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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. - PowerPoint PPT Presentation
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Chromospheric reflection layer for high-frequency acoustic wave
Takashi Sekii
Solar Physics Division, NAOJ
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
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
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
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
• 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
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
From Jefferies et al (1997)
• Second- and third-skip features found → partial reflection at the photosphere
• Satellite features
The First Far Eastern Workshop on Helioseismology
• What makes the satellite features?
From Jefferies et al (1997)
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 actua
l wording and have not ruled out the TL solution
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
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?
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
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
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
Intensity
Velocity
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
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
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
The First Far Eastern Workshop on Helioseismology
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
The First Far Eastern Workshop on Helioseismology
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
V I LD
70/140 9.7% 9.4% 10.3%
80/160 9.1% 9.0% 10.2%
90/180 9.4% 8.1% 9.8%
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?
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
The First Far Eastern Workshop on Helioseismology
% ls -1tf970701tf970702・・・bb970709・・・% cd tf970701% ls -1slcrem.1839380slcrem.1839381・・・
1024×1024 CCD image
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)
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
The First Far Eastern Workshop on Helioseismology
Apodization mask
• A cosine-bell mask
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
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
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
The First Far Eastern Workshop on Helioseismology
Daily k-ω power maps(3)
apodization: cosine-bell
long-term detrending: Legendre
rotation removal
N/A
The First Far Eastern Workshop on Helioseismology
Daily k-ω power maps(4)
apodization: cosine-bell
long-term detrending: Legendre
rotation removal
by bins
The First Far Eastern Workshop on Helioseismology
Daily k-ω power maps(4’)
Linear scale!
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)
The First Far Eastern Workshop on Helioseismology
What’s wrong?
• Sasha Serebryanskiy produced cleaner power
• Should the short-term detrending be subtractive?
• Apodization?
• SHT?
The First Far Eastern Workshop on Helioseismology
Daily k-ω power maps(4”)
subtractive detrending
The First Far Eastern Workshop on Helioseismology
Daily k-ω power maps(4”’)
different apodization
The First Far Eastern Workshop on Helioseismology
Spherical harmonic transform
• Leakage for l=10, m=3
• They make sense
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
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
SP data
• The original SP data obtained– 18 days, 42-second
cadence– l=0-250
• Time-distance ACF produced
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SP t-d ACF at 6.75mHz
• The double-ridge structure non-existent
The First Far Eastern Workshop on Helioseismology
SP t-d ACF at 6.125mHz
• Voila!
The First Far Eastern Workshop on Helioseismology
Reflection rates?
• 30/60-degree pair– requires double-gauss
ian fitting– composite rate ~10%
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%(!)
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%(!)
The First Far Eastern Workshop on Helioseismology
Then what about MDI?
• I did look at different frequencies before without any success, but this time…
The First Far Eastern Workshop on Helioseismology
The First Far Eastern Workshop on Helioseismology
MDI reflection rates?
• After geometrical correction:– 10% for the main ridge– ~50%(!) for the satellite
ridge
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 powe
r leaked into chromosphere
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