1. 4/10/20101 OMSI Workshop Detecting Exo-Planet Transits: Adventures in Milli-mag Photometry Ken Hose 4/10/2010

2. 4/10/2010OMSI Workshop2 Agenda Transit detection concepts Equipment required Reducing the data Optimal aperture photometry Noise sources and dealing with noise References

3. 4/10/2010OMSI Workshop3 Dimming During a Transit Dimming K FG M Jupiter. Earth ~0.5%~0.8%~1.1%~2.1%

4. 4/10/2010OMSI Workshop4 WASP-12b Transit ST-402 Camera No Guiding No Filter 60 Sec Exposures Published Data: Transit End: 10:12PM Transit Depth: 0.015 mag WASP-12b Transit ~10:14 PM Julian Date (Add 2455269) Relative Magnitude

5. 4/10/2010OMSI Workshop5 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

6. 4/10/2010OMSI Workshop6 Star Field Around HD209458 V C K 41,314 ADU 810,930 ADU 23,744 ADU 15 Second Exposure – Red Filter HD209458

7. 4/10/2010OMSI Workshop7 What’s a Milli-mag? One-thousandth of a magnitude unit (0.001 mag) Dimming due to transit of HD 209458b ~ 0.016 mag 22 orders of magnitude Brightness difference Differential Magnitude:

8. 4/10/2010OMSI Workshop8 What Can We Detect? Adapted from Howell, ASP Conference Series, Vol. 189, 1999 Neptune F GKM Scintillation Limit Earth Large StarsSmall Stars HD 209458 is type F7 Amount of Dimming (mag) □ Amount of Dimming vs. Spectral Type (Size) Easy Jupiter

9. 4/10/2010OMSI Workshop9 Exoplanet Transit Database http://var2.astro.cz/ETD/predictions.php

10. 4/10/2010OMSI Workshop10 Amateur Equipment in Use Amateur Equipment in Use First exo-planet Detected (RV Method) in 1995 20002002 200420062008 1998 WATTS 300mm 0.005mag XO Project 200mm 0.009mag MEarth Project 40cm <0.002mag? Howell LX200 0.003mag Hudgins LX200 0.003mag Telescope Aperture (inches) 2 4 6 8 10 12 14 16 Canon B. Gary RCX400 0.003mag WASP 200mm 0.009mag

11. 4/10/2010OMSI Workshop11 My Setup Paramount ME RCOS 12.5” QSI 516 wsg SSAG

12. 4/10/2010OMSI Workshop12 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

13. 4/10/2010OMSI Workshop13 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

14. 4/10/2010OMSI Workshop14 Aperture 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 From AIP4WIN, Maxim DL, etc. Picking the right aperture is key!

15. 4/10/2010OMSI Workshop15 Differential Aperture Photometry V C K 41,314 810,930 23,744 15 Second Exposure – Red Filter HD209458 Differential Photometry:

16. 4/10/2010OMSI Workshop16Workflow AIP4WIN Raw Aperture Photometry Output Perl Script Output (csv) Excel Flux Diff Mag

17. 4/10/2010OMSI Workshop17 Noise 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 

18. 4/10/2010OMSI Workshop18 Scintillation 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 * Function of: Aperture of scope Altitude Air Mass A Fundamental Limiter!  Kepler

19. 4/10/2010OMSI Workshop19 Noise Terms V C One Single 15-second Raw Exposure.0007.004 K.007.03

20. 4/10/2010OMSI Workshop20 1-Sigma Error vs. # Photoelectrons Want > 1E6 photoelectrons For Bright Stars: Noise = 1.0857/sqrt(N*) C V

21. 4/10/2010OMSI Workshop21 Differential 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

22. 4/10/2010OMSI Workshop22 Differential Extinction BVIR Atmospheric Extinction vs. Wavelength As compared To start value

23. 4/10/2010OMSI Workshop23 Exposure 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 so Data valid for my setup—your mileage will vary

24. 4/10/2010OMSI Workshop24 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

25. 4/10/2010OMSI Workshop25 Reducing the Data (cont) Uncertainty (mag) 168 images combined using script for Maxim DL for experiment below Differential photometry done with AIP4WIN using 5-pixel radius (5/16/20)

26. 4/10/2010OMSI Workshop26 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(σ v 2 + σ c 2 ) = sqrt(0.000734 2 + 0.00368 2 ) σ(diff) = 0.0038 mag or 3.8 parts per 1000 Reduces σ c by ~1/sqrt(N) for multiple comp stars (same mag) i.e.: σ c (10 comp) = 0.31 * σ c (1 comp)

27. 4/10/2010OMSI Workshop27 Raw Data (After Calibration) σ = 0.008 One observation every 21 sec Air mass = 1.28 Air mass = 1.17 Differential Magnitude HD 209458

28. 4/10/2010OMSI Workshop28 After Some Filtering Each observation: 5 x 15 sec images stacked and median-combined Running average: [(x-1)+(x)+(x+1)]/3 Average = -3.239 σ = 0.003 σ = 0.0027 10 mmag

29. 4/10/2010OMSI Workshop29 SNR vs. Aperture Dilemma Best SNR gives wrong Magnitude (Δmag=0.209) Best SNR = 4 pixels 7.978 7.750 7.653 7.615 Flux Ratio Variable Star SNR Comp Star ΔMag = 0.209 FWHM = 3.6 pix 7.824

30. 4/10/2010OMSI Workshop30 Curve of Growth Relates Flux to Max Flux At Full Aperture. Gc, Gv ~cancel Normalized Flux Good Matching Best SNR G = 1-(1/(1+(r 2 /4.9) 1.2 )) Depends on Seeing

31. 4/10/2010OMSI Workshop31 Use Aperture for Best SNR 1.4 * FWHM Uncertainty (mag) Aperture (pixels) Measurement Uncertainty vs. Aperture Inner annulus = 16 Outer annulus = 20 (Koppelman)

32. 4/10/2010OMSI Workshop32 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)

33. 4/10/2010OMSI Workshop33 Other Sources of Noise Focus drift –Check focus every so often –Causes variations in flux measurements –Choice of Annulus and Aperture radius

34. 4/10/2010OMSI Workshop34 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/http://var2.astro.cz/ETD/ 5.Gary, Bruce. Exoplanet Observing for Amateurs. http://brucegary.net/book_EOA/x.htm 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

35. 4/10/2010OMSI Workshop35 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 24 th 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

36. 4/10/2010OMSI Workshop36 Backup Slides

37. 4/10/2010OMSI Workshop37 Camera Linearity Find out where your camera saturates in ADUs Be sure your exposures are below saturation Characterize using light box Linear up to ~ 60,000 ADU 59,581 ADU QSI 516 wsg

38. 4/10/2010OMSI Workshop38 g * N * + npix * npix ann_pix ( 1 + ) * [ g * ann_adu ann_pix () + g * dc + ro^2 + quant ] SNR = g *N * Signal to Noise Ratio Sky Noise Dark Current Readout Noise Noise Terms σ = 1.0857/SNR (mag)

39. 4/10/2010OMSI Workshop39 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

40. 4/10/2010OMSI Workshop40 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