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Effective wavelength

Effective wavelength.  eff is mean  of detected photons:  eff depends on both: Passband P(  ) Spectrum shape N(  ). What if N(  ) is unknown? Then  eff is unknown too. Defining broad-band fluxes. Passband function P(  ) = probability of detecting a photon of wavelength  . x.

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Effective wavelength

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  1. Effective wavelength • eff is mean  of detected photons: • eff depends on both: • Passband P() • Spectrum shape N(). • What if N() is unknown? Then eff is unknown too.

  2. Defining broad-band fluxes • Passband function P() = probability of detecting a photon of wavelength .

  3. x CCD imaging and photometry • Image calibration: • Noise model: • Find objects: • Sort pixels by DN • Set thresholds • Decrease toward sky level.

  4. Aperture photometry • Define apertures • round / square / partial pixels allowed • Sum counts in aperture: • PROBLEM: • Noise increases with aperture size • So use smallish aperture to maximise S/N • Calibrate bias using bright stars.

  5. PSF fitting • PSF = point spread function = image of star. • Use analytic model, e.g.: • Gaussian: • DoPHOT: • 4 = 6 = 1 gives truncated series of Gaussian.

  6. Optimal extraction of stellar flux • If P(x,y) is known, scale this to fit the sky-subtracted star image: Iterate

  7. x • x0 (xi-x0)P(xi-x0) x PSF fitting • We want to find F but must also find • NUISANCE PARAMETERS: • Centroid:x0, y0 • Shape parameters:x, y, xy, 4, 6, etc. • How to find centroid: • Rough: • Refine:

  8. x x x • x0 • x0 • x0 Shape parameters • Orthogonality: • Centroid and shape parameters are roughly orthogonal to area, so small errors won’t affect photometry • true only for isolated stars Same area under fitted curves:

  9.  galaxies stars cosmics mag = -2.5 log F faint bright Automated photometry of crowded fields • e.g. DoPHOT, DAOPHOT • Set threshold, find objects. • Many objects, often overlapping • Make object list. • Store parameters F, x0, y0 , x, y, ... • Classify objects based on size/shape parameters: • star • double star • galaxy: big, not round • blemish, cosmic: small, saturated • -clip thresholds set to divide categories • Flag cosmics, saturated pixels; ignore flagged pixels

  10. Automated photometry -- continued • Find mean PSF shape parameters by weighted averages over all objects classified as stars • May be functions of position and/or brightness • Scale PSF to measure star fluxes. • Subtract all “nearby” objects before scaling. • Perform aperture photometry if desired • ITERATE!

  11. Problems with crowded-field photometry • Phantom stars • residual PSF structure near bright objects • Crowding errors/incompleteness/mis-classification • use Monte carlo tests • inject “fake” stars or other objects at random positions • see what fraction are recovered correctly with what errors in flux • Sky levels • PSF wings and large numbers of faint stars merge to create bumpy pseudo-sky • Solution: use local sky level, e.g. median of pixels in ring around object • Fit polynomial or spline to local sky levels • Boost error bars accrodingly

  12. 0 2 Non-stellar images • Design and fit appropriate models • e.g. Ellipse fitting (structure of elliptical galaxies) • Aim: find ellipses that fit image contours at specified brightnesses • Sample data around a trial ellipse • Fit truncated sin/cos series: • A: If mean contour level too high/low, expand/shrink ellipse • B, C: If ellipse not centred, adjust x0, y0 • D, E: If shape/orientation not correct, adjust ellipticity/position angle. • Plot ellipse parameters vs size or contour level to quantify radial brightness profile, twists, shifts, etc

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