Hot interstellar tunnels. 1. Simulation of interacting supernova remnants

The theory required to build a numerical simulation of interacting supernova remnants is developed. The hot cavities within a population of remnants will become connected, with varying ease and speed, for a variety of assumed conditions in the outer shells of old remnants. Apparently neither radiative cooling nor thermal conduction in a large-scale galactic magnetic field can destroy hot cavity regions, if they grow, faster than they are reheated by supernova shock waves, but interstellar mass motions disrupt the contiguity of extensive cavities necessary for the dispersal of these shocks over a wide volume. Monte Carlo simulations show that a quasi-equilibrium is reached in the test space within 10 million years of the first supernova, and is characterized by an average cavity filling fraction of the interstellar volume. Aspects of this equilibrium are discussed for a range of supernova rates. Two predictions are not confirmed within this range: critical growth of hot regions to encompass the entire medium, and the efficient quenching of the expansion of a remnant by interaction with other cavities