Magnetars vs. high magnetic field pulsars: a theoretical interpretation of the apparent dichotomy

Highly magnetized neutron stars (NSs) are characterized by a bewildering range of astrophysical manifestations. Here, building on our simulations of the evolution of magnetic stresses in the NS crust and its ensuing fractures (Perna & Pons 2011), we explore in detail, for the middle-age and old NSs, the dependence of starquake frequency and energetics on the relative strength of the poloidal (B_p) and toroidal (B_tor) components. We find that, for B_p >~10^{14}G, since a strong crustal toroidal field B_tor B_p is quickly formed on a Hall timescale, the initial toroidal field needs to be B_tor >> B_p to have a clear influence on the outbursting behaviour. For initial fields B_p <~ 10^{14}G, it is very unlikely that a middle-age (t~10^5 years) NS shows any bursting activity. This study allows us to solve the apparent puzzle of how NSs with similar dipolar magnetic fields can behave in a remarkably different way: an outbursting 'magnetar' with a high X-ray luminosity, or a quiet, low-luminosity, "high-$B$" radio pulsar. As an example, we consider the specific cases of the magnetar 1E2259+586 and the radio pulsar PSRJ1814-1744, which at present have a similar dipolar field ~6x10^{13}G. We determine for each object an initial magnetic field configuration that reproduces the observed timing parameters at their current age. The same two configurations also account for the differences in quiescent X-ray luminosity and for the 'magnetar/outbursting' behaviour of 1E2259+586 but not of PSRJ1814-1744. We further use the theoretically predicted surface temperature distribution to compute the light-curve for these objects. In the case of 1E2259+586, for which data are available, our predicted temperature distribution gives rise to a pulse profile whose double-peaked nature and modulation level is consistent with the observations.