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An intermediate mass black hole (IMBH) may have a dark matter (DM) mini-haloaround it and develop a spiky structure within less than a parsec from theIMBH. When a stellar mass object is captured by the mini-halo, it eventuallyinfalls into such an IMBH due to gravitational wave back reaction which in turncould be observed directly by future space-borne gravitational wave experimentssuch as eLISA/NGO. In this paper, we show that the GW detectability stronglydepends 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 veryaccurately. The DM density distribution obtained would make it clear how theIMBH has evolved from a seed BH and whether the IMBH has experienced majormergers in the past. Unlike the gamma ray observations of DM annihilation, GWis just sensitive to the radial profile of the DM distribution and even tonon-interacting DM. Hence the effect we demonstrate here can be used as a newand powerful probe into DM properties.

A new probe of dark matter properties: gravitational waves from an intermediate mass black hole embedded in a dark matter mini-spike