Why do fast-spinning accreting neutron stars evade the r-mode instability?
In plain words
Theory says certain sloshing oscillations called r-modes should grow on their own in fast-spinning neutron stars, radiate gravitational waves and slow the stars down. Yet many observed stars spin fast in the region where this should happen.
Precise statement
With standard shear and bulk viscosity, low-mass X-ray binaries spinning at $300\ \text{to}\ 700\ \mathrm{Hz}$ with inferred core temperatures of about $1e8\ \mathrm{K}$ lie inside the r-mode instability window. Determine the extra damping (viscous crust-core boundary layer, hyperon or quark bulk viscosity, superfluid mutual friction, resonances) or the low saturation amplitude that reconciles theory with the observed spin and temperature distribution.
What would settle it
A calculation of r-mode damping and nonlinear saturation in realistic stellar models that places the observed systems outside the window or predicts their spin-temperature distribution.