Looking for Hall attractor in astrophysical sources

Recently, numerical calculations of the magnetic field evolution in neutron stars demonstrated the possible existence of a Hall attractor, a stage at which the evolution of the field driven by the Hall cascade ends. The existence of such a stage in neutron star magnetic evolution is very important, and can be potentially probed by observations. Here we discuss three types of objects which could have reached this stage. First, we briefly describe the evolution of normal radio pulsars with ages about a few hundred thousand years. Then we analyse in more detail observations of RX J1856.5-3754, one of the Magnificent Seven, focusing on the surface temperature distribution and comparing model predictions with the temperature map inferred from X-ray observations. Finally, we discuss the necessity of the Hall attractor stage to explain the hypothetical existence of accreting magnetars. We conclude that at the moment there is no direct confirmation of the Hall attractor stage in known sources. However, more detailed observations in the near future can demonstrate existence (or absence) of this stage of the crustal magnetic field evolution.