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

##### Abstract

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.