Magnetic field evolution of accreting neutron stars

We discuss the effect of accretion on the evolution of the magnetic field of a neutron star and highlight the main unresolved issues. Charged, accreted matter is funneled towards the magnetic poles where it heats the stellar surface and alters its magnetic structure resulting in an overall reduction of the magnetic dipole moment. Mechanisms for accretion‐induced field reduction include accelerated Ohmic decay, vortex‐fluxoid interactions, and magnetic burial or screening. We discuss how these can be integrated into a global model and detail recent self‐consistent, three‐dimensional, magneto‐hydrodynamic, calculations (using analytic Grad‐Shafranov methods and the numerical solver ZEUS‐MP) which incorporate global resistive instabilities. These models can explain why neutron stars in binaries have systematically lower magnetic dipole moments than isolated neutron stars. Finally we discuss applications including the evolution of accreting millisecond pulsars and type‐I X‐ray bursts, magnetars, and gravitational waves.