On the detectability of a rotation rate gradient in the solar core

We consider the problem of uncovering a possible gradient of rotation in the solar core using seismic frequency splittings of low-degree p-modes. The data are presumed to come from full-disc observations of the Sun. In particular, we formulate an approach for determining the diagnostic potential of a low-l splitting set to uncover, by inversion, a difference in rotation between two target radii: one deep in the core, the other in the mid-regions of the radiative zone. Our formulation assumes the underlying rotation rate to be flat in the outer part of the zone, but to vary linearly in the core (with the breakpoint in behaviour located between the two target radii). Artificial data are used to test the formulation, and to investigate the relative importance at low l of deeply penetrating, high-order modes and relatively shallow, low-order modes. Our results suggest that in order to detect a significant difference between the rotation at r = 0.1R and 0.35R - with the input splitting data coming from a 10-yr set of high-quality observations - that difference would need to be a significant fraction of the rotation rate itself.