Gravitational-wave bursts and stochastic background from superfluid vortex avalanches during pulsar glitches

The current-quadrupole gravitational-wave signal emitted during the spin-up phase of a pulsar glitch is calculated from first principles by modeling the vortex dynamics observed in recent Gross-Pitaevskii simulations of pinned, decelerating quantum condensates. Homogeneous and inhomogeneous unpinning geometries, representing creep- and avalanche-like glitches, provide lower and upper bounds on the gravitational wave signal strength respectively. The signal arising from homogeneous glitches is found to scale with the square root of glitch size, whereas the signal from inhomogeneous glitches scales proportional to glitch size. The signal is also computed as a function of vortex travel distance and stellar angular velocity. Convenient amplitude scalings are derived as functions of these parameters. For the typical astrophysical situation, where the glitch duration (in units of the spin period) is large compared to the vortex travel distance (in units of the stellar radius), an individual glitch from an object $1\,\rm{kpc}$ from Earth generates a wave strain of $10^{-24} [(\Delta\omega/\omega) / 10^{-7}] (\omega/10^2 \rm{rad s}^{-1})^3 (\Delta r / 10^{-2} \rm{m})^{-1}$, where $\Delta r$ is the average distance travelled by a vortex during a glitch, $\Delta\omega/\omega$ is the fractional glitch size, and $\omega$ is the pulsar angular velocity. The non-detection of a signal from the 2006 Vela glitch in data from the fifth science run conducted by the Laser Interferometer Gravitational-Wave Observatory implies that the glitch duration exceeds $\sim 10^{-4}\,\rm{ms}$. This represents the first observational lower bound on glitch duration to be obtained.