Evolutionary deformation toward the elastic limit by a magnetic field confined in the neutron--star crust

Occasional energetic outbursts and anomalous X-ray luminosities are expected to be powered by the strong magnetic field in a neutron star. For a very strong magnetic field, elastic deformation becomes excessively large such that it leads to crustal failure. We studied the evolutionary process driven by the Hall drift for a magnetic field confined inside the crust. Assuming that the elastic force acts against the Lorentz force, we examined the duration of the elastic regime and maximum elastic energy stored before the critical state. The breakup time was longer than that required for extending the field to the exterior, because the tangential components of the Lorentz force vanished in the fragile surface region. The conversion of large magnetic energy, confined to the interior, into Joule heat is considered to explain the power for central compact objects. This process can function without reaching its elastic limit, unless the magnetic energy exceeds $2\times 10^{47}$ erg, which requires an average field strength of $2\times10^{15}$ G. Thus, the strong magnetic field hidden in the crust is unlikely to cause outbursts. Furthermore, the magnetic field configuration can discriminate between central compact objects and magnetars.