  An intermediate mass black hole (IMBH) may have a dark matter (DM) mini-halo
around it and develop a spiky structure within less than a parsec from the
IMBH. When a stellar mass object is captured by the mini-halo, it eventually
infalls into such an IMBH due to gravitational wave back reaction which in turn
could be observed directly by future space-borne gravitational wave experiments
such as eLISA/NGO. In this paper, we show that the GW detectability strongly
depends on the radial profile of the DM distribution. So if the GW is detected,
the power index, that is, the DM density distribution would be determined very
accurately. The DM density distribution obtained would make it clear how the
IMBH has evolved from a seed BH and whether the IMBH has experienced major
mergers in the past. Unlike the gamma ray observations of DM annihilation, GW
is just sensitive to the radial profile of the DM distribution and even to
non-interacting DM. Hence the effect we demonstrate here can be used as a new
and powerful probe into DM properties.
