UNCERTAINTIES FOR 2-DIMENSIONAL MODELS OF SOLAR ROTATION FROM HELIOSEISMIC EIGENFREQUENCY SPLITTING

Observed solar p-mode frequency splittings can be used to estimate ang ular velocity as a function of position in the solar interior. Formal uncertainties of such estimates depend on the method of estimation (e. g., feast-squares), the distribution of errors in the observations, an d the parameterization imposed on the angular velocity. We obtain lowe r bounds on the uncertainties that do not depend on the method of esti mation; the bounds depend on an assumed parameterization, but the fact that they are lower bounds for the ''true'' uncertainty does not. Nin ety-five percent confidence intervals for estimates of the angular vel ocity from 1986 Big Bear Solar Observatory (BBSO) data, based on a 365 9 element tenser-product cubic-spline parameterization, are everywhere wider than 120 nHz, and exceed 60,000 nHz near the core. When compare d with estimates of the solar rotation, these bounds reveal that usefu l inferences based on pointwise estimates of the angular velocity usin g 1986 BBSO splitting data are not feasible over most of the Sun's vol ume. The discouraging size of the uncertainties is due principally to the fact that helioseismic measurements are insensitive to changes in the angular velocity at individual points, so estimates of point value s based on splittings are extremely uncertain. Functionals that measur e distributed ''smooth'' properties are, in general, better constraine d than estimates of the rotation at a point. For example, the uncertai nties in estimated differences of average rotation between adjacent bl ocks of about 0.001 solar volumes across the base of the convective zo ne are much smaller, and one of several estimated differences we compu te appears significant at the 95% level.