Photometric Methods and Sources of Noise

1. Photometric Methods and Sources of Noise • CCD Detectors • Photometric measurements • Sources of Noise

2. Photometric detectors of the past: photomultipliers. Not good for transit work because you could only observe one star at a time. In 1907 Joel Stebbins pioneered the use of photoelectric devices in Astronomy

3. Charge Coupled Devices The two dimensional format makes these ideal detectors for photometry over a wide field. Keplers‘s 42 CCDs CoRoT‘s 4 CCDs

4. A „3-phase CCD“ Reading out a CCD Figure from O‘Connell‘s lecture notes on detectors Parallel registers shift the charge along columns There is one serial register at the end which reads the charge along the final row and records it to a computer For last row, shift is done along the row Columns

5. Important Parameters for Photometry • Quantum Efficiency (QE): fraction of incoming photons that are detected. • Bandpass: wavelength region for which a CCD is sensitive. Not so important for ground-based observations where you use filters, but important for space-based observations (e.g. CoRoT) that use no filters • Gain: Number of electrons needed to generate 1 data number (DN) of the output of the device. Needed to convert your recorded counts to actual photons • Charge Transfer Efficiency (CTE): Fraction of the total charge in a pixel that is transfered during the readout process. This is something like 99.999% • Readout noise: The noise introduced by reading out the device. • Bias Level: Constant voltage value added to the data to ensure that there are no negative values • Dark Current (noise): Electrons caused by thermal motion in the device • Full well: Maximum number of pixels that can be stored in a pixel before the potential well overflows or too large for the Analog to Digital Converter (ADC) • Linearity: Over what count range that the CCD output is proportional to the exposure time.

6. Bandpass: The Quantum Efficiency as a function of Wavelength The real power of CCDs is their high quantum efficiency

7. Values for a CCD used at McDonald Observatory: Gain = 0.56 ± 0.015 e–1/ADU Readout Noise = 3.06 electrons Bias level = 1024 Most of these parameters can be measured and this should be done at the start of each observing run to ensure that the device is performing as expected.

8. Overscan region Bias Level Pixel Most CCDs have an overscan region, a portion of the chip that is not exposed so as to record the bias level. You can use this so long as the bias value is completely flat across the CCD. The prefered way is to record a separate bias (a dark with 0 sec exposure) frame and fit a polynomial 2-D surface to this. This is then subtracted from every frame as the first step in the reduction. If the bias changes with time then it is better to use the overscan region

9. Mean Intensity 1.5 x 105 If the curve followed the red line at the high count rate end (and some CCDs do!) then you would know to keep your exposure to under 150.000. Otherwise for brighter stars this can affect your photometry Linearity Take a series of frames of a low intensity lamp and plot the mean counts as a function of exposure time

10. CCD GAIN For Photon statistics the variance, s = √Photons. Therefore s2 should be a measure of the number of detected photons • Take a series of frames at with a constant light level • Compute s for frames • Change the exposure time and take another series of frames calculating a new s • Plot the observed mean intensity versus the variance squared (s2) • The slope is a measure of the gain

11. CCD Gain 1.5 x 105 Mean Intensity

12. Readout Noise Signal-to-Noise Ratio Readout noise in electrons 1 0 3 10 Intensity High readout noise CCDs (older ones) could seriously affect your Signal-to-Noise ratios of observations. Readout noise is not a concern with modern CCD systems.

13. Some Problems and Pitfalls of CCD Usage Saturation If too many electrons are produced (too high intensity level) then the full well of the CCD is reached and the maximum count level will be obtained. Additional detected photons will not increase the measured intensity level: 65535 16-bit AD converter ADU Exposure time

14. Blooming: If the full well is exceeded then charge starts to spill over in the readout direction, i.e. columns. This can destroy data far away from the saturated pixels.

15. Blooming columns Saturated stars

16. Anti-blooming CCD can eliminate this effect: No blooming Blooming

17. Residual Images If the intensity is too high this will leave a residual image. Left is a normal CCD image. Right is a bias frame showing residual charge in the CCD. This can effect photometry Solution: several dark frames readout or shift image between successive exposures

18. Fringing CCDs especially back illuminated ones are bonded to a glass plate SiO2 10 mm Glue 1 mm Glass When the glass is illuminated by monochromatic light it creates a fringe pattern. Fringing can also occur without a glass plate due to the thickness of the CCD

19. l (Å) 6600 6760 6920 7080 7280 7460 7650 7850 8100 8400 Depending on the CCD fringing becomes important for wavelengths greater than about 6500 Å. For example, for the Tautenburg TEST we get better precision in a V filter rather than an R filter

20. Basic CCD reductions • Subtract the Bias level. The bias level is an artificial constant added in the electronics to ensure that there are no negative pixels • Divide by a Flat lamp to ensure that there are no pixel to pixel variations • Optional: Removal of cosmic rays. These are high energy particles from space that create „hot pixels“ on your detector. Also can be caused by natural radiactive decay on the earth.

21. Flat Field Division Flat Field Raw Frame Raw divided by Flat Every CCD has different pixel-to-pixel sensitivity, defects, dust particles, etc that not only make the image look bad, but if the sensitivity of pixels change with time can influence your results. Every observation must be divided by a flat field after bias subtraction. The flat field is an observation of a white lamp. For imaging one must take either sky flats, or dome flats (an illuminated white screen or dome observed with the telescope). For spectral observations „internal“ lamps (i.e. ones that illuminate the spectrograph, but not observed through the telescope are taken. Often even for spectroscopy „dome flats“ produce better results, particularly if you want to minimize fringing.

22. Make sure you do not have multiple readout amplifiers! Typical CCD readout times are 90 – 240 secs, depending on the size of the CCD. This is for single amplifier CCDs. To reduce the readout time some devices can have 4 channels (amplifiers) for readout: Serial register with one amplfier 4 Serial registers with 4 amplfiers 4 Channel CCD Normal readout 4 channel CCD cuts readout time by a factor of 4. Problem: each quadrant usually behaves differently, with its own bias, flat field response, etc. In the data reduction 4 channel CCDs have to be reduced as if they were 4 independent frames.

23. CCD Photometry CCD Imaging photometry is at the heart of any transit search program • Color photometry • Aperture photometry • PSF photometry • Difference imaging

24. Filter Characteristics of Astronomical Photometry Systems

25. But first a few words about color photometry From http://cas.sdss.org/dr5/en/proj/advanced/color/making.asp Color indices are a measure of the shape of the black body curve and thus the temperature. In transit searching you need to find the right kind of stars (cool main sequence stars). Often you have to rely on color photometry

26. But for cool stars there is a degeneracy between main sequence and giant stars. You should see 2 branches if you can measure the color or brightness Avoid stars with B–V values lower than 0.5 For detecting transiting planets you should avoid giant stars as well as early-type main sequence stars Color photometry is a poor persons way of getting a crude spectral type. Done for faint stars or over a wide field where you can get classifications of many stars

27. Giants (most likely) If all works well the B–V should tell you the luminosity class If you really want to get the spectral type of a star get a spectrum!

28. From http://www.ucolick.org/~kcooksey/CTIOreu.html Giant stars Main sequence stars For field stars the apparent magnitude does not tell you the true luminosity. Therefore, color-color magnitude diagrams are often employed, and infrared colors being the best

29. Photometry gives the spectral type as a K0 Main Sequence star But this does not fit the spectrum

30. It is a giant!

31. Spectral determination Photometric determination Interstellar redening can affect the colors of stars. It is best to take a spectrum

32. Get data (star) counts Get sky counts Aperture Photometry Magnitude = constant –2.5 x log [Σ(data – sky)/(exposure time)] Instrumental magnitude can be converted to real magnitude by looking at standard stars

33. Aperture photometry is useless for crowded fields

34. Term: Point Spread Function PSF: Image produced by the instrument + atmosphere = point spread function Camera Atmosphere Most photometric reduction programs require modeling of the PSF

35. Crowded field Photometry: DAOPHOT Computer program developed to obtain accurate photometry of blended images (Stetson 1987, Publications of the Astronomical Society of the Pacific, 99, 191) DAOPHOT software is part of the IRAF (Image Reduction and Analysis Facility) IRAF can be dowloaded from http://iraf.net (Windows, Mac) or http://star-www.rl.ac.uk/iraf/web/iraf-homepage.html (mostly Linux) In iraf: load packages: noao -> digiphot -> daophot Users manuals: http://www.iac.es/galeria/ncaon/IRAFSoporte/Iraf-Manuals.html

36. In DAOPHOT modeling of the PSF is done through an iterative process: • Choose several stars as „psf“ stars • Fit psf • Subtract neighbors • Refit PSF • Iterate • Stop after 2-3 iterations

38. Original Data Data minus stars found in first star list Data minus stars found in second determination of star list

40. S ([R*K](xi,yi) – I(xi,yi))2 i Image Subtraction If you are only interested in changes in the brightness (differential photometry) of an object one can use image subtraction (Alard, Astronomy and Astrophysics Suppl. Ser. 144, 363, 2000) • Get a reference image R. This is either a synthetic image (point sources) or a real data frame taken under good seeing conditions (usually your best frame). • Find a convolution Kernal, K, that will transform R to fit your observed image, I. Your fit image is R*Iwhere * is the convolution (i.e. smoothing) • Solve in a least squares manner the Kernal that will minimize the sum: Kernal is usually taken to be a Gaussian whose width can vary across the frame.

41. Observation Reference profile: e.g. Observation taken under excellent conditions Smooth your reference profile with your Kernel function. This should look like your observation In a perfect world if you subtract the two you get zero, except for differences due to star variabiltiy In pictures:

43. These techniques are fine, but what happens when some light clouds pass by covering some stars, but not others, or the atmospheric transparency changes across the CCD? You need to find a reference star with which you divide the flux from your target star. But what if this star is variable? In practice each star is divided by the sum of all the other stars in the field, i.e. each star is referenced to all other stars in the field. T: Target, Red: Reference Stars T/A = Constant T/B = Constant T/C = variations C is a variable star T A B C

44. Sources of Noise in Light Curves :The Good, The Bad, and The Ugly • White Noise (The Good). Noise due to photon statistics that does not produce false transit signals. If you want to decrease your noise and improve your chances of detecting a transit, just collect more photons. This is uncorrelated noise. • Red Noise (The Bad): Noise that is correlated and not random often associated with atmospheric extinction. Collecting more photons will not decrease your noise. Not only does red noise mask signals, it can create false transit signals. • Intrinsic Stellar Noise (The Ugly): Noise that is associated with intrinsic variability on the star (e.g. spots or pulsations). This is difficult to quantify and can be difficult to remove from your data. It is often periodic and associated with stellar rotation, oscillations, etc.

45. White Noise versus Red Noise White noise Red noise In Fourier space correlated noise has an amplitude spectrum that has structure in it. Often this rises to low frequency and is thus called „red“ noise. This is the Fourier spectrum of the same random noise as the right panel, but with a trend. In Fourier space (frequency) white noise has an amplitude spectrum is constant as a function of frequency. This is the Fourier amplitude spectrum of random noise

46. Fourier Noise versus Noise FT of a time series twice as long, but with the same level of random noise FT of a time series of random noise With constant noise in the time domain with rms s, the more data you take, the noise level is still the same, i.e. s does not change. In the Fourier domain the Fourier noise floor becomes less the more data. This is why the more data you take, the easier it will be for you to detect a periodic signal above the noise level (which is dropping). Rule of thumb: a peak that has an amplitude 4 times the surrounding noise level has a false alarm probability of 0.01 (99% chance it is a real signal).

47. Sources of White Noise photometric noise: 1. Photon noise: error = √Ns (Ns = photons from source) Signal to noise ratio = Ns/ √ Ns = √Ns rms scatter in brightness = 1/(S/N) Photon noise is often referred to as Gaussian, White, or Uncorrelated noise (i.e. independent of other parameters like air mass). Note: your counts detected by your CCD need to be multiplied by the gain to get real photons detected.

48. Sources of White Noise 2. Sky: Sky is bright, adds noise, best not to observe under full moon or in downtown Jena. Error = (Ndata + Nsky)1/2 S/N = (Ndata)/(Ndata + Nsky)1/2 rms scatter = 1/(S/N) Ndata = counts from star Nsky = background

49. Nsky = 1000 Nsky = 100 Nsky = 10 Nsky = 0 rms Ndata

50. Sources of White Noise 3. Dark Counts and Readout Noise: Electrons dislodged by thermal noise, typically a few per hour. This can be neglected unless you are looking at very faint sources Readout Noise: Noise introduced in reading out the CCD: Typical CCDs have readout noise counts of 3–11 e–1 (photons). This can also be neglected