Polarization of the radiation scattered in conical magnetized envelopes

We analyze the polarization effects of the radiation scattered in conical optically thin plasma envelopes. The density of free electrons in the envelope is assumed to decrease in inverse proportion to the square of the distance from the radiation source. The magnetic field, radial or azimuthal, is also assumed to vary in inverse proportion to the square of the distance from the center of the system. We take into account the fact that the scattered radiation near the surface of a star or a quasar is virtually unpolarized (the model of a nonpoint star). The spectra of linear polarization and its position angle are given for conical-envelope opening half-angles of 7.5°, 15°, and 30°. The inclination of the cone axis with respect to the observer’s direction took on values of 30°, 45°, 60°, 90°, 120°, 135°, and 150°. We allowed for the fact that part of the envelope is screened from the observer by the star itself. We also give polarization spectra for the radiation scattered in two mutually opposite conical envelopes. We use the results of our theoretical calculations to analyze the polarimetric observations of relativistic jets in cosmic gamma-ray bursts and active galactic nuclei. As a result, we estimated the magnetic fields in these objects. The constraint on the density of relativistic electrons is <10⁷ cm^?3.