The density contrast of the Shapley supercluster

We calculate the density contrast of the Shapley supercluster (SSC) based on the enhanced abundance of X-ray clusters in it using the extended Press-Schechter formalism. We derive a total SSC mass of M_tot = (4.4 +/- 0.44) × 10¹⁶M_solar within a sphere of 50Mpc centred at a distance of about 160Mpc. The non-linear fractional density contrast of the sphere is (1 + δ) = 1.76 +/- 0.17 relative to the mean matter density in the Universe, but the contrast increases in the interior of the SSC. Including the cosmological constant, the SSC region is found to be gravitationally unbound. The SSC contributes only a minor portion (9.0 +/- 2.1 per cent) of the peculiar velocity of the Local Group.