Ring-diagram Frequency Shifts, Again Rachel Howe December 2005 02/13/20 Rachel Howe, December 2005 1 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 02/13/20 Rachel Howe, December 2005 2
The Data Standard 15-degree dense pack fits MDI dynamics runs, 1996-2004 GONG+, 2001 August 2004 Oct Magnetograms from MDI 02/13/20
Rachel Howe, December 2005 3 Fitting the frequency shifts Express frequencies as =0+a1x+a2x2+a3y+a4y2+a5B+a6B2 Where x, y 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. 02/13/20 Rachel Howe, December 2005 4 Geometric terms, MDI 02/13/20 Rachel Howe, December 2005
5 Comments on MDI geometric terms Geometric terms are mostly quite small only a few Hz 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. 02/13/20
Rachel Howe, December 2005 6 Geometric terms -- GONG 02/13/20 Rachel Howe, December 2005 7
Comments on GONG geometric terms No obvious year-to-year changes Quite marked seasonal variations For d/dydy, lowest frequencies vary in phase with semidiameter, higher with B0. Why? 02/13/20 Rachel Howe, December 2005 8
Geometric terms for CR1988 02/13/20 Rachel Howe, December 2005 9 Comments on CR1988 geometric terms Note structure in MDI d/dy not seen in GONG.
GONG terms go wild at high-k ends of ridges. 02/13/20 Rachel Howe, December 2005 10 Magnetic Terms MDI (top) GONG (bottom)
Color-coded by year 02/13/20 Rachel Howe, December 2005 11 Comments on magnetic terms 1996, 1997 look different. Weak activity in those years, so quadratic fit picks up downshifted frequency for highfrequency modes in weak regions.
02/13/20 Rachel Howe, December 2005 12 Asymptotic frequency fitting Frequency differences from model can be expressed as H1, H2 can be obtained from cubic spline fitting
02/13/20 Rachel Howe, December 2005 13 Asymptotic fitting with ring frequencies For each CR, fit to obtain 0 and coefficients. Try asymptotic fit on 0 Compare with global frequencies (also with magnetic term removed).
02/13/20 Rachel Howe, December 2005 14 Scaled frequency differences Scaled frequency differences for global (filled) and
local (open) modes. 02/13/20 Rachel Howe, December 2005 15 H1 term Crosses global modes Open circles
local modes Filled circles fit to local 02/13/20 Rachel Howe, December 2005 16 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). 02/13/20 Rachel Howe, December 2005 17 Dependence of H1 term on magnetic index GONG
crosses MDI -circles 02/13/20 Rachel Howe, December 2005 18 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 activitydependence in the depth-dependent H1 term. Is it real? Or is it an artifact? 02/13/20 Rachel Howe, December 2005 19 Next Step? Some authors have used extra, /dyL
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. 02/13/20 Rachel Howe, December 2005 20