Source identification

For our simulations we produced cluster catalogues by running a friends-of-friends

(FoF) group finder (e.g., Davis et al. 1985) with a linking length ofb= 0.2 in units

of the mean inter-particle spacing. The FoF algorithm links together all particle

pairs separated by less than a distanceb and identifies, as halos, candidate groups

that contains more than 32 particles. We define the centre of a halo as the posi- tion of the minimum of its gravitational potential; this proves very robust and is insensitive to the particle distribution near the outskirts of the halo. The centre

Figure 3.6 Thermal SZ sources identified with SExtractor_{. A circle is drawn for each}

source, with area equal to the area determined by the source-detection software.

100 1000 10000 Mass recovered 0 10 20 30 40 contaminations [ % ] z = 1.5 10-5 ₁₀-4 ₁₀-3 ₁₀-2 Y recovered 0 5 10 15 20 contaminations [ % ] ΛCDM DECDM w=-0.8 EDE1 Wetterich EDE2 Wetterich EDE3 Linder EDE4 Linder EDE3DR Doran K08 Komatsu

Figure 3.7Contamination rate of the detected cluster sample as a function of the recovered mass (left panel) and SExtractor _{flux (right panel) for all the different cosmologies we}

examined. The sources are considered true detections when the peak in the map and the matching cluster from the catalogue are within a 24 pixel distance of each other. Atz= 1.5 our sample shows only 5% percent contamination from false-positive matches down toY = 1.0×10−5_.

defined in this way also coincides closely with the density maximum of the group found with the shrinking sphere method. For each of the halos we also computed spherical overdensity (SO) mass estimates, i.e. the mass enclosed in a sphere with

a prescribed mean density ∆_×ρcrit, where ρcrit is the critical density and ∆ de-

scribes a characteristic virial overdensity. In particular, we consider the massM200

enclosed within the virial radius,r200, interior to which the density contrast is 200

times the critical density. Where appropriate, we also consider different values of ∆ motivated by the generalized spherical collapse model in general cosmologies.

Besides this source identification in the three-dimensional raw simulation data, we independently detected and determined the photometry of extended sources in

our SZ maps. To this end we used the software SExtractor _{(Bertin and Arnouts,}

1996), a source extraction code based on a connected-pixel algorithm which opti- mally detects, deblends and measures sources in a given map. The analysis begins with an iterative estimation of the ‘sky’ background, and then proceeds with an identification of the locations of the brighter sources, building a catalogue of ob- jects from the image map. Thresholding is applied to isolate connected groups of pixels, and to find the approximate positions and shapes of individual detections that will be further processed. A crucial parameter is the threshold level, in particu- lar the minimum number of pixels above the background required before a source is considered as an object. Finally, the total integrated flux for each source is obtained by summing up the contributions of all the pixels centered on the known location of the clusters. The detection itself is more complicated because it depends on the morphology of a cluster. Following the simplest characterization for an extended

SZ source,SExtractor _{evaluates the flux inside an elliptical aperture around every}

detected object, described by a characteristic Kron radius that includes 90% of an

object’s light. We have tried to optimize the parameter settings of SExtractor _in

order to avoid source confusion and to robustly identify most of the brighter sources at all redshifts.

Figure 3.6 shows a typical source detection map. We have drawn circles with

areas equal to the areas of the ellipses matched by SExtractor _{to each identified}

source. We here used default settings for the detection algorithm but we tuned the detection threshold such that only the more massive halos are found and confusion with the background is avoided, a consideration that becomes especially important for the high redshift partial maps, where we have a dominant contribution from small and faint sources. The threshold cut we apply is 10.5 times the standard deviation on the filtered map (the algorithm estimates the background and noise level automatically). We remark that our maps are in principle noise-free, so what it is interpret here as ‘noise’ is effectively due to source confusion and alignment of clusters along the line-of-sight.

In a typical coadded map, more than 40% of the total thermal SZ signal can be resolved into isolated sources. For a detailed analysis, we would like to associate

each of the bright sources we observe in the SZ maps with a massive halo in the underlying three-dimensional simulation catalogue. This allows a comparison of the intrinsic halo properties with the quantities that can be extracted from an observed SZ map. From the cluster catalogue derived from the FoF algorithm, we choose a

sub-sample of halos with mass>1012_h−1_M

⊙ to stay well above our mass limit of

1.3_×1010_h−1_M

⊙. All selected clusters contain at least 3500 particles within the

virial radius and are hence well resolved. Using again our map making procedure we found all the clusters in the catalogue that fall within a particular map.

We identified as a match all the input clusters that were located within a distance

of at most 24 pixels from aSExtractor_{flux peak in the 2D map-plane. This distance}

corresponds to _∼1 arcmin, which is the typical cluster size in the 3 square degree

maps. We do not allow for multiple catalogue clusters matching a single detection. If no input clusters is found for a given source in the map, we flag the nearest object as a false detection. We have verified that this procedure avoids misclassifications even in the moderately crowded fields at high redshifts, where sometimes several candidates are associated to a single cluster within a larger search radius.

After running through all the candidates, we can identify as true detections in the simulated maps about 90% of the clusters at each redshift with mass above 13h−1_M

⊙. Figure 3.7 shows the contamination level at z = 1.5 in different cos-

mological models derived as a function of the recovered cluster mass (left panel), and the SZ flux (right panel). The total flux here means the flux decrement inte-

grated by SExtractor _{over the entire cluster profile, which we express just as the}

Compton-Y parameter, independently of the frequency. Interestingly, the ΛCDM

map appears systematically ‘cleaner’ than the maps of EDE cosmologies, in terms of the fraction of peaks that correspond to real clusters as a function of mass. On the other hand, in the contamination versus flux plot all the models show a sharp

decline from_∼20% to_∼1% in the contamination rate aroundY _∼10−5_{, indicating}

that confusion effects in our maps are unimportant for bright sources. The maps show a slightly higher contamination level when we consider the biggest objects. In the early dark energy model EDE3 we could not identify one of the extended clusters, and this is the reason of the higher contamination. In general, we note that in order to detect extended clusters, direct profile fitting is a good alternative compared to the peak pixel finding procedure (Sehgal et al., 2007).

If we disregard the slightly higher contamination level at large fluxes due to rare and extended clusters, our sample of detected clusters is 95% complete down to

Y = 2_×10−5_{at all redshifts. For the EDE2 model, there are more than 3000 halos}

more massive than 1012_h−1_M

⊙ in the z = 1.5 three-dimensional catalogue for a 3

square degree map. There is still the possibility that some peaks match clusters in the catalogue just by chance alignments. However, we consider only clusters that should give a visible contribution to the Comptonization parameter, and the analysis is performed on single partial maps in the simulation, before to construct

the coadded maps. Then, such misclassification should be very rare.