2022MNRAS.515.3014A

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_γ. Models with and without hyperon cores match L_γ of young magnetars (with poloidal-dipolar field B_dip ≳ 10¹⁴ G at the polar surface and L_γ ≳ 10³⁴ erg s^–1 at t ≲ 10⁵ yr) as well as mature, moderately magnetized stars (with B_dip ≲ 10¹⁴ G and 10³¹ erg s^–1 ≲ L_γ ≲ 10³² erg s^–1 at t ≳ 10⁵ 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_γ in the same range and are almost indistinguishable. Likewise, L_γ data of neutron stars with B_dip ≲ 10¹⁴ 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 ≈1 MeV.