4.4 The Microwave Deblender
4.4.2 Statistics of tSZ Detections
The very strength that makes the SZ effect a powerful probe of cosmology, the redshift indepen- dence of the SZ source flux, means that the SZ sky will comprise not only well-defined sources but a plethora of weak signals super-imposed on one another, due mainly to unresolved clusters and groups spanning a range of masses and redshifts (Holder et al., 2007). To understand this effect, we created a≈200deg2 map containing tSZ halos and2µK per beam instrumental noise.
The map contained halos ranging in mass from 2×1011M¯to 2×1015M¯within the redshift range 0 < z < 3. Since the survey mass limit is significantly higher than the minimum mass object present in the maps, the data represents an adequate sample to study projection effects.
The particular mass threshold chosen for the maps does not significantly effect the results, since the SZ power spectrum is dominated by clusters of the order of1014M¯(see Holder et al., 2007, and references therein).
To compare the efficiencies and accuracies of both algorithms in recovering cluster fluxes, we utilised the same object catalogue for both algorithms. To explain further,SExtractor was first run on the composite map. An output catalogue consisting of the positions of objects detected above3σwere created and then passed to the deblender. The catalogue created in this way was
4.4 The Microwave Deblender 83
Figure 4.2: Flux recovery statistics for SExtractor. The solid lines in the right panel indicate 20% errors.
found to have approximately80%purity. This technique ensures our conclusions are not biased by the cluster sample or by any other selection criteria. Photometric analysis was then performed by bothSExtractor and the deblender, with the analysed halos matched to the simulation input catalogue to produce completeness and flux recovery statistics. Catalogue matching was per- formed using a matching length of≈ 1.80 – which corresponds to the central radius of a typical cluster (similar to the half-light radius). All catalogue halos within this radius were flagged as candidates. The final match was taken to be the candidate whose mass was highest. If two ob- jects were matched to the same object, the closest match was kept and the other was flagged as a contaminant. The recovered cluster fluxes (Y) obtained bySExtractor and the deblender are plotted against the halo catalogue fluxes (Yo) to produce the left hand panels of Figs. 4.2 and 4.3 while the relative error given by:
error = Y −Yo
Yo , (4.4.8)
is plotted in the right hand panel.
4.4 The Microwave Deblender 84
Figure 4.3: Flux recovery statistics for the deblender. The solid lines in the right panel indicate 20% errors.
The bias in the flux error forSExtractor, particularly at low fluxes, suggests that lower mass halos extracted by this algorithm suffer from contamination due to projection effects along the line of sight. The deblender has the same problem but to a lesser extent. The relative error for the latter indicates a more uniform distribution about the zero level. To quantify this error further, in Figs. 4.4-4.5, we present a histogram containing the errors in various mass bins for each of the algorithms. Also presented is the skewness (presented as a dimensionless quantity rescaled to the standard deviation) of the total error distribution. In the case of the deblender the skewness was found to be 0.0027, while in the case of SExtractor it was 0.0048–almost a factor of two larger, indicating that the deblender provides more uniform flux errors, particularly noticeable at low masses. Both algorithms do exhibit a slightly positive tail, particularly in the low mass bins.
This is due to unresolved low mass halos that could not be removed, and thus caused a small projection effect.
The ability to measure low mass objects has a compounding effect on the quality of the overall catalogue. Moreover, the accurate description of these low mass objects allows one to
4.4 The Microwave Deblender 85
Figure 4.4: Histogram of flux recovery errors for SExtractor in five mass bins (signified by the different linestyles in the legend). The rescaled skewness of the total distribution is also presented.
Figure 4.5: Histogram of flux recovery errors for the deblender in five mass bins (signified by the different linestyles in the legend). The rescaled skewness of the total distribution is also presented.
4.4 The Microwave Deblender 86
remove their contamination effects from higher mass objects, thus creating a cleaner catalogue throughout a large mass range. It must be said, that current telescope sensitivity is not at the level where these issues will skew results significantly, however, next generation experiments reaching sensitivities of a fewµK will have to take into account such effects.
Another important attribute of the deblender is the ability to accurately probe the outer re- gions of clusters, which is especially useful when estimating radial profiles of objects. After a cluster has been detected, its centre is found by a simple centroiding algorithm. Concentric annuli, of thickness equal to the pixel resolution of the map in question (or the beam width in the case of beam-convolved maps), are then constructed around this centre. To estimate the sky level in each annulus, we place up to30annuli (analogous to dithering) around the local region of the cluster. We found that a minimum of20 dithers were required for sky level convergence. We then take the median, in a pixel-by-pixel basis, of the set of annuli and subtract this final annulus from the object flux annulus yielding the final flux for that particular aperture.
The total error associated with each bin in the radial profile was calculated to be the sum- mation (in quadrature) of the sky annulus error as well as the error in the estimation of the total background sky. The latter was determined by the standard deviation of the map pixels contained within an annulus extending from√
3Rvirto2Rviraway from the cluster centre. The sky annulus error was determined using a similar method as the sky estimation discussed above. After dither- ing the set of annuli, each annulus was totalled to yield a set of sky values. We then calculated the standard deviation of this distribution to yield the sky error in each annulus. In Fig. 4.6 we illustrate the binned radial profile error for the deblender against direct profile extraction (where the profile is measured directly from the map without source removal) for two different mass bins. The radial profiles were extracted from a slightly larger area of sky than discussed previ- ously, in order to increase the number of statistics. The fractional error,δ(r), was calculated as follows:
δ(r) = P
Nhalo
¯¯
¯∆Tmap∆T(r)−∆Tmodel(r)model(r)
¯¯
¯ Nhalo
, (4.4.9)
4.4 The Microwave Deblender 87
Figure 4.6: Direct (solid line) versus deblended (dotted line) radial profile extraction for two mass bins. The top panel illustrates the binned fractional error for the two extraction techniques, while the bottom panel expresses the error, compared to the average model profile (dot-dashed line). The lefthand side represents the mass bin2×1014M¯−4×1014M¯, while the righthand side pertains to4×1014M¯−1×1015M¯.
where∆Tmodel is the model tSZ profile, ∆Tmap is the extracted tSZ profile andNhalo is the number of halos in the particular bin. The fractional error shown in the top panel is significantly smaller for the deblender (dotted line) across the entire radial range. In the bottom panel we express this error as a fraction of the average SZ profile within the bin. At the centre of each halo the errors are comparable, however in the outskirts, the deblended profile is more accurate since contaminating objects are deblended out of each halo profile.
Although the overall integrated flux estimated from the blended or deblended profiles will be similar, owing to the low flux in the outskirts, the accuracy of profile estimation is improved. This is due to the fact that one is able to fit over a larger dynamic range. Furthermore, contamination removal allows more accurate shape fitting, which effects parameters such asβin the well known
‘beta model’. As alluded to earlier, many studies of clusters currently do not use deblending since