A two dimensional regularized least-squares inversion code with expansion of the solution in B-splines has been presented. It includes a condition that insures the regularity of the solution at the center and provides the possibility of adding surface constraints on the rotation rate.
We have inverted the two year LOWL rotational splitting dataset to derive the rotation rate of the solar interior matched to the observed plasma surface rotation rate. Both the inversion of the three a-coefficients and of the individuals splittings reconstructed from these a-coefficients have been performed. The comparison of the results gives an estimation of the improvement of the latitudinal resolution which could be obtained by the knowledge of the individual splittings.
Between 0.4 and , our results are in good agreement with the previous work of Tomczyk et al. (1995b) who have used the first three month dataset. The small maximum at obtained previously is however smoothed for polar latitudes and disappears for equatorial rotation.
The 2 year dataset allows a description of the internal rotation rate with depth and latitude from 0.4 up to 0.95 solar radii with increasing radial resolution. At the base of the convection zone, the width of the transition zone is found to be smaller than 0.1 solar radii, in agreement with Thompson et al. (1996). We have shown that the LOWL data are compatible with the surface rotation estimated by plasma observations and confirm an increase of the rotation below the surface up to values measured by magnetic feature observations for equatorial latitudes.
Our solution is compatible with a solar core that rotates slower than the radiative interior. However, improved observations are needed to sound the region below more accurately and with latitudinal resolution. In addition to the ground based networks, the instruments aboard the SOHO satellite will hopefully provide these observations in the near future and add the possibility of detecting low frequency p-modes as well as g-modes which have their maximum amplitude in the solar core.
© European Southern Observatory (ESO) 1997
Online publication: May 26, 1998