Origin and evolution of two-component debris discs and an application to the q$^1$ Eridani system

Many debris discs reveal a two-component structure, with an outer Kuiper-belt analogue and a warm inner component whose origin is still a matter of debate. One possibility is that warm emission stems from an "asteroid belt" closer in to the star. We consider a scenario in which a set of giant planets is formed in an initially extended planetesimal disc. These planets carve a broad gap around their orbits, splitting up the disc into the outer and the inner belts. After the gas dispersal, both belts undergo collisional evolution in a steady-state regime. This scenario is explored with detailed collisional simulations involving realistic physics to describe a long-term collisional depletion of the two-component disc. We find that the inner disc may be able to retain larger amounts of material at older ages than thought before on the basis of simplified analytic models. We show that the proposed scenario is consistent with a suite of thermal emission and scattered light observational data for a bright two-temperature debris disc around a nearby solar-type star q$^1$ Eridani. This implies a Solar System-like architecture of the system, with an outer massive "Kuiper belt", an inner "asteroid belt", and a few Neptune- to Jupiter-mass planets in between.