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It was found that dark matter(DM)in an intermediate-mass-ratio-inspiral(IMRI)system has a signific-ant enhancement effect on the orbital eccentricity of a stellar massive compact object,such as a black hole(BH),which may be tested by space-based gravitational wave(GW)detectors,including LISA,Taiji,and Tianqin in fu-ture observations.In this paper,we study the enhancement effect of the eccentricity for an IMRI under different DM density profiles and center BH masses.Our results are as follows:(1)in terms of the general DM spike distribution,the enhancement of the eccentricity is basically consistent with the power-law profile,which indicates that it is reas-onable to adopt the power-law profile;(2)in the presence of a DM spike,the different masses of the center BH will affect the eccentricity,which provides a new way for us to detect the BH's mass;and(3)considering the change in the eccentricity in the presence and absence of a DM spike,we find that it is possible to distinguish DM models by measuring the eccentricity at a scale of approximately l05GM/c2.