2021ApJ...913L..12M

Anomalous X-ray pulsars and soft gamma repeaters are slowly rotating, young, and isolated neutron stars exhibiting sporadic outbursts and high X-ray quiescent luminosities. They are believed to be powered by ultrastrong magnetic fields, B ∼ 10¹⁴-10¹⁵ G, associated with "magnetars." In the peculiar case of SGR 0418+5729, timing parameters imply a dipolar B-field of 6.1 x 10¹² G. This discovery has challenged the traditional picture of magnetars in terms of B-field strengths, evolutionary stages, and ages. Here we provide a novel approach to estimate a magnetar's age by considering the self-consistent time evolution of a plasma-filled oblique pulsar with the state-of-the-art magnetospheric particle acceleration gaps. The rotational period of magnetars increases over time due to angular momentum extraction by gravitational-wave radiations, magnetic dipole radiations, and particle winds. These torques also change the obliquity angle between the magnetic and rotation axes. For SGR 0418+5729, we obtain a dipolar B-field of 1.0 x 10¹⁴ G, and a realistic age of ∼18 kyr, consistent within the magnetar paradigm.