Magnetic field decay in neutron stars: From soft gamma repeaters to 'weak-field magnetars'

The recent discovery of the 'weak-field, old magnetar' soft gamma repeater (SGR) J0418+5729, whose dipole magnetic field, B _dip, is less than 7.5 × 10 ¹²G, has raised perplexing questions: how can the neutron star produce SGR-like bursts with such a low magnetic field? What powers the observed X-ray emission when neither the rotational energy nor the magnetic dipole energy is sufficient? These observations, which suggest either a much larger energy reservoir or a much younger true age (or both), have renewed the interest in the evolutionary sequence of magnetars. We examine here a phenomenological model for the magnetic field decay: and compare its predictions with the observed period, P, the period derivative, and the X-ray luminosity, L _X, of magnetar candidates. We find a strong evidence for a dipole field decay on a time-scale of ∼10 ³yr for the strongest (B _dip∼ 10 ¹⁵G) field objects, with a decay index within the range 1 ≤α < 2 and more likely within 1.5 ≲α≲ 1.8. The decaying field implies a younger age than what is implied by Surprisingly, even with the younger age, the energy released in the dipole field decay is insufficient to power the X-ray emission, suggesting the existence of a stronger internal field, B _int. Examining several models for the internal magnetic field decay, we find that it must have a very large (≳ 10 ¹⁶G) initial value. Our findings suggest two clear distinct evolutionary tracks - the SGR/anomalous X-ray pulsar branch and the transient branch, with a possible third branch involving high-field radio pulsars that age into low-luminosity X-ray dim isolated neutron stars.