Point Spread Functions. Aperture Photometry. Obs Tech Obs Tech 26 Sep 2017

Transcription

1 Point Spread Functions & Aperture Photometry Obs Tech Obs Tech 26 Sep 2017

2 Point Spread Functions (PSFs) Stars are far away (typically d >> 3x10 15 km) Stars are relatively small (D ~ 10 6 km) Angular spread D/d = 3x10-10 rad < 60 microarcsec This is very close to "point-like" Atmospheric turbulence blurs this to ~1 arcsec The shape of the blur is the "point spread function" p p p (how the light from a point is spread out)

3 What do PSFs look like? Surface plot of bright star in skysubtracted version of pstds.0001 Axi-symmetric, centrally peaked Basically 2-D Gaussian

4 PSF: Real vs. Gaussian Real Star 2-D Gaussian Difference

5 Implications Atmospheric turbulence produces Gaussian profiles (Central Limit Theorem) If turbulence dominates (typically true), we can understand PSFs Light from stars spread all over the place 1 radius 67% insideid 2 radius 95% inside 3 radius 99.8% inside

6 Why ydo brighter big stars appear larger than fainter stars? Hint1: The turbulence is the same PSF is the same Hint2: We don't see starlight everywhere. A Question:

7 Stellar Photometry We want the starlight, the whole starlight, and nothing but the starlight We went to great efforts to get rid of nonstarlight effects But the whole starlight Gaussian PSF means light spread all over the sky (with exponentially decaying amplitude) What do we do?

8 Gaussian-Selected Aperture Photometry If we select a fiducial radius in terms of the Gaussian, we know what fraction of the total signal is inside that radius So... we measure the Gaussian shape using a bright star in the image (gauss2dfit.pro) We then measure the total number of ADU inside id some radius r As long as r is constant in (not necessarily in pixels), we can compare fluxes between images

9

10

11 How many?(cont.) So, the best number depends on the star But, we MUST choose 1 value for consistency Note that even for bright stars, ~2-3 gives near maximum Signal/Noise Also, must deal with other real-world effects (e.g. crowding/overlap)

12 One last thing IR sky varies fast (remember?) So: Image 0001 has 2.7 ADU/pixel residual sky background 0002 has -1.0 ADU/pix 0003 has has has has -0.3 etc.

13 Aperture Photometry (finally) Use bright star to get (why bright?) using gauss2dfit Pick fiducial num_sigma Find star center (not usually integer pixels) Get total flux inside num_sigma radius, and num_pixels Get average sky flux per pixel from annulus Subtract num_pixels*sky_ave from total flux Done! (Sort of...)

14 Practical points Getting ggaussian fits Getting star centers (gaussian fit or centroid?) Centroid: i c = ( i j i*im(i,j))/(σ i Σ j im(i,j)) j c = (Σ i Σ j j*im(i,j))/(σ i Σ j im(i,j)) Choosing annular regions for background

15 PSF-Fitting Fitting Photometry Obs Tech 24 Sep 2013

16 WhydoPSF-fitting? Star light not uniformly distributed inside aperture 2-D Gaussian (duh) Sky noise is uniformly distributed So, points far from center of aperature have much lower signal-to-noise noise ratio why give them equal weight? PSF-fitting (Gaussian fitting) gives lower weight to pixels expected to have lower SNR

17 PSF-Fitting Fitting Theory Amplitude = F pix /e -(r2/2* 2) Optimal weighting 1/ 2 2 A = 2 pix (e r2/2* 2 ) 2 For star flux dominated (bright star), this simplifies to simple aperture photometry For sky noise dominated (faint star), this simplifies to Gaussian weighting So, aperture photometry often OK PSF-fitting i photometry sometimes better...

18 PSF-Fitting Fitting Application Need to develop model for PSF usually NOT a simple Gaussian in real life PSF often changes across field of view as well Very hard to do by hand Typically rely on DAOPhot or similar code

19 Photometric Calibration: How bright IS it?

20 A Photometric Summary: We've subtracted sky background, electronic offsets, dark current We've corrected small-scale gain & QE variations iti We've corrected bad pixels and cosmic rays We've measured the (correct) number of ADU/s from a star Now, we need to convert this number of ADU to a physical flux standard star calibration

21 Photometric units Flux is energy per unit area per unit time ergs cm -2 s -1 W m -2 ADU/s (relative units) Absolute calibration is tough (sky and optical transmission, detector QE calibration, etc.) Vega ( Lyra) is THE standard star best absolute calibration (~10%) All other standard stars calibrated RELATIVE to Vega, using the magnitude system

22 Stellar Magnitudes Thus, stellar magnitudes are excellent relative brightness measurements, but mediocre absolute measurements Given two stars with fluxes (ADU or other units) we calculate the magnitudes m 2 -m 1 = -2.5 log(f 1 /F 2 ) mag g = 2.5 factor of 10 mag = 1.0 factor of 2.5 Larger mag fainter star (and vice versa)

23 Standard Star Calibration Measure ADU/s from target (F targ ) Measure ADU/s from standard star (F std ) Standard star has known magnitude (m std ) relative to Vega Magnitude of target is: m targ = -2.5*log(F targ /F std ) + m std

24 It's not quite that easy... This calibrates out the optical transmission, overall gain & QE, and rough atmospheric transmission Optical system, gain, QE generally constant Atmosphere roughly constant on good nights, but transmission depends on airmass (sec z) [explain airmass] Need atmospheric correction mag(z) = mag 0 + *sec(z)

25 Some common calibration mistakes Always compare ADU/s; same band; same telescope/instrument Always compare same aperture size (in ) Use normalized flatfield (or same flatfield image) Use same filter band Use band-dependent depe de atmospheric correction (varies night to night)

26 Extended Object Photometry Obs Tech Obs Tech 26 Sep 2017

27 Observing Extended Objects For point sources, we combine dithered images to get sky frames For this to work, most of the pixels in the image must be "sky-only" (no starlight); thus, median will pick the sky value For large extended targets (comparable to the field of view), this won't be the case So, the "standard" dither approach we have used will not work

28 Extended Targets - Solutions Sol'n 1: Dither around on target; move completely off-target and repeat dither; median-combine off-target frames for sky background; subtract this from individual ontarget frames; [why dither target?] Sol'n 2: Suck it up [meaning: do lots of ontarget dithering and median-combine; this will smooth out the pseudo-sky frame; this frame will have some residual target flux in each pixel; if this is small OK (?)]

29 Galaxy Photometry Stars are intrinsically "point-like" if you know the PSF shape (2-D Gaussian), measure some portion of it and extrapolate to total flux (e.g. 2 Galaxies are not point-like; in addition to the PSF, they have their own distribution of light F(x,y) Galaxy light comes from stars, clouds, etc. lumpy But, ~10 11 stars, etc. averages to smooth

30 Surface brightness Measure brightness per unit area as a function of position = "surface brightness" Typically units are magnitudes per square arcsecond Why use this? Because integrated brightness difficult/impossible to measure (vs. stars) More below...

31 "Iso" = same "phote" = light "Isophote" = same light Contours of equal light levels (units of mag per sq. arcsec) Useful for defining light profiles of galaxies - F sb (R) Isophotes

32 Types of Galaxies ë Elliptical Galaxy Spiral Galaxy ë R = sqrt(r 1 *r 2 ) R = radius ë Includes inclination Inclination elliptical

33 Galaxy Profiles "de Vaucouleurs law" F sb (R) ] exp(-r 1/4 ) Applies to elliptical galaxies; (Why?) Spiral galaxies have two components: bulge follows de Vaucouleurs law; disk follows F sb (R) ] exp(-r); (Why?) These are NOT caused by statistical averages of atmospheric turbulence, they are intrinsic to the galaxies Thus, they are typical approximations, NOT exact/correct; sometimes dead wrong

34 Isophotal Exceptions Foreground stars (can subtract using PSF model) dl) Nebulae in the galaxy ("valid" light) Dust lanes in the galaxy (ditto) Azimuthal asymmetry (e.g. Spiral galaxies) Irregular galaxies Isophote twists in otherwise "normal" galaxies

35 Misfit Galaxies - I

36 Misfit Galaxies - II

37 Misfit Galaxies - III Isophote twists in a spiral lbulge

38 So, now what? Given their limitations, isophote analysis is still useful Galaxy "effective radius" radius which encloses 50% of the total light Problem: How do you know light distribution shape (necessary for knowing "total light")? Answer: Assume de Vaucouleurs and/or exponential profiles But... are these correct? Probably not...

39 Other isophotal parameters Radius at the xx th mag isophote E.g. radius at V= 25 mag/sq. arcsec isophote This is an easily-definable quantity observationally Problem: To what physical quantity does this correspond? How does that complicate things?

40 Summary Very extended objects require different data- taking approaches Important concept for analysis are surface brightness and isophotes Surface brightness profiles have descriptive "laws" (which are broken more often than not) Isophote analysis can help quantify things, but is far from perfect This is all FAR more complicated than stars...