Magnetic field decay in neutron stars: from Soft Gamma Repeaters to "weak field magnetars"

The recent discovery of the "weak field, old magnetar", the soft gamma repeater SGR 0418+5729, whose dipole magnetic field is less than 7.5 \times 10^{12} G, 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 are sufficient? These observations, that 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: B_dip} \propto (B_dip)^{1+a} and compare its predictions with the observed period, P,the period derivative, \dot{P}, and the X-ray luminosity, L_X, of magnetar candidates. We find a strong evidence for a dipole field decay on a timescale of \sim 10^3 yr for the strongest (\sim 10^{15} G) field objects, with a decay index within the range 1 \leq a < 2 and more likely within 1.5\lesssim a \lesssim 1.8. The decaying field implies a younger age than what is implied by the spinown age. 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^{16} G) initial value. Our findings suggest two clear distinct evolutionary tracks -- the SGR/AXP 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.