5.4 Depth and completeness limits

The depth is measured the same way as in Section 4.3. The completeness limits and galaxy count plots are available in the synoptic table.

The depths of D-25 and D-85 are given in Tables 17 and 18 for the median combined stacks and Tables 19 and 20 for the sigma-combined stacks. These numbers are also presented in the synoptic table. The errors quoted for the completeness limits in the Tables are dominated by the fitting error. For the 80% and 50% values, this is due to sparse sampling of the curve in the magnitude range where the variations of the completeness as a function of magnitude are important.

From Figure 47, the 80% completeness limits of stellar sources is a good indicator of the turn-over magnitude for the galaxy counts. Similarly, the 80% completeness limits of extended sources corresponds well to the turnover point where the galaxy counts begin to be incomplete. This is however not true for the u*-band data, where both depth parameters have similar values and also for the z-band, where the completeness limit value is lower than the turnover point and appears to be a pessimistic estimate of depth.

We note that the completeness limit measurements with simulated sources in the Deep data seem to be in poorer agreement with the galaxy counts plots in comparison to the Wide survey (see Fig. 28). Furthermore, the Deep D-25 estimates are closer to expectations than D-85. This is most likely a consequence of increased crowding in deeper images. In these D-85 images, the fraction of blended sources indeed increases and makes the unambiguous detection of simulated sources more and more difficult.

The D2-u* should be interpreted with caution. As it contains a mix of CFHTLS and cosmos images that are shifted by 30 arc-minutes, the center of the stacks is deeper and the corners are shallower than the mean depth of the stack (see Fig. 45). Note that the total exposure times and the depths quoted in the Tables and on the figures for the D2-25-u* and D2-85-u* do not apply to the entire image.

Figure 45: Weightmap images of the D2 CFHTLS_D-85_u_100028+021230_T0007 (left) and CFHTLS_D-85_i_100028+021230_T0007(right) stacks. The mosaicing of the D2-u* field by CFHTLS and COSMOS data produces a heterogeneous stack, with significant variations of the exposure times and depths over the field. The contrast with the i-band (and other filters) is striking. The innermost bright region of the D2-u* weight-map corresponds to the central squares inside the bold contours drawn on Fig. 46, and the numbers quoted on Tables 17 and 18 for the D2-u* stacks are only relevant for the regions inside the black contours.

The D2-u* is the only Deep stack with a non-uniform field coverage. The observing sequences were split into five positions of MegaCam with respect to the Deep D2 center field. They are referenced as:

Figure 46: Locations of u*-band pointings used to produced the D2-u* stack. The colored squares represent the different MegaCam fields, and the colored points are the center positions of each CFHTLS and COSMOS images that are combined to produce the D-25-u* and D-85u* images. The dark squares are located at the D2 center position and outline the contour of the final D2-u*. The D2-u* characteristics quoted in Tables 17 and 18 only refer to the central regions delimited by the black squares. The bold squares show the central region containing all exposures. The stacks inside this narrow region are extremely deep: 51012 s. for D2-u*-25, and 142970 s. for D2-u*-85.

The relative positions of D2-cc, D2-ul, D2-ur, D2-ll and D2-lr are shown on Fig. 46. The black contours outline the shape of the D2-u* stacks. All colored areas located inside are combined to produce the D-25-u* and D-85u*, which explains the complex weightmap shown on the left panel of Fig. 45.

The complex mosaic pattern and the division of observations amongst several observing runs results in a non-uniform completeness for the D2-u* stacks. The exposure time and depth can only be defined locally over for the D2-u* MegaCam field. Table 22 describes the observations in sub-quadrants drawn on Fig. 46. Each quadrant of D-25-u* and D-85-u* combines the cc images with either D2-ul, or D2-ur, or D2-ll, or D2-lr, while the central part combines them all. A global estimation of exposure time and depth for D2-u* is clearly impossible. Note that the exposure times inside the bold contours of Fig. 46 are 51012 s. and 142970 s., for the D2-u*-25 and D2-u*-85 stacks, respectively.

In contrast, the seeing is more uniform. The last column of Table 22 provides the mean seeing, as derived from the median seeing value of the single MegaCam exposures comprising D2-cc, D2-ul, D2-ur, D2-ll and D2-lr. The errors are the rms of the mean. None of the seeing values are further than 1-σ from the mean.

Stacks labelled SIGWEI have been combined using a sigma-clipping method. Sources in such a sigma-clipped image combination should have slightly better signal-to-noise ratios (around 20%) compared to a median-combined image. Our results do show a modest improvement in u and z (0.1 to 0.2 mag) but almost no improvement within the error bars in r and i. We note that this result has to be considered with caution since the gri bandpasses suffer from crowding, and the technique of adding simulated objects to a field where a large fraction of pixels are already masked (due to the presence of objects) is necessarily problematic. Other methods should be investigated to test the improvement of depth with the combination method.

cfhtls+cosmos Reference center Number of Total Exp. Mean Seeing rms
D2-u* field ra ; dec Exposures time
name [J2000] [s] ["]

D2-cc-25 10:00:28.00 ; +02:12:30 37 19663 0.827 0.133
D2-cc-85 37 19663 0.827 0.133
D2-ul-25 10:01:48.00 ; +02:24:44 15 6393 0.812 0.019
D2-ul-85 61 31004 0.909 0.080
D2-ur-25 09:58:50.00 ; +02:24:44 15 12482 0.730 0.059
D2-ur-85 58 27892 0.853 0.099
D2-ll-25 10:01:48.00 ; +01:49:47 15 19299 0.716 0.019
D2-ll-85 64 32805 0.840 0.098
D2-lr-25 09:58:50.00 ; +01:49:47 15 12866 0.690 0.044
D2-lr-85 62 28325 0.865 0.124

Table 22: Overview of the mosaicing of u*-band observations over the five pointings that are used to produce D-25-u* and D-85-u*. The total field of view covered by the five pointings is 1.4×1.4 deg2, but we only keep the 1.×1. deg2 field at the D2 T0007 reference position. Only the very central region of stacks contains all data and corresponds to the D2-u* properties quoted in Tables 17 and 18. This region is roughly contained within the bold squares of Fig. 46. The seeing is not the same, but the scatter is large and all stacks agree with the same mean seeing, within 1-σ.


Figure 47: Galaxy counts for the deep, sigma-weighted stacks in all bands for each of the four fields. The dotted lines show the 80% completeness for galaxies described in Section 5.4.