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Astron. Astrophys. 329, 1-13 (1998)

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1. Introduction

The tremendous growth of observational data during the last few years has strongly changed our insight into the structure and evolution of the universe. The large scale matter distribution of the universe has been predicted by the nonlinear theory of gravitational instability of Zeldovich (1970), and the Large Scale Structure (LSS) has already been identified in the first wedge diagrams of galaxy redshift surveys (Gregory  &  Thompson 1978) underlining qualitatively the theoretical picture.

During the last decade such phenomena as the Great Void (Kirshner et al. 1983), the Great Attractor (Dressler et al. 1987) and the Great Wall (de Lapparent et al. 1988) were extraordinary examples of the hugest observed structures in the Universe. However, the analysis of the presently largest galaxy catalogue - the Las Campanas Redshift Survey (Shectman et al. 1996) - demonstrates clearly that distinguished very large structure elements accumulate about 50% of all galaxies of the survey (Doroshkevich et al. 1996, 1997b). These structure elements are in many respects similar to the Great Wall and the superclusters of galaxies, we call them super-large scale structure (SLSS). The existence of these structures needs to be studied theoretically and in simulations in order to understand and to explain an essential feature of the universe.

The large scales (about 100 [FORMULA] Mpc) by which the SLSS is characterized make this problem especially enigmatic, since the galaxy correlation length is smaller than 10 [FORMULA] Mpc, and the cluster correlation length is smaller than 25 [FORMULA] Mpc. The matter distribution is, according to the general conviction, approximately homogeneous at larger scales. This point of view now needs to be revised. Perhaps, however, the galaxy concentration within the SLSS elements is not accompanied by a similar concentration of dark matter (see discussion in Piran et al. 1993, Demianski & Doroshkevich 1997), i.e. a large scale bias between dark matter and galaxies could exist.

The formation of the SLSS elements can be explained by matter infall into large scale gravitational wells. Undoubtedly, this explanation is valid for the description of the formation of a single wall and, hence, the observed galaxy distribution maps the well distribution. Therefore, the main problem in question is the origin of such wells, and the explanation of their spatial distribution. This aspect becomes especially important in view of new huge redshift surveys under preparation.

Apparently potential, velocity and density provide us with formal equivalent descriptions of the matter evolution because they are related by well known equations. For example, the adhesion approach, which operates only with the initial potential, describes very detailed the matter evolution (see, e.g., Shandarin & Zeldovich 1989). On the other hand, in a seminal paper, Bardeen et al. (1986) consider the same problem using the density field.

However, all previous experience in physics shows, that seemingly equivalent descriptions emphasize different aspects of the same problem and, thus, they are supplementary to each other. In practice the density field is more representative for the small scale evolution while the potential is more suited for the investigations of large scale matter evolution. Both descriptions need to be used together to reveal the interaction and the mutual influence of long and short wave perturbations and to obtain the general description of the matter evolution.

It is important that due to very slow evolution of the large scale spatial distribution even the initial potential field can be used for the prediction and explanation of properties of the matter distribution at later evolutionary stages. In particular, such analysis allows us to specify the large scale perturbations responsible for the SLSS formation (Demianski & Doroshkevich 1997).

A short theoretical analysis of the possible impact of the potential perturbations on the structure evolution has been given by Buryak et al. (1992) and by Demianski  &  Doroshkevich (1992). There a correlation of potential and density perturbations during all evolutionary periods was demonstrated quantitatively, and the typical scale of the potential perturbations was derived. Doroshkevich et al. (1997a) have improved some of the relations describing the potential perturbations. On the basis of six numerical simulation we will demonstrate here the close links of the spatial distribution of matter density with the potential distribution. Further we propose some quantitative characteristics of this correlation.

This paper is organized as follows. In Sect. 2 we describe the numerical models utilized for further analysis. In Sect. 3 the simulated potential distributions are discussed and characterized quantitatively. In Sect. 4 the link of potential and density perturbations is considered and some quantitative characteristics of this interactions are found. In Sect. 5 we summarize and discuss our results.

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© European Southern Observatory (ESO) 1998

Online publication: November 24, 1997