Chromospheric reflection layer for high-frequency acoustic wave

Chromospheric reflection layer for high-frequency acoustic wave

Takashi Sekii

Solar Physics Division, NAOJ

The First Far Eastern Workshop on Helioseismology

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


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



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)


• Peak spacing and width better explained by Kumar’s model

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


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)


From Jefferies et al (1997)

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

• Satellite features


• What makes the satellite features?

From Jefferies et al (1997)


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 actua

l wording and have not ruled out the TL solution


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


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?


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




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


Intensity

Velocity



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)


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



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



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

V I LD

70/140 9.7% 9.4% 10.3%

80/160 9.1% 9.0% 10.2%

90/180 9.4% 8.1% 9.8%


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?


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


% ls -1tf970701tf970702・・・bb970709・・・% cd tf970701% ls -1slcrem.1839380slcrem.1839381・・・

1024×1024 CCD image


Analysis procedure

1. one-day string by one-day string (about 10 hours)

2. pixel-by-pixel short time-scale detrending renormalization by 15-point running mean

⇒detrended images

3. cosine-bell apodization+SH transform ⇒SHT (spherical harmonic time-series)


4. long time-scale detrending+FFT of SHT ⇒power spectra

5. m-averaging+rotational splitting correction

⇒k-ω diagram

6. Fourier-Legendre transform ⇒time-distance autocorrelation

7. repeat the above for many other days and take the average


Apodization mask

• A cosine-bell mask


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


Daily k-ω power maps(1)

apodization: N/A

long-term detrending: N/A

rotation removal

N/A



apodization: cosine-bell

long-term detrending: N/A

rotation removal

N/A




long-term detrending: Legendre

rotation removal

N/A




long-term detrending: Legendre

rotation removal

by bins


Daily k-ω power maps(4’)

Linear scale!


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)


What’s wrong?

• Sasha Serebryanskiy produced cleaner power

• Should the short-term detrending be subtractive?

• Apodization?

• SHT?


Daily k-ω power maps(4”)

subtractive detrending


Daily k-ω power maps(4”’)

different apodization


Spherical harmonic transform

• Leakage for l=10, m=3

• They make sense


• AS says: analysis without GRASP has led to a noisy power diagram– is GRASP doing something clever?

• Well…let us do the averaging anyway



SP data

• The original SP data obtained– 18 days, 42-second

cadence– l=0-250

• Time-distance ACF produced


SP t-d ACF at 6.75mHz

• The double-ridge structure non-existent


SP t-d ACF at 6.125mHz

• Voila!


Reflection rates?

• 30/60-degree pair– requires double-gauss

ian fitting– composite rate ~10%


• 40/80-degree pair– Composite reflection rate between the first & the

second ridge ~12%– But, from the second & third

• Main ~ 40%(!)

• Satellite ~ 75%(!)


• 45/90-degree pair– Composite reflection rate between the first & the

second ridge ~14%– But, from the second & third

• Main ~ 26%(!)

• Satellite ~ 50%(!)


Then what about MDI?

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



MDI reflection rates?

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

ridge


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 powe

r leaked into chromosphere


• Reflection-rate measurement still requires careful check– High reflection rate at large angular distances may

be due to over-compensation

Documents

Chromospheric reflection layer for high-frequency acoustic wave