Ringdiagram Frequency Shifts, Again

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Ring-diagram Frequency Shifts, Again

• Rachel Howe
• December 2005

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Synopsis

• The Data
• Fitting the frequency shifts
• Geometric Variations
• Year-to-year changes (MDI)
• Seasonal changes (GONG)
• MDI vs GONG
• Active-region changes
• Asymptotic fitting

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The Data

• Standard 15-degree dense pack fits
• MDI dynamics runs, 1996-2004
• GONG, 2001 August 2004 Oct
• Magnetograms from MDI

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Fitting the frequency shifts

• Express frequencies as nn0a1rxa2rx2a3rya4ry2
  a5Ba6B2
• Where
• rx, ry are fractional distances from disk
  center,
• B is magnetic index (mean unsigned field strength
  in patch).
• Repeat fit for every patch, one CR at a time.

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Geometric terms, MDI
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Comments on MDI geometric terms

• Geometric terms are mostly quite small only a
  few mHz across the disk.
• They change from year to year.
• Some years, limb has higher frequency. than disk
  center, some years the reverse.
• They vary with both wave number and frequency, so
  could mimic structural changes.

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Geometric terms -- GONG
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Comments on GONG geometric terms

• No obvious year-to-year changes
• Quite marked seasonal variations
• For dn/dy, lowest frequencies vary in phase with
  semidiameter, higher with B0. Why?

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Geometric terms for CR1988
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Comments on CR1988 geometric terms

• Note structure in MDI dn/dy not seen in GONG.
• GONG terms go wild at high-k ends of ridges.

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Magnetic Terms

• MDI (top)
• GONG (bottom)
• Color-coded by year

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Comments on magnetic terms

• 1996, 1997 look different.
• Weak activity in those years, so quadratic fit
  picks up downshifted frequency for high-frequency
  modes in weak regions.

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Asymptotic frequency fitting

• Frequency differences from model can be expressed
  as
• H1, H2 can be obtained from cubic spline fitting

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Asymptotic fitting with ring frequencies

• For each CR, fit to obtain n0 and coefficients.
• Try asymptotic fit on n0
• Compare with global frequencies (also with
  magnetic term removed).

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Scaled frequency differences

• Scaled frequency differences for global (filled)
  and local (open) modes.

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H1 term

• Crosses global modes
• Open circles local modes
• Filled circles fit to local

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Does H1 vary with activity?

• Do asymptotic fit for each patch in the rotation
  after subtracting geometric terms
• Do regression with B as independent variable, H1
  as independent variable, for each (n,k).

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Dependence of H1 term on magnetic index

• GONG crosses
• MDI -- circles

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Comments on spline fitting

• There are obvious discontinuities between local
  and global frequencies
• There is structure in the local frequency
  differences that does not fit the two-term model
• There appears to be some activity-dependence in
  the depth-dependent H1 term.
• Is it real? Or is it an artifact?

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Next Step?

• Some authors have used extra, n/L dependent terms
  for the surface part at high degree.
• So far, we have been unable to make this work
  properly, but this may not be an intrinsic
  problem.