2.4 Estimating rotation properties directly from coefficients

It is possible to make some inferences about the rotation profile without carrying out a full-scale inversion. Simple examination of the odd-order coefficients, sorted by the lower turning-point radius of the modes, reveals the existence of the near-surface shear, the differential rotation within the convection zone, and a discontinuity in the differential rotation at the base of the convection zone, as shown in Figure 9View Image. More sophisticated analysis is also possible. For example, Wilson and Burtonclay (1995Jump To The Next Citation Point) gave approximate expressions for the rotation profile at different latitudes as sensed by a particular n,l multiplet, nl ¯Ω, as follows:
¯Ωnl0 ≈ anl1 + an3l+ anl5 , (7 ) nl nl ¯Ωn3l0 ≈ an1l− a3-− 19a5-, (8 ) 4 16 ¯nl nl 3an3l 3an5l Ω45 ≈ a1 − 2 − 4 , (9 ) nl nl ¯Ωnl60 ≈ an1l − 11a3- + 37a-5 . (10 ) 4 16
These estimates, where the subscripts on the LHS refer to the latitude in degrees, are noisy for individual multiplets, but Wilson and Burtonclay (1995) were able to build up a picture of the internal rotation from BBSO data by forming cumulative averages with the input data sorted in ascending order of ν∕L.

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