Checks on Photometry

Systematic errors
External comparisons
Star Colours
Limiting Magnitudes
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Systematic Errors

The photometry for the D2 and D3 is directly tied to the SDSS photometry. There are a thousand or so standards in every field. Thus, the systematic errors between the SDSS and the CFHTLS are effectively nil, with the possible exception of some aperture effects. The systematic errors in the SDSS are quoted as 2-3%.

The systematics for the D1 and D4 which are not in the SDSS will be larger. Over several photometric nights, "secondary standards" were set up the these fields using the SDSS fields as "primary standards". The night-to-night scatter for the secondary standards, (typically 0.02 to 0.03 magnitudes) is an indicator of the potential systematic error. However, since the magnitude of the "secondary standards" are averaged over several nights, the systematic error on the average should be lower. Adding in quadrature SDSS systematic error (0.025 mags) to the systematic error in transferring from the "primary" to "secondary" standards (0.025 mags) we get 0.035 magnitudes of total systetmatic error.

External comparisons

The D2 and D3 fields lie within the SDSS. This makes it possible to directly compare the magnitudes in those fields to an external reference. The figure at right shows the difference between the SDSS (transformed to the MegaCam system as described here) and the CFHTLS for the 5 bands. The agreement is very good. At bright magnitudes, for g, r and i bands, there are deviations. This is caused by the brightest stars saturating. There is no evidence for systematic shifts greater than 0.01 magnitudes There is also relatively little scatter (at least at moderate magnitudes). This argues that the colour terms in the SDSS-MegaCam transformation are fairly accurate.

Star Colours

A useful diagnostic of photometry is to examine the colours of stars. Stars have a relatively constrained locus in colour space. Any offsets between the observed and synthetic colours indicates a zeropoint error. This test can be applied to the D1 and D4 fields that do not lie in the SDSS cannot be checked directly.

The top left panel of the figure at right illustrates the selection of stars. The plot shows half-light radius plotted as magnitude. On this plot, the galaxies occupy a range of magnitudes and radii while the stars show up as a well defined horizontal locus, turning up at the bright end where the stars saturate. The red points indicate the very conservative cuts in magnitude and radius to select stars for further analysis.

The other 3 plots plots show the colours of the stars selected from the CFHTLS in this manner in black overlaid on top of the transformed SDSS star colours shown in green. No systematic shifts seem to be visible.

Limiting Magnitudes

The limiting magnitudes of the images were tested by adding fake galaxies to the images and then trying to recover them using the same parameters used to generate the real image catalogues.

The fake galaxies used were taken from the images themselves, rather than adding completely artificial galaxies. A set of 40 bright, isolated galaxies was selected out of the field and assembled into a master list. Postage stamps of these galaxies were cut out of the field. The galaxies were faded in both surface brightness and magnitude through a combination of scaling the pixel values and resampling the images.

To test the recovery rate at a given magnitude and surface brightness, galaxy postage stamps are selected from the master list, faded as described above to the magnitude and surface brightness in question and then added to the image at random locations. SExtractor is then run on new image. The fraction of fake galaxies found gives the recovery rate at that magnitude and surface brightness, An illustration of adding the galaxies is shown at right. The same galaxy has been added multiple times to the image. The galaxy has faded to various magnitudes and surface brightnesses. The red boxes contain the galaxy. The boxes are labeled by mag/surface brightness. Note the galaxy at I=23, μ_I=25 accidentally ended up near a bright galaxy and is only partially visible. Normally of course, the galaxies are not placed in such a regular grid.

To test the false-positive rate, The original image was multiplied by -1; the noise peaks became noise troughs and vice-versa. SExtractor was run, using the same detection criteria. Since there are no real negative galaxies, all the objects thus detected are spurious.

The magnitude/surface brightness plot at right shows the results of such simulations. The black points are real objects. The bottom edge of the black points is the locus of point-like objects. The green points show the false-positive detections. The red numbers show the percent of artificial galaxies that were recovered at that magnitude/surface brightness. The blue contour line shows the 80% completeness level.

Limiting magnitude and surface brightness

Deriving a single limiting magnitude from such a plot is slightly difficult. The cleaner cut in the false positives seems to be in surface brightness. Extended objects become harder to detect at brighter magnitudes whereas stellar objects are detectable a magnitude or so fainter.

The limiting magnitudes quoted on each of the Deep Field webpages represents the intersection of the 80% completeness contour (blue) with the approximate middle of the locus of detected objects (black). It it estimated by eye to the nearest half magnitude. This estimate is more vague than something like ''3% sigma detection of point sources at magnitude XYZ'' but is a more relevant measure of limiting magnitude for galaxies. For those who need a more careful measure of the detection limits of the sample, a limiting magnitude is not sufficient since surface brightness limits are clearly relevant.

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