Powering Central Compact Objects with a Tangled Crustal Magnetic Field

Central Compact Objects (CCOs) are X-ray sources with luminosity ranging between $10^{32}$-$10^{34}$ erg~s$^{-1}$, located at the centres of supernova remnants. Some of them have been confirmed to be neutron stars. Timing observations have allowed the estimation of their dipole magnetic field, placing them in the range $\sim10^{10}$-$10^{11}$ G. The decay of their weak dipole fields, mediated by the Hall effect and Ohmic dissipation, cannot provide sufficient thermal energy to power their X-ray luminosity, as opposed to magnetars whose X-ray luminosities are comparable. Motivated by the question of producing high X-ray power through magnetic field decay while maintaining a weak dipole field, we explore the evolution of a crustal magnetic field that does not consist of an ordered axisymmetric structure, but rather comprises a tangled configuration. This can be the outcome of a non-self-excited dynamo, buried inside the crust by fallback material following the supernova explosion. We find that such initial conditions lead to the emergence of the magnetic field from the surface of the star and the formation of a dipolar magnetic field component. An internal tangled magnetic field of the order of $10^{14}$ G can provide sufficient Ohmic heating to the crust and power CCOs, while the dipole field it forms is approximately $10^{10}$ G, as observed in CCOs.