4/10/20104/10/2010 11OMSI WorkshopOMSI Workshop
Detecting Exo-Planet Transits: Detecting Exo-Planet Transits: Adventures in Milli-mag PhotometryAdventures in Milli-mag Photometry
Ken HoseKen Hose4/10/20104/10/2010
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AgendaAgenda• Transit detection concepts• Equipment required• Reducing the data• Optimal aperture photometry• Noise sources and dealing with noise• References
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Dimming During a TransitDimming During a Transit
Astar
Aplanet
I
I
Dimming
KF G M
Jupiter
.Earth
~0.5% ~0.8% ~1.1% ~2.1%
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WASP-12b TransitWASP-12b TransitWASP-12b Transit
0.990
0.995
1.000
1.005
1.010
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)
Re
lati
ve
Ma
gn
itu
de
ST-402 CameraNo GuidingNo Filter60 Sec Exposures
Published Data:Transit End: 10:12PMTransit Depth: 0.015 mag
WASP-12b Transit
~10:14 PM
Julian Date (Add 2455269)
Rel
ati
ve
Mag
nit
ud
e
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Typical Transit: HD209458Typical 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 HD209458Star Field Around HD209458
V
C
K
41,314 ADU
810,930 ADU
23,744 ADU
15 Second Exposure – Red Filter
HD209458
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What’s a Milli-mag?What’s a Milli-mag?
• One-thousandth of a magnitude unit (0.001 mag)• Dimming due to transit of HD 209458b ~ 0.016 mag
2
1log*5.221
Flux
Fluxmm -26 Sun
-4 Venus-2 Jupiter0 Vega6 Limiting Mag (dark)
7.65 HD20945830 Dimmest Hubble
Apparent Magnitude Object
22 orders of magnitude Brightness difference
Differential Magnitude:
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What Can We Detect?What Can We Detect?
Adapted from Howell, ASP Conference Series, Vol. 189, 1999
Precision Required to Detect vs. Spectral Type
0.0000
0.0001
0.0010
0.0100
0.1000
1.0000
Req
uir
ed P
reci
sio
n (
mag
)
Neptune
F G K M
Scintillation LimitEarth
Large Stars Small Stars
HD 209458 is type F7
Am
ou
nt
of
Dim
min
g (
ma
g)
□
Amount of Dimming vs. Spectral Type (Size)
EasyJupiter
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Exoplanet Transit DatabaseExoplanet Transit Database
http://var2.astro.cz/ETD/predictions.php
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Amateur Equipment in UseAmateur Equipment in UseFirst exo-planet Detected (RV Method) in 1995
2000 2002 2004 2006 20081998
WATTS300mm0.005mag
XO Project200mm0.009mag
MEarth Project40cm<0.002mag?
HowellLX2000.003mag
HudginsLX2000.003mag
Tel
esco
pe A
pert
ure
(inch
es)
2
4
6
8
10
12
14
16
Canon
B. GaryRCX4000.003mag
WASP200mm0.009mag
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My SetupMy Setup
• Paramount ME• RCOS 12.5”• QSI 516 wsg• SSAG
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StepsSteps• 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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Data Taking (HD209458)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– 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 PhotometryAperture Photometry• Integrate star flux in aperture• Measure sky background between inner and outer
annulus• Subtract sky background from star• Calculate magnitude
Aperture
Inner Annulus
Outer Annulus
ADU # Pixels ADU/PixelStar 400,000 300 1333Sky 20,000 600 33Star - Sky 390,000 300 1300
From AIP4WIN, Maxim DL, etc.
Picking the right aperture is key!
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Differential Aperture PhotometryDifferential Aperture Photometry
V
C
K
41,314
810,930
23,744
15 Second Exposure – Red Filter
HD209458
)log(*5.2FluxC
FluxVmag
232.3)314,41
930,810log(*5.2 mag
Differential Photometry:
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WorkflowWorkflowAIP4WIN
Raw AperturePhotometryOutput
Perl ScriptOutput (csv)
Excel
Flux
DiffMag
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Noise in Time Series MeasurementsNoise in Time Series Measurements
Noise is measured as the 1-sigma variation in magnitude
+0.008 Mag
-0.008 Mag
+1σ
-1σ
Raw Time Series Differential Magnitude Data For HD209458
Average
Time
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Scintillation NoiseScintillation Noise• Buchheim explains it as small thermal fluctuations that act like
weak lenses to cause stars to brighten and dim randomly—Causes twinkling
ϕ
Air mass = 1 / cos ϕ
zenith
*Scintillation Magnitude
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0 10 20 30 40 50 60 70
Exposure (sec)
Ma
g
Airmass = 1
Airmass = 2
Airmass = 3
Airmass = 4
Function of:Aperture of scopeAltitudeAir Mass
A Fundamental Limiter! Kepler
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Noise TermsNoise TermsNoise Terms vs. Magnitude
0%
20%
40%
60%
80%
100%
120%
6 7 8 9 10 11 12 13 14 15 16 17
Raw Instrumental Magnitude
Pe
rce
nt Signal
Sky
Dark
Readout
sum
readoutdarkskysignal
signalSNR
V
C
One Single 15-second Raw Exposure
.0007
.004
K.007
.03
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1-Sigma Error vs. # Photoelectrons1-Sigma Error vs. # Photoelectrons
1-Sigma Error (Magnitude) vs. # Photoelectrons
0.0000
0.0010
0.0020
0.0030
0.0040
0.0050
0.0060
0.0070
1.00E+04 5.10E+05 1.01E+06 1.51E+06 2.01E+06
# Photoelectrons
1-S
igm
a E
rro
r (m
ag
)
Want > 1E6 photoelectrons
For Bright Stars: Noise = 1.0857/sqrt(N*)
C
V
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Differential ExtinctionDifferential Extinction
V
C
K
From SkyMap Pro
• As air mass changes, differential magnitude will change if stars are not the same color– Red filter minimizes the effect
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Differential ExtinctionDifferential ExtinctionAtmospheric Extinction vs. Wavelength
0
0.1
0.2
0.3
0.4
0.5
0.6
300 400 500 600 700 800 900 1000
Wavelength (nm)
Ma
gn
itu
de
pe
r A
irm
as
s
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
BV
RI
Roque de Los Muchachos
Palomar
B V IR
Air Mass Ext. Coef. Total Ext. Ext. Coef. Total Ext. Δ ErrorStart 1.5 0.3 0.45 0.1 0.15 0.3 0End 2.5 0.3 0.75 0.1 0.25 0.5 0.2
Star1: Blue Star2: Red
Atmospheric Extinction vs. Wavelength
As comparedTo start value
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Exposure Time vs. ErrorExposure Time vs. Error
Red: Greater than 5 minutes—may under sample transit Exposure time in seconds with red filter
Should be able to image down to magnitude >=12 or soData valid for my setup—your mileage will vary
6 7 8 9 10 11 12 13 14 15 160.0005 7 18 46 120 330 1012 3704 16643 88135 513747 31352110.0010 2 5 12 30 83 255 929 4165 22039 128443 7838090.0020 0 1 3 8 22 66 236 1046 5515 32117 1959580.0030 0 1 1 4 10 30 107 468 2455 14278 870970.0040 0 0 1 2 6 18 62 266 1384 8035 489960.0050 0 0 1 2 4 12 41 172 889 5145 313600.0060 0 0 0 1 3 9 29 121 619 3576 217800.0070 0 0 0 1 3 7 23 91 457 2629 160040.0080 0 0 0 1 2 6 18 71 351 2015 122550.0090 0 0 0 1 2 5 15 57 279 1593 96850.0100 0 0 0 1 1 4 12 47 227 1292 78460.0150 0 0 0 0 1 2 7 23 105 579 34920.0200 0 0 0 0 1 2 5 15 62 329 1968
Raw Instrumental Magnitude
1-S
igm
a E
rro
r
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Reducing the DataReducing 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)Reducing the Data (cont)
Uncertainty vs. # Combined Raw Images
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0 1 2 3 4 5 6 7 8 9 10 11
# Combined Raw Images (Binning)
Unce
rtai
nty
(mag
) Measured
Model
Un
ce
rta
inty
(m
ag
)
168 images combined using script for Maxim DL for experiment belowDifferential photometry done with AIP4WIN using 5-pixel radius (5/16/20)
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Noise CalculationsNoise 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 + σc
2) = 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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Raw Data (After Calibration)Raw Data (After Calibration)
Differential Magnitude vs. Observation Number
-3.28
-3.27
-3.26
-3.25
-3.24
-3.23
-3.22
-3.21
-3.2
0 20 40 60 80 100 120 140 160 180
Observation Number
Diff
eren
tial M
agnitu
de
σ = 0.008
One observation every 21 secAir mass = 1.28 Air mass = 1.17
Dif
fere
nti
al M
agn
itu
de
HD 209458
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After Some FilteringAfter Some FilteringEach observation: 5 x 15 sec images stacked and median-combinedRunning average: [(x-1)+(x)+(x+1)]/3
Differential Magnitude vs. Observation Number
-3.28
-3.27
-3.26
-3.25
-3.24
-3.23
-3.22
-3.21
-3.2
0 5 10 15 20 25 30 35
Observation Number
Diff
eren
tial M
agnitu
de
Diff_Mag
Running_AvgAverage = -3.239
σ = 0.003
σ = 0.0027 10 mmag
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SNR vs. Aperture DilemmaSNR vs. Aperture Dilemma
• Best SNR gives wrong Magnitude (Δmag=0.209)
Best SNR = 4 pixels
SNR & Flux Ratio vs. Aperture Radius
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
0 5 10 15 20 25
Aperture Radius (pixels)
Flu
x R
atio
50
100
150
200
250
300
SN
R C
om
p S
tar
Flux Var
SNR Comp
7.978
7.750
7.653
7.615
Flu
x R
ati
o V
ari
ab
le S
tar
SN
R C
om
p S
tar
ΔMag = 0.209
FWHM = 3.6 pix
7.824
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Curve of GrowthCurve of Growth
FluxCapertureGv
FluxVapertureGcMag
*)(
*)(log*5.2 Relates Flux to Max Flux
At Full Aperture. Gc, Gv ~cancel
Curve of Growth vs. Aperture
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1 2 3 4 5 6 7 8 9 1011 12 13 14 15 1617 18 19 20
Aperture Radius (pixels)
Norm
aliz
ed F
lux
V, Mag 7.65
C, Mag 10.1
Mag14.5 Star
Mag13.1 Star
No
rma
lize
d F
lux
Good MatchingBest SNR
G = 1-(1/(1+(r2/4.9)1.2))Depends on Seeing
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Use Aperture for Best SNRUse Aperture for Best SNR
Measurement Uncertainty vs. Aperture
0.0025
0.0030
0.0035
0.0040
0.0045
0.0050
0.0055
0.0060
2 3 4 5 6 7 8 9 10 11 12
Aperture (pixels)
Un
cert
ain
ty (
mag
)
C - K
V -C
V - Ensemble
1.4 * FWHM
Un
ce
rta
inty
(m
ag
)
Aperture (pixels)
Measurement Uncertainty vs. Aperture
2
1)( )(
1
1xx
N
N
iiKC
Inner annulus = 16Outer annulus = 20
(Koppelman)
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GuidingGuiding
• 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 NoiseOther 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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ReferencesReferences
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.htm6. 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.)References (cont.)
8. Howell, Steve B. Two-Dimensional Aperture Photometry: Signal-to-Noise Ratio of Point-Source Observations And Optimal Data-Extraction 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 Sun-Like 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 SlidesBackup Slides
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Camera LinearityCamera Linearity• Find out where your camera saturates in ADUs• Be sure your exposures are below saturation• Characterize using light box
Time ADU % Error0.50 609 7.085%0.96 981 3.596%2.00 1825 1.119%4.00 3455 -0.035%8.00 6734 -0.379%
16.00 13309 -0.429%24.00 19934 -0.194%32.00 26527 -0.197%40.00 33196 0.031%48.00 39818 0.065%56.00 46437 0.082%64.00 53037 0.060%72.00 59581 -0.052%
Linear up to ~ 60,000 ADU
ADU Divided by Exposure Time
600
700
800
900
1000
1100
1200
1300
0 10 20 30 40 50 60 70 80
Exposure Time (sec)
AD
Us
pe
r S
ec 59,581 ADU
QSI 516 wsg
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g * N* + npix * npixann_pix( 1 + ) * [ g *
ann_aduann_pix( ) + g * dc + ro^2 + quant ]
SNR = g *N*
Signal to Noise RatioSignal to Noise Ratio
Variable Definition NotesN* Total sky-subtracted flux (ADU) (1)
g Conversion gain (e-/ADU) (2)
npix # pixels in aperture (1)
ann_pix # pixels in annulus (1)
ann_adu Total ADU in annulus (1)
dc Dark current per pixel for exposure time (2)
ro RMS readout noise per pixel (2)
quant Quantization noise. Use 0.289*g2
(1) Measure using photometry software (AIP4WIN)(2) From CCD characterization (AIP4WIN)
Sky Noise
Dark Current
Readout Noise
Noise Terms
σ = 1.0857/SNR (mag)
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Probability of DetectionProbability 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 CalibrationMy 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