Two-dimensional inversion of rotational splitting data
We solve a two-dimensional inverse problem of the rotational frequency splitting to infer the rotation rate in the sun as a function of both the radius and the latitude. We use Libbrecht's (1989) observational data of the solar p-mode frequency splitting. We discretize a set of linear integral equations for rotational splittings and reduce them a set of linear algebraic equations. We solve the resultant algebraic equations by imposing an error-weighted least squares condition cooperated with boundary constraint at the surface. In order to stabilize the solution to observational and numerical errors, we discard small singular values of the coefficient matrix, and this keeps some parameters undetermined. To determine these parameters we impose a flatness condition. The inverted results show the solar internal rotation becomes slower at low latitudes and faster at high latitudes with increasing depth. The most significant deviation from this trend is that rotation is slow at low latitudes in the convection zone.
KeywordsRotation Rate Convection Zone Frequency Splitting Flatness Condition Inverted Result
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