The Theory of Synchrotron Radiation from Stars with Dipole Magnetic Fields

Abstract

A simple model of a star whose radiation is partially due to the synchrotron mechanism is analyzed. The model consists of a normal star with a strong dipole magnetic field outside its surface, in which ultrarelativistic electrons are spiraling. The polarization and intensity of the synchrotron component of the radiation are calculated as functions of the frequency of the radiation, the observer's orientation, the energy distribution of the ultra-relativistic electrons, and their pitch-angle distribution. The degree of polarization of the synchrotron component from the most plausible models is found to be 20 to 40 per cent for an observer located in the equatorial plane and to drop off in a 5in2 00-like curve to 0 per cent for an observer located on the polar axis. The spectrum of the synchrotron component is characterized by a (l/ ) dependence; n remains constant (about 13 or 31) except at high frequencies, where it begins to increase gradually. The maximum power is emitted at the lower end of the high-frequency region, where n 1. The characteristics of the combined synchrotron and thermal radiation are examined for various stellar models, and lower limits are placed on the surface magnetic-field strengths required to produce a given degree of polarization. The lower limit is 100 gauss for a polarization of 0.05 per cent and 1000 gauss for 10 per cent. The dependence of the polarization of the combined radiation on frequency is examined. The degree of polarization and the color excess of the combined radiation are correlated for main-sequence stars using a U, B, V diagram. The characteristics of the emission from an oblique rotator containing significant amounts of synchrotron radiation are examined and compared with the emission from the star HD 71866. The synchrotron radiation from objects with turbulent magnetic fields is compared with that from a number of randomly oriented dipole magnetic fields.