We present a search for periodic gravitational waves from the neutron star in the supernova remnant Cassiopeia
A. The search coherently analyzes data in a 12 day interval taken from the fifth science run of the Laser
Interferometer Gravitational-Wave Observatory. It searches gravitational-wave frequencies from 100 to 300 Hz
and covers a wide range of first and second frequency derivatives appropriate for the age of the remnant and
for different spin-down mechanisms. No gravitational-wave signal was detected. Within the range of search
frequencies, we set 95% confidence upper limits of (0.7–1.2) × 10^(−24) on the intrinsic gravitational-wave
strain, (0.4–4) × 10^(−4) on the equatorial ellipticity of the neutron star, and 0.005–0.14 on the amplitude of
r-mode oscillations of the neutron star. These direct upper limits beat indirect limits derived from energy
conservation and enter the range of theoretical predictions involving crystalline exotic matter or runaway r-modes.
This paper is also the first gravitational-wave search to present upper limits on the r-mode amplitude