Angular Dependence of Coherent Radio Emission from Magnetars with Multipolar Magnetic Fields

The recent detection of a Fast Radio Burst (FRB) from a Galactic magnetar secured the fact that neutron stars (NSs) with super-strong magnetic fields are capable of producing these extremely bright coherent radio bursts. One of the leading mechanisms to explain the origin of such coherent radio emission is the curvature radiation process within the dipolar magnetic field structure. It has, however, already been demonstrated that magnetars likely have a more complex magnetic field topology. Here we critically investigate curvature radio emission in the presence of inclined dipolar and quadrupolar ("quadrudipolar") magnetic fields and show that such field structures differ in their angular characteristics from a purely dipolar case. We analytically show that the shape of open field lines can be modified significantly depending on both the ratio of quadrupole to dipole field strength and their inclination angle at the NS surface. This creates multiple points along each magnetic field line that coincides with the observer's line of sight, and may explain the complex spectral and temporal structure of the observed FRBs. We also find that in quadrudipole, the radio beam can take a wider angular range and the beam width can be wider than in pure dipole. This may explain why the pulse width of the transient radio pulsation from magnetars is as large as that of ordinary radio pulsars.