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Chromospheric reflection layer for high-frequency acoustic wavePowerPoint Presentation

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 wave

- 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 wave

- 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? wave

- 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 wave
- For a quantitative account, partial reflection (not necessarily at the TL) is important too

The First Far Eastern Workshop on Helioseismology

South Pole Observation wave

- 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? reflection at the photosphere

From Jefferies et al (1997)

The First Far Eastern Workshop on Helioseismology

Chromospheric reflection reflection at the photosphere

- 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 reflection at the photosphere

- 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 reflection at the photosphere

- 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 reflection at the photosphere

- 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 reflection at the photosphere

The First Far Eastern Workshop on Helioseismology reflection at the photosphere

Geometrical factor reflection at the photosphere

- 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

The First Far Eastern Workshop on Helioseismology reflection at the photosphere

Were SP reflection rates correct? reflection at the photosphere

- 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 reflection at the photosphere

- 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 reflection at the photosphere

MDI reflection rate reflection at the photosphere

- 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 reflection at the photosphere

And the answer is… reflection at the photosphere

- 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? reflection at the photosphere

- 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 reflection at the photosphere

- 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 reflection at the photosphere

tf970701

tf970702

・・・

bb970709

・・・

% cd tf970701

% ls -1

slcrem.1839380

slcrem.1839381

・・・

1024×1024 CCD image

The First Far Eastern Workshop on Helioseismology

Analysis procedure reflection at the photosphere

- 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 reflection at the photosphere
⇒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 reflection at the photosphere

- A cosine-bell mask

The First Far Eastern Workshop on Helioseismology

Spherical-harmonic timeseries reflection at the photosphere

- 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

- FFT in φ-direction after zero-padding

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Daily reflection at the photospherek-ωpower maps(1)

apodization: N/A

long-term detrending: N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(2)

apodization: cosine-bell

long-term detrending: N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(3)

apodization: cosine-bell

long-term detrending: Legendre

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(4)

apodization: cosine-bell

long-term detrending: Legendre

rotation removal

by bins

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(4’)

Linear scale!

The First Far Eastern Workshop on Helioseismology

Problems? reflection at the photosphere

- 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? reflection at the photosphere

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

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(4”)

subtractive detrending

The First Far Eastern Workshop on Helioseismology

Daily reflection at the photospherek-ωpower maps(4”’)

different apodization

The First Far Eastern Workshop on Helioseismology

Spherical harmonic transform reflection at the photosphere

- 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

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SP data diagram

- 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 diagram

- The double-ridge structure non-existent

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Reflection rates? diagram

- 30/60-degree pair
- requires double-gaussian fitting
- composite rate ~10%

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- 40/80-degree pair diagram
- 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 diagram
- 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? diagram

- I did look at different frequencies before without any success, but this time…

The First Far Eastern Workshop on Helioseismology

MDI reflection rates? diagram

- 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 diagram

- 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 diagram
- High reflection rate at large angular distances may be due to over-compensation

The First Far Eastern Workshop on Helioseismology

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