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Chromospheric reflection layer for high-frequency acoustic wave

Chromospheric reflection layer for high-frequency acoustic wave. Takashi Sekii Solar Physics Division, NAOJ. Outline. Introduction on high-frequency oscillations What Jefferies et al (1997) did Our attempt with MDI data Ongoing effort with TON data SP data revisited.

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Chromospheric reflection layer for high-frequency acoustic wave

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  1. Chromospheric reflection layer for high-frequency acoustic wave Takashi Sekii Solar Physics Division, NAOJ

  2. Outline • Introduction on high-frequency oscillations • What Jefferies et al (1997) did • Our attempt with MDI data • Ongoing effort with TON data • SP data revisited The First Far Eastern Workshop on Helioseismology

  3. High-frequency oscillations • Jefferies et al 1988: peaks in power spectra above the acoustic cut-off frequency • Cannot be eigenmodes in the normal sense of the word, because the sun does not provide a cavity in this frequency range The First Far Eastern Workshop on Helioseismology

  4. The First Far Eastern Workshop on Helioseismology

  5. What are they? • Balmforth & Gough 1990: partial reflection at the transition layer • Kumar et al 1990: interference of the waves from a localized source (HIP) The First Far Eastern Workshop on Helioseismology

  6. Peak spacing and width better explained by Kumar’s model • For a quantitative account, partial reflection (not necessarily at the TL) is important too The First Far Eastern Workshop on Helioseismology

  7. South Pole Observation • Jefferies et al 1997 • South Pole, K line intensity • Time-distance diagram for l=125, ν=6.75mHz with Gaussian filtering (Δl=33, Δν=0.75mHz) The First Far Eastern Workshop on Helioseismology

  8. Second- and third-skip features found → partial reflection at the photosphere • Satellite features From Jefferies et al (1997) The First Far Eastern Workshop on Helioseismology

  9. What makes the satellite features? From Jefferies et al (1997) The First Far Eastern Workshop on Helioseismology

  10. Chromospheric reflection • Satellite features → another reflecting layer in the chromosphere • From the travel time differences, Jefferies et al estimated that the layer is ~1000km above the photosphere i.e. in the middle of the chromosphere • In fact, they are a bit more cautious about the actual wording and have not ruled out the TL solution The First Far Eastern Workshop on Helioseismology

  11. Wave reflection rates • Amplitude ratios between ridges give reflection rates • 13~22% (photosphere) • 3~9% (chromosphere) • Consistent with Kumar(1993) • JCD’s model used • Some version of mixing-length theory gives higher reflection rate due to steeper gradient The First Far Eastern Workshop on Helioseismology

  12. Atmospheric reflection • Why are the South Pole results important? • Photospheric reflection rate determined by thermal structure of the surface layer, which is (at least in part) determined by convective transport • If there is a reflection layer in the middle of the chromosphere, WHY? • Perhaps worth having another look with MDI data? The First Far Eastern Workshop on Helioseismology

  13. Analysis of MDI data • We had a look at MDI data • V, I (61d, #1564) & LD (63d,#1238) • m-averaged power spectra produced up to l=200 • calculate ACF of SHT • LD data seems the best suited • Geometrical effect observed The First Far Eastern Workshop on Helioseismology

  14. The First Far Eastern Workshop on Helioseismology

  15. The First Far Eastern Workshop on Helioseismology

  16. Geometrical factor • Observed signal strength depends on skip angle • Geometrical factor = Sum of the products of projection factor for all the visible pairs of points • l=18, ν~3mHz → skip angle ~ 90º The First Far Eastern Workshop on Helioseismology

  17. Intensity Velocity The First Far Eastern Workshop on Helioseismology

  18. The First Far Eastern Workshop on Helioseismology

  19. Were SP reflection rates correct? • Was the geometrical factor taken into account? Nobody remembers for sure • Inclusion of the geometrical factor would push up the reflection rates • Then they might become inconsistent with Kumar(1993) The First Far Eastern Workshop on Helioseismology

  20. MDI time-distance diagram • Power spectra converted to time-distance autocorrelation after Gaussian filtering in both l and ν • Parameters same as the SP analysis The First Far Eastern Workshop on Helioseismology

  21. The First Far Eastern Workshop on Helioseismology

  22. MDI reflection rate • Slices at fixed travel times made • Amplitudes compared and corrected by the geometrical factor • Apodization not taken into account • Satellite features unseparated from mains The First Far Eastern Workshop on Helioseismology

  23. The First Far Eastern Workshop on Helioseismology

  24. And the answer is… • Reflection rate ~ 10% in all the datasets after corrected for the geometrical factor • Lower than SP results (13-22%) • But it was supposed to be HIGHER The First Far Eastern Workshop on Helioseismology

  25. Implicatations? • Analysis simply too crude? (maybe) • Solar cycle effect? (unlikely) • SP data acquired during Dec 1994 to Jan 1995 • MDI V&I: Apr to Jun 1997, LD: May to Jul 1996 • Unseparated satellite features push down the number (chromospheric reflection rate lower) • No separation due to observing different lines? • Can we try TON data for comparison? The First Far Eastern Workshop on Helioseismology

  26. TON data • Remapped images • “remapped”= in solar coordinate • 1024×1024 • image flattening done (projection, limb darkening) • 1 minute cadence • No merging of data strings from different stations The First Far Eastern Workshop on Helioseismology

  27. % ls -1 tf970701 tf970702 ・・・ bb970709 ・・・ % cd tf970701 % ls -1 slcrem.1839380 slcrem.1839381 ・・・ 1024×1024 CCD image The First Far Eastern Workshop on Helioseismology

  28. Analysis procedure • one-day string by one-day string (about 10 hours) • pixel-by-pixel short time-scale detrending renormalization by 15-point running mean ⇒detrended images • cosine-bell apodization+SH transform ⇒SHT(spherical harmonic time-series) The First Far Eastern Workshop on Helioseismology

  29. long time-scale detrending+FFT of SHT ⇒power spectra • m-averaging+rotational splitting correction ⇒k-ω diagram • Fourier-Legendre transform ⇒time-distance autocorrelation • repeat the above for many other days and take the average The First Far Eastern Workshop on Helioseismology

  30. Apodization mask • A cosine-bell mask The First Far Eastern Workshop on Helioseismology

  31. Spherical-harmonic timeseries • Spherical harmonic transform • FFT in φ-direction after zero-padding • otherwise only even-m appears • equivalent with the direct projection • (associated-)Legendre transform in θ-direction The First Far Eastern Workshop on Helioseismology

  32. Daily k-ωpower maps(1) apodization: N/A long-term detrending: N/A rotation removal N/A The First Far Eastern Workshop on Helioseismology

  33. Daily k-ωpower maps(2) apodization: cosine-bell long-term detrending: N/A rotation removal N/A The First Far Eastern Workshop on Helioseismology

  34. Daily k-ωpower maps(3) apodization: cosine-bell long-term detrending: Legendre rotation removal N/A The First Far Eastern Workshop on Helioseismology

  35. Daily k-ωpower maps(4) apodization: cosine-bell long-term detrending: Legendre rotation removal by bins The First Far Eastern Workshop on Helioseismology

  36. Daily k-ωpower maps(4’) Linear scale! The First Far Eastern Workshop on Helioseismology

  37. Problems? • Noise level high even in the 5-min band, and there is some structure • Broad peak in sub-1mHz region (also in SP data) The First Far Eastern Workshop on Helioseismology

  38. What’s wrong? • Sasha Serebryanskiy produced cleaner power • Should the short-term detrending be subtractive? • Apodization? • SHT? The First Far Eastern Workshop on Helioseismology

  39. Daily k-ωpower maps(4”) subtractive detrending The First Far Eastern Workshop on Helioseismology

  40. Daily k-ωpower maps(4”’) different apodization The First Far Eastern Workshop on Helioseismology

  41. Spherical harmonic transform • Leakage for l=10, m=3 • They make sense The First Far Eastern Workshop on Helioseismology

  42. AS says: analysis without GRASP has led to a noisy power diagram • is GRASP doing something clever? • Well…let us do the averaging anyway The First Far Eastern Workshop on Helioseismology

  43. The First Far Eastern Workshop on Helioseismology

  44. SP data • The original SP data obtained • 18 days, 42-second cadence • l=0-250 • Time-distance ACF produced The First Far Eastern Workshop on Helioseismology

  45. SP t-d ACF at 6.75mHz • The double-ridge structure non-existent The First Far Eastern Workshop on Helioseismology

  46. SP t-d ACF at 6.125mHz • Voila! The First Far Eastern Workshop on Helioseismology

  47. Reflection rates? • 30/60-degree pair • requires double-gaussian fitting • composite rate ~10% The First Far Eastern Workshop on Helioseismology

  48. 40/80-degree pair • Composite reflection rate between the first & the second ridge ~12% • But, from the second & third • Main ~ 40%(!) • Satellite ~ 75%(!) The First Far Eastern Workshop on Helioseismology

  49. 45/90-degree pair • Composite reflection rate between the first & the second ridge ~14% • But, from the second & third • Main ~ 26%(!) • Satellite ~ 50%(!) The First Far Eastern Workshop on Helioseismology

  50. Then what about MDI? • I did look at different frequencies before without any success, but this time… The First Far Eastern Workshop on Helioseismology

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