Joule heating in magnetized NS

Joule heating in the crustal layers due to Ohmic decay was thought to affect only the late photon cooling era in old NS (10^7 yr), and to be an efficient mechanism to maintain the surface temperature as high as 10^{4-5} K for a long time (Miralles & Urpin, 1998). Now we have revisited the problem and found that for strongly magnetized NS (B~10^14 G) Joule heating can be important much earlier in the evolution. The magnetic field decay energy could modify or even control the cooling of a magnetized NS, rather independently from the stellar structure or matter composition. We have performed first 2D simulations keeping the geometry of the magnetic field fixed. Coupled magneto-thermal evolution calculations are needed.