lecture 11 - users-phys.au.dk · 02-06-2014 11 h k j dmc dj dj t k 1 sin( 2 ) cos( 2) 1 1 i j n i i...
TRANSCRIPT
![Page 1: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/1.jpg)
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![Page 2: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/2.jpg)
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![Page 3: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/3.jpg)
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![Page 4: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/4.jpg)
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Bridge vibrations
![Page 5: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/5.jpg)
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![Page 6: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/6.jpg)
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Filtering
• Transit-removal filter
• Pulsation-removal filter
![Page 7: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/7.jpg)
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![Page 8: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/8.jpg)
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Randomizephases
![Page 9: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/9.jpg)
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Randomizephases
H
kj
DMCjj kTdd
1
)( Transit searchfor deep transits
![Page 10: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/10.jpg)
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H
kj
DMCjj kTdd
1
)(
)2(cos)2(sin11
ji
N
iiji
N
iij
CLEANj tftfdd
Niiiif ,1),,( CLEANing forstrong coherent
oscillations
H
kj
DMCjj kTdd
1
)(
)2(cos)2(sin11
ji
N
iiji
N
iij
CLEANj tftfdd
cutfCLEANjlow dFTFT 0)(
)( randomlowrandom FTFT
Randomize phasesbelow cut-frequency
![Page 11: Lecture 11 - users-phys.au.dk · 02-06-2014 11 H k j DMC dj dj T k 1 sin( 2 ) cos( 2) 1 1 i j N i i j i N i j i CLEAN dj d f t f t fcut CLEAN FTlow FT(dj)0 FTrandom FTlow( random)](https://reader035.vdocuments.pub/reader035/viewer/2022081407/60520720d631682a95212d92/html5/thumbnails/11.jpg)
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H
kj
DMCjj kTdd
1
)(
)2(cos)2(sin11
ji
N
iiji
N
iij
CLEANj tftfdd
cutfCLEANjlow dFTFT 0)(
)( randomlowrandom FTFT
)()( 11randomlow
CLEANj
Randomj FTFTFTFTdd
Randomizephases
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γ Doradus star SIMULATION
Match filter
Wavelet analysis (Band-pass filter)
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Match filter
Wavelet analysis (Band-pass filter)
Match filter
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Band-pass filter
Band-pass filterTransit detection
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Transit depth
Band-pass filter
Transit depth
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Transit depth
Transit depth
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Time Series Data
Match Filter
Period Search
Planet Detection
High-pass Filter
γ Doradus star SIMULATION
High-pass Filter
Match Filter
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Period Search
Time Series Data
Match Filter
Period Search
Planet Detection
High-pass Filter
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Time Series Data
Match Filter
Period Search
Planet Detection
High-pass Filter
High-pass Filter
CLEANing forStellar Pulsations
2
1 1
)2cos()()2sin()()(
N
j
n
ijiijiij tttf
An efficient Stellar Pulsation Band-pass filter:Spectral CLEANing
• Oscillations are coherent over a long timescale compared to the duration of a planet transit
• We may measure amplitude, frequency and phase for those oscillations and correct for them
• We shall minimize the following term, given N data points and n frequencies
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High-pass Filter
Match Filter
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High-pass Filter
Match Filter
Period Search
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Transit depth
Band-pass filter
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High-pass Filter Match Filter
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Match FilterHigh-pass Filter
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CLEANing forStellar Pulsations
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CLEANing forStellar Pulsations High-pass Filter Match Filter
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High-pass Filter
Match Filter
Observational Asteroseismology:Observables
• Oscillation frequencies and frequency differences/ratios/splittings
• Oscillation mode identification (degree, order and mode type; g/p/f, mixed)
• Oscillation mode properties (amplitude, amplitude ratios, phase, phase differences, life time, …)
• Changes (short term and long term) in mode parameters (frequencies, amplitudes, …)
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Non-radial modes
Mode degree: ℓ
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ℓ= 1 1 2
0 2 2 3Radial
3 3 3
5 10 10
ℓ= 1 1 2
0 2 2 3Radial
3 3 3
5 10 10
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Radial order: nn = 17
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Radial Modes
02δν13δν
0νp-mode oscillations:Large separationSmall separation
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0ν
p-mode oscillations:Large separationSmall separation
0ν 0ν 0ν 0ν
19n 20n 21n 22n
0ν
p-mode oscillations:Large separationSmall separation
2
0 0 0 0
2 2 2
HydrogenXconst .δν02
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p-mode oscillations:Large separationSmall separation
3
1 1 1 1
3 3 3
HydrogenXconst .δν13
Jørgen Christensen-Dalsgaard et al.
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Jørgen Christensen-Dalsgaard et al.
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Large separations
106 μHz
135 μHz
161 μHz
0
Large separations
106 μHz
135 μHz
161 μHz
Small separations
6.6 μHz
9.2 μHz
11.3 μHz
0 02
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The Sun
The Sun
α Centauri A
The Sun
α Cen A
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α Centauri B
The Sun
α Cen A
α Cen B
CoRoT: HD 49933
Appourchaux, Michel, Auvergne, Baglin et al. 2008
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HD 49933
The Sun
HD 49933α Cen A
α Cen B
%10)(
MSAge
Age
%5M
M%3
R
R
The Sun
α Cen A
α Cen B
HD 49933
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Chaplin et al. 2011
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White et al. 2011
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450 d, mag: 7.18
G main sequence
Kepler
540 d, mag: 9.27
subgiant
Kepler
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White et al. 2012
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90
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H
He
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Guggenberger et al., 2012