8.4 Redshift Determination
9.1.2 Cluster number counts
The cumulative raw XDCP cluster number counts in the 0.5–2.0 keV band for distant cluster candidates (top blue line) and all identified cluster candidate sources (top green line) are shown in Fig. 9.2, where the lighter lines indicate the distribution for a core survey restriction with a maximum off-axis angle of 120. This logN–logS (see Equ. 3.45) is to be considered as raw in the following sense: (i) the number counts are not normalized to a unit solid angle, (ii) the candidate sample still contains false positives, (iii) the flux determination is based on fiducial values for the Energy Conversion Factor (see Sect. 6.3.3) and the β parameter (Equ. 2.6), and (iv) fluxes are consistently determined for the PN detector, which is not available for about 10% of the (missing) candidate sources due to a non-imaging operation mode of the PN for this fraction of all observations.
The overall shape of the cumulative number count distribution yields important di- agnostic information for the survey sensitivity characteristics. The flux level where the logN–logS slope starts deviating from the observed number counts in deeper surveys (see Fig. 4.6) indicates the approximate flux limit of the survey below which the source counts become incomplete. In Fig. 9.2 this estimated XDCP completeness level is represented by the red dashed line at fcom
X '1×10−14erg s−1cm−2. The logN–logS approaches a con-
stant value, i.e. no additional sources are found at lower flux levels, at the point where the effective sky coverage of the survey at the given limit drops rapidly towards zero. This approximate minimum survey sensitivity is indicated by the second dashed line at fmin
X '5×10−15erg s−1cm−2. At the bright end, the observed cumulative number count
distribution appears to be (artificially) truncated for the most luminous clusters. This effect can be attributed to two features of the source detection algorithm which (i) has a fixed upper size limit of 8000 for the core radius in the XDCP pipeline setup and (ii) the intrinsic tendency of the eboxdetect task to split very extended cluster sources into several sub-clumps.
Figure 9.2: Raw logN–logS of XDCP candidates and identified clusters. The total number of objects is shown as a function of the 0.5–2.0 keV flux measured for the PN detector, which is available for about 90% of all sources. The green lines display all identified clusters and distant candidates for the full XMM detector area (top green line) and the FoV restricted to 120 off-axis angle (lower green line). The blue lines illustrate the cumulative distribution of the distant cluster candidates only. Vertical red lines indicate the position where the logN–logS curves start to turn over at approximately1×10−14erg s−1cm−2and the flux level where the effective area becomes small around 5×10−15erg s−1cm−2.
With the total number of cluster candidates and the survey area available, we can now estimate the observed XDCP galaxy cluster surface density. In total, the full XDCP sample contains 990 unique cluster candidates, 276 of which aredistant cluster candidates and 714 are DSS-identified cluster sources. For the restricted core survey at off-axis angles of less than 120, the 226 distant and 526 DSS-identified candidates make up a combined core sample of 752 sources. Subtracting the approximate false positive fraction of 1/3 for distant and 1/6 for low redshift candidates, the expected sample size ofrealgalaxy clusters is obtained as ∼780 for the full region of 79.3 square degrees and ∼590 objects for the core survey area of 50.6 square degrees. Note that this cluster sample size is comparable to the largest local all-sky surveys (see Sect. 4.2), with the difference that the XDCP survey is not aiming at a full identification of all clusters.
The approximate average XDCP surface density is thus ∼9.8 clusters per square degree for the overall area and∼11.6 clusters per square degree for the more sensitive core survey area with Θ≤120. From the observed logN–logSof Fig. 4.6, a cluster surface density of 10 objects per square degree is obtained at a flux limit of 1×10−14erg s−1cm−2. The identified
Figure 9.3: XDCP distant cluster candidates in the 0.5-2.0 keV flux versus core radius plane. The parameter space of detected candidates is confined by the XMM resolution limit (vertical red line) at core radii of about 600 and the background limit (lower red line), where the cluster surface brightness drops below the detection threshold. Green diamonds indicate the positions of three most distant spectroscopically confirmed clusters in the Southern hemisphere (using the source parameters of the XDCP X-ray pipeline), from left to right: XMMU J2235-25 at z= 1.39, XCS J2215-17 at z= 1.45, and RDCS J1252-29 atz= 1.24, see Sect. 9.5 for references.
sensitivity of ¯flim
X '1×10−14erg s−1cm−2 for the full survey area and slightly below this
value for the core sample.
The estimated XDCP sensitivity limits from the raw logN–logS and the total candi- date numbers in this section are about 30% lower than the conservative median sensitivities derived in the previous section. This apparent discrepancy originates from the attempt to characterize an XMM serendipitous surveys with a single number, the flux limitflim
X . The
difficulties arising from this concept of a global survey flux limit will be briefly discussed in the next sub-section.