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Detecting Exo-Planet Transits: Adventures in Milli-mag Photometry

Detecting Exo-Planet Transits: Adventures in Milli-mag Photometry. Ken Hose 4/10/2010. Agenda. Transit detection concepts Equipment required Reducing the data Optimal aperture photometry Noise sources and dealing with noise References. Jupiter. K. M. F. G. Earth. ~0.5%. ~0.8%.

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Detecting Exo-Planet Transits: Adventures in Milli-mag Photometry

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

  2. Agenda • Transit detection concepts • Equipment required • Reducing the data • Optimal aperture photometry • Noise sources and dealing with noise • References OMSI Workshop

  3. Jupiter . K M F G Earth ~0.5% ~0.8% ~1.1% ~2.1% Dimming During a Transit Dimming OMSI Workshop

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

  5. 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 OMSI Workshop

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

  7. 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: 22 orders of magnitude Brightness difference OMSI Workshop

  8. Amount of Dimming vs. Spectral Type (Size) HD 209458 is type F7 Easy □ Jupiter Amount of Dimming (mag) Neptune Earth Scintillation Limit F G K M Large Stars Small Stars Adapted from Howell, ASP Conference Series, Vol. 189, 1999 What Can We Detect? OMSI Workshop

  9. http://var2.astro.cz/ETD/predictions.php Exoplanet Transit Database OMSI Workshop

  10. 16 14 12 10 8 6 4 2 Amateur Equipment in Use First exo-planet Detected (RV Method) in 1995 MEarth Project 40cm <0.002mag? B. Gary RCX400 0.003mag Hudgins LX200 0.003mag Howell LX200 0.003mag Telescope Aperture (inches) Canon WATTS 300mm 0.005mag XO Project 200mm 0.009mag WASP 200mm 0.009mag 1998 2000 2002 2004 2006 2008 OMSI Workshop

  11. My Setup • Paramount ME • RCOS 12.5” • QSI 516 wsg • SSAG OMSI Workshop

  12. 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 OMSI Workshop

  13. 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 OMSI Workshop

  14. Inner Annulus Outer Annulus Aperture 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. Picking the right aperture is key! OMSI Workshop

  15. Differential Photometry: V 810,930 C 41,314 K 23,744 Differential Aperture Photometry HD209458 15 Second Exposure – Red Filter OMSI Workshop

  16. AIP4WIN Raw Aperture Photometry Output Perl Script Output (csv) Excel Flux Diff Mag Workflow OMSI Workshop

  17. Raw Time Series Differential Magnitude Data For HD209458 +0.008 Mag +1σ Average -0.008 Mag -1σ Time  Noise in Time Series Measurements Noise is measured as the 1-sigma variation in magnitude OMSI Workshop

  18. zenith * ϕ Air mass = 1 / cos ϕ Scintillation Noise • Buchheim explains it as small thermal fluctuations that act like weak lenses to cause stars to brighten and dim randomly—Causes twinkling A Fundamental Limiter!  Kepler Function of: Aperture of scope Altitude Air Mass OMSI Workshop

  19. One Single 15-second Raw Exposure V .0007 .004 C .007 K .03 Noise Terms OMSI Workshop

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

  21. From SkyMap Pro V C K Differential Extinction • As air mass changes, differential magnitude will change if stars are not the same color • Red filter minimizes the effect OMSI Workshop

  22. B V R I Differential Extinction Atmospheric Extinction vs. Wavelength As compared To start value OMSI Workshop

  23. Exposure Time vs. Error Should be able to image down to magnitude >=12 or so Data valid for my setup—your mileage will vary Red: Greater than 5 minutes—may under sample transit Exposure time in seconds with red filter OMSI Workshop

  24. 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 OMSI Workshop

  25. Uncertainty (mag) 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) OMSI Workshop

  26. 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) OMSI Workshop

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

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

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

  30. G = 1-(1/(1+(r2/4.9)1.2)) Normalized Flux Good Matching Best SNR Curve of Growth Depends on Seeing Relates Flux to Max Flux At Full Aperture. Gc, Gv ~cancel OMSI Workshop

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

  32. 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) OMSI Workshop

  33. Other Sources of Noise • Focus drift • Check focus every so often • Causes variations in flux measurements • Choice of Annulus and Aperture radius OMSI Workshop

  34. References • Howell, Steve B. Introduction to Time-Series Photometry Using Charge-Coupled Devices. J. AAVSO volume 20, 1991 • Castellano et al. Detection of Extrasolar Giant Planets With Inexpensive Telescopes and CCDs. J. AAVSO Volume 33, 2004 • 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 • Exoplanet Transit Database. http://var2.astro.cz/ETD/ • Gary, Bruce. Exoplanet Observing for Amateurs. http://brucegary.net/book_EOA/x.htm • Buchheim, Robert. The Sky is Your Laboratory. • 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 OMSI Workshop

  35. References (cont.) • 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 • Koppelman, Michael. Uncertainty Analysis in Photometric Observations. The Society for Astronomical Sciences 24th Annual Symposium. SAS, 2005, p.107 • Charbonneau, et al. Detection of Planetary Transits Across a Sun-Like Star. The Astrophysical Journal. 2000 January 20 • 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 OMSI Workshop

  36. Backup Slides OMSI Workshop

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

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

  39. 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 OMSI Workshop

  40. 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 OMSI Workshop

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