摘要
For synchrotron radiation from relativistic electrons having a power-law energy distribution with a power-law index p in an optically thin medium with a locally uniform magnetic field, it is generally adopted that the spectral index and the degree of linear polarization, and hence that. These (,; p) relations are derived assuming that the electrons have an isotropic momentum distribution and a power-law energy distribution, and they have been used, almost universally, in the interpretation of polarimetry observations. In this study, we assess the validity of the (,; p) relations in different scenarios, such as anisotropic electron momenta and non-power-law distributions of electron energy. We calculate the synchrotron radiation and polarization spectra for power-law, kappa, and log-parabola electron-energy distributions, with isotropic and two anisotropic (beamed and loss cone) electron-momentum distributions. Our calculations show that when the electron momenta are isotropic, the usual (,; p) relations are generally applicable. However, if the electrons are anisotropic, the usual (,; p) relations could break down. Applying the usual (,; p) relations indiscriminately without caution on anisotropy in the electron momentum distribution, would lead to incorrect interpretatsions of polarimetry data.