Solar activity and helioseismology show the limitation of the standard solar model and call for the inclusion of dynamical processes in both convective and radiative zones. In this paper, we concentrate on the radiative zone. We first recall the sensitivity of boron neutrinos to the microscopic physics included in solar standard and seismic models. We confront the neutrino predictions of the seismic model with all the detected neutrino fluxes. Then, we compute new models of the Sun including a detailed transport of angular momentum and chemicals due to internal rotation that includes meridional circulation and shear-induced turbulence. We use two stellar evolution codes: CESAM and STAREVOL to estimate the different terms. We follow three temporal evolutions of the internal rotation which differ by their initial conditions: very slow, moderate, and fast rotation, with magnetic braking at the arrival on the main sequence for the last two. We find that the meridional velocities in the present solar radiative zone are extremely small in comparison with those of the convective zone (smaller than 10-6 cm s-1 instead of m s-1). All models lead to a radial differential rotation profile in the radiative zone but with a significantly different contrast. We compare these profiles to the presumed solar internal rotation and show that if meridional circulation and shear turbulence were the only mechanisms transporting angular momentum within the Sun, a rather slow rotation in the young Sun is favored. We confirm the small influence of the transport by rotation on the sound speed profile but its potential impact on the chemicals in the transition region between radiation and convective zones. These models are physically more representative of the real Sun than the standard or seismic solar models but a high initial rotation, as has been considered previously, increases the disagreement with neutrinos and the sound speed in the radiative zone. This present work pushes us to pursue the inclusion of the other dynamical processes to better reproduce the observed solar profile in the whole radiative zone and to better describe the young active Sun. We also need to get a better knowledge of solar gravity mode splittings to use their constraints.
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