Gravitational waves from neutron stars with large toroidal $B$ fields

We show that NS’s with large toroidal B fields tend naturally to evolve into potent gravitational-wave (GW) emitters. The toroidal field $B_t$ tends to distort the NS into a prolate shape, and this magnetic distortion dominates over the oblateness “frozen into” the NS crust for $B_t\gtrsim 3.4\times {10}^{12}\mathrm{G}({\nu }_s/300\mathrm{}\mathrm{Hz}{)}^2.$ An elastic NS with frozen-in B field of this magnitude is clearly secularly unstable: the wobble angle between the NS’s angular momentum $J^i$ and the star’s magnetic axis $n_B^i$ grows on a dissipation time scale until $J^i$ and $n_B^i$ are orthogonal. This final orientation is clearly the optimal one for GW emission. The basic cause of the instability is quite general, so we conjecture that the same final state is reached for a realistic NS, with superfluid core. Assuming this, we show that for LMXB’s with $B_t\sim 2\times {10}^{12}-2\times {10}^{14}\mathrm{G},$ the spindown from GW’s is sufficient to balance the accretion torque—supporting a suggestion by Bildsten. The spindown rates of most millisecond pulsars can also be attributed to GW emission sourced by toroidal B fields, and both these sources could be observed by LIGO II. While the first-year spindown of a newborn NS is most likely dominated by electromagnetic processes, reasonable values of $B_t$ and the (external) dipolar field $B_d$ can lead to detectable levels of GW emission, for a newborn NS in our own Galaxy.