  The axion or axion-like particle motivated from a natural solution of strong
CP problem or string theory is a promising dark matter candidate. We study the
new observational effects of ultralight axion-like particles by the space-borne
gravitational wave detector and the radio telescope. Taking the neutron
star-black hole binary as an example, we demonstrate that the gravitational
waveform could be obviously modified by the slow depletion of the axion cloud
around the black hole formed through the superradiance process. We compare
these new effects on the binary with the well-studied effects from dynamical
friction with dark matter and dipole radiation in model-independent ways.
Finally, we discuss the constraints from LIGO/Virgo and study the detectability
of the ultralight axion particles at LISA and TianQin.
