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Bridge vibrations

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Filtering

• Transit-removal filter

• Pulsation-removal filter

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Randomizephases

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Randomizephases

H

kj

DMCjj kTdd

1

)( Transit searchfor deep transits

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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

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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