6.1 Observations

While the bulk of radiative interior appears to rotate almost as a solid body, the base of the convection zone at 0.71 R⊙ coincides with a region of strong radial shear, above which the convection zone exhibits a differential rotation pattern that depends strongly on latitude and only weakly on depth. This shear layer is known as the tachocline, a term introduced to the literature by Spiegel and Zahn (1992Jump To The Next Citation Point), who attribute to D.O. Gough the correction of the earlier term “tachycline” (Spiegel, 1972). As is evident from the date of the latter reference, the notion of a shear layer at the bottom of the convection zone had been present in models for some time prior to its observational discovery, though its exact location was somewhat uncertain.

The existence of a layer of radial shear around the base of the convection zone, with approximately solid-body rotation below it, was first demonstrated by Brown et al. (1989Jump To The Next Citation Point), using the data of Brown and Morrow (1987Jump To The Next Citation Point); however, the significance of their results was quite low and they were at pains to point out that other interpretations of the data were possible. Dziembowski et al. (1989Jump To The Next Citation Point) used BBSO data to improve the picture of rotation at the base of the convection zone, again finding that the low-latitude rotation rate increased, and the high-latitude rate decreased, towards a common value at the base of the convection zone. The position of the base of the convection zone was determined by Christensen-Dalsgaard et al. (1991) using sound-speed inversions of helioseismic frequencies from the work of Duvall Jr et al. (1988) and Libbrecht and Kaufman (1988); their value of 0.713 R ⊙, confirmed by Basu and Antia (1997), has been accepted ever since.

The discovery of this shear layer (as pointed out by Brown et al.) offered a solution to the puzzle of the apparent absence of a radial gradient of rotation in the convection zone that could drive a solar dynamo, leading to speculation that the dynamo must operate in the tachocline region instead of in the bulk of the convection zone.

The tachocline lies in the region where modes of l ≈ 20 have their lower turning points, and the resolution of the inversions is quite low – about 5 – 10% of the solar radius in the radial direction. The thickness of the shear layer is therefore likely not to be resolved in inversions, and some ingenuity (and forward modeling) is required to estimate it and account for the effect of the finite-width averaging kernels in smoothing out the inversion inferences. The results of various efforts to parameterize the tachocline shape at the equator are summarized in Table 2. They mostly concur in placing the centroid of the shear layer slightly below the seismically-determined base of the convection zone, and its thickness at around 0.05 R⊙. The largest value for the thickness, that of Wilson et al. (1996b), was obtained using forward calculation and direct combination of splitting coefficients rather than a true inversion, while the very low value of Corbard et al. (1999Jump To The Next Citation Point) was obtained using an inversion technique specifically designed to allow a discontinuous step in the rotation rate at the tachocline. The analysis of Elliott and Gough (1999Jump To The Next Citation Point) was somewhat different from the others, in that it involved calibrating a particular model of the tachocline against the inferred sound-speed rather than against a rotation profile.

Table 2: Tachocline radius r and width Γ.
Reference r ∕R ⊙ σr ∕R ⊙ Γ ∕R ⊙ σ Γ ∕R ⊙ Project
Kosovichev (1996) 0.692 0.005 0.09 0.04 BBSO
Wilson et al. (1996a) 0.68 0.01 0.12 BBSO
Basu (1997) 0.705 0.0027 0.0480 0.0127 GONG
Antia et al. (1998Jump To The Next Citation Point) 0.6947 0.0035 0.033 0.0069 GONG
Corbard et al. (1998a) 0.695 0.005 0.05 0.03 LOWL
Corbard et al. (1999Jump To The Next Citation Point) 0.691 0.004 0.01 0.03 LOWL
Charbonneau et al. (1999Jump To The Next Citation Point) 0.693 0.002 0.039 0.002 LOWL
Elliott and Gough (1999) 0.697 0.002 0.019 0.001 MDI
Basu and Antia (2003Jump To The Next Citation Point) 0.6916 0.0019 0.0162 0.0032 MDI, GONG

Antia et al. (1998) and Corbard et al. (1999) found no significant evidence for a variation in the position or thickness of the tachocline with latitude, but Charbonneau et al. (1999) found a significant prolateness, with the tachocline (0.024 ± 0.004 )R ⊙ shallower at latitude 60° than at the equator. Basu and Antia (2003Jump To The Next Citation Point) also found a slightly thicker and shallower tachocline at high latitudes, and speculated that the tachocline location might be discontinuous at the latitude (around 30°) where the shear vanishes and changes sign.

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