Non-LTE line formation in a magnetic field

Theoretical line contours calculated for fixed values of the line constants and a given model atmosphere show an increase of the Stokes parameters Q, U, and V but a decrease of I if the portion of non-coherent scattering increases. These effects increase from the centre of the solar disk to the limb. The action of scattering may be approximately simulated in LTE contours by increasing the gradient of the source function and fitting in this way theoretical contours to observed ones. There remains, however, the effect of V-reversal near the line core, which is caused by anomalous dispersion and is abnormally increased by scattering.     

Quantum theory of line formation in a magnetic field

The transfer equations for the Stokes parameters in the presence of magnetic field and under the hypothesis of LTE are derived in an original way by the use of density matrix techniques.The results are substantially the same as those previously obtained by other authors. We finally compare our results to the previous ones in order to clarify some discrepancies still present in the literature.     

On the mean depth of line formation in a magnetic field

Probability interpretation of radiative transfer is used to calculate the contribution of different layers of the solar atmosphere to the emergent intensity. Generally the mean depths of line formation increase with increasing intensity; this is valid also for arbitrarily polarized constituents of a line formed in a magnetic field.     

A generalized theory for line formation in a homogeneous magnetic field

The formation of spectral lines in a homogeneous magnetic field has been studied. A new method for solving the transfer equations for polarized light has been found. Using this method, the Stokes parameters may be derived without any special assumptions regarding the model atmosphere. With the line formed by pure absorption, the expressions for the Stokes parameters may easily be adapted to numerical calculations. In order to illustrate the method, the line profile for the Zeeman triplet 5250 has been calculated using a photospheric model atmosphere.     

Line formation in a magnetic field

The effect of noncoherent scattering is examined for an absorption line formed in a uniform magnetic field. It is shown that the Stokes parameters of the line radiation may be computed by using the line source function in the absence of a magnetic field as a first approximation for that in the presence of a magnetic field.     

The magnetic field in some prominences measured with the He I, 5876 Å line

Observations of the longitudinal magnetic field of several prominences were made with the D₃, H, and H lines. There is no significant difference in the magnetic field measured with the helium and hydrogen lines. The possibility of a true difference in the fields on a scale much finer than that of our observations is not excluded.     

Photon dispersion in a strong magnetic field with positronium formation: Theory

Positrinium atom is considered in a strong magnetic field in a vector-potential gauged asA _x =–By. The energy spectrum is obtained including its dependence on the centre-of-mass wave vector across the magnetic field. The pole-like contributions into the photon polarization operator coming from the positronium states are calculated and dispersion curves of joint photon-positronium states are obtained as trajectories of poles of the photon Green function in momentum space.When propagating in a strong magnetic field (B0.1B _cr 4×10¹² G) with curved lines of force, a photon is canalized along the magnetic field by adiabatically transforming into a bound electron-positron pair, which is a stronger effect than the analogous photon capture by transforming into an unbound pair at the edge of the continuum discussed previously by the authors. The effect of bound pair formation by-quanta in a strong magnetic field may be important near pulsars,-burst sources, powerful X-ray sources in close binary systems and other astronomical objects, recognized as magnetic neutron stars.     

Line formation in a magnetic field and the interpretation of magnetographic measurements

The strong temperature dependence of the line Fei 5250.2 has been studied by calculating line contours and magnetographic calibration curves for different spot models and the BCA. Line contours calculated for arbitrary depth dependence of the magnetic field vector show depolarization effects within the Zeeman components for transversal fields with variable direction and changes of the observed plane of polarization if anomalous dispersion is taken into account.The observed anomalous splitting of the -component may be interpreted best by suggesting discrete inhomogeneities of the magnetic field within sunspots.     

On the magnetic field line topology in solar active regions

The field lines of closed magnetic structures above the photosphere define a mapping from the photosphere to itself. This mapping is discontinuous, and the field line connectivity to the boundary can change discontinuously in response to continuous changes of field strength and direction, if field lines either end in a singular point of the field or are tangential to the photosphere at one end. Whereas the general existence of singular points is questionable, the field has typically a cell structure due to the presence of segments of the zero line of the photospheric longitudinal field on which the transversal field is directed from negative (pointing into the Sun) to positive fields. The cell boundaries are made up of field lines which all touch the photosphere on one of these line segments. Within each of the cells the field line mapping is continuous. When during a slow evolution a substantial part of a coronal loop or of an arcade has passed from one cell into another a fast dynamic instability may set in which was previously prevented by the anchoring of field lines in the dense photosphere.     

The flow field in a force-free magnetic field

We have obtained a complete set of the zeroth-order equations for a force-free field at large magnetic Reynolds numbers. One of the equations has often been overlooked in previous works. We discuss the question of uniqueness of solution of the Cauchy problem and outline a general method of solution in the plane and axisymmetric cases.     

Remarks on the one-photon-pair annihilation in strong magnetic fields

We report specifically on a quantum electrodynamic feature of the one-photon-pair annihilation. Most of the calculation related with this process (not excluding other ones) have been carried out usually utilizing the wave functions obtained from the Dirac equation in the Landau gauge A = (0,Bx, 0), where B is oriented along the z-axis (Johnson and Lippman, 1949). Although, the eigenstates of the Dirac Hamiltonian as it was introduced by Johnson and Lippman, do not consider the coupling to the radiation field and consequently they reflect only forp _z = 0 the same linear combination of the two degenerate polarization states.We report the transition rate function for the one-photon-pair annihilation in a strong magnetic field by using the Sokolov and Ternov eigenstate |± as far asp _z = 0 andN > 0 is concerned. The difference between the expression for the transition rate by using the Sokolov and Ternov eigenstates and the one calculated by (Wunneret al., 1986), is just the functionI _s,s which corresponds to the degeneracy of the orbit center of the electrons characterized by the quantum numberss ands. Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9-13 November, 1992.     

Mechanism of formation of a dipole magnetic field in the central regions of active galaxies

A model of the formation of large-scale magnetic fields of dipole configuration in the central regions (r 100 pc) of active galaxies is studied. It is assumed that these regions contain a rapidly rotating, highly ionized gas ( 5·10^–15 sec, N_e 10³ cm^–3). Ionized matter escapes from the center of the region with a velocity of several hundred km/sec and is entrained by the rotation of the surrounding medium. Biermann's "battery" effect [L. Biermann, Z. Naturforsch., 5a, 65 (1950)] operates under such conditions, and circular electric currents are formed in the medium, which amplify the dipole magnetic fields. During the active phase of a galaxy, about 10⁸ years, the magnetic field strength at the boundary of this region may reach 10^–4–10^–3 G.Translated from Astrofizika, Vol. 39, No. 1, pp. 111–119, January–March, 1996.     

Remarks on the magnetic support of quiescent prominences

The development of magnetic field structures which can lead to prominence configurations of the Kuperus-Raadu type is discussed. Starting from streamer type configurations and preserving the total current in the system we find that simple two-dimensional static configurations lead to prominences which in general lie systematically much lower than the heights found from observations. We therefore conclude that either more complex field configurations are needed to explain the recent observations by Leroy et al. (1983) or the initial configurations must be very special.     

The role of a magnetic field in the formation of jet-like features in the crab nebula

The toroidal magnetic field frozen in the relativistic plasma ejected by pulsars must play a significant role in the formation of jet-like features observed in the central parts of plerions. We performed a semiquantitative analysis and calculations of the plasma flow in a plerion using the perturbation theory. We show that for the latitudinal magnetic-field distribution expected during the interaction of the pulsar wind with the interstellar medium, the magnetic field will have an appreciable effect on the flow primarily near the rotation axis. In the equatorial region, the effect of the magnetic field is negligible up to distances of 7r_sh.     

Spectral line formation in a mesoturbulent atmosphere

The formation of spectral lines in a turbulent atmosphere with a spatially correlated velocity field is examined. A new approach for solving this problem is proposed which is not based on the Fokker-Planck formalism. The invariant imbedding method makes it possible to reduce the problem of finding the mean radiant intensity observed in a line to solving a system of differential equations. This possibility is based on determining the mean intensity of the radiation emerging from the medium for a fixed value of the turbulent velocity at its boundary. A separate integral equation is derived for this quantity. The dependence of the line profile, integrated intensity, and width on the mean correlation length and the average value of the hydrodynamic velocity is studied. It is shown that the transition from a microturbulent regime to a macroturbulent regime occurs within a comparatively narrow range of variation in the correlation length. The proposed method yields a solution to the problem for a family of inhomogeneous atmospheres with different optical thicknesses, which makes it easy to determine the radiation field inside the turbulent medium. This approach can be generalized in various ways, in particular, it can be applied without significant changes to the case where the correlation length depends on position within the atmosphere. __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 219–232 (May 2007).