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. 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


Chromospheric reflection layer for high frequency acoustic wave

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


Chromospheric reflection layer for high frequency acoustic wave

  • 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)

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

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

  • Satellite features

From Jefferies et al (1997)

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

  • 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?

The First Far Eastern Workshop on Helioseismology


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


Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

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

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

Intensity

Velocity

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


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?

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

% ls -1

tf970701

tf970702

・・・

bb970709

・・・

% cd tf970701

% ls -1

slcrem.1839380

slcrem.1839381

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1024×1024 CCD image

The First Far Eastern Workshop on Helioseismology


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)

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

  • 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

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Daily k power maps 1

Daily k-ωpower maps(1)

apodization: N/A

long-term detrending:N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology


Daily k power maps 2

Daily k-ωpower maps(2)

apodization: cosine-bell

long-term detrending:N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Spherical harmonic transform

Spherical harmonic transform

  • Leakage for l=10, m=3

  • They make sense

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

  • 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


Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


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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Chromospheric reflection layer for high frequency acoustic wave

  • 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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Chromospheric reflection layer for high frequency acoustic wave

  • 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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Chromospheric reflection layer for high frequency acoustic wave

The First Far Eastern Workshop on Helioseismology


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

The First Far Eastern Workshop on Helioseismology


Chromospheric reflection layer for high frequency acoustic wave

  • 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


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