The role of magnetic damping in the r-mode evolution of accreting neutron stars

The magnetic damping rate was introduced in the evolution equations of r-modes, which shows that r-modes can generate strong toroidal magnetic fields in the core of accreting millisecond pulsars inducing by differential rotation. With consideration of the coupling evolution of r-modes, spin and thermal evolution, we investigated the influence of the magnetic damping on the differential rotation of nonlinear r-modes of accreting neutron stars. We derived the coupling evolution equations of the star involving the magnetic damping rate in the framework of second-order r-mode theory. The numerical results show that the magnetic damping suppressed the nonlinear evolution of r-modes since the saturation amplitude is reduced to a great extent. In particular, because of the presence of the generated toroidal magnetic field, the spin-down of the stars is terminated and the viscous heating effects are also weakened. Moreover, we could obtain a stronger generated toroidal magnetic field in the second-order r-mode theory. The gravitational radiation may be detected by the advanced laser interferometer detector LIGO if the amount of differential rotation is small when the r-mode instability becomes active and the accretion rate is not very high.