Global Rotation

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Global Rotation

• Rachel Howe, NSO

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How deep is the tachocline, how wide is the shear?

• With almost a whole cycle of observations from
  GONG and MDI, we can look at the stationary part
  of the rotation.
• Forward-modeling exercises help to establish
  robustness of results.

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The Questions

• How well can we measure the near-surface shear?
• Is the slant in the convection-zone rotation
  real?
• How well can we measure the shape of the
  tachocline?

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The Data

• 106 overlapping 108-day sets from GONG, covering
  10.5 years 1995-2006.
• 0?l150, coefficients up to a16
• 49 72-day sets from MDI, starting May 1996.
• 0l300, coefficients up to a36

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Analysis

• Fit 11yr sinusoid to each coefficient
• Use stationary part of fit
• 2dRLS and 2dOLA inversions
• Convolve averaging kernels with test profiles to
  simulate inversions.

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Analysis the inversion problem
Kernel
Averaging Kernel
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Generating Artificial Data
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Generating Artificial Data

• The long way around
• Use Eq. 1 to calculate di from the desired W.
• Add ei with the correct s.
• Do the inversion.
• Repeat for each realization.
• The shortcut
• Calculate the K once for a grid of (r,q).
• Convolve with each W to get noise-free profile
• Add in noise.

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Generating Artificial Data
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Coefficients
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Results profiles
GONG
MDI
6,2 RLS
7,3 RLS
OLA
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Results profiles
GONG
MDI
7,3 RLS
6,2 RLS
OLA
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Global Rotation Profile

• Dashed lines inclined at 25 degrees to rotation
  axis.

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Slope of Isorotation Contours

• Dashed line shows slope of radial lines.
• Gilman Howe, 2003 (BB proceedings).

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Results Synthetic Profiles
GONG
MDI
6,2 RLS
7,3 RLS
OLA
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Results Synthetic Profiles
GONG
MDI
6,2 RLS
7,3 RLS
OLA
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Results Synthetic Profiles
GONG
MDI
6,2 RLS
7,3 RLS
OLA
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Results Synthetic Profiles
GONG
MDI
6,2 RLS
7,3 RLS
OLA
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Discussion

• Slope in convection zone looks robust
• Near-surface shear already resolved in single-set
  data
• But reversal at high latitudes may be MDI(CA)
  artefact.
• Some sensitivity to different tachcocline
  thickness.

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Calibrating the Tachocline

• Charbonneau et al (1999) used fits with error
  function model convolved with 1d averaging kernel
• Tried this using OLA inversions, checking against
  synthetic profiles.

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Fit Results (MDI OLA)
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But

• We know rotation isnt quite depth-independent in
  convection zone.
• What does technique do with tilted-contour model
  and no thickness?

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Aha!
Fits to tilted-contour model
Fits to real data
Fits to dashed-contour model
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So

• Try fitting model with slope in convection zone
  taken into account, combined with error-function
  tachocline.

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And we get this
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From which we conclude

• Deconvolution fitting does not work perfectly.
• Forward modeling is only useful if the model is
  appropriate!
• The tachocline could be quite thin,
  (0.030.04)Rsun once the slanted rotation
  contours are taken into account.
• However, this still needs more study.