Issues related to dynamo, meridional circulation and diffusion at tachocline interface

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Issues related to dynamo, meridional circulation
and diffusion at tachocline interface

• Peter A. Gilman, Mausumi Dikpati
• High Altitude Observatory, NCAR

March 2005
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Topics

• Problems with interface dynamo for the Sun
  (Mausumi)
• Boundary Layers (Peter)
• Diffusion of toroidal fields into interior
  (Peter)

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Peter Gilman, Mausumi dikpati

March 2005
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Problems with interface dynamo for the Sun
Shaded shell thin layer where temp gradient
is same as both radiative and
adiabatic gradient
Bounded on top by level where
temperature gradient adiabatic
value only (Schwarzschild boundary
r(sb) ) and on bottom by radiative
zone boundary r(rz) Dashed
line is helioseismically determined base
of solar convection zone where
temperature gradient changes
from adiabatic to strongly
subadiabatic
M. Dikpati, P. A. Gilman K. B. MacGregor, 2005
(submitted)
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Location of the tachocline
Most of tachocline is in the strongly
subadiabatic radiative interior (extending below
the gray shade). Magnetic diffusivity declines
toward molecular value in radiative
interior. From Garaud (1999) skin-depth of
poloidal field generated above is no more than a
few hundredths of a percent of solar
radius. Therefore may not be available for
shearing by most of the Tachocline. So can a
pure interface dynamo work for the Sun?
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Assumptions for interface dynamo calculation
(a) Magnetic diffusivity with depth
(b) alpha-effect and differential rotation
with depth at 45-degrees latitude
(c) alpha-effect and differential rotation with
latitude at interface
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Results

• Interface dynamo with
• tachocline

(b) Interface dynamo without tachocline
( c) Interface dynamo without tachocline, but
with meridional circulation
(d) Dynamo with both interface and
Babcock-Leighton alpha-effects and without
tachocline but with meridional circulation
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Penetration of Meridional Circulation below the
Convection Zone

• Model
• HD, imposed, steady meridional circulation at
  top of slab or shell
• (non-rotating or rotating)
• Thin shell, Boussinesq, applied to tachocline
  above
• Vertical shear does not change result
  qualitatively
• Latitudinal force balance coriolis, pressure
  gradient, vertical
• diffusion
• Vertical force balance hydrostatic
• Reduces to 6th order PDE for latitudinal flow
• In which

interior rotation rate eddy diffusivities of
momentum, entropy gravity coefficient of
volume expansion departure from adiabatic
gradient
(Gilman and Miesch (ApJ 611, 568, 2004))
Peter Gilman

March 2005
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Penetration of Meridional Circulation below the
Convection Zone (continued)

• Can get separable solution of form
• Yields bicubic
• Can take separate limits of small to
  get pure cases
• Small leads to classical Ekman layer
• Small leads to non-rotating, stratified
  diffusion layer

(Gilman and Miesch (ApJ 611, 568, 2004))
Peter Gilman

March 2005
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Penetration of Meridional Circulation below the
Convection Zone (continued)

• Spherical case similar
• Dimensional boundary layer thickness
• !
• Very insensitive to v, values
• If compared to overshoot and radiative
  tachoclines, get
• overshoot
• radiative
• Ekman layer thickness
• overshoot 140km
• radiative
• Therefore no significant penetration below
  overshoot lower boundary, or therefore below

(Gilman and Miesch (ApJ 611, 568, 2004))
Peter Gilman

March 2005
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Diffusion of toroidal fields into interior

• Could solar cycle dynamo be a source
• for deep interior magnetic fields?
• Noticed flux-transport dynamo model
• diffusing toroidal field into low-diffusivity
• domain below tachocline. Artifact, or reality?
• Long-term transient or permanent?
• Nonreversing fields, but structure dependent
• on initial phase of cycle when diffusion starts?

Dikpati Gilman (in preparation)