The Effects of the Peak-Peak Correlation on the Peak Model of Hierarchical Clustering

In two previous papers a semianalytical model was presented for the hierarchical clustering of halos via gravitational instability from peaks in a random Gaussian field of density fluctuations. This model is better founded than the extended Press-Schechter model, which is known to agree with numerical simulations, and it makes similar predictions. The specific merger rate, however, shows a significant departure at intermediate captured masses. The origin of this was suspected to be the rather crude approximation used for the density of nested peaks. Here, we seek to verify this suspicion by implementing a more accurate expression for the latter quantity, which accounts for the correlation among peaks. We confirm that the inclusion of the peak-peak correlation improves the specific merger rate, while the good behavior of the remaining quantities is preserved.