On Singular Points of the Radiation Polarization Tensor

M. M. Molodenskii and L. I. Starkova

Institute of Terrestrial Magnetism, Aeronomy, and Radio Wave Propagation,
Russian Academy of Sciences, Troitsk, Moscow oblast, 142092 Russia

Received July 21, 1994

Abstract—The problem of determining the magnetic field above the chromosphere from data on the orienta-
tion of the vector = B_t / B_t can be solved in various approximations. The direction field is not the only field
accessible to observation. The Stokes parameters (components of the radiation tensor) can be measured at each
point in the plane of the sky. The directions of the eigenvectors of this tensor define two orthogonal systems of
integral curves in the plane of the sky. These curves have singular points, generally of a type different from those
in a vector field. It is shown that (1) all first-order singular points are associated with structures observed in the
Crab nebula, but the inverse problem for the magnetic field cannot be solved if the radiation is assumed to be
caused by the synchrotron mechanism; (2) the difference in the polarization patterns observed with high and
low spatial resolutions can be explained by the presence of node–saddle associations; and (3) the existence of
singular points with topological indices of ±1/4 is not ruled out.

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