Photometry La Palma trip 2014 Lecture 2 Prof. S.C. Trager
Photometry is the measurement of magnitude from images technically, it s the measurement of light, but astronomers use the above definition these days This sounds simple, but there are several steps required! We ll focus here on photometry of objects from twodimensional images (detectors) similar (if not all) steps are needed when using singlepixel detectors like photomultiplier tubes
The process of photometry 1. Find the location(s) of the object(s) of interest (perhaps all) 2. Determine the background level(s) B of the object(s) (per pixel) 3. Calculate the integrated source intensity I for each object. To do this, sum S counts from N pixels. Then I = S N B
The process of photometry 4. Determine the magnitude: m = 2.5 log 10 I + C where C is the photometric zero point 5. Determine the photometric zeropoint(s), airmass correction(s), and color term(s) (if needed) using photometry of standard objects (almost always these are standard stars)
Background estimation It is always preferable to find the background as close to the object as possible When measuring magnitudes of compact objects (stars, small galaxies), it is common to determine the background in an annulus around the object object sky annulus
Background estimation the annulus is often circular or elliptical, but can be more complicated shape not done when doing surface photometry object sky annulus
Background estimation Once the counts in the sky annulus have been measured, compute a histogram of these values then take the mode of the distribution (the most probable value) to determine the background level per pixel #of pixels Mode (peak of this histogram) Median (1/2 above, 1/2 below) Counts Arithmetic mean Because essentially all deviations from the sky are positive counts (stars and galaxies), the mode is the best approximation to the sky.
Background estimation For surface photometry, you should fit a constant value or a plane or a surface to blank regions of the image and subtract this from the entire image Note: surface photometry is the measurement of magnitudes per unit area (on the sky)
Determining source intensity There are two approaches to this step, depending on need and source type: aperture photometry PSF (fitting) photometry (which we ll skip for now )...and there s also surface photometry, which we ll describe briefly below
Aperture photometry In this case, we count the flux from the object and the sky within some aperture typically we use circular apertures for stellar photometry, but the apertures can be arbitrarily shaped for, say, complex galaxies Then the source intensity X is I = aperture I ij B N aperture
Aperture photometry Problems... How big should the apertures be? Ideally, you d like to get all of the light from your object... but even stars have very extended images Profile of a stellar image on a photographic plate (King 1971)
Aperture photometry Note that a Gaussian profile contains 99% of its light within 10σ 4 FWHM (because FWHM=2.355σ) But! As the aperture grows, S = P aperture I ij increases, but so does Naperture B (because N gets bigger) therefore the noise increases, because N r 2, where r is the radius (size) of the aperture therefore the maximum S/N occurs at some intermediate radius, depending on FWHM
Aperture photometry If we restrict size to maximize S/N, we re not measuring all of the flux Either measure and compare all objects through the same aperture...or... Use the fact that the profile is the same for all stars (hopefully!) and measure a bright, well-exposed, unsaturated, isolated star out to 4 FWHM. Then use the magnitude between this aperture and your smaller aperture to correct all the photometry
Curve-of-growth analysis 0.05!mag[aper(n+1) - aper(n)] 0-0.05-0.10-0.15 5 10 15 20 25 30 Aperture Radius
Aperture photometry More problems... Cosmic rays or bad pixels contaminating your aperture just discard this object why didn t you take multiple images? Nearby stars (or other objects) contaminate your aperture not a problem for sky estimate because we used the mode but if your aperture is contaminated, need to discard object
Surface photometry Like aperture photometry on a large scale Determines intensity per unit (angular) area on the sky:!! X SB = I ij B N aperture /area aperture Often use elliptical apertures for this Surface photometry gives light profile and shape information (using parameters of aperture fits)
Surface brightness profiles The surface brightness of a galaxy I(x) is the amount of light contained in some small area at a particular point x in an image Consider a square area with a side of length D of a galaxy at distance d. This length will subtend an angle = D/d If the total luminosity of the galaxy in that area is L, then the received flux is F = L/(4 d 2 )
So the surface brightness is! I(x) =F/ 2 = L/(4 d 2 )(d/d) 2 = L/(4 D 2 ) which is independent of distance note that this is not true at cosmological distances! The units of I(x) are usually given in L pc 2
Often the magnitude per square arcsecond is quoted as the surface brightness:! µ (x) = 2.5 log I (x) + constant In the B-band, the constant is 27 mag/arcsec 2, which corresponds to 1 L pc 2 Thus I B = 10 0.4(µ B 27) L,B pc 2
Photometric calibration To determine our photometric zeropoints,! m = 2.5 log 10 I + ZP we need to observe objects usually stars of known magnitudes and colors at many different hour angles
Photometric calibration We need to correct three major effects: 1. overall magnitude offset: what magnitude corresponds to, say, one e /s at X=1? 2. color shifts between your filters and the standard stars filters 3. atmospheric extinction note that there will also be different k λ for different-colored stars, because of the width of the broadband filter compared to the slope of k λ and the shape of the stars spectra
Color terms
Photometric calibration Combining 1) and 2), we have m! true = m 0,inst + b 0 + b 1 c + b 2 c 2 + where c is the color of your object And 3) means V=v 1 +a 0! m 0,inst = m X kx + k 0 cx where c is the color, k is the extinction coefficient, k is the differential color extinction coefficient, and m X is the magnitude observed at airmass X just magnitude zeropoint RMS=0.055
Photometric calibration Combining 1) and 2), we have m! true = m 0,inst + b 0 + b 1 c + b 2 c 2 + where c is the color of your object And 3) means V=v inst + c 0 + c 1 X! m 0,inst = m X kx + k 0 cx where c is the color, k is the extinction coefficient, k is the differential color extinction coefficient, and m X is the magnitude observed at airmass X zeropoint and airmass RMS=0.032
Photometric calibration Combining 1) and 2), we have m! true = m 0,inst + b 0 + b 1 c + b 2 c 2 + where c is the color of your object And 3) means V=v inst +c 0 +c 1 X+c 2 (B-V)! m 0,inst = m X kx + k 0 cx where c is the color, k is the extinction coefficient, k is the differential color extinction coefficient, and m X is the magnitude observed at airmass X RMS=0.021 zeropoint, airmass, and color
Photometric calibration Thus, for a star of known mtrue and c observed at X,! m true = m X + a 0 + a 1 X + a 2 c + a 3 cx + a 4 c 2 + Since each star satisfies this equation, a system of linear polynomial equations exist, and we can invert this system to get our necessary coefficients ai Lists of standard stars can be found in papers by Landolt, Graham, and Stetson, and should be available at any observatory!
The photometry Golden Rules Always observe standard stars with colors bracketing the colors of the objects you want to calibrate Always observe standard stars at airmasses spanning the airmasses of your target exposures Only use very clear (photometric) weather! No clouds.
The photometry Golden Rules Use blue filters at low X and least moon Save red filters for higher airmasses and more moon Try to work at X<1.5 On big telescopes (>2m) with CCD cameras, standard stars are very easy to saturate Use short exposures to get bright standard stars but not too short to avoid scintillation (>5 10 s) Use longer exposures to get faint standard stars