First search for gravitational waves from r-modes of the Crab Pulsar

Neutron stars are the most dense form of matter, the density being comparable to the density of an atomic nucleus. If the neutron star is rotating, then, just like Rossby waves in Earth’s atmosphere, motion of this fluid will be susceptible to the Coriolis force and associated oscillations. These non-radial oscillations, known as r-modes, can be very long lived—perhaps thousands of years. Because the fluid is so dense, these r-modes may be viable sources of continuous gravitational waves. R-modes are current quadrupoles which oscillate at four thirds the star’s spin frequency. The modes are damped by viscosity, but can be unstable to gravitational radiation via the Chandrasekhar-Friedman- Schutz instability. When relativistic corrections are taken into consideration, the mode frequency can be 1.39 to 1.57 times the spin frequency of the star, and the frequency derivative can be roughly estimated in terms of the star’s measured spin-down parameter. We show for the first time how to construct searches over appropriate ranges of frequencies and spin-down parameters to target r-modes from known pulsars. We present the first searches for gravitational waves from r-modes of the Crab pulsar, coherently and separately integrating data from three stretches of the first two observing runs of Advanced LIGO using the F-statistic. The second run was divided in two by a glitch of the pulsar roughly halfway through. The frequencies and derivatives searched were based on radio measurements of the pulsar’s spin-down parameters as described in Caride et al., Phys. Rev. D 100, 064013 (2019). We did not find any evidence of gravitational waves. The best 95% confidence upper limits on the gravitational wave intrinsic strain were 1.6 × 10 −25 for the first run, 1.5 × 10 −25 for the first stretch of the second run, and 1.2 × 10 −25 for the second stretch of the second run. These are the first upper limits on gravitational waves from r-modes of a known pulsar to beat its spin- down limit, and they do so by more than an order of magnitude in amplitude or two orders of magnitude in luminosity.