Digital Aperture Photometry ASTR 3010 Lecture 10 Textbook 9.5

Photometry How bright is the object? How bright is the object? In an object frame… In an object frame… measured brightness = source + background background (or “sky”) : all unwanted light not originated from the source  foreground + background scattered light  glow of the atmosphere  radiation from the telescope, etc. In this lecture, we will focus only on the tasks of separating signals from background and getting uncertainty of the measurement.

Digital Apertures Aperture : a circular area centered on the centroid of the object Aperture : a circular area centered on the centroid of the object Three computations in the aperture photometry: 1.Add up all pixel values inside the aperture: take into account of fractional pixels (A is a fraction of pixel’s area inside the aperture) 2.Estimate the value of the sky emission per pixel 3.Subtract the sky emission from the total count. A=1.0 A=0.7 A=0.05

When does the Aperture Photometry fails? when star images (i.e., PSFs) seriously overlap… when star images (i.e., PSFs) seriously overlap… PSF fitting photometry is better in this case! PSF fitting photometry is better in this case!  fitting a PSF to each star image and the source brightness will be the summation of “scaled” PSF pixel values.

PSF fitting versus Aperture photometry PSF fitting ≈ infinite aperture size PSF fitting ≈ infinite aperture size PSF fit Aperture background level How do we choose the right aperture size? Gaussian + constant

Best aperture size? Large Aperture include more light  larger S include more light  larger S more contamination more contamination added noise from the sky added noise from the sky  lower S/N Small Aperture less contamination less contamination losing source signal losing source signal  lower S/N

Good Aperture Size Typical choice of apertures: 0.75 to 4 times FWHM Typical choice of apertures: 0.75 to 4 times FWHM Best S/N  about 2 times the HWHM (or 1 FWHM) Best S/N  about 2 times the HWHM (or 1 FWHM) radial profile of the object (i.e., 1D PSF)

Python HW #3 (x2 weight) Using one of FITS files from HW#2, create a Python script that generates a radial profile. Using one of FITS files from HW#2, create a Python script that generates a radial profile.

Measuring Sky Sky measurement : Sky measurement : o Need to measure the sky level at the location of the source  impossible. o So, we assume that the sky does not change with location (i.e., homogeneous sky).

Measuring Sky Typically measuring the sky level from a sky annulus Typically measuring the sky level from a sky annulus o inner sky radius : as small as possible yet large enough away from the source o outer sky radius : large enough to include significant # of pixels in statistics, but not too far from the source o Not the mean pixel value: Or from a dedicated sky region Or from a dedicated sky region meanmedianmode

Measuring Sky What about the case like Super Nova embedded in a rapidly varying background? What about the case like Super Nova embedded in a rapidly varying background?

How about non-variable objects in the non-uniform sky?

1.Find all sources with PSF fitting 2.Remove detected sources 3.heavily smooth the residual image 4.subtract the smoothed residual from the source image 5.do photometry original image source subtracted image Bright sources are not perfectly subtracted. Why?

Signal and noise in an aperture see textbook pp for a detailed derivation

CCD equation log (time) log (SNR) bright source sky-limited faint star readout noise limited faint star

In summary… Important Concepts CCD equation (consult textbook!) Aperture photometry PSF fitting photometry Important Terms photon-noise limited sky-limited readout noise limited Chapter/sections covered in this lecture : 9.5