Asteroseismic hare & hound exercises: the case of β Cephei stars

The β Cephei pulsating stars present a unique opportunity to test and probe our knowledge of the interior of massive stars. The information that we can get depends on the quality and number of observational constraints, both seismic and classical ones. The asteroseismology of β Cephei stars proceeds by a forward approach, which can result in multiple solutions, without clear indication on the level of confidence. We seek a method to derive confidence intervals on stellar parameters and investigate how these latter behave depending on the seismic data accessible to the observer. We realise forward modelling with the help of a grid of pre-computed models. We also use Monte-Carlo simulations to build confidence intervals on the inferred stellar parameters. We apply and test this method in a series of hare and hound exercises on a subset of theoretical models simulating observed stars. Results show that a set of 5 frequencies (with knowledge of their associated angular degree) yields precise seismic constraints. Significant errors on the determination of the extent of the central mixed region may result when the theoretical models do not present the same chemical mixture as the observed star.