Anomalous diffusion across a tera-Gauss magnetic field in accreting neutron stars

When mass falls on the polar regions of a neutron star in a binary X-ray source system, it tends to spread out over the entire surface. A long-standing question in research on this problem is: will the mass be anchored on the magnetic field lines and drag the field with it or is there a special mechanism that allows the mass to slip through the magnetic field lines, leading to much less distortion? As the amount of mass falling on the neutron star can actually be comparable with the neutron star mass, the question of which alternative holds is very important. We suggest an efficient mechanism that will allow the mass to slip through the lines. The mechanism is based on a strong ideal Schwarzschild (Structure and Evolution of the Stars. Princeton University Press, 1958) instability. As the instability itself is ideal, it cannot directly force the mass to slip though the lines. However, it can create a cascade of eddies whose scale extends down to a resistive scale, at the same time mixing the field lines up without breaking them. On this scale the mass can cross the lines. This instability is efficient enough that it can produce a mass flow in the plasma without growing to a large amplitude but saturates at a small one. The instability determines the mass per flux distribution of the accumulated material on different lines so that the equilibrium is marginal to the instability on every line. This makes the equilibrium unique. Thus, as the extra mass on the neutron star grows, the state of the outer shell proceeds through a sequence of unique critically unstable equilibria. In an appendex, an attempt is made to track the critical equilibria over long times.