detecting exo-planet transits: adventures in milli-mag photometry

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

4/10/20104/10/2010 OMSI WorkshopOMSI Workshop 22

AgendaAgenda• Transit detection concepts• Equipment required• Reducing the data• Optimal aperture photometry• Noise sources and dealing with noise• References


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%


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


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


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


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:


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


Exoplanet Transit DatabaseExoplanet Transit Database

http://var2.astro.cz/ETD/predictions.php


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


My SetupMy Setup

• Paramount ME• RCOS 12.5”• QSI 516 wsg• SSAG


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


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


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!


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:


WorkflowWorkflowAIP4WIN

Raw AperturePhotometryOutput

Perl ScriptOutput (csv)

Excel

Flux

DiffMag


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


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


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


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


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


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


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


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


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)


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)


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


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


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


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


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)


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)


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


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


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


Backup SlidesBackup Slides


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


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)


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


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

detecting exo-planet transits: adventures in milli-mag photometry

Documents

sample transit exposure

hd209458the transit

transit of hd

starcalculate magnitude

magnitude unit

omsi workshopreducing

right aperture

best exposure