THE CONFLUENT SYSTEM FORMALISM .2. THE GROWTH HISTORY OF OBJECTS

We conclude the presentation of a semianalytical model of hierarchical clustering of bound virialized objects formed by gravitational instab ility from a random Gaussian field of density fluctuations. In the fir st paper of this series, we introduced the basic tool, the so-called c onfluent system formalism, able to follow the evolution of bound viria lized objects in the peak model. This was applied to derive the mass f unction of objects. In the present paper, we calculate other important quantities that characterize the growth history of objects. This mode l is compared with a similar one obtained by Lacey St. Cole following the Press-Schechter approach. The interest of the new modeling present ed here is twofold: (1) it is formally better justified, as far as pea ks are more reasonable seeds of objects than the undetermined regions in the Press-Schechter prescription, and (2) it distinguishes between merger and accretion, enabling us to unambiguously define the formatio n and destruction of objects and to estimate growth rates and characte ristic rimes not available in the previous approach.