inversion technique without iterations. The time taken for computation is only 1/100 the time that the iterative algorithm takes. In addition, it can provide available initial values even in cases with lower spectral resolutions. This strategy is useful for a filter-type Stokes spectrograph, such as SDO/HMI and the developed two-dimensional real-time spectrograph(2DS).  相似文献   

7.
A functional analytic method of solution of the operator equations is used to obtain a solution of the radiative transfer equation in spectral lines. A problem of scattering in the spectral line with frequency redistribution in an isotropic scattering medium is considered.  相似文献   

8.
We study in some detail one-dimensional NLTE effects in solar Fei lines. The lines selected are frequently used in solar polarimetry, and also in studies of line asymmetries and for abundance determinations. Our model atom for Fei–Feii–Feiii is realistic: it takes account of multiplet structure and it includes over 200 bound–bound and bound–free transitions in detail. We use very efficient iterative methods for the self-consistent solution of the kinetic and radiative transfer equations (Auer, Fabiani Bendicho, and Trujillo Bueno, 1994). We have applied these fast methods of solution because they are suitable for the investigation of 2D and 3D NLTE transfer effects with multilevel atoms, which constitutes the next step of our ongoing research project on the iron line formation problem.  相似文献   

9.
Spectra of a 2B flare on 3 February, 1983 were observed simultaneously at H, H, and Can H, K lines with a multichannel spectrograph in the solar tower telescope of Nanjing University. The flare occurred in an extended region of penumbra at S 17 W07 from 05 : 41 to 07 : 00 UT. By use of an iterative method to solve the equations describing hydrostatic, radiative, and statistical equilibrium for hydrogen and ionized calcium atoms, five semi-empirical models corresponding to different times of the chromospheric flare have been computed. The results show that after the beginning of the flare, the heating of the chromosphere starts and the transition layer begins to be displaced downwards. However, during the impulsive phase the flare chromospheric region has a rapid outward expansion followed by a quick downward contraction. At the same time the transition layer starts to ascend and then descend again. After the H intensity maximum, the flare chromospheric region continues to condense and attains its most dense phase more than ten minutes after the maximum. Finally, the flare chromospheric region returns slowly to the normal chromospheric situation.  相似文献   

10.
B. Schmieder 《Solar physics》1978,57(2):245-253
In a previous paper (Schmieder, 1977), we solved simultaneously the hydrodynamical and radiative transfer equations, so we do not have to assume any relaxation time of the atmosphere. In this paper, we use that theory to interpret photospheric observations of the Mg i line at 5172 Å.For periods between 400 and 140 s, the phase-shifts observed between velocities and the phase shifts between intensity and velocity fluctuations are explained by the existence of radiative dissipation coupled with evanescent waves or upward propagating waves, according to the frequency.For smaller periods partial or total reflections must be considered.The results relative to radiative dissipation are expressed in terms of the variation of a relaxation time with frequency through the atmosphere (10–3<5000<1).  相似文献   

11.
Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M1?10 and unperturbed gas densities σ1=10?10 g cm?3, the Doppler shift is approximately one third of the shock velocity U1. The FWHM of the emission-line profile δ ? is related to the shock velocity by δ ? ≈ k ? U1, where k ? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.  相似文献   

12.
On the ground of the proper wave representation the general theory is developed of radiative transfer in a homogeneous plasma with the strong magnetic field ( B /1). The linear and nonlinear equations are derived which generalize the corresponding equations of scalar radiative transfer theory in isotropic media. The solutions of some problems are given for the cases when the magnetic field is perpendicular to the surface: diffuse reflection of radiation from a semiinfinite medium, provided the sources are placed far from the surface (Milne's problem) and have constant intensity, increase linearly or quadratically with the optical depths, or decrease exponentially from the surface.  相似文献   

13.
Radiative transfer equation in a plane-parallel medium with isotropic boundary conditions for linearly anisotropic scattering phase function is considered. Two coupled integral equations for total density of radiation and total radiation flux are obtained. The Galerkin method is used to solve these equations. Numerical results for the radiative fluxes at the boundaries show that the Galerkin method yields accurate results compared well with other exact methods.  相似文献   

14.
Shved  G. M.  Semenov  A. O. 《Solar System Research》2001,35(3):212-226
The standard problem of radiative transfer in a rovibrational band is formulated for an optically semi-infinite plane-parallel planetary atmosphere using a model of a linear molecule with two vibrational states. The solution of the problem describes the variation with height of the population of the excited vibrational state due to the existence of the upper boundary of the atmosphere. We seek this solution as a function of the specially introduced dimensionless parameters—the atmosphere depth and four similarity parameters—and study it for the parameter values that can be realized in the planetary atmospheres, including the atmospheres of extrasolar planets. It is shown that an increase in the optical density of the atmosphere can reduce the population of an excited vibrational state in the band at the upper boundary of the atmosphere by as much as several orders of magnitude as compared to the population corresponding to the optically thin band limit. The anomalous decrease in the opacity of the atmosphere, when only several lines of the band are involved in radiative transfer, is predicted. We also determined the accuracy of calculating the population in the approximation of the Doppler line profile. An approximate formula is obtained for the dimensionless height of the boundary of the layer in which the local thermodynamic equilibrium exists for vibrational states. We propose a model and the formula following from this model to roughly evaluate the decrease in this height due to the impact on the population of additional radiative transitions between the state being considered and the underlying state belonging to another vibrational mode of the molecule.  相似文献   

15.
Generalization of the escape probability method introduced by Sobolev allows us to study the transfer of spectral line radiation for a resonance doublet in rapidly expanding envelopes.For the cases of outward-accelerating (or equivalently inward-decelerating) and outward-decelerating (or equivalently inward-accelerating) envelopes we derive, in the frame of a three-level atom model, the expressions for the spectral radiation fieldsJ 12 andJ 13, for the resulting radiative force FRE exerted per atom and for the resonance doublet profileE(X)/C c; we take into account the complex radiative coupling, in both resonance transitions 12 and 13, between distant parts of the atmosphere.For various physical and geometrical conditions prevailing in the expanding media, we illustrate and discuss the behaviours of those quantities as well as their dependence on the parameters of the model. Namely, we deduce criteria under which resonance doublet profiles formed in outward-accelerating and/or outward-decelerating envelopes would appear to be resolved into double P Cygni profiles.We also stress the importance of treating a resonance doublet as being formed by two distinct resonance transitions when evaluating the resulting radiative force FRE acting on an atom. It is indeed shown that if we use a two-level atom model to represent a resonance doublet-i.e., assigning to it an oscillator strength equal to the sum of the oscillator strengths of both resonance transitions-the amplitude of the resulting radiative force can be underestimated by factors reaching 100% and more in the regions of the expanding envelope which are optically thick to the spectral line radiation. In this context, it would be essential to revise the previous models of radiation-driven winds developed for early-type stars in which the lines belonging to any multiplet were treated as a single line.Also, Aspirant au Fonds National de la Recherche Scientifique (Belgium).  相似文献   

16.
D. E. Rees  G. Geers 《Solar physics》1996,164(1-2):103-116
This paper looks at three aspects of numerical methods for solving polarized radiative transfer problems associated with spectral line formation in the presence of a magnetic field. First we prove Murphy's law for Stokes evolution operators which is the basis of the efficient algorithm used in the SPSR software package to compute the Stokes line depression contribution functions. Then we use a two-stream model to explain the efficacy of the field-free method in which the non-LTE line source function in a uniform magnetic field is approximated by the source function neglecting the magnetic field. Finally we introduce a totally new and computationally efficient approach to solving non-LTE problems based on a method of sparsely representing integral operators using wavelets. As an illustration, the wavelet method is used to solve the source function integral equation for a two-level atomic model in a finite atmosphere with coherent scattering, ignoring polarization.  相似文献   

17.
Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa 1 anda 3, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a 1,a 3) phase space, and of botha 1 and the total central pressureP c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha 1 andP c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea 1 oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea 1 andP c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea 1 oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.  相似文献   

18.
V. P. Grinin 《Astrophysics》1984,20(2):190-223
Conclusions It can be seen from the above review that the theory of radiative transfer in moving media in its classical field of applications is a well-developed branch of theoretical astrophysics. Studies i n recent years have clarified important questions such as the asymptotic behavior of the kernel functions and the characteristic lengths of the theory. It has been established that there are two types of radiative coupling, and the influence of nonlocal radiative coupling on the formation of spectral lines and radiation pressure has been investigated. The theory now has at its disposal a large selection of asymptotic, approximate, and numerical methods for solving different applied problems.Despite the competition from numerical methods, the overwhelming majority of calculations of emission spectra in the region of supersonic motions has been made on the basis of the escape-probability method and its generalization to the case of nonlocal radiative coupling. This is explained not only by the simplicity and economy of the method but even more by the fact that the greater accuracy of the calculations that can be achieved by using numerical methods is frequently spurious, since it certainly exceeds the accuracy of the basic assumptions. The real way to increase the reliability in the diagnosis of a radiating gas is, first, to solve simultaneously many-level problems for the group of elements whose lines are observed in the spectrum of the object. Second, where possible, one must solve simultaneously the stationary equations and the heat balance equations.Crimean Astrophysical Observatory. Translated from Astrofizika, Vol. 20, No. 2, pp. 365–417, March–April, 1984.  相似文献   

19.
We present a cylindrically symmetric model for a sunspot atmosphere using the similarity principle of Schlüter and Temesvary for the magnetic field configuration. The equations of magnetostatic equilibrium are used, augmented by a radial Evershed flow. The LTE radiative transfer equations for the Stokes vector were solved under a variety of conditions for a ray emerging from a typical penumbral point. The contribution from isolated lines to the broadband circular polarization in sunspot penumbrae is evaluated using a more realistic model sunspot atmosphere than has hitherto been considered. Results indicate that the inclusion of a velocity field along B is unable to give a net circular polarization of sufficient magnitude, although the variation with the angle between the line-of-sight and B is in qualitative agreement with observations. The corresponding results for the net linear polarization are satisfactory.  相似文献   

20.
Datlowe  D. W.  Hudson  H. S.  Peterson  L. E. 《Solar physics》1974,34(1):193-206
We simultaneously solve the equations of radiative transfer and statistical equilibrium for a model hydrogen atom including Lyman-, Lyman-, Balmer- and the Lyman, Balmer and Paschen continua. The model atmospheres we use are the results of Nakagawa et al. (1973) for a kinematic model of the chromospheric solar flare.We find that the models adequately predict the total intensity of B, its wing broadening, the presence of a red-shifted wing, the maximum electron density, the total line-of-sight second-level population and the narrowness in height of the B emitting region. The profile of B is strongly self-reversed, however, and agrees with observations only in the presence of 40–70 km s–1 macroturbulent motion.We find that Nakagawa et al. (1973) seriously overestimate the radiative loss function, which will have a large effect on their models. Proper radiative loss calculations must be included in any physically realistic model.The National Center for Atmospheric Research is sponsored by the National Science Foundation.  相似文献   

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