normalizing datanormalizing data • variable sensitivity • high-pass filter • moving median...
TRANSCRIPT
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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
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kN
ikNi
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11
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Auto-correlation
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kN
xxxxkr
Nkki
kN
ikNi
1
11
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Analysis of time series data for exoplanet transits
• Alternative: correlation analysis (using a model with parameters)
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yyxxr i
N
ii
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Correlation between x and y
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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
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Moving Median Filter: …
n=25
Moving Median Filter: …
n=25
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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
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TrES-2
TrES-3
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HAT-P-7
27 cm telescope
COROT (CNES)2006
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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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Koch et al. 2010
Kepler Photometer
1.4
m P
rim
ary
Mir
ror
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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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60 80 100 120 140 160 180 200 220 240 2600
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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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Kepler-10b
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Kepler-11
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Kepler-36
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95
96
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98
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