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 $h_0$ as a function of

the spin frequency $f$ and distance $D$ from the Earth is bounded above by $h_0

= 1.2substack{+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 = 1.8substack{+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 = 7.3substack{+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 ${N_{rm v}} leq 5times10^3$

vortices and extrapolated to the astrophysical regime ${N_{rm v}} sim 10^{17}

(f/30;{rm Hz})$. The scaling is provisional, pending future computational

advances to raise ${N_{rm v}}$ and include three-dimensional effects such as

vortex tension and turbulence.

Superfluid vortices in neutron stars evolve through metastable spatial configurations, emitting gravitational waves. The characteristic gravitational wave strain $h_0$ is bounded above and below by specific equations. N-body point vortex simulations predict an intermediate scaling. However, the scaling is provisional and further computational advances are needed.

## Future Roadmap

**Challenge 1:**Increase computational capabilities to raise the number of vortices (${N_{rm v}}$) included in simulations.**Challenge 2:**Incorporate three-dimensional effects such as vortex tension and turbulence into simulations.**Opportunity 1:**Conduct simulations with ${N_{rm v}} leq 5times10^3$ to calibrate the scaling.**Opportunity 2:**Extrapolate the scaling to the astrophysical regime with ${N_{rm v}} sim 10^{17} (f/30;{rm Hz})$.

The future roadmap involves tackling the challenges of increasing computing power and incorporating additional factors into the simulations. By conducting simulations with a smaller number of vortices, the scaling can be calibrated. Then, with the help of computational advances, the scaling formula can be extrapolated to larger astrophysical scenarios. This process will provide a better understanding of superfluid vortices in neutron stars and their associated gravitational wave emission.

**Note:** The conclusions in this text are highly technical and specialized. Additional context and background information may be required for a comprehensive understanding of the topic.