Most matter in the Universe is invisible and unknown, and is called dark matter. A candidate of dark matter is the axion, which is an ultralight particle motivated as a solution for the $CP$ problem. Axions form clouds in a galactic halo, and amplify and delay a part of gravitational waves propagating in the clouds. The Milky Way is surrounded by the dark matter halo composed of a number of axion patches. Thus, the characteristic secondary gravitational waves are always expected right after the reported gravitational-wave signals from compact binary mergers. In this paper, we derive a realistic amplitude of the secondary gravitational waves. Then we search the gravitational waves having the characteristic time delay and duration with a method optimized for them. We find no significant signal. Assuming the axions are a dominant component of dark matter, we obtain the constraints on the axion coupling to the parity-violating sector of gravity for the mass range, $[1.7\times {10}^{-13},8.5\times {10}^{-12}]\mathrm{eV}$, which is at most $\sim 10$ times stronger than that from Gravity Probe B.

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• Gravitational wave detection
• Gravitational wave sources
• Gravitational waves
• Particle dark matter