Asteroseismology of evolved stars to constrain the internal transport of angular momentum: IV. Internal rotation of Kepler-56 from an MCMC analysis of the rotational splittings

Context. The observations of global stellar oscillations of post-main-sequence stars by space-based photometry missions have allowed us to directly determine their internal rotation. These constraints have pointed towards the existence of angular momentum transport processes not accounted for in theoretical models. Constraining the properties of their internal rotation thus appears to be the golden path to determine the physical nature of these missing dynamical processes. Aims. Our aim is to determine the robustness of a new approach to study the internal rotation of post-main-sequence stars, using parametric rotation profiles coupled to a global optimization technique. Methods. We tested our methodology on Kepler-56, a red giant observed by the Kepler mission. First, we carried out an extensive modelling of the star using global and local minimizations techniques, and seismic inversions. Then, using our best model, we study in details its internal rotation profile, we adopted a Bayesian approach to constrain stellar parametric predetermined rotation profiles using a Markov chain Monte Carlo analysis of the rotational splittings of mixed modes. Results. Our Markov chain Monte Carlo analysis of the rotational splittings allows us to determine the core and envelope rotation of Kepler-56 and gives us hints about the location of the transition between the slowly rotating envelope and the fast-rotating core. We are able to discard a rigid rotation profile in the radiative regions followed by a power law in the convective zone, and we show that the data favours a transition located in the radiative region, as predicted by processes originating from a turbulent nature such as for example magnetic instabilities. Conclusions. Our new approach to studying the internal rotation of red giants constitutes a viable option to analyse Kepler targets and allows us to put stringent constraints on the properties of the missing angular momentum transport process acting in post-main-sequence stars. Our analysis of Kepler-56 indicates that turbulent processes whose transport efficiency is reduced by chemical gradients are favoured, while large-scale fossil magnetic fields are disfavoured as a solution to the missing angular momentum transport.