The Distribution of Matter in the Virgo Supercluster

Abstract

A spherically symmetric mass distribution centred on the Virgo cluster is fitted to de Vaucouleurs' survey of the distribution of galaxies within 15 Mpc of the Local Group. Each galaxy is assigned an approximate distance on the basis of its probable ‘ membership ’ of some group or cluster (without, however, implying any dynamical association). Two models are constructed with group distances based respectively on the mean recession velocity of the group and on the bright end of the group luminosity function. Using Shapiro's luminosity function, the mass distribution in consecutive shells centred on the Virgo cluster is determined and fitted with a simple model. Over most of the survey volume, the spatial mass density falls off roughly as r^–3 from the Virgo cluster. The mean cosmic mass density at the distance of the Local Group is 0·35 × 10^–31 g cm^–3 (on the assumption that (ℳ/ℒ)_s = 7, (ℳ/ℒ)_E = 50 and H₀ = 100 km s^–1 Mpc^–1). The mean cosmic mass density over the whole survey volume is 2·0 × 10^–31 g cm^–3 and the density of the Virgo supercluster falls to this value at ~ 5 Mpc from the Virgo cluster centre. On the basis of the model, the mean density of the cluster averaged over a volume of ~ 2 Mpc radius is $$2 \times 10^{-29} \,\text{g cm}^{-3},$$ and so this is the dynamical radius for the cluster under the present assumptions. The deviations from the Hubble flow are small (< 15 per cent) over a volume of 10 Mpc radius centred on the Local Group. Since there is considerable variation in density over this volume, a low value $$q_{0} \lesssim 0 \cdot 05$$ is implied for the deceleration parameter of the supercluster material.