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

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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

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


  • 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


  • 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 actual 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

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 -1

tf970701

tf970702

・・・

bb970709

・・・

% cd tf970701

% ls -1

slcrem.1839380

slcrem.1839381

・・・

1024×1024 CCD image

The First Far Eastern Workshop on Helioseismology


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


  • 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

  • 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-ωpower maps(1)

apodization: N/A

long-term detrending:N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology


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-ωpower maps(3)

apodization: cosine-bell

long-term detrending:Legendre

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology


Daily k-ωpower maps(4)

apodization: cosine-bell

long-term detrending:Legendre

rotation removal

by bins

The First Far Eastern Workshop on Helioseismology


Daily k-ωpower 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-ωpower maps(4”)

subtractive detrending

The First Far Eastern Workshop on Helioseismology


Daily k-ωpower 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

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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%(!)

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 power 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

The First Far Eastern Workshop on Helioseismology


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