2024ApJ...974...89W

It is generally recognized that the electromagnetic multipolar emission from magnetars can be used to explain radiation from soft gamma repeaters or anomalous X-ray pulsars, but they have little impact on the spin-down of magnetars. We here present an analytical solution for the neutron star multipolar electromagnetic fields and their associated expected luminosities. We find that for newborn millisecond magnetars, the spin-down luminosity from higher multipolar components can match or even exceed that from the dipole component. Such high-intensity radiation will undoubtedly affect related astrophysical phenomena at the birth of a magnetar. We show that the spin-down luminosity from multipoles can well explain the majority of gamma-ray burst (GRB) afterglows, from the plateau starting at several hundred seconds until the normal decay phase lasting for many years. The fitted magnetar parameters for GRB afterglows are all typical values, with spins in the millisecond range and magnetic field strengths on the order of 10¹⁴-10¹⁵ G. Our results, in turn, provide support for the hypothesis that GRBs originate from the birth of magnetars with a period of a few milliseconds, thus deepening our understanding of the complex magnetic field structure and the equation of state of magnetars.