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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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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

- 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 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

- 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

- 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

- 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

- A cosine-bell mask

The First Far Eastern Workshop on Helioseismology

- 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

The First Far Eastern Workshop on Helioseismology

apodization: N/A

long-term detrending:N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

apodization: cosine-bell

long-term detrending:N/A

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

apodization: cosine-bell

long-term detrending:Legendre

rotation removal

N/A

The First Far Eastern Workshop on Helioseismology

apodization: cosine-bell

long-term detrending:Legendre

rotation removal

by bins

The First Far Eastern Workshop on Helioseismology

Linear scale!

The First Far Eastern Workshop on Helioseismology

- 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

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

The First Far Eastern Workshop on Helioseismology

subtractive detrending

The First Far Eastern Workshop on Helioseismology

different apodization

The First Far Eastern Workshop on Helioseismology

- 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

- The original SP data obtained
- 18 days, 42-second cadence
- l=0-250

- Time-distance ACF produced

The First Far Eastern Workshop on Helioseismology

- The double-ridge structure non-existent

The First Far Eastern Workshop on Helioseismology

- Voila!

The First Far Eastern Workshop on Helioseismology

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

The First Far Eastern Workshop on Helioseismology

- 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

- 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

- After geometrical correction:
- 10% for the main ridge
- ~50%(!) for the satellite ridge

The First Far Eastern Workshop on Helioseismology

- 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