Previrialization

The relation between the virialized mass concentrations produced in a hierarchical gravitational instability picture and the amplitude of the primeval mass fluctuations is estimated under the Ansatz that one can choose an epoch a = aₓ_ that marks the transition between the growth of small departures from homogeneity and the final production of a virialized cluster, and such that at a = aₓ_ the mass distribution is usefully approximated as loosely concentrated but discrete protoclusters. The orbits that lead to this configuration are computed by minimizing the action, and the departures of these orbits from homogeneous expansion at high redshifts are used to find the primeval mass fluctuation needed to produce the postulated distribution at a = aₓ_. This procedure has the advantage that the primeval density fluctuation that produced the protocluster can be reliably measured and the evolution followed in a way that suppresses artificial two- body relaxation. In the computations presented here, the test protocluster at a = aₓ_ is modeled by 50 particles randomly placed in a sphere at mean density 3 times the background. When this test system is isolated, the orbits trace back to primeval density contrast consistent with the spherical model. In the presence of neighboring protoclusters, one sees the effects of previrialization: matter moves in a decidedly nonradial way, increasing the primeval contrast and reducing the collapse factor after the system stops expanding. The protoclusters virialize at half mass density β ~ 30 times the background, and the primeval mass contrast extrapolated to the epoch of virialization in linear perturbation theory is α ~ 8, about 5 times the prediction of the spherical model. It is not yet possible to check whether this is an artifact of the model: it is conceivable that the protoclusters in the model develop out of highly special initial conditions. However, since the nonradial motions leading to previrialization are what one would expect to see in a growing clumpy distribution, the model result seems to be well worth considering, and, if true, would be important for theories of galaxy formation. For example, it would imply that if the dark halo of a giant spiral galaxy formed out of dissipationless matter, the mass would have been assembled at redshift 1 + z ~ 7OMEGA^-1/2^, where OMEGA is the mass density parameter.