  Recent studies show that an intermediate mass black hole (IMBH) may develop a
dark matter (DM) mini-halo according to some BH formation scenarios. We
consider a binary system composed of an IMBH surrounded by a DM mini-spike and
a stellar mass object orbiting around the IMBH. The binary evolves due to
gravitational pull and dynamical friction from the DM mini-spike and
back-reaction from its gravitational wave (GW) radiation which can be detected
by future space-borne GW experiments such as eLISA/NGO. We consider a single
power-law model for the DM mini-spike which is assumed to consist of
non-annihilating DM particles and demonstrate that an eLISA/NGO detection of GW
from such a binary enables us to measure the DM mini-spike parameters very
accurately. For instance, in our reference case originally advocated by Zhao
and Silk (2005) and Bertone et al. (2005), we could determine the power-law
index $\alpha$ of the DM mini-spike radial profile with a 1 $\sigma$ relative
error of $\pm 5\times 10^{-6}$ for a GW signal with signal-to-noise-ratio 10
and assuming a 5 year observation with eLISA. We also investigate how
accurately the DM parameters can be determined for various DM parameters and
the masses of the IMBH-stellar mass object binary surrounded by a DM
mini-spike. We find that we can determine the power-law index $\alpha$ at 10 %
level even for a slightly flatter radial distribution of $\alpha \sim 1.7$.
