Simulating observable comets - I. The effects of a single stellar passage through or near the Oort cometary cloud

This is the first of a series of papers presenting an attempt to reproduce the mechanisms acting currently on the Oort cloud of comets and producing the observed long-period comets. In this first part we give a short review of papers on the stellar perturbations on the cometary cloud and on the observed long-period comet perihelia/aphelia directions distribution. We present in detail the effects of a single stellar passage through or near the cometary cloud by means of a Monte Carlo simulation based on the improved impulse approximation. The simulations are performed for two different steady-state numerical models of the Oort cloud and for different parameters of the stellar passage. Among others, we calculate the probabilities of producing an observable comet as well as ejecting it from the cloud, we characterize cometary shower resulting from the close stellar passage and discuss anisotropies in the observable sample of comets, produced by a simulated single stellar perturbation.