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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.

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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
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
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

what are they
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

slide6
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
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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slide8
Second- and third-skip features found → partial reflection at the photosphere
  • Satellite features

From Jefferies et al (1997)

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slide9
What makes the satellite features?

From Jefferies et al (1997)

The First Far Eastern Workshop on Helioseismology

chromospheric reflection
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

wave reflection rates
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
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
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

geometrical factor
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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slide17

Intensity

Velocity

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were sp reflection rates correct
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
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
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
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

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implicatations
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
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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slide27
% ls -1

tf970701

tf970702

・・・

bb970709

・・・

% cd tf970701

% ls -1

slcrem.1839380

slcrem.1839381

・・・

1024×1024 CCD image

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analysis procedure
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)

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slide29
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

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apodization mask
Apodization mask
  • A cosine-bell mask

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spherical harmonic timeseries
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 power maps 1
Daily k-ωpower maps(1)

apodization: N/A

long-term detrending: N/A

rotation removal

N/A

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daily k power maps 2
Daily k-ωpower maps(2)

apodization: cosine-bell

long-term detrending: N/A

rotation removal

N/A

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daily k power maps 3
Daily k-ωpower maps(3)

apodization: cosine-bell

long-term detrending: Legendre

rotation removal

N/A

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daily k power maps 4
Daily k-ωpower maps(4)

apodization: cosine-bell

long-term detrending: Legendre

rotation removal

by bins

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daily k power maps 41
Daily k-ωpower maps(4’)

Linear scale!

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problems
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
What’s wrong?
  • Sasha Serebryanskiy produced cleaner power
  • Should the short-term detrending be subtractive?
  • Apodization?
  • SHT?

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daily k power maps 42
Daily k-ωpower maps(4”)

subtractive detrending

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daily k power maps 43
Daily k-ωpower maps(4”’)

different apodization

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spherical harmonic transform
Spherical harmonic transform
  • Leakage for l=10, m=3
  • They make sense

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slide42
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
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
SP t-d ACF at 6.75mHz
  • The double-ridge structure non-existent

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sp t d acf at 6 125mhz
SP t-d ACF at 6.125mHz
  • Voila!

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reflection rates
Reflection rates?
  • 30/60-degree pair
    • requires double-gaussian fitting
    • composite rate ~10%

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slide48
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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slide49
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
Then what about MDI?
  • I did look at different frequencies before without any success, but this time…

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mdi reflection rates
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
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

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slide54
Reflection-rate measurement still requires careful check
    • High reflection rate at large angular distances may be due to over-compensation

The First Far Eastern Workshop on Helioseismology