The rotational shear layer inside the early red-giant star KIC 4448777

We present the asteroseismic study of the early red-giant star KIC 4448777, complementing and integrating a previous work (Di Mauro et al. 2016), aimed at characterizing the dynamics of its interior by analyzing the overall set of data collected by the {\it Kepler} satellite during the four years of its first nominal mission. We adopted the Bayesian inference code DIAMOND (Corsaro \& De Ridder 2014) for the peak bagging analysis and asteroseismic splitting inversion methods to derive the internal rotational profile of the star. The detection of new splittings of mixed modes, more concentrated in the very inner part of the helium core, allowed us to reconstruct the angular velocity profile deeper into the interior of the star and to disentangle the details better than in Paper I: the helium core rotates almost rigidly about 6 times faster than the convective envelope, while part of the hydrogen shell seems to rotate at a constant velocity about 1.15 times lower than the He core. In particular, we studied the internal shear layer between the fast-rotating radiative interior and the slow convective zone and we found that it lies partially inside the hydrogen shell above $r \simeq 0.05R$ and extends across the core-envelope boundary. Finally, we theoretically explored the possibility for the future to sound the convective envelope in the red-giant stars and we concluded that the inversion of a set of splittings with only low-harmonic degree $l\leq 3$, even supposing a very large number of modes, will not allow to resolve the rotational profile of this region in detail.