Thermal luminosity degeneracy of magnetized neutron stars with and without hyperon cores

The dissipation of intense crustal electric currents produces high Joule heating rates in cooling neutron stars. Here, it is shown that Joule heating can counterbalance fast cooling, making it difficult to infer the presence of hyperons (which accelerate cooling) from measurements of the observed thermal luminosity L-gamma. Models with and without hyperon cores match L-gamma of young magnetars (with poloidal-dipolar field B-dip greater than or similar to 10(14) G at the polar surface and L-gamma greater than or similar to 10(34) erg s(-1) at t less than or similar to 10(5) yr) as well as mature, moderately magnetized stars (with B-dip less than or similar to 10(14) G and 10(31) erg s(-1) less than or similar to L-gamma less than or similar to 10(32) erg s(-1) at t greater than or similar to 10(5) yr). In magnetars, the crustal temperature is almost independent of hyperon direct Urca cooling in the core, regardless of whether the latter is suppressed or not by hyperon superfluidity. The thermal luminosities of light magnetars without hyperons and heavy magnetars with hyperons have L-gamma in the same range and are almost indistinguishable. Likewise, L-gamma data of neutron stars with B-dip less than or similar to 10(14) G but with strong internal fields are not suitable to extract information about the equation of state as long as hyperons are superfluid, with maximum amplitude of the energy gaps of the order approximate to 1 MeV.