2000ApJ...537L..73S

We have determined the mass profiles of dark halos in 83 objects observed by ASCA. The point-spread function of the X-ray telescope was deconvoled by the Richardson-Lucy algorithm, and the temperature profiles were calculated to obtain the mass profiles. The derived mass profiles are consistent with the Navarro, Frenk, & White model in (0.01-1.0)r_virial. We found a good correlation between the scale radius r_s and the characteristic mass density δ_c, which indicates the self-similarity of dark halos. The spectrum index of primordial density fluctuation, P(k)∝kⁿ, was determined from the slope of the r_s-δ_c relation. For M₂₀₀=10¹²-10¹⁵ M_☉, our analysis gives n=-1.2±0.3 with a confidence level of 90%. The mass density of dark halos is a good indicator of the mean mass density of the universe at the time when the halos were assembled, z=z_f. Assuming δ_c∝(1+z_f)³, we have determined the epoch when each dark halo was assembled. Our analysis indicates that the field elliptical galaxies and groups of galaxies formed approximately at 1+z_f≃15 and at 1+z_f≃7-10, respectively.