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
  Kumars 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 l125, ?6.75mHz with
  Gaussian filtering (?l33, ??0.75mHz)

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• Second- and third-skip features found ?
  partial reflection at the photosphere
• Satellite features

From Jefferies et al (1997)
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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
  actual wording and have not ruled out the TL
  solution

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Wave reflection rates

• Amplitude ratios between ridges give reflection
  rates
• 1322 (photosphere)
• 39 (chromosphere)
• Consistent with Kumar(1993)
• JCDs 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 l200
• 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
• l18, ?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 ?
• 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 VI 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
• 10241024
• image flattening done (projection, limb
  darkening)
• 1 minute cadence
• No merging of data strings from different
  stations

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• ls -1
• tf970701
• tf970702
• bb970709
• cd tf970701
• ls -1
• slcrem.1839380
• slcrem.1839381

10241024 CCD image
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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 apodizationSH transform
• ?SHT (spherical harmonic time-series)

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• long time-scale detrendingFFT of SHT
• ?power spectra
• m-averagingrotational splitting correction
• ?k-? diagram
• Fourier-Legendre transform
• ?time-distance autocorrelation
• 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 f-direction after zero-padding
• otherwise only even-m appears
• equivalent with the direct projection
• (associated-)Legendre transform in ?-direction

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Daily k-? power maps(1)

• apodization N/A
• long-term detrending N/A
• rotation removal
• N/A

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Daily k-? power maps(2)

• apodization cosine-bell
• long-term detrending N/A
• rotation removal
• N/A

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Daily k-? power maps(3)

• apodization cosine-bell
• long-term detrending Legendre
• rotation removal
• N/A

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Daily k-? power maps(4)

• apodization cosine-bell
• long-term detrending Legendre
• rotation removal
• by bins

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Daily k-? 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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Whats wrong?

• Sasha Serebryanskiy produced cleaner power
• Should the short-term detrending be subtractive?
• Apodization?
• SHT?

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Daily k-? power maps(4)

• subtractive detrending

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Daily k-? power maps(4)

• different apodization

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Spherical harmonic transform

• Leakage for l10, m3
• They make sense

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• AS says analysis without GRASP has led to a
  noisy power diagram
• is GRASP doing something clever?
• Welllet us do the averaging anyway

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SP data

• The original SP data obtained
• 18 days, 42-second cadence
• l0-250
• 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-gaussian 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

• Im 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

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• Reflection-rate measurement still requires
  careful check
• High reflection rate at large angular distances
  may be due to over-compensation