Details

Autor(en) / Beteiligte

• Hanami, Hitoshi

Titel

Statistics of merging peaks of random Gaussian fluctuations: skeleton tree formalism

Ist Teil von

• Monthly notices of the Royal Astronomical Society, 2001-11, Vol.327 (3), p.721-738

Ort / Verlag

Oxford, UK: Blackwell Science Ltd

Erscheinungsjahr

2001

Link zum Volltext

Quelle

Wiley Online Library - AutoHoldings Journals

Beschreibungen/Notizen

• Cosmological bound objects are generally considered to be formed from the local maxima of cosmological density fluctuations, which are often assumed to be Gaussian random fields. In order to study the statistics of those objects that are the result of hierarchical merging, we propose skeleton tree formalism, which can analytically distinguish episodic merging from continuous accretion in the mass-growth processes. This distinction was not clear in the extended Press–Schechter (PS) formalism. Skeleton tree formalism is a natural extension of peak theory, which is an alternative formalism for the statistics of bound objects. Fluctuation-field smoothing with a Gaussian filter produces a landscape by adding the extra dimension of the filter-resolution scale to the spatial coordinate of the fluctuation. In this landscape, a smoothed peak is nesting alongside the neighbouring peak and appears as a critical point called a sloping saddle, which can be interpreted as a destroyed object during a merger event in the context of the hierarchical structure formation. The topological properties of the landscape can be abstracted as skeleton trees, which consist of the line process of the smoothing peaks and the point process of the sloping saddles. According to this abstract topological picture, in this paper, we present the concept and the basic results of skeleton tree formalism in describing (1) the distinction between accretion and a merger in the hierarchical structure formation from various initial random Gaussian fields; (2) the instantaneous number density of the sloping saddles, which gives the destruction rate in the mergers; (3) the number densities of all the peaks, nesting and non-nesting, with simple and analytical distinguishing definitions; (4) the self-consistency of the formalism in reproducing the statistics, including the conservation equation, of all the peaks; (5) the instantaneous number density of the reforming objects, which is derived from the conservation formula of the non-nesting peak; and (6) the mean growth history of the objects, which is reproduced from the rates of destruction, reformation, and from the relative accretion growth.