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

The observations of global stellar oscillations of post main-sequence stars by space-based photometry missions allowed to directly determine their internal rotation. These constraints have pointed towards the existence of angular momentum transport processes unaccounted for in theoretical models. Constraining the properties of their internal rotation thus appears as the golden path to determine the physical nature of these missing dynamical processes. We wish 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. We test our methodology on Kepler 56, a red giant observed by the Kepler mission. First, we carry 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 Monte Carlo Markov Chain analysis of the rotational splittings of mixed modes. Our Monte Carlo Markov Chain analysis of the rotational splittings allows to determine the core and envelope rotation of Kepler 56 as well as give 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 show that the data favours a transition located in the radiative region, as predicted by processes originating from a turbulent nature. 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.