Angular momentum redistribution by mixed modes in evolved low-mass stars. II. Spin-down of the core of red giants induced by mixed modes

The detection of mixed modes in subgiants and red giants by the CoRoT and \emph{Kepler} space-borne missions allows us to investigate the internal structure of evolved low-mass stars. In particular, the measurement of the mean core rotation rate as a function of the evolution places stringent constraints on the physical mechanisms responsible for the angular momentum redistribution in stars. It showed that the current stellar evolution codes including the modelling of rotation fail to reproduce the observations. An additional physical process that efficiently extracts angular momentum from the core is thus necessary. Our aim is to assess the ability of mixed modes to do this. To this end, we developed a formalism that provides a modelling of the wave fluxes in both the mean angular momentum and the mean energy equations in a companion paper. In this article, mode amplitudes are modelled based on recent asteroseismic observations, and a quantitative estimate of the angular momentum transfer is obtained. This is performed for a benchmark model of 1.3 $M_{\odot}$ at three evolutionary stages, representative of the evolved pulsating stars observed by CoRoT and Kepler. We show that mixed modes extract angular momentum from the innermost regions of subgiants and red giants. However, this transport of angular momentum from the core is unlikely to counterbalance the effect of the core contraction in subgiants and early red giants. In contrast, for more evolved red giants, mixed modes are found efficient enough to balance and exceed the effect of the core contraction, in particular in the hydrogen-burning shell. Our results thus indicate that mixed modes are a promising candidate to explain the observed spin-down of the core of evolved red giants, but that an other mechanism is to be invoked for subgiants and early red giants.