Understand
In most astrophysical processes involving synchrotron radiation, the pitch-angle distribution of the electrons is assumed to be isotropic.
- However, if electrons are accelerated anisotropically, e.g, in a relativistic shock wave with an ordered magnetic field or in magnetic reconnection regions, the electron pitch angles might be anisotropic.
- In this work, we study synchrotron radiation from electrons with a pitch-angle distribution with respect to a large-scale uniform magnetic field.
- Assuming that the pitch-angle distribution is normal with a scatter of $\sigma_p$ and that the viewing direction is where the pitch-angle direction peaks, we find that for electrons with a Lorentz factor $\gamma$, the observed flux satisfies $F_\nu\propto\nu^{2/3}$ for $\nu\ll\nu_{\rm cr}$ ($\nu_{\rm cr}$ is the critical frequency of synchrotron), if $\sigma_p\lesssim1/\gamma$ is satisfied.