Chromospheric reflection layer for high-frequency acoustic wave
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Transcript of Chromospheric reflection layer for high-frequency acoustic wave
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Chromospheric reflection layer for high-frequency acoustic wave
Takashi Sekii
Solar Physics Division, NAOJ
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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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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
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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)
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• Peak spacing and width better explained by Kumar’s model
• For a quantitative account, partial reflection (not necessarily at the TL) is important too
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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)
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From Jefferies et al (1997)
• Second- and third-skip features found → partial reflection at the photosphere
• Satellite features
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• What makes the satellite features?
From Jefferies et al (1997)
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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
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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
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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?
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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
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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
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Intensity
Velocity
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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)
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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
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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
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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%
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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?
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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
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% ls -1tf970701tf970702・・・bb970709・・・% cd tf970701% ls -1slcrem.1839380slcrem.1839381・・・
1024×1024 CCD image
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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)
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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
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Apodization mask
• A cosine-bell mask
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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
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Daily k-ω power maps(1)
apodization: N/A
long-term detrending: N/A
rotation removal
N/A
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Daily k-ω power maps(2)
apodization: cosine-bell
long-term detrending: N/A
rotation removal
N/A
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Daily k-ω power maps(3)
apodization: cosine-bell
long-term detrending: Legendre
rotation removal
N/A
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Daily k-ω power maps(4)
apodization: cosine-bell
long-term detrending: Legendre
rotation removal
by bins
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Daily k-ω power maps(4’)
Linear scale!
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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)
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What’s wrong?
• Sasha Serebryanskiy produced cleaner power
• Should the short-term detrending be subtractive?
• Apodization?
• SHT?
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Daily k-ω power maps(4”)
subtractive detrending
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Daily k-ω power maps(4”’)
different apodization
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Spherical harmonic transform
• Leakage for l=10, m=3
• They make sense
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• AS says: analysis without GRASP has led to a noisy power diagram– is GRASP doing something clever?
• Well…let us do the averaging anyway
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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
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SP t-d ACF at 6.125mHz
• Voila!
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Reflection rates?
• 30/60-degree pair– requires double-gauss
ian fitting– composite rate ~10%
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• 40/80-degree pair– Composite reflection rate between the first & the
second ridge ~12%– But, from the second & third
• Main ~ 40%(!)
• Satellite ~ 75%(!)
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• 45/90-degree pair– Composite reflection rate between the first & the
second ridge ~14%– But, from the second & third
• Main ~ 26%(!)
• Satellite ~ 50%(!)
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Then what about MDI?
• I did look at different frequencies before without any success, but this time…
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MDI reflection rates?
• After geometrical correction:– 10% for the main ridge– ~50%(!) for the satellite
ridge
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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
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• Reflection-rate measurement still requires careful check– High reflection rate at large angular distances may
be due to over-compensation