The Density Profiles of Massive, Relaxed Galaxy Clusters. I. The Total
  Density Over Three Decades in Radius
  Clusters of galaxies are excellent locations to probe the distribution of
baryons and dark matter (DM) over a wide range of scales. We study a sample of
seven massive, relaxed galaxy clusters with centrally-located brightest cluster
galaxies (BCGs) at z=0.2-0.3. Using the observational tools of strong and weak
gravitational lensing, combined with resolved stellar kinematics within the
BCG, we measure the total radial density profile, comprising both dark and
baryonic matter, over scales of ~3-3000 kpc. Lensing-derived mass profiles
typically agree with independent X-ray estimates within ~15%, suggesting that
departures from hydrostatic equilibrium are small and that the clusters in our
sample (except A383) are not strongly elongated along the line of sight. The
inner logarithmic slope gamma_tot of the total density profile measured over
r/r200=0.003-0.03, where rho_tot ~ r^(-gamma_tot), is found to be nearly
universal, with a mean <gamma_tot> = 1.16 +- 0.05 (random) +0.05-0.07
(systematic) and an intrinsic scatter of < 0.13 (68% confidence). This is
further supported by the very homogeneous shape of the observed velocity
dispersion profiles, obtained via Keck spectroscopy, which are mutually
consistent after a simple scaling. Remarkably, this slope agrees closely with
numerical simulations that contain only dark matter, despite the significant
contribution of stellar mass on the scales we probe. The Navarro-Frenk-White
profile characteristic of collisionless cold dark matter is a better
description of the total mass density at radii >~ 5-10 kpc than that of dark
matter alone. Hydrodynamical simulations that include baryons, cooling, and
feedback currently provide a poorer match. We discuss the significance of our
findings for understanding the assembly of BCGs and cluster cores, particularly
the influence of baryons on the inner DM halo. [abridged]
