r-Mode Oscillations and Spin-down of Young Rotating Magnetic Neutron Stars

Recent work has shown that a young, rapidly rotating neutron star loses angular momentum to gravitational waves generated by unstable r-mode oscillations. We study the spin evolution of a young, magnetic neutron star including the effects of both gravitational radiation and magnetic braking (modeled as magnetic dipole radiation). Our phenomenological description of nonlinear r-modes is similar to, but distinct from, that given by Owen and colleagues in 1998, in that our treatment is consistent with the principle of adiabatic invariance in the limit when direct driving and damping of the mode are absent. We show that while magnetic braking tends to increase the r-mode amplitude by spinning down the neutron star, it nevertheless reduces the efficiency of gravitational wave emission from the star. For B ≳ 10¹⁴(ν_s/300 Hz)² G, where ν_s is the spin frequency, the spin-down rate and the gravitational waveforms are significantly modified by the effect of magnetic braking. We also estimate the growth rate of the r-mode due to electromagnetic (fast magnetosonic) wave emission and due to Alfvén wave emission in the neutron star magnetosphere. The Alfvén wave driving of the r-mode becomes more important than the gravitational radiation driving when B ≳ 10¹³(ν_s/150 Hz)³ G; the electromagnetic wave driving of the r-mode is much weaker. Finally, we study the properties of local Rossby-Alfvén waves inside the neutron star and show that the fractional change of the r-mode frequency due to the magnetic field is of order 0.5(B/10¹⁶ G)²(ν_s/100 Hz)^-2.