The life cycle of magnetars: a novel approach to estimate their ages

Abstract

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, $B\sim10^{14}-10^{15}$ G, associated with `magnetars'. In the peculiar case of SGR 0418+5729, timing parameters imply a dipolar $B$-field of $6.1\times10^{12}$ 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 $1.0\times10^{14}$ G, and a realistic age of $\sim18$ kyr, consistent within the magnetar paradigm.