4.5 Physical Properties of Clusters and Groups
4.5.1 Statistics of tSZ Detections
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on our results in a forthcoming paper. We expect flux and purity statistics to be adversly effected by their inclusion.
Figure 4.7: The multi-frequency Wiener filter weights plotted against multipole, l. We have multiplied the weights by `(`+1)2π to compare to the conventional way of plotting the CMB power spectrum. The weights for 148 GHz, 219 GHz and 277 GHz are signified by the solid, dotted and dashed lines respectively.
We considered an experiment with three frequency channels, namely, 148 GHz, 219 GHz and 277 GHz, the same as those used in the ACT experiment (Kosowsky, 2006). The filter profile for each frequency channel was generated by modelling the power spectra of each foreground component (see Moodley et al., 2009, for a detailed discussion). Fig. 4.7 presents the filter weights, W`, that are applied to the maps in each frequency band. We note that in the case of the 148 GHz and 277 GHz channels the weight function is peaked, but with opposite sign (due to the change in sign of the tSZ signal), at multipoles in the region of a few thousand where the tSZ signal template (taken to be that of a4×1014M¯ cluster at z = 0.1) peaks, whereas it is practically zero over this range of multipoles for the 219 GHz channel, since at these frequencies the tSZ signal is null. At low multipoles (` < 2000) the filter weights tend to zero to suppress
4.5 Physical Properties of Clusters and Groups 90
Figure 4.8: The 200 deg2input tSZ map (left) and filtered tSZ map (right) in Compton parameter units.
contributions from the primary CMB and galactic dust, moreover the weights in the 219 GHz and 277 GHz channels are opposite in sign to the weights in the 148 GHz channel to allow delicate cancellations of the CMB and galactic dust signals that are, respectively, constant and increasing in thermodynamic temperature of the CMB. At high multipoles (` >10000) the filter weights go to zero to suppress the contamination from detector noise, if we were to include point sources in our filter then the filter weights would go to zero more rapidly at high multipoles.
The Wiener filter was applied in harmonic space to each of the three frequency maps, which were then summed and inverse Fourier transformed to obtain the filtered tSZ map in real space.
We considered three tSZ surveys, a deep survey (ACT-Deep), a wide survey (ACT-Wide) with the same experimental sensitivities as those achieved by the ACT survey (Fowler et al., 2010) and similar to the SPT surveys (Lueker et al., 2009), and an extended deep (ACT-Extended) survey over the same area as the ACT-Deep survey but with greater sensitivity (as considered in Moodley et al. (2009) and Sehgal et al. (2007)). The experimental specifications for each of these surveys is given in Table 4.1.
The200 deg2 Wiener filtered tSZ map for the ACT-Deep survey is shown in the right panel of Fig. 4.8 where it is compared to the input tSZ map in the left panel. The input tSZ map is not
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Table 4.1: Experimental specifications for a wide, deep and extended survey using ACT
Experiment Area (deg2)a ν (GHz)b σp (µK/beam)c FWHM(0)d
148.0 28.6 1.4
ACT-Wide 800 219.0 53.5 1.1
277.0 133.8 0.9
148.0 14.3 1.4
ACT-Deep 200 219.0 26.8 1.1
277.0 66.9 0.9
148.0 2.0 1.4
ACT-Extended 200 219.0 5.2 1.1
277.0 8.8 0.9
aSky area for particular survey.
bInstrumental frequency.
cPixel noise per beam width.
dFull width at half-maximum of the beam related to the Gaussian beam width,√ θb,byFWHM = 8 ln 2θb.
convolved with the beam, unlike the filtered map, and both have the same pixelisation scale of 0.50. The dominant feature in the filtered tSZ map is the presence of detector noise on small scales which makes the smooth tSZ signals appear noisier. An examination of the power spectrum of the filtered tSZ map shows that there is a slight excess of power on large scales but this is hardly discernible in the map. Overall, halos in the input tSZ map with a central Compton distortion of y ≈ 4×10−5 or higher stand out in the filtered tSZ map while halos with distortions as low as y≈2×10−5 are also visible.
To detect clusters in the filtered tSZ maps we first ran the source detection algorithm de- scribed in the previous section to identify peaks in the tSZ maps. We set the threshold high enough to increase the purity i.e., the ratio of true detections to total detections, in each of the maps to approximately 85% or better. We have considered two sets of maps for the different surveys corresponding to the standard and adiabatic model simulations described in Bode et al.
(2009) and summarised in Appendix B. In the case of the standard model map, Fig. 4.9 illustrates that the wide survey only becomes complete at7×1014M¯ while the deep survey is complete
4.5 Physical Properties of Clusters and Groups 92
Figure 4.9: Completeness statistics for the ACT-Wide, ACT-Deep and ACT-Extended surveys using a standard model (red lines) and adiabatic model (blue lines) filtered tSZ map.
at5×1014M¯. Both of these surveys do not detect many low mass clusters and groups below 1×1014M¯, though at lower masses the completeness of the deep survey is greater than that of the wide survey due to its lower pixel noise. The extended survey with its higher sensitivity is able to detect groups at 5×1013M¯ with 10% completeness and clusters at 1×1014M¯ with 40% completeness. The extended ACT survey becomes complete at approximately2×1014M¯, which agrees with the completeness reported for ACT by Sehgal et al. (2007) and Moodley et al.
(2009) due to the consistency of the noise levels assumed in these papers.
To determine how many galaxy groups and clusters will be used for model parameter con- straints in §4.5.3, we computed the abundance of detected tSZ halos in the standard model maps for the wide, deep and extended surveys. Fig. 4.10 displays the abundances as a function of mass above a mass limit of1×1014M¯. We note that the deep survey contains more low mass clusters above the detection threshold, while the wide survey has more high mass clusters detected result- ing from the larger area. Due to the sensitivity to low mass clusters and the steep mass function for galaxy clusters overall, the deep survey comprises more clusters detections, approximately
4.5 Physical Properties of Clusters and Groups 93
100 in total, in comparison to the wide survey, which has approximately 40 in total. The ex- tended survey, which contains much lower pixel noise, has significantly more cluster detections, over 700 in total, than both the wide and deep surveys. The majority of these clusters, roughly 550, are at masses below2×1014M¯with few objects detected at the highest masses, due to the smaller area of sky covered in comparison to the wide survey.
Fig. 4.9 also shows the completeness of the adiabatic filtered tSZ maps for the different sur- veys. We expect that the adiabatic model map should contain a larger number of detected clus- ters in comparison to the standard model map as there is neither star formation in the adiabatic model, which increases the average entropy in the cluster centre, nor AGN and supernovae feed- back, which pushes gas into the outskirts of the halo. Both these effects, which are present in the standard model map, reduce the central Compton distortion, making these halos harder to detect.
The differences between the number of detections in the adiabatic and standard model maps are in fact quite small for the different surveys, with the completeness of the adiabatic model map not significantly higher than that of the standard model map. This could be due to the fact that the effects of star formation and feedback only slightly change the integrated Compton distortion i.e., the tSZ flux, in clusters as has been demonstrated in Motl et al. (2005); Nagai (2006); Reid and Spergel (2006) using numerical simulations.
As we will see in §4.5.2 the effects of star formation and feedback are more pronounced on the Compton profile, which suggests that this observable is more sensitive to physical cluster pa- rameters, such as the feedback energy and the amount of star formation. For the halos detected in these maps we will use their radial Compton profiles to probe the underlying physical parameters that determine the distribution of hot gas in each cluster. In the next section we describe how the Compton profiles for each of the detected tSZ halos were extracted from the maps.