4.3 Depth and completeness limits

The depth of the survey tile is measured by the completeness limit. It is determined for each stack and each filter separately. The depth is also checked by using the galaxy counts computed after the production of each stack, as part of the QualityFITS analysis. All completeness galaxy count plots are available from the T0007 synoptic table22 .

To compute the completeness limit, we used image simulations produced by SkyMaker(?). Noiseless images of point-like (stars or galaxy bulges) and disk-like (spiral galaxies) sources have been simulated by combining spheroid and disk models, using de Vaucouleur and exponential light profiles, respectively. The star and galaxy number densities of simulated sources correspond to the expectations for typical CFHTLS exposure times. Their slope and normalization are based on realistic luminosity function in a standard Λ-CDM cosmology (for galaxies), and are produced according to the transmission of the MegaCam filters.

The sources are then convolved by a PSF that takes into account the pupil of the CFHT telescope (mirrors and arms) and other components of the PSF. The PSF is built by using the diffraction and the simplest aberration components of the CFHT telescope, as well as the typical atmospheric contributions that degrade long exposures. A set of simulations are produced with PSF FWHM ranging from 0.4′′ to 1.3′′. For each stack, the simulated images with the closest PSF in FWHM size is then used to compute the final completeness. This “adaptive FWHM” method gives rise to larger dispersion in the completeness distribution compared to T0006. The T0007 completeness encompass both the exposure time and depth effect, as well as the image quality. The point source completeness is therefore more affected than the extended objects one.


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Figure 28: Completeness calculation for the W3 stack CFHTLS_W_i_142939+514231. Left panel: The blue and red lines shows the completeness for point-like and extended sources respectively. The green dots show the best fitting functions which are used to derive the completeness values. Right panel: galaxy counts derived automatically by QualityFITS from this stack. The red line shows the expectations for the MegaCam i-filter. The green line is the 80% completeness limit of extended objects.

The completeness limit is then derived from the averaged completeness value over the central 10000×10000 MegaCam fields. The statistics are computed in each field separately and for each filter. The output is the fraction of sources detected and measured as a function of magnitude. The magnitudes at 80% and 50% completeness are given for point-like (star or bulge) and for extended (disks) sources.

The 80% and 50% completeness values are calculated from an automated fitting process applied to the catalogues of real and simulated sources without tuning. The limiting magnitudes are derived automatically by an empirical two parameter (x0; α) fitting function

           (                   )
               erf [x-- x0]α +-1.0
y = 100.0 ×  1-        2.0
(12)

where x0 provides the turn-over position of the completeness function and α is the function slope at x0. The parameters (x0; α) are found from a standard χ2 minimization. The 50% and 80% completeness limits are derived from a linear interpolation. An example of fit is given in Fig. 28. In some cases, the fit and the interpolation are not good and the completeness value is then poorly estimated.

The completeness distributions over all the Wide fields and inside a Wide field are presented in Table ??. The left panel of Figure 29 shows the completeness distribution for the entire Wide survey for all four fields. Figure 30 shows the completeness distributions for each of the four Wide patches.

The histograms coupled to a detailed inspection of the data show that the mean scatter in completeness is 0.20 magnitudes, with significant variations from filter to filter. The completeness distribution in z-band is broader than other filters, with a tail that extends over one magnitude. In contrast, the r band distribution is narrower ( 0.15 mag.). This is due primarily to the large variations of the sky brightness through the years in that photometric band (OH emission lines), causing the variable depth on observations following a fixed exposure time model. Erratic behavior of the OH emission lines also leads to poorer correction of the fringes, aggravating the situation in the z-band.

Figure 32 shows a series of completeness maps over the entire Wide fields. The maps are produced for each Wide field and for each filter.

The left and right panels of Figure 31 shows that the completeness distribution are dominated by seeing, both for point sources and extended objects : better image quality corresponds to deeper images. Compared to the seeing contribution, the exposure time (even with double exposure time) has a smaller influence on the final depth measurement. For the u* band, the range of limiting depth is likely broadened by the diversity of observing conditions (Moon, extinction, seeing). Nevertheless, (other than exposure time) the main factor affecting image completeness is the Seeing FWHM.

The comparison with T0006 completeness is not straightforward. In T0006, the simulations were produced using a PSF of fixed FWHM equal to 0.9 arcsec. In T0007, the simulated PSF size matches the real PSF size of each tile. Since the actual seeing distribution peaks at an image quality better than 0.9 arcsec, the T0007 measured completeness of point sources is deeper than T0006. This increase in depth (around 0.02 to 0.03mag in riyz) is therefore largely due to the measurement technique rather than changes in the images.



Figure 29: Left panel: overall distribution of completeness on the Wide fields. Right panel: completeness limit of Wide stacks as a function of exposure time. A trend of increasing depth with increasing observing time is apparent. There is however a broad spread in depths at a given exposure time. due to other factors such as image quality, sky brightness and weather conditions (cirrus). The depth of some z-band stacks is also reduced by residuals from the fringe subtraction.


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Figure 30: Distribution of 80% stellar completeness over the Wide fields. The horizontal axes are MegaCam AB magnitudes.


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Figure 31: Left and right panels respectively: Stellar and extended sources completeness limit of Wide stacks as a function of seeing FWHM. As expected, the point source completeness is a clear function of the image quality: the better the seeing, the deeper the image.


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Figure 32: Maps of 80% completeness limits in W1, W2, W3 and W4 (from left to right). Each colored square represents a 1×1 deg2 tile. Square color indicates the seeing value, with darker squares have poorer seeing. From top to bottom: u*,g,r,i,y and z bands.

Finally, Figure 33 shows the galaxy counts for the four Wide patches for each of the six bands, appropriately normalized in each case to the effective area after masking. The field-to-field agreement between the different patches is excellent, as is the match to the literature values.


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Figure 33: Galaxy counts for the four Wide patches in all bands. The dotted red line corresponds to the 80% completeness for extended sources computed from the simulations. In r and i band counts are compared those in the VLT-VIRMOS deep field (?).