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\section*{ \large\bf Diagnosis of the Structure and 
Dynamics at the Base of the Convection Zone}

\noindent
{\bf Lead Investigator:} A.G. Kosovichev\\
{\bf Other Team Members:} T.L. Duvall, P. Giles, D.O. Gough, G. Roumeliotis, 
T. Sekii\\

\noindent
{\large\bf Abstract/Technical Summary}\\
Determine properties of convective overshoot and the transition layer
at the lower boundary of the convection zone, and find the shape
of the boundary, and investigate their variations with time 
from MDI Medium-l data by local smoothness map methods
complemented by the 3D tomographic imaging technique.

\subsection*{Investigation Plan}

The structure of the transition region between the zones of radiative and
convective energy transport is of particular interest in  solar physics and
astrophysics. It is generally
expected that convective elements penetrate into  the convectively-stable
radiative zone forming a zone of convective overshoot and contributing
to the development of turbulence and mixing in the upper radiative
zone. This effect might be responsible for the observed deficit of lithium and
beryllium in the Sun. The zone of convective overshoot is also a place
with  strong radial gradient of angular velocity, and therefore is considered
in  modern theories as a place where the solar dynamo 
might operate (e.g. Parker, 1994).
Within this layer,
the toroidal magnetic flux that appears at the surface in various 
forms of solar activity is generated from the radial component of 
the poloidal field. The toroidal flux is believed to be
mainly accumulated in a thin layer just beneath the convection zone 
because convection would quickly destroy the toroidal flux
if the layer were widely extended into the convection zone. 
However, as recently argued by R\"udiger and Brandenburg (1995), 
this layer cannot be very thin because the period of the solar cycle,
which depends on the turbulent magnetic diffusion time through the layer, 
would be too short. They estimated the thickness to be at least
 35 Mm $\approx \frac{1}{2}H_p$, where $R$ is the
solar radius and $H_p$ is the local pressure scale height.

Estimates of the thickness and precise location of the transition 
layer by standard helioseismic techniques from rotational 
splitting of oscillation p modes are rather uncertain. Attempts to resolve 
the layer under global smoothness constraints lead to either an oversmoothed
angular velocity profile or to spurious oscillations around the 
transition layer.


We propose a complex study of radial and latitudinal variations of the structure
and rotation in the transition region between the radiative and convection zones
by using local smoothness map methods complemented by the helioseismic
tomography technique.

The investigation plan is:
\begin{enumerate}
\item
investigate properties of the transition region between the radiative and
convective zones by studying the variations of the parameter of convective
stability, $A$, using local smoothness map techniques;
\item
compare the results with theoretical models
based on non-local theories of convection (e.g. Schmitt et al, 1984) and on
direct numerical simulations (Hurlburt, et al, 1994);
\item
study of the role of the overshoot in the evolution of the chemical composition of
the upper radiative zone;
\item
study the latitudinal dependence of the depth of the convection zone;
\item 
study the gradient of the azimuthal flow velocity in the transition zone;
\item
investigate possibilities for 3D tomographic imaging of 3D structure 
and flows in the transition region.
\end {enumerate}
\begin{thebibliography}
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extent of overshoot below the solar convection zone, {\it Mon. Not. of the Royal Astron. Soc.},
{\bf 269}, 1137-1144.
\bibitem{} Duvall, T.L., Jr, Jefferies, \& Harvey, J.W., 1995, Mapping wave speed
in the outer convection zone, {\it Bull. Am. Astr. Soc.}, {\bf 27}, 950
\bibitem{} Gough, D.O.,  Kosovichev, A.G., Sekii, T., Libbrecht, K. \&
Woodard, M., 1993,
Seismic evidence of modulation of
the structure and angular
 velocity of the sun
associated with the solar cycle,
in: Proc. IAU Colloquium 137 {\it Inside the stars},
the Conference Series of the Astronomical Society of the Pacific,
eds. A.Baglin and W.Weiss,  93-96.
\bibitem{} Gough, D.O. \& Kosovichev, A.G. 1995, An attempt to measure latitudinal 
variation of the depth of the convection zone, in: Proc. 4th SOHO Workshop, 
{\it Helioseismology}, ESA SP-376, ESTEC, Noordwijk
\bibitem{} Hurlburt, N.E., Toomre, J., Massaguer, J.M. \& Zahn, J.-P.,
1994, Penetration below a convective zone,
{\it Astrophys. J.}, {\bf 421}, 245-260.
\bibitem{} Kosovichev, A.G., 1988, 
Determination of the internal rotation of the Sun from
the frequency splitting of acoustic modes, 
{\it Bull. Crimean Astrophys. Obs.}, {\bf 80},  167-179.
\bibitem{} Kosovichev, A.G., 1994, 
Helioseismic evidences for mixing in the radiative interior,
in: Proc. Seventh Europ. Meeting on Solar Phys. `Advances in Solar Physics',
Catania, 1993, {\it Lect. Not. Phys.}, {\bf 432}, 47 -- 52
 \bibitem {} Parker, E.N., 1993, A solar dynamo surface wave at the 
interface between convection and nonuniform rotation, {\it Astrophys. J.},
{\bf 408}, 707-719.
\bibitem{} R\"udiger, G. and Brandenburg, A. 1995, 
A solar dynamo in the overshoot layer: cycle period
       and butterfly diagram{\it Astron. Astrophys.}, {\bf 296}, 557.
\bibitem {} Schmitt, J.H.M.M., Rosner, R., \& Bohn, H.U., 1984, 
The overshoot region at the bottom of the solar convection zone,
{\it Astrophys. J.}, {\bf 282}, 316-329.
 \bibitem {} Skaley D. \& Stix M., 1991, 
The overshoot layer at the base of the solar 
      convection zone, {\it Astron. Astrophys.}, {\bf 241}, 227
\bibitem{} Spiegel, E.A. \& Zahn, J.-P., 1992, The solar tachocline, 
{\it Astron. \& Astrophys.},
{\bf 265}, 106
\end{thebibliography}{}
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