Persistent gravitational radiation from glitching pulsars. II. Updated scaling with vortex number

Superfluid vortices pinned to nuclear lattice sites or magnetic flux tubes in a neutron star evolve abruptly through a sequence of metastable spatial configurations, punctuated by unpinning avalanches associated with rotational glitches, as the stellar crust spins down electromagnetically. The metastable configurations are approximately but not exactly axisymmetric, causing the emission of persistent, quasimonochromatic, current quadrupole gravitational radiation. The characteristic gravitational wave strain h0 as a function of the spin frequency f and distance D from the Earth is bounded above by $h_0 = 1.2\substack{+1.3 \\-0.9} \times 10^{-32} (f/30\,\,{\rm Hz})^{2.5} (D/1\,\,{\rm kpc})^{-1}$, corresponding to a Poissonian spatial configuration (equal probability per unit area, i.e. zero inter-vortex repulsion), and bounded below by $h_0 = 1.8\substack{+2.0 \\-1.5} \times 10^{-50} (f/30\,\,{\rm Hz})^{1.5} (D/1\,\,{\rm kpc})^{-1}$, corresponding to a regular array (periodic separation, i.e. maximum inter-vortex repulsion). N-body point vortex simulations predict an intermediate scaling, $h_0 = 7.3\substack{+7.9 \\-5.4} \times 10^{-42} (f/30\,\,{\rm Hz})^{1.9} (D/1\,\,{\rm kpc})^{-1}$, which reflects a balance between the randomizing but spatially correlated action of superfluid vortex avalanches and the regularizing action of inter-vortex repulsion. The scaling is calibrated by conducting simulations with Nv ≤ 5 × 103 vortices and extrapolated to the astrophysical regime Nv ∼ 1017(f/30 Hz). The scaling is provisional, pending future computational advances to raise Nv and include three-dimensional effects such as vortex tension and turbulence.