Effect of a fossil magnetic field on the structure of a young Sun

We study the impact of a fossil magnetic field on the physical quantities which describe the structure of a young Sun of 500 Myr. We consider for the first time a non-force-free field composed of a mixture of poloidal and toroidal magnetic fields and propose a specific configuration to illustrate our purpose. In this paper, we estimate the relative role of the different terms which appear in the modified stellar structure equations. We note that the Lorentz tension plays a non-negligible role in addition to the magnetic pressure. This is interesting because most of the previous stellar evolution codes ignored that term and the geometry of the field. The solar structure perturbations are, as already known, small and consequently we have been able to estimate each term semi-analytically. We develop a general treatment to calculate the global modification of the structure and of the energetic balance. We also estimate the gravitational multipolar moments associated with the presence of a fossil large-scale magnetic field in radiative zone. The values given for the young Sun help the future implementation in stellar evolution codes. This work can be repeated for any other field configuration and prepares the achievement of a solar magnetohydrodynamic model where we will follow the transport of such field on secular time-scales and the associated transport of momentum and chemicals. The described method will be applied at the present Sun and the results will be compared with the coming balloon or space measurements.