2011ApJ...741..123P

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, we explore in detail, for the middle-aged 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 ≳ 10¹⁴ 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{Gt} B_p to have a clear influence on the outbursting behavior. For initial fields B_p≲ 10¹⁴ G, it is very unlikely that a middle-aged (t ∼ 10⁵ 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 1E 2259+586 and the radio pulsar PSR J1814-1744, which at present have a similar dipolar field ∼6x10¹³ 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" behavior of 1E 2259+586 but not of PSR J1814-1744. We further use the theoretically predicted surface temperature distribution to compute the light curve for these objects. In the case of 1E 2259+586, for which data are available, our predicted temperature distribution gives rise to a pulse profile whose double-peaked nature and modulation level are consistent with the observations.