Detecting Exo-Planet Transits:
Adventures in Milli-mag Photometry
Ken Hose
4/10/2010
4/10/2010
OMSI Workshop
1
Agenda
•
•
•
•
•
•
Transit detection concepts
Equipment required
Reducing the data
Optimal aperture photometry
Noise sources and dealing with noise
References
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OMSI Workshop
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Dimming During a Transit
Dimming
I Aplanet

I
Astar
Jupiter
.
F
G
K
M
Earth
~0.5%
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~0.8%
OMSI Workshop
~1.1%
~2.1%
3
WASP-12b Transit
WASP-12b Transit
WASP-12b
Transit
0.990
Relative Magnitude
Magnitude
Relative
0.995
Published Data:
Transit End: 10:12PM
Transit Depth: 0.015 mag
1.000
1.005
1.010
~10:14 PM
ST-402 Camera
No Guiding
No Filter
60 Sec Exposures
1.015
1.020
1.025
0.725
0.730
0.735
0.740
0.745
0.750
0.755
0.760 0.765
0.770
0.775
0.780
0.785
0.790
0.795
0.800
0.805
Julian Date
(Add
2455269)
Julian Date
(Add
2455269)
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OMSI Workshop
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Typical Transit: HD209458
• The transit lasts about 4 hours
• The period is about 3.5 days
• Dimming is about 1.5% during the transit
– Magnitude drop ~ 0.016 mag
Charbonneau et al. 2000
Charbonneau et al. 2000
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Star Field Around HD209458
HD209458
V
810,930 ADU
C
41,314 ADU
K
23,744 ADU
15 Second Exposure – Red Filter
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What’s a Milli-mag?
• One-thousandth of a magnitude unit (0.001 mag)
• Dimming due to transit of HD 209458b ~ 0.016 mag
Differential Magnitude:
Apparent
Magnitude
-26
-4
-2
0
6
7.65
30
 Flux1 
m1  m2  2.5 * log

 Flux2 
22 orders of magnitude
Brightness difference
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Object
Sun
Venus
Jupiter
Vega
Limiting Mag (dark)
HD209458
Dimmest Hubble
7
What Can We Detect?
Amount
Dimming
Spectral
Type (Size)
PrecisionofRequired
tovs.
Detect
vs. Spectral
Type
1.0000
Required
(mag)
Dimming(mag)
Amount ofPrecision
HD 209458 is type F7
0.1000
Easy
□
Jupiter
0.0100
Neptune
0.0010
Earth
Scintillation Limit
0.0001
F
0.0000
G
K
Large Stars
M
Small Stars
Adapted from Howell, ASP Conference Series, Vol. 189, 1999
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Exoplanet Transit Database
http://var2.astro.cz/ETD/predictions.php
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Amateur Equipment in Use
First exo-planet Detected (RV Method) in 1995
MEarth Project
40cm
<0.002mag?
B. Gary
RCX400
0.003mag
Telescope Aperture (inches)
16
14
12
10
Howell
LX200
0.003mag
8
Hudgins
LX200
0.003mag
Canon
6
XO Project
200mm
0.009mag
4
WATTS
WASP
300mm
200mm
0.005mag
0.009mag
2
1998
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2000
2002
OMSI Workshop
2004
2006
2008
10
My Setup
•
•
•
•
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OMSI Workshop
Paramount ME
RCOS 12.5”
QSI 516 wsg
SSAG
11
Steps
• Pick an object from ETD that will be transiting on
a given night
• Take exposures continuously during the transit
and one hour on either side
• Calibrate your images
• Use photometry tool like AIP4WIN or MaxIm DL
to extract differential magnitudes
• Use EXCEL spreadsheet to evaluate,
manipulate, and filter your data
• Plot the light curve
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OMSI Workshop
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Data Taking (HD209458)
• I used continuous 15 second exposures which kept the
target just below the saturation level of my CCD
• You will need to experiment to find the best exposure for
your target
• I used a red filter to maximize exposure time (to defeat
scintillation noise) and to minimize the effects of
extinction
• Camera data
–
–
–
–
4/10/2010
Dark Current: 0.021 e/pix/sec
Readout Noise: 17.7 e RMS
Gain: 2.7 e/ADU
Sky Background ~ 3.9 ADU/pix/sec
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Aperture Photometry
• Integrate star flux in aperture
• Measure sky background between inner and outer
annulus
• Subtract sky background from star
• Calculate magnitude
From AIP4WIN, Maxim DL, etc.
Star
Sky
Star - Sky
ADU
400,000
20,000
390,000
# Pixels ADU/Pixel
300
1333
600
33
300
1300
Picking the right aperture is key!
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Inner Annulus
Outer Annulus
Aperture
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Differential Aperture Photometry
HD209458
Differential Photometry:
V
810,930
C
mag  2.5 * log(
41,314
m ag  2.5 * log(
K
23,744
FluxV
)
FluxC
810,930
)  3.232
41,314
15 Second Exposure – Red Filter
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OMSI Workshop
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Workflow
AIP4WIN
Raw Aperture
Photometry
Output
Perl Script
Output (csv)
Excel
Flux
Diff
Mag
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Noise in Time Series Measurements
Noise is measured as the 1-sigma variation in magnitude
Raw Time Series Differential Magnitude Data For HD209458
+0.008 Mag
+1σ
Average
-0.008 Mag
-1σ
Time 
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Scintillation Noise
• Buchheim explains it as small thermal fluctuations that act like
weak lenses to cause stars to brighten and dim randomly—
Causes twinkling
zenith
Scintillation Magnitude
A Fundamental Limiter!  Kepler
0.030
ϕ
0.025
*
Airmass = 1
Airmass = 2
Mag
0.020
Air mass = 1 / cos ϕ
Airmass = 3
Airmass = 4
0.015
0.010
0.005
0.000
0
10
20
30
40
50
60
70
Function of:
Aperture of scope
Altitude
Air Mass
Exposure (sec)
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Noise Terms
Noise Terms vs. Magnitude
One Single 15-second Raw Exposure
120%
100%
SNR 
V
.0007
80%
Percent
signal
signal  sky  dark  readout
.004
60%
Signal
Sky
40%
Dark
Readout
C
.007
K
sum
20%
.03
0%
6
7
8
9
10
11
12
13
14
15
16
17
Raw Instrumental Magnitude
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1-Sigma Error vs. # Photoelectrons
1-Sigma Error (Magnitude) vs. # Photoelectrons
0.0070
For Bright Stars: Noise = 1.0857/sqrt(N*)
1-Sigma Error (mag)
0.0060
0.0050
0.0040
C
0.0030
Want > 1E6 photoelectrons
0.0020
V
0.0010
0.0000
1.00E+04
5.10E+05
1.01E+06
1.51E+06
2.01E+06
# Photoelectrons
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Differential Extinction
• As air mass changes, differential magnitude will change
if stars are not the same color
– Red filter minimizes the effect
From SkyMap Pro
V
C
K
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Differential Extinction
Atmospheric Extinction vs. Wavelength
Atmospheric
Extinction vs. Wavelength
0.6
2
1.8
1.6
Roque de Los Muchachos
Palomar
1.4
0.4
1.2
B
0.3
V
R
I
BVRI
Magnitude per Airmass
0.5
1
0.8
0.2
0.6
0.4
0.1
0.2
0
300
400
500
600
700
800
0
1000
900
As compared
To start value
Wavelength (nm)
Start
End
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Star1: Blue
Star2: Red
Air Mass Ext. Coef. Total Ext. Ext. Coef. Total Ext.
1.5
0.3
0.45
0.1
0.15
2.5
0.3
0.75
0.1
0.25
OMSI Workshop
Δ
0.3
0.5
E
r
r
o
r
0
0.2
22
Exposure Time vs. Error
Should be able to image down to magnitude >=12 or so
Data valid for my setup—your mileage will vary
Raw Instrumental Magnitude
1-Sigma Error
6
0.0005
0.0010
0.0020
0.0030
0.0040
0.0050
0.0060
0.0070
0.0080
0.0090
0.0100
0.0150
0.0200
7
2
0
0
0
0
0
0
0
0
0
0
0
7
18
5
1
1
0
0
0
0
0
0
0
0
0
8
46
12
3
1
1
1
0
0
0
0
0
0
0
9
120
30
8
4
2
2
1
1
1
1
1
0
0
10
330
83
22
10
6
4
3
3
2
2
1
1
1
11
1012
255
66
30
18
12
9
7
6
5
4
2
2
12
13
14
15
16
3704 16643 88135 513747 3135211
929 4165 22039 128443 783809
236 1046 5515 32117 195958
107
468 2455 14278
87097
62
266 1384
8035
48996
41
172
889
5145
31360
29
121
619
3576
21780
23
91
457
2629
16004
18
71
351
2015
12255
15
57
279
1593
9685
12
47
227
1292
7846
7
23
105
579
3492
5
15
62
329
1968
Red: Greater than 5 minutes—may under sample transit
Exposure time in seconds with red filter
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OMSI Workshop
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Reducing the Data
• I combined every 5 raw exposures which gave
effective data points every 1.75 minutes
– Referred to as “binning” in the literature
– This reduces the measurement uncertainty by
1/Sqrt(N) where N is the number of images combined
• Further smoothing can be achieved by taking a
running average
• Caution: These actions low-pass filter the data
– Could affect slope and duration of transit
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Reducing the Data (cont)
168 images combined using script for Maxim DL for experiment below
Differential photometry done with AIP4WIN using 5-pixel radius (5/16/20)
Uncertainty vs. # Combined Raw Images
Uncertainty(mag)
(mag)
Uncertainty
0.009
0.008
0.007
Measured
Model
0.006
0.005
0.004
0.003
0.002
0.001
0
0
1
2
3
4
5
6
7
8
9
10
11
# Combined Raw Images (Binning)
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Noise Calculations
• Noise calculations in differential photometry must
account for both the variable and the comp star
• Noise adds in quadrature
– The square root of the sum of the squares
•
•
•
•
Variable: 2.16e6 e-, σ = 0.000734 mag
Comp: 1.10e5 e-, σ = 0.00368 mag
σ(diff) = sqrt(σv2 + σc2) = sqrt(0.0007342 + 0.003682)
σ(diff) = 0.0038 mag or 3.8 parts per 1000
Reduces σc by ~1/sqrt(N) for multiple comp stars (same mag)
i.e.: σc(10 comp) = 0.31 * σc(1 comp)
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OMSI Workshop
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Raw Data (After Calibration)
HD 209458
Differential Magnitude vs. Observation Number
-3.2
Differential Magnitude
Magnitude
Differential
-3.21
-3.22
-3.23
-3.24
-3.25
-3.26
σ = 0.008
-3.27
-3.28
0
20
40
60
80
100
120
140
160
180
Observation Number
Air mass = 1.28
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One observation every 21 sec
OMSI Workshop
Air mass = 1.17
27
After Some Filtering
Each observation: 5 x 15 sec images stacked and median-combined
Running average: [(x-1)+(x)+(x+1)]/3
Differential Magnitude vs. Observation Number
-3.2
Diff_Mag
Differential Magnitude
-3.21
Average = -3.239
Running_Avg
-3.22
σ = 0.003
-3.23
-3.24
-3.25
-3.26
σ = 0.0027
10 mmag
-3.27
-3.28
0
5
10
15
20
25
30
35
Observation Number
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SNR vs. Aperture Dilemma
• Best SNR gives wrong Magnitude (Δmag=0.209)
SNR & Flux Ratio vs. Aperture Radius
ΔMag = 0.209
FluxVariable
Ratio
Star
Flux Ratio
1.1
300
7.615
1
250
0.9
7.653
0.8
Flux Var
SNR Comp
7.750
0.7
200
150
7.824
0.6
7.978
SNRComp
Comp Star
Star
SNR
Best SNR = 4 pixels
100
0.5
FWHM = 3.6 pix
0.4
50
0
5
10
15
20
25
Aperture Radius (pixels)
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Curve of Growth
Curve of Growth vs. Aperture
1.1
Normalized Flux
Flux
Normalized
1
0.9
G = 1-(1/(1+(r2/4.9)1.2))
0.8
V, Mag 7.65
Depends on
Seeing
C, Mag 10.1
0.7
Mag14.5 Star
0.6
0.5
Mag13.1 Star
Good Matching
Best SNR
0.4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Aperture Radius (pixels)
 Gc(aperture) * FluxV 

Gv
(
aperture
)
*
FluxC


Mag  2.5 * log
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OMSI Workshop
Relates Flux to Max Flux
At Full Aperture.
Gc, Gv ~cancel
30
Use Aperture for Best SNR
Measurement Uncertainty vs. Aperture
Measurement
Uncertainty vs. Aperture
0.0060
(mag)
Uncertainty
Uncertainty (mag)
0.0055
C-K
 (C  K ) 
V -C
0.0050
V - Ensemble
0.0045
1 N
( xi  x) 2

N  1 i 1
(Koppelman)
1.4 * FWHM
0.0040
Inner annulus = 16
Outer annulus = 20
0.0035
0.0030
0.0025
2
3
4
5
6
7
8
9
10
11
12
Aperture
(pixels)
Aperture (pixels)
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Guiding
• Different photo sites have different sensitivity
– Need perfect flat-field master to compensate
– Good flat fields are difficult to make
• It is best to keep your image on the same photo
sites throughout the entire observing run
– Accurate guiding is a must
– Watch out for field rotation due to imperfect polar
alignment (an issue mentioned in a couple of papers)
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Other Sources of Noise
• Focus drift
– Check focus every so often
– Causes variations in flux measurements
– Choice of Annulus and Aperture radius
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References
1. Howell, Steve B. Introduction to Time-Series Photometry Using
Charge-Coupled Devices. J. AAVSO volume 20, 1991
2. Castellano et al. Detection of Extrasolar Giant Planets With
Inexpensive Telescopes and CCDs. J. AAVSO Volume 33, 2004
3. Hudgins, et al. Photometric Techniques Using Small College
Research Instruments of Study of the Extrasolar Planetary Transits
of HD 209458. Astronomical Society of Australia, 2002
4. Exoplanet Transit Database. http://var2.astro.cz/ETD/
5. Gary, Bruce. Exoplanet Observing for Amateurs.
http://brucegary.net/book_EOA/x.htm
6. Buchheim, Robert. The Sky is Your Laboratory.
7. Howell, Steve B. Photometric Search for Extra-Solar Planets. ASP
Conference Series, Vol. 189, 1999
This research has made use of NASA's Astrophysics Data System
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References (cont.)
8.
Howell, Steve B. Two-Dimensional Aperture Photometry: Signal-toNoise Ratio of Point-Source Observations And Optimal DataExtraction Techniques. PASP volume 101, June 1989
9. Koppelman, Michael. Uncertainty Analysis in Photometric
Observations. The Society for Astronomical Sciences 24th Annual
Symposium. SAS, 2005, p.107
10. Charbonneau, et al. Detection of Planetary Transits Across a SunLike Star. The Astrophysical Journal. 2000 January 20
11. Oetiker, Brian et. al. Wide Angle Telescope Transit Search
(WATTS): A Low-Elevation Component of the TrEs Network. PASP,
vol 122, January 2010
This research has made use of NASA's Astrophysics Data System
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Backup Slides
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Camera Linearity
• Find out where your camera saturates in ADUs
• Be sure your exposures are below saturation
• Characterize using light box
QSI 516 wsg
Time
0.50
0.96
2.00
4.00
8.00
16.00
24.00
32.00
40.00
48.00
56.00
64.00
72.00
ADU Divided by Exposure Time
1300
ADUs per Sec
1200
59,581 ADU
1100
1000
900
800
700
ADU
609
981
1825
3455
6734
13309
19934
26527
33196
39818
46437
53037
59581
% Error
7.085%
3.596%
1.119%
-0.035%
-0.379%
-0.429%
-0.194%
-0.197%
0.031%
0.065%
0.082%
0.060%
-0.052%
600
0
10
20
30
40
50
60
70
80
Exposure Time (sec)
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OMSI Workshop
Linear up to ~ 60,000 ADU
37
Signal to Noise Ratio
g *N*
SNR =
npix
g * N* + npix * ( 1 + ann_pix
)*[
g*
(
ann_adu
ann_pix
Noise Terms
Variable
N*
g
npix
ann_pix
ann_adu
dc
ro
quant
(1)
(2)
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Definition
Total sky-subtracted flux (ADU)
Conversion gain (e-/ADU)
# pixels in aperture
# pixels in annulus
Total ADU in annulus
Dark current per pixel for exposure time
RMS readout noise per pixel
Quantization noise. Use 0.289*g2
) + g * dc + ro^2 + quant ]
Sky Noise
Notes
(1)
(2)
(1)
(1)
(1)
(2)
(2)
Dark Current
Readout Noise
σ = 1.0857/SNR (mag)
Measure using photometry software (AIP4WIN)
From CCD characterization (AIP4WIN)
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Probability of Detection
• About 1/10 stars has a hot Jupiter
• The probability that alignment is correct is about 1/100
• So the probability that a given star will have a hot Jupiter
is about 1/1000
• Such a star will be in transit about 15% of the time
• You will need to survey lots of stars to make a single
detection and view it at the right time
• Start with known exo-planets
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My Calibration
• It is important to use full calibration
• Darks were taken with same exposure as the
images no bias frames required
• Image: 15 sec gives ~50,000ADU max PV
• Dark: 30 x 15 sec
• Flats: 30 x 30 sec
• Remember: Calibration adds noise
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