Effects of nonuniform structure on the derived physical parameters of compact synchrotron sources

Abstract

The time-independent theory of a compact incoherent synchrotron radio source which contains gradients in magnetic field and in relativistic electron distribution is developed and discussed. Analytic expressions for the frequency spectrum are obtained, and we demonstrate the dependence of the spectral index below the synchrotron self-absorption turnover frequency on the gradients in the source and on the source geometry. We show that at high frequencies the existence of a gradient in the magnetic field causes a gradual bend (a steepening) in the spectrum owing to a decrease in effective source radius with increasing frequency. The theoretical interferometric fringe visibility function is computed for a nonuniform source, and it is shown that the characteristic Gaussian angular size derived from this function increases with decreasing frequency below the spectral turnover.We discuss how the important physical parameters of a nonuniform source can be directly derived from observable quantities. The results indicate that the existence of steep gradients in the magnetic field strength and/or the distribution of relativistic electrons can alleviate somewhat the energetic and inverse Compton difficulties of some compact sources, while the presence of moderate gradients only aggravates these problems relative to the homogeneous model.The theory of nonuniform components is applied tomore » the compact radio sources 1633+38 and OQ 172. We find that the radio spectrum of these objects can be interpreted as arising in simple nonuniform sources as opposed to the multiple source models that are necessary when homogeneous components are used. However, the inverse Compton optical and X-ray fluxes in the case of 1633+38 and the predicted minimum angular size in the case of OQ 172 are similar to those obtained via the uniform models.« less