The Gravitational Instability Picture and the Formation of the Local Group

If galaxy clustering grew by gravity, and galaxies trace mass, galaxy orbits can be estimated by adjusting them to make the action stationary. Derived redshifts of five outlying members of the Local Group are in remarkably good agreement with the observations if Hubble's constant is in the range h = 0.75 to 1 (H = 100h km s^-1^ Mpc^-1^) in a low density universe, or if h ~ 0.5 in an Einstein-de Sitter universe. The galaxy N6822 is close enough that it may already have passed by; the passing orbit gives a reasonable fit to its redshift. With density parameter {OMEGA} ~ 0.1 the predicted peculiar motion of the Sculptor Group is toward us, as observed. A fit to the redshift of the Maffei Group requires that it be at distance >~ 2h^-1^ Mpc, which may prove to be a problem. In the best solution the present ratio of kinetic to potential energy in the Local Group is close to virial equilibrium; the present relative transverse velocity of the Andromeda nebula is ~110 km s^-1^, about the same as the radial component; and the Milky Way and M31 will reach minimum separation ~ 160 kpc and then (in the absence of other masses) move apart. The Local Group grows out of an initial contrast {DELTA} ~ 4 +/- 1 (δρ/ρ extrapolated to the present in linear perturbation approximation). This would be a fluctuation ~ 1 σ if the primeval mass distribution has a white noise spectrum. In the {OMEGA} = 0.1 solution the Local Group plus the Maffei and Sculptor Groups were collected from a sphere with diameter HD ~ 1000 km s^-1^, large enough to empty the nearby voids. A problem with the {OMEGA} = 1 case is that the mean mass density within the local galaxy concentration would be lower than the background, which would be difficult to reconcile with the fact that we are in a distinct galaxy concentration.