HELIOSEISMIC CONSTRAINTS ON THE GRADIENT OF ANGULAR VELOCITY AT THE BASE OF THE SOLAR CONVECTION ZONE

ABSTRACTThe layer of transition from the nearly rigid rotation of the radiative interior to the latitudinal differentialrotation of the convection zone plays a significant role in the internal dynamics of the Sun. Using rotationalsplitting coefficients of the p-mode frequencies, obtained during 1986-1990 at the Big Bear Solar Observatory,we have found that the thickness of the transitional layer is 0.09 _+ 0.04 solar radii (63 _+28 Mm), and that mostof the transition occurs beneath the adiabatically stratified part of the convection zone, as suggested by thedynamo theories of the 22 yr solar activity cycle.Subject headings., convection -- methods: data analysis -- Sun: activity -- Sun: interior -- Sun: oscillations --Sun: rotation 1. INTRODUfTION Helioseismology has established the existence of a layer ofstrong gradients of angular velocity at the base of the solarconvection zone (e.g., Brown et al. 1989; Goode et al. 1991;Tomczyk, Schou, & Thompson 1995). This layer separates theconvection zone exhibiting strong latitudinal differential rota-tion from the radiative interior rotating almost rigidly. Turbu-lence generated in the layer is likely to mix material in theupper radiative zone, resulting in the observed deficit of Li andBe (see, e.g., Zahn 19921. However, the theoretical estimatesof the precise location and the thickness of the transition layer("tachocline") depend on details of turbulent energy andmomentum transport, and are uncertain (Spiegel & Zahn1992).Perhaps of the greatest interest, the transition layer is themost likely place for the solar dynamo (see, e.g., Weiss 1994).Within this layer, the toroidal magnetic flux that appears at thesurface in various forms of solar activity is generated from theradial component of the poloidal field (Brandcrburg 1994).The toroidal flux is believed to bc mainly accumulated in a thinlayer just beneath the convection zone because convectionwould quickly destroy the toroidal flux if the layer were widelyextended into the convection zone. However, as recentlyargued by Riidiger & Brandenburg (1995), this layer cannot bevery thin because the period of the solar cycle, which dependson the turbulent magnetic diffusion time through the layer,would bc too short. They estimated the thickness to be at least0.05R _ 35 Mm _TH,,, where R is the solar radius and//,, isthe local pressure scale height.Estimates of the thickness and precise location of thetransition layer by standard helioseismic inversion techniquesfrom rotational splitting of oscillation p-modes are ratheruncertain. Attempts to resolve the layer under global smooth-ness constraints lead to either an oversmoothed angularvelocity profile or to spurious oscillations around the transitionlayer (cf. Goode ct al. 1991). Thompson (19901 has demon-strated that even if the transition were discontinuous theformal helioscismic inversions still produce a broad smoothregion. To overcome these difficulties, Goode et al. (1991)assumed that the transition layer is, in fact, discontinuous andL61found that their model fits the helioseismic data best when thediscontinuity coincides with the base of the convection zone.In this Letter, we demonstrate that the discontinuous model ofsolar rotation is not the best fit to the data and that a modelwith a transitional layer of finite thickness (_0.09 + 0.04R)fits the data more accurately than the discontinuous model.The midpoint of this layer is found at 0.692 _+ 0.005R, slightlybelow the convection zone.