SYNCHROTRON POLARIZATION AND SYNCHROTRON SELF-ABSORPTION SPECTRA FOR A POWER-LAW PARTICLE DISTRIBUTION WITH FINITE ENERGY RANGE

We have derived asymptotic forms for the degree of polarization of the optically thin synchrotron and for synchrotron self-absorption (SSA) spectra assuming a power-law particle distribution of the form N(gamma) similar to gamma(-p) with gamma(1) < gamma < gamma(2), especially for a finite high-energy limit, gamma(2), in the case of an arbitrary pitch angle. The new results inferred concern more especially the high-frequency range x >> eta(2) with parameter eta = gamma(2)/gamma(1). The calculated SSA spectra concern instantaneous photon emission where cooling effects are not considered. They have been obtained by also ignoring likely effects such as Comptonization, pair creation and annihilation, as well as magnetic photon splitting. To that aim, in addition to the two usual absorption frequencies, a third possible one has been derived and expressed in terms of the Lambert W function based on the analytical asymptotic form of the absorption coefficient, alpha(nu), for the high-frequency range nu >> nu(2) (with nu(2) the synchrotron frequency corresponding to gamma(2)). We have shown that the latter frequency may not have realistic applications in astrophysics, except in the case of an adequate set of parameters allowing one to neglect Comptonization effects. More detailed calculations and discussions are presented.