  Context. Using asteroseismic techniques, it has recently become possible to
probe the internal rotation profile of low-mass (~1.1-1.5 Msun) subgiant and
red giant stars. Under the assumption of local angular momentum conservation,
the core contraction and envelope expansion occurring at the end of the main
sequence would result in a much larger internal differential rotation than
observed. This suggests that angular momentum redistribution must be taking
place in the interior of these stars. Aims. We investigate the physical nature
of the angular momentum redistribution mechanisms operating in stellar
interiors by constraining the efficiency of post-main sequence rotational
coupling. Methods. We model the rotational evolution of a 1.25 Msun star using
the Yale Rotational stellar Evolution Code. Our models take into account the
magnetic wind braking occurring at the surface of the star and the angular
momentum transport in the interior, with an efficiency dependent on the degree
of internal differential rotation. Results. We find that models including a
dependence of the angular momentum transport efficiency on the radial
rotational shear reproduce very well the observations. The best fit of the data
is obtained with an angular momentum transport coefficient scaling with the
ratio of the rotation rate of the radiative interior over that of the
convective envelope of the star as a power law of exponent ~3. This scaling is
consistent with the predictions of recent numerical simulations of the
Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular
momentum transport process whose efficiency varies during the stellar evolution
through a dependence on the level of internal differential rotation is required
to explain the observed post-main sequence rotational evolution of low-mass
stars.
