3D Magneto-thermal Simulations of Tangled Crustal Magnetic Field in Central Compact Objects

Central compact objects are young neutron stars emitting thermal X-rays with bolometric luminosities $L_X$ in the range $10^{32}$-$10^{34}$ erg/s. Gourgouliatos, Hollerbach and Igoshev recently suggested that peculiar emission properties of central compact objects can be explained by tangled magnetic field configurations formed in a stochastic dynamo during the proto-neutron star stage. In this case the magnetic field consists of multiple small-scale components with negligible contribution of global dipolar field. We study numerically three-dimensional magneto-thermal evolution of tangled crustal magnetic fields in neutron stars. We find that all configurations produce complicated surface thermal patterns which consist of multiple small hot regions located at significant separations from each other. The configurations with initial magnetic energy of $2.5-10\times 10^{47}$ erg have temperatures of hot regions that reach $\approx 0.2$ keV, to be compared with the bulk temperature of $\approx 0.1$ keV in our simulations with no cooling. A factor of two in temperature is also seen in observations of central compact objects. The hot spots produce periodic modulations in light curve with typical amplitudes of $\leq 9-11$ %. Therefore, the tangled magnetic field configuration can explain thermal emission properties of some central compact objects.