The dynamics of luminous galaxies in isothermal halos

We examine the dynamics of luminous galaxies in singular isothermal mass distributions by fitting the line-of-sight velocity dispersion profiles of 37 elliptical galaxies assuming that the galaxies are spherical, are non-rotating, and have a constant velocity anisotropy. We find that the observed central velocity dispersion, σ_c_, is a good estimate for the velocity dispersion of the halo σ_DM_. If the σDM are fitted with a power law of the luminosity, σ_DM_ = σ_DM*_(L/L_*_)^1/γ^, we find σ_DM*_ = 225 +/- 10 km s^- 1^ and 1/γ = 0.24 +/- 0.05, compared to σ_c*_ = 228 +/- 14 km s^-1^ and 1/γ = 0.29 +/- 0.07 for the central velocity dispersions. The scatter about the power law correlated with the central surface brightness and the effective radius (the "fundamental plane") and is uncorrelated with ellipticity and rotation. The existence of a fundamental plane that causes intrinsic scatter about the power-law relations significantly modifies the number counts of galaxies as a function of velocity dispersion.