Solar Mean Magnetic Field Near the Surface and its Variation During a Cycle

The unsigned mean magnetic field characterizes the magnetic energy settled in the region near the solar surface. It is one of the determinant ingredients that govern the turbulence in the photosphere, and the magnetic heating of upper layers. The acoustic eigenmodes are directly sensitive to this mean magnetic energy, via the magnetic pressure, and thanks to their trajectories sweeping entirely this region. We use the local-wave formalism to calculate the p-mode frequencies of the Saclay seismic solar model. Then, by comparing them to the LOWL observed frequencies, the l-independent differences (up to 40 microHz) can be attributed to the existence of a magnetic pressure that modifies the pressure, the density and the sound speed, taking also into account the additional Alfven speed. A profile of unsigned mean magnetic field is deduced, increasing from zero at the surface to 2.5e4 G, 5600 km deeper. Next, by applying the same method, the l-independent variations in frequency due the solar cycle (up to 0.4 microHz) is used to deduce the change of the magnetic profile. This change presents two distinctive parts: a plateau of only 2-3 G from the surface down to 2100 km, and a very narrow peak of 55 G, 220 km thick, right at the surface. Due to the non-linear effect of the magnetic field, comparing only the frequencies between minimum and maximum activity is not sufficient to deduce the magnetic variation. The additional knowledge of the magnetic field at minimum activity is necessary. If the latter is ignored, an extra variation of up to 130 G would be found. Finally, our results are compared to magnetic field estimates by other helioseismic and spectroscopic methods.