Helioseismic constraints on the structure of the solar tachocline

This paper presents a series of helioseismic inversions aimed at determinin g with the highest possible confidence and accuracy the structure of the ro tational shear layer (the tachocline) located beneath the base of the solar convective envelope. We are particularly interested in identifying feature s 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 Re gularized Least-Squares (RLS) and Subtractive Optimally Localized Averages (SOLA), the latter formulated in terms of either the rotation rate or its r adial gradient. We also perform nonlinear parametric least-squares fits usi ng 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 equato rial central radius r(c)/R-. = 0.693 +/- 0.002 All three techniques also in dicate 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 degr ees and the equator. Assuming uncorrelated and normally distributed errors, a strictly spherical tachocline can be rejected at the 99% confidence leve l. No statistically significant variation in tachocline thickness with lati tude is found. Implications of these results for hydrodynamical and magneto hydrodynamical models of the solar tachocline are discussed.