Helioseismic constraints on the structure of the solar tachocline

This paper presents a series of helioseismic inversions aimed at determining with the highest possible confidence and accuracy the structure of the rotational shear layer (the tachocline) located beneath the base of the solar convective envelope. We are particularly interested in identifying features of the inversions that are robust properties of the data, in the sense of not being overly influenced by the choice of analysis methods. Toward this aim we carry out two types of two-dimensional Linear inversions, namely Regularized Least-Squares (RLS) and Subtractive Optimally Localized Averages (SOLA), the latter formulated in terms of either the rotation rate or its radial gradient. We also perform nonlinear parametric least-squares fits using a genetic algorithm-based forward modeling technique. The sensitivity of each method is thoroughly tested on synthetic data. The three methods are then used on the LOWL 2 yr frequency-splitting data set. The tachocline is found to have an equatorial thickness of w/R-. = 0.039 +/- 0.013 and equatorial central radius r(c)/R-. = 0.693 +/- 0.002 All three techniques also indicate that the tachocline is prolate, with a difference in central radius Delta r(c)/R-. similar or equal to 0.024 +/- 0.004 between latitude 60 degrees and the equator. Assuming uncorrelated and normally distributed errors, a strictly spherical tachocline can be rejected at the 99% confidence level. No statistically significant variation in tachocline thickness with latitude is found. Implications of these results for hydrodynamical and magnetohydrodynamical models of the solar tachocline are discussed.