Extended Data Figure 6: Various properties of our optimal model.

a, Normalized weight function plotted against the normalized radius. Each individual weight function for the eight gravity modes of interest from the optimal model of KIC08626021 is normalized to a maximum value of 1.0. The weight function of a mode indicates the layers contributing most to the integral, giving the frequency (period) of the mode according to a well known variational principle in linear pulsation theory. The middle panel illustrates the chemical stratification of the model. All of the identified modes are useful probes of the core composition. b, Internal rotation profile. Contour map of the two-dimensional merit function that optimizes the match between the observed spacings in the three frequency multiplets with computed spacings on the basis of our seismic model. This is shown in terms of depth (expressed as the normalized radius) and in terms of the local rotation period of the inner region in the two-zone approach of ref. 45. The best-fitting solution is illustrated by the nearly vertical white curve about the solid-body solution (vertical dot-dashed white line). The dotted white curves on both sides of the solution depict its associated 1σ, 2σ and 3σ uncertainty contours. The fact that these contours diverge out at the greater depths considered here indicates that the rotationally split gravity modes available here lose their capacity to measure the local rotation rate at greater depths (indeed, their rotation kernels have negligible amplitudes at such depths). The horizontal white dot-dashed lines indicate the layer below which there is 99%, 90% and 10% of the mass of the star, from top to bottom. c, Comparison between the ranges of detected and excited periods in KIC08626021. The panel shows the detected periods (thick lines) with the bands of excited periods (thin lines) in two models similar to the optimal seismic model, but computed with the higher convective efficiency of ML2/α?=?1.5 (above) and ML2/α?=?1.6 (below). The reduced period is used as the abcissa in order to have comparable values for both dipole mode (in red) and quadrupole mode (in blue). The radial order k is indicated at both ends of each range.