Proto-galactic perturbations

In the gravitational instability picture of galaxy formation, the precursor of a galaxy or a cluster of galaxies is a region with a significantly perturbed mean density or velocity field. This region may, and generally does, have considerable substructure. To relate the early perturbations to the currently observable structures it is necessary to distinguish between perturbations which merge with other perturbations and those, more encompassing ones, which form galaxies by themselves. The latter can be thought of as ‘isolated’ fluctuations; they conserve mass during their evolution so that the present distribution of over-dense regions provides a direct record of these fluctuations at earlier epochs. The relationship between isolated fluctuations and current observations is discussed in general terms in this paper and is explored in more detail elsewhere. One of the main focuses of the present work is the computation of the mass spectra of ‘extremal mass’ fluctuations for a Poisson distribution of point masses. The spectra of isolated fluctuations can be derived from the spectra of extremal fluctuations when the dynamics of small perturbations in a uniform background is determined. It is found that the space density of extremal perturbations is nearly constant per logarithmic mass interval at low masses and then falls off sharply.