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Ring-diagram Frequency Shifts, Again

Ring-diagram Frequency Shifts, Again. Rachel Howe December 2005. 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. The Data. Standard 15-degree dense pack fits

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Ring-diagram Frequency Shifts, Again

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  1. Ring-diagram Frequency Shifts, Again Rachel Howe December 2005 Rachel Howe, December 2005

  2. 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 Rachel Howe, December 2005

  3. The Data • Standard 15-degree dense pack fits • MDI dynamics runs, 1996-2004 • GONG+, 2001 August – 2004 Oct • Magnetograms from MDI Rachel Howe, December 2005

  4. Fitting the frequency shifts • Express frequencies as n=n0+a1rx+a2rx2+a3ry+a4ry2+a5B+a6B2 • 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. Rachel Howe, December 2005

  5. Geometric terms, MDI Rachel Howe, December 2005

  6. 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. Rachel Howe, December 2005

  7. Geometric terms -- GONG Rachel Howe, December 2005

  8. 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? Rachel Howe, December 2005

  9. Geometric terms for CR1988 Rachel Howe, December 2005

  10. 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. Rachel Howe, December 2005

  11. Magnetic Terms • MDI (top) • GONG (bottom) • Color-coded by year Rachel Howe, December 2005

  12. 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. Rachel Howe, December 2005

  13. Asymptotic frequency fitting • Frequency differences from model can be expressed as • H1, H2 can be obtained from cubic spline fitting Rachel Howe, December 2005

  14. 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). Rachel Howe, December 2005

  15. Scaled frequency differences • Scaled frequency differences for global (filled) and local (open) modes. Rachel Howe, December 2005

  16. H1 term • Crosses – global modes • Open circles – local modes • Filled circles – fit to local Rachel Howe, December 2005

  17. 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). Rachel Howe, December 2005

  18. Dependence of H1 term on magnetic index • GONG – crosses • MDI -- circles Rachel Howe, December 2005

  19. 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? Rachel Howe, December 2005

  20. 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. Rachel Howe, December 2005

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