The Observed Mass Profiles of Dark Halos and the Formation Epoch of Galaxies

We have determined the mass profiles of dark halos in 83 objects observed byASCA. The point spread function of X-ray telescope was deconvoled by theRichardson-Lucy algorithm and the temperature profiles were calculated toobtain the mass profiles. The derived mass profiles are consistent with the NFWmodel in 0.01-1.0 r_virial. We found a good correlation between the scaleradius r_s and the characteristic mass density \delta_c, which indicates theself-similarity of dark halos. The spectrum index of primordial densityfluctuation, P(k) \propto k^n, was determined from the slope of r_s - delta_crelation. For M_200=10^12-10^15 M_solar, our analysis gives n=-1.2 +/- 0.3 witha confidence level of 90%. The mass density of dark halos is a good indicatorof the mean mass density of the universe at the time when the halos wereassembled, z=z_f. Assuming delta_c \propto (1+z_f)^3, we have determined theepoch when each dark halo was assembled. Our analysis indicates that the fieldelliptical galaxies and groups of galaxies formed approximately at 1+z_f ~ 15and at 1+z_f ~ 7-10 respectively.Comment: 11 pages, 5 figures. Accepted for the publication in Astrophysical Journal Letter