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

2. The First Far Eastern Workshop on Helioseismology 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

3. The First Far Eastern Workshop on Helioseismology 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

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)

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

7. The First Far Eastern Workshop on Helioseismology 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)

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

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

10. The First Far Eastern Workshop on Helioseismology 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

11. The First Far Eastern Workshop on Helioseismology 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

12. The First Far Eastern Workshop on Helioseismology 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?

13. The First Far Eastern Workshop on Helioseismology 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

14. 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

17. The First Far Eastern Workshop on Helioseismology Intensity Velocity

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)

20. The First Far Eastern Workshop on Helioseismology 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

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

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 VILD 70/1409.7%9.4%10.3% 80/1609.1%9.0%10.2% 90/1809.4%8.1%9.8%

25. The First Far Eastern Workshop on Helioseismology 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?

26. The First Far Eastern Workshop on Helioseismology 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

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

28. The First Far Eastern Workshop on Helioseismology Analysis procedure 1.one-day string by one-day string (about 10 hours) 2.pixel-by-pixel short time-scale detrending renormalization by 15-point running mean ⇒ detrended images 3.cosine-bell apodization+SH transform ⇒ SHT (spherical harmonic time-series)

29. The First Far Eastern Workshop on Helioseismology 4.long time-scale detrending+FFT of SHT ⇒ power spectra 5.m-averaging+rotational splitting correction ⇒ k-ω diagram 6.Fourier-Legendre transform ⇒ time-distance autocorrelation 7.repeat the above for many other days and take the average

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

31. The First Far Eastern Workshop on Helioseismology 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

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

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

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

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

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

37. The First Far Eastern Workshop on Helioseismology 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)

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

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

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

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

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

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

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

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

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

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

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

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

51. The First Far Eastern Workshop on Helioseismology

52. MDI reflection rates? After geometrical correction: –10% for the main ridge –~50%(!) for the satellite ridge

53. The First Far Eastern Workshop on Helioseismology So, what is the situation now I’m still digesting all this myself! Still no distinct double-ridge structure around originally reported 6.75mHz We do find them around 6.125mHz (and very likely in other frequencies) both in SP and in MDI –Lower frequency implies higher rate of wave power leaked into chromosphere

54. The First Far Eastern Workshop on Helioseismology Reflection-rate measurement still requires careful check –High reflection rate at large angular distances may be due to over-compensation