Figure 6.1: Two-dimensional weight function prescribed for the ACT data map, where the units are arbitrary. This particular filter weight uses the data within the filter description. The use of a two dimensional filtering scheme is motivated by the presence of asymmetric structure in the filter.
6.4 Detection Statistics: ACT and Simulated Maps
Once filtering of the simulated or data maps was completed, we applied a simple cluster detection algorithm to the maps, which detected all sources above a given signal-to-noise limit. We simply thresholded the filtered maps and enforced that candidate objects should have a minimum of ten connected pixels above a threshold of3.5σ(whereσis the standard deviation of the filtered map).
As alluded to earlier, nine templates were used in the filtering process. In cases where an object was detected in multiple templates, only the highest signal-to-noise detection was included in the final catalogue of cluster candidates. To remove any spurious detections related to noise
6.4 Detection Statistics: ACT and Simulated Maps 148
Figure 6.2: Sub-region of the filtered ACT data map at148GHz. The well known Bullet cluster (bottom left) and Abell S0592 (top right) are clearly discernible.
fluctuations, we utilised a data weight map in the detection process. A region of the weight map corresponding to the filtered region displayed above is presented in Fig. 6.3. The weight map comprises the number of times a pixel had been observed (defined as H in the figure).
Consequently, high signal-to-noise regions were weighted more significantly than lower ones, reducing effects of noise stripes which are common in data, particularly in the outskirts of the survey region. The weight map was also used to produce signal-to-noise estimates for each of the cluster candidates, allowing one to produce completeness estimates as well as purity and number counts as a function of signal-to-noise.
In order to produce purity and completeness statistics, detected objects in the simulated maps were matched to the input cluster catalogue for the specified region. This was achieved by
6.4 Detection Statistics: ACT and Simulated Maps 149
Figure 6.3: Sub-region of the ACT weight map at148GHz. The units are in terms of hit counts, designated by the variable,H.
locating all catalogue clusters contained within a radius of≈ 1.20 from the detected object. The matched cluster was chosen to be the catalogue cluster with the highest mass found within the matching radius. The purity (P˜), above a particular signal-to-noise,σjSN, was then calculated by the following
P˜(> σSNj ) = 100× Nmatchj
Nobsj , (6.4.2)
where Nmatchj andNobsj are the number of matched and detected objects, respectively, above a signal-to-noise limit. The completeness (C) for the sample (above a particular mass) is given by˜
C(> M˜ i) = Nmatchi
Ncati , (6.4.3)
6.4 Detection Statistics: ACT and Simulated Maps 150
where Ncati and Nmatchi are the number of catalogue and matched halos respectively, above a given mass,Mi.
In Fig. 6.4 we present the purity of the cluster sample from the simulated maps of the ACT strip. We also present the number of matched clusters as a function of signal-to-noise. The black lines reflect the case where the data was used in the filter construction, while the red lines depict the case where models for the sky sources were used instead. Slightly more true clusters are
Figure 6.4: Cluster sample purity and true number counts versus signal-to-noise for the simulated ACT map. Black lines describe the case where data was used in the filter construction while the red lines indicate the scenario where astrophysical models were used instead.
detected in the simulation in the case where a model was used for the filter, with a relatively unchanged purity level. Considering the fact that we used the same source models (dust and lensed CMB) in the construction of the simulated map, this behaviour is not unexpected.
Studies of the completeness of the cluster sample, displayed in Fig. 6.5, show that we are approximately80%complete above7×1014M¯ with a total contamination of70%. The com- pleteness and overall contamination proved to be approximately independent of filter construc- tion (i.e. data or model used in the filter). The dip in the completeness at high mass is due to a single cluster that is asymmetric in shape. Thus, although we do detect this object, the peak is
6.4 Detection Statistics: ACT and Simulated Maps 151
located sufficiently far away from the position given in the input catalogue, that it is not flagged as a match.
Figure 6.5: Cluster sample completeness and overall contamination for both filter construction cases.
The simulated cluster analysis is vital in quantifying the cluster detection results from the ACT data maps. In Fig. 6.6 we present the number counts from the ACT simulated and data maps. In both filter construction cases we see that the simulated maps produced more cluster de- tections. This discrepancy is more prominent in the situation where a model is used in the filter construction. This suggests that we are over-performing in the simulations with this assump- tion, and under-performing in the real data. Using the data in the filter construction produced a closer correlation between the real and simulation number counts. This can be explained by the fact that we are using the actual data properties to minimise noise sources, so both situations include the same priors. The fact that the simulation does not match the data precisely is due to a number of factors. Firstly, the noise properties (e.g. noise level) in the simulations could be slightly different from the real maps, which would translate into offset number counts. Secondly, the simulation has not been mapped in the same way as the ACT data, which could introduce noise correlations and other artifacts, which might impinge on detection statistics. Thirdly, the simulated galaxy clusters could have a larger than expected SZ signal, which would lead to an