normalizing datanormalizing data • variable sensitivity • high-pass filter • moving median...

1

Normalizing data

• Variable Sensitivity

• High-pass Filter

• Moving Median Filter

• Moving Mean Filter

• Sigma-clipping

Analysis of time series data for exoplanet transits

• Gab-filling and transfer to regular grid

2

kN

xxxxkr

Nkki

kN

ikNi

1

11

)(

Auto-correlation

3

kN

xxxxkr

Nkki

kN

ikNi

1

11

)(

Analysis of time series data for exoplanet transits

• Alternative: correlation analysis (using a model with parameters)

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yyxxr i

N

ii

1

Correlation between x and y

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6

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Normalizing data

• Variable Sensitivity

• High-pass Filter

• Moving Median Filter

• Moving Mean Filter

• Sigma-clipping

Kepler-7

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Moving Median Filter: …

n=2

Moving Median Filter:

n=2

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w(data)=0, w(median)=1

w(data)=1w(median)=0

w(data)=0, w(median)=1

Removal of noise peaks: ∙ ∙

n=2

10

Moving Median Filter: …

n=25

Moving Median Filter: …

n=25

11

Moving Mean Filter: …

n=25

Normalizing: /

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Normalizing: /

Auto-Correlation

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Analysis of time series data for exoplanet transits

• Basic analysis

Analysis of time series data for exoplanet transits

• Basic analysis

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Analysis of time series data for exoplanet transits

• Gab-filling and transfer to regular grid

Analysis of time series data for exoplanet transits

• Phase-folded and search for transit timing variations (TTV)

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Analysis of time series data for exoplanet transits

• Filter the data before correlation analysis (e.g. in time domain)

Lowpass filter

Pla

net T

rans

it

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Highpass filter

Pla

net T

rans

itP

lane

t Tra

nsit

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Analysis of time series data for exoplanet transits

• Filter the data before correlation analysis (e.g. in time domain – moving mean filter)

Examples of search for correlations in time series analysis

• Planet Transit Searches from ground

• CoRoT

• Kepler

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TrES: 10 cm

XO: 11 cm

SuperWASP: 11 cm

OGLE: 1.3 m

HAT: 11 cm

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XO-2

21

22

TrES-2

TrES-3

23

24

25

HAT-P-7

27 cm telescope

COROT (CNES)2006

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27

28

29

CoRoT: 27 December 2006

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COROT (CNES)2007

CoRoT-1

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CoRoT-2

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CoRoT-3

CoRoT-4

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P(rot) = 23 days

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35

Koch et al. 2010

Kepler Photometer

1.4

m P

rim

ary

Mir

ror

36

95 cm Schmidt Corrector

One Kepler CCD:50x25 mm (2200x1024 pixels)

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Koch et al. 2010

Focal Plane Assembly42 CCDs with Field Flattener Lenses

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7 marts 2009

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Kepler Field of View: 110 square degrees

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41

60 80 100 120 140 160 180 200 220 240 2600

10

20

30

40

50

Days Since Launch

Max

imum

Atti

tude

Res

idua

l (m

illip

ixel

s)

Q2Q1 Q3

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Jenkins et al. 2010

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44

Kepler-10b

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46

Kepler-11

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Kepler-36

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95

96

49

98

50

51

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