Stellar Photometry: I. Measuring. Ast 401/Phy 580 Fall 2014

Transcription

1 What s Left (Today): Introduction to Photometry Nov 10 Photometry I/Spectra I Nov 12 Spectra II Nov 17 Guest lecture on IR by Trilling Nov 19 Radio lecture by Hunter Nov 24 Canceled Nov 26 Thanksgiving Dec 1 Astrometry/Trip to Chile Dec 3 Variability Dc 8 Review + PHY 590 presentation Dec 10 Review + PHY 590 presentation Dec 15 Final

2 Stellar Photometry: I. Measuring Ast 401/Phy 580 Fall 2014

3 Quiz List the steps necessary to reduce CCD data, and explain WHY each step is necessary.

4 Quiz List the steps necessary to reduce CCD data, and explain WHY each step is necessary.

5 A quick recap 1) Identify what part of the image we want to save ( trimsec in IRAFese) and where the overscan is located ( biassec in IRAF-ese) 2) Remove the overscan from all of the images by fitting a constant (probably) or a small gradient. 3) Average a zillion (okay, 9) bias frames, and see if there s any bias structure. If so, remove it by subtracting off the master bias frame. 4) Check that we didn t have to remove darks. 5) Combine flats (either dome flats or sky flats) filter-by-filter. 6) Divide the data by the normalized flat. 7) Check that blank sky or program frames are flat-flat.

6 Photometry Photometry means measuring how bright something is. Typical goal for photometric precision is 1%, or 0.01 magnitudes. Basically two types: Stellar photometry (point sources) Surface photometry (magnitudes per square arc sec)

7 Photometry Stellar photometry: Aperture photometry. Good in sparse fields. Point-spread-function (PSF) fitting. Needed for crowded fields

8 Aperture photometry The basic idea is that you add up all the counts within a radius of R (where R seeing disk), and then subtract sky. As always, the devil is in the details.

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10 Measuring aperture radius R

11 975 Sky annulus Measuring aperture radius R

12 Aperture photometry 1) You add up all of the counts within the measuring aperture. Call this Sum_all. 2) You use a modal definition to determine the best estimate of the sky using an annulus far from the star. Call this Sky. 3) You subtract Sky x (number of pixels) from Sum_all to get the number of counts above sky. Call this Sum_above_sky. 4) Instrumental magnitude is = -2.5log(Sum_above_sky/exptime) + C. Usually C is 20 or 25 just to make the numbers look sensible.

13 Some of the devils How large a measuring aperture should you use? Should you try to get all of the light? At what radius r does a Gaussian drop to zero?

14 r=

15 Huh? Yes, the light from a star just keeps on going, but getting fainter and fainter until it gets lost in the photon noise from the sky itself. Wow. Cosmic.

16 Aperture size Stellar profiles are not really Gaussian. There s an inner core that s dominated by seeing and guiding, an exponential drop (dominated by diffraction), and an inverse-square halo (King 1971).

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18 Core Exponential drop inverse-square

19 Aperture size Stellar profile: the inner part (core) is affected by the seeing and guiding. But the outer two parts are caused by the diffraction of light by dust particles on the mirror (and in the atmosphere).

20 So how does photometry ever work? You can never include ALL of the light of a star you re trying to measure. But you can exclude the same fraction as whatever you re using for a reference (such as a standard star). You just need to be sure you re well out on the diffraction part of the profile.

21 Aperture size So, what size aperture should you use? What to minimize the errors: If too small, too little light and errors go up. up. If too large, too much sky and the errors go Optimize size is with a radius about the same as the FWHM.

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23 Aperture size In this case, one might choose to make R be 5 pixels.

24 Another devil: the center One of the GREAT things about CCD photometry vs the old photoelectric photometry is the issue of centering the aperture on the star digitally rather than trying really, really hard to center the aperture (attached to the telescope) on the star. But, you still need a good center. Easiest thing is to determine a centroid. centroid_x = (intensity times X)/ (intensity) centroid_y = (intensity times Y)/ (intensity)

25 centroids So, a centroid definition works well unless the object is crowded.

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27 Aperture center In a crowded field, it s better to identify stars and then NOT centroid. Popular star-finding routines that are good to 1/3rd of a pixel include daofind in IRAF, and the linux Source-Extractor (SExtractor).

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29 Another devil: the sky Yet another advantage CCDs have is the ability to determine the sky values locally and simultaneously: Locally: Very useful when the background is complicated. Simultaneously: the sky brightness is constantly changing by small amounts.

30 Example of variable background

31 Sky annulus So, keep the sky annulus close to the star, but not too close. If R=5 pixels, sky annulus of is pretty good. N.B.: LOTS of pixels in that annulus: 3.14 x ( ) = 254 pixels

32 Sky annulus The other issues in the sky annulus is the issue of other stars. Consider the following example:

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34 Sky annulus The result is that the distribution of sky values is not Gaussian. So, we typically take the mode or median of the sky values.

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36 Mode

37 Aperture photometry Summary: Define center of star by centroid (if uncrowded) or adopt. Needs to be accurate to 1/10th of measuring radius. Define measuring aperture. Want to minimize errors. To minimize error, radius should be similar to the fwhm. Define sky annulus and algorithm (mode or median are good choice).

38 Aperture photometry not always a good choice

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41 Crowded field photometry Could use smaller apertures.

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43 Crowded field photometry That helps some but the light of one star is still contaminating the light of the other star.

44 Crowded field photometry An alternative to aperture photometry: pointspread-function fitting.

45 Point-spread-function (PSF) The premise of PSF fitting is that the shapes of stars are the same across the entire frame, and regardless of brightness. In other words, bright stars are not actually bigger than faint stars. The shape is

46 Bright star

47 Fainter star

48 Much fainter star

49 PSF-fitting The shape stays the same! But it gets noiser!

50 PSF-fitting First, find the stars using some mechanism, like daofind. 2) Do aperture photometry so that you know the sky value and the approximate intensity relative to the stars you ll use to define the PSF. 3) Define a good clean PSF from bright isolated stars on the frame.

51 PSF-fitting 4) Now you can fit all of the stars on the frame simultaneously. There are three parameters: x, y, and Intensity, where the Intensity is the scaling factor between the sample PSF and the star.

52 PSF-fitting 5) You can subtract the fitting PSFs from the frame to see how well you did. Also it lets you find additional stars that were hidden under the other stars.

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55 Signal-to-Noise and Magnitudes Signal-to-noise (S/N): The SIGNAL will be Number of counts above sky x gain=n_star The noise will have two components: Photon noise for Total number of photons in aperture (star+sky): sqrt (N_star+sky) Read-noise within the aperture: sqrt(p) x readnoise where p is the number of pixels within the measuring aperture, xR 2 Total Noise = sqrt( (photon_noise) 2 + (read-noise_within_aperture) 2 ) S/N = N_star / total noise.

56 Signal-to-noise Example: Your chip has a gain of 2.0 e/adu. You measure 1000 counts (ADUs) in your measuring aperture with a radius of 5 pixels. The average sky is 5.5 ADUs. The readnoise is 6 e. What s the S/N? Number of pixels is 3.14 x 25 = Sky contribution to aperture is 78.5 pixels x 5.5 ADUs = ADUs Counts above sky ( Sum_above_sky ) = = Signal is thus ADUs x 2e/ADU = e Noise: Photon noise = sqrt( 1000ADUs x 2) = 44.7 e read-noise within the aperture: sqrt(78.5) x 6e = 53.1 e Total noise = sqrt(44.7 S/N = / 69.4 = )= 69.4e In magnitudes, this corresponds to 1/16.4 = 0.06 mag

57 Signal-to-noise Wait, what? How can the uncertainty in magnitude just be 1./(S/N) in magnitudes? sigma (mag) = -2.5 log ((S ± N)/S))=-2.5 log(1+n/s) The fact that 2.5 is very similar to Euler s number e once again saves us

58 Summary Instrumental magnitude: -2.5 log (counts_above_sky/exptime)+c signal-to-noise S/N: (Sum_above_sky) x gain / total noise where total noise= sqrt( (Sum_all x gain)+npixel x readnoise 2 ) Uncertainity in magnitudes = 1.08 x (1/(S/N))

59 Homework_9 Due Nov 17 You use LMI (gain 3.0 e/adu, 6 e read-noise) to measure a star. The seeing is about 1.2, i.e., 5 pixels. a) What radius aperture should you use for measuring the star? You obtain 2000 ADUs in your measuring aperture. The average sky value is 4.5 ADUs. b) What is the S/N? c) What is the uncertainty in the magnitude? d) The exposure time was 10 seconds. What instrumental magnitude would you assign if you assume 1 ADU/sec corresponds to 25th mag?