GALAXY CLUSTERS DISCOVERED WITH A SUNYAEV–ZEL'DOVICH EFFECT SURVEY

The first step in the data reduction process is to identify the data that will be included in each single-observation map. For every observation, a set of well-performing detectors is identified, primarily by assessing each detector's response to the chopped thermal source, its response to atmospheric emission during the ∼2 deg elevation nods, and its noise in the frequency band appropriate for cluster signals. Performance is also assessed based on the shape of the individual detector's noise power spectrum. If the power spectrum has too many lines or other deviations from the expected functional form, that detector is omitted from that observation's analysis. The median number of detectors stated in Section 2.2 is obtained after the application of these criteria.

In addition to cutting all data from individual detectors with anomalous noise power spectra, a small amount of bandwidth is cut from all detectors in certain observations. The receiver exhibits sensitivity to the pulse-tube cooler, resulting in occasional lines in the detector noise power spectra at frequencies corresponding to the pulse-tube frequency (approximately 1.6 Hz) and its harmonics. In every observation, all detectors' noise power spectra are combined in quadrature, and a search is performed for features in the resulting spectrum at every harmonic of the pulse-tube frequency. If a high-significance feature is found at any harmonic, a notch filter around that harmonic is applied to every detector's timestream. The width of the notch is determined by the fit, with a maximum of 0.007 Hz full width. The maximum amount of bandwidth that could be cut with this filter is 0.4%, but the actual amount is far smaller.

The data are eventually parsed into individual azimuth scans and are further selected for inclusion in the analysis on a scan-by-scan basis. Only the constant-azimuthal-velocity portion of each scan is eligible for inclusion; data taken while the telescope is accelerating are omitted. Scans during which there were data acquisition problems or large (>20 arcsec) instantaneous pointing errors—roughly 5% of total scans—are flagged for omission. For each detector, data from an individual scan are flagged if the detector or its associated readout channel exhibits high noise, if the demodulated detector output comes close to the limits of the analog-to-digital converter, if the readout SQUID associated with the detector exhibits an anomalously large DC offset, or if the detector demonstrates any cosmic-ray-like events in its time-ordered data. Typically about 5% of all otherwise well-performing bolometers are flagged within a given scan for one of these reasons. Data that remain unflagged after all of these cuts have been applied are processed and included in the maps.

Finally, individual observations are assessed for quality before inclusion in the final coadded maps. Observations are excluded if the thermal conditions of the receiver were not sufficiently stable, if the number of well-performing detectors was anomalously low, or if the observation was not fully completed. Individual observation maps are also excluded from the final maps if the rms in the single-observation map exceeds an empirically determined threshold. Of the complete observations of the BCS5h30 field, approximately 77% (270/350) of the 2007 observations and 83% (314/377) of the 2008 observations are included in the final maps.

The relative gains of the detectors, and their gain variations over time, are estimated using measurements of their response to a chopped thermal source taken before every observation. This relative calibration is used to "flat-field" the array before estimation of any common-mode timestream signal and before mapmaking. For the relative calibration step before mapmaking, we apply corrections to account for variations in illumination of the thermal source across the focal plane. These are measured by calculating the ratio of each detector's response to the thermal source to its response to the galactic H ii region RCW38, averaged over many measurements.

We convert the RCW38-corrected relative calibration into an absolute calibration by comparing our measurements of RCW38 with published flux measurements in our observing bands. For 150 and 225 GHz, we compare to the RCW38 flux reported by ACBAR (Runyan et al. 2003), which was recently linked to the WMAP5 calibration at 150 GHz (Reichardt et al. 2009). In order to use the ACBAR calibration, we smooth the SPT map of RCW38 to match the ACBAR resolution. We then compare the flux within the inner 8 arcmin of the SPT map with the ACBAR-determined flux. For the 95 GHz calibration, we use the flux reported by BOOMERANG (Coble et al. 2003). In this case, we smooth the SPT RCW38 map to match the BOOMERANG resolution and then compare the flux within two times the Gaussian width (σ) of the BOOMERANG beam.

This calibration method does not correct for temporal variations in atmospheric opacity between SPT measurements of RCW38. This results in a slightly suboptimal weighting of detectors during mapmaking, but does not bias the absolute calibration. The added absolute calibration uncertainty from ignoring atmospheric opacity corrections is small relative to our overall calibration uncertainty. For each of our bands over both seasons, the rms variation in the brightness of RCW38 is measured to be <5%, even without correcting for differences in atmospheric opacity or changes in the relative response of the bolometers.

We estimate the calibration uncertainty of the 95, 150, and 225 GHz bands to be 13%, 8%, and 16%, respectively. At these levels of uncertainty, the RCW38-based calibration is consistent with other cross-checks of our calibration, including initial CMB power spectrum estimates and observations of Neptune.

In addition to the notch filtering described in Section 2.3.1, the timestream processing of detector data consists of deconvolution of the detector response function, low-pass filtering, and projecting out long-timescale drifts due to atmosphere and readout 1/f noise.

Detector-response deconvolution and low-pass filtering are done in a single step. The detector temporal-response functions are measured periodically by sweeping the chop frequency of the thermal calibration source and measuring the amplitude and phase of each detector's response. These temporal-response functions are fit adequately by a single-pole low-pass filter, and the time constants do not vary significantly from observation to observation. Across the focal plane, the time constants ranged from 5 to 10 ms in 2007 and from 10 to 20 ms in 2008. The cutoff for the applied low-pass filter is set at 40 Hz for the 2007 data and 25 Hz for the 2008 data, such that in conjunction with a digital filter already applied by the data acquisition computer, they filter approximately the same spatial scales (≲0.5 arcmin), given the different scan speeds for each season. This combination acts as an anti-aliasing filter for our eventual resampling of the data onto 0.25 arcmin map pixels but does not suppress power on scales of the SPT beams.

For every scan, each detector's timestream is then fit simultaneously to a number of slowly varying template functions, and the best fit to each template is subtracted from that detector's timestream. This time-domain filter reduces the effect of low-frequency noise in the detector timestreams due to readout noise or to atmospheric fluctuations. For this analysis, we use a combination of Legendre polynomials and an array common mode as the templates. The highest order of Legendre polynomial used is 19 for the 2008 data and 11 for the 2007 data, resulting in a characteristic filter scale of roughly one-half degree for both seasons.

The common-mode template is constructed from the mean across all the well-performing detectors in the array at a given observing frequency, using a nominal relative calibration. Removing this common mode should eliminate the majority of the atmospheric fluctuation power in the detector timestreams, because this atmospheric signal is highly correlated between detectors. The common-mode subtraction acts as a spatial high-pass filter with a characteristic scale that roughly corresponds to the 1 deg angular size of the array.

In order to avoid contamination of the best-fit common mode and polynomial by bright point sources, sources were detected in a preliminary set of maps, and the locations of those sources were masked in the common mode and polynomial subtraction algorithm. A total of 92 sources were masked in this analysis, 35 of which lie in the ∼40 deg² BCS5h30 field. A mask radius of 5 arcmin was used for the five brightest sources (including the three brightest in the BCS5h30 field), and a mask radius of 2 arcmin was used for the rest.

For every observation, a map is made for each observing frequency using the processed data for all detectors in that band. Pointing information (R.A. and decl.) is calculated for each detector using focal-plane offsets measured in observations of the galactic H ii regions, and boresight pointing calculated using data from the telescope pointing readout system, with a set of corrections described below. Pointing coordinates are converted to pixel number using a Sanson–Flamsteed projection (Calabretta & Greisen 2002) with 0.25 arcmin pixels, and all measurements of a given pixel's brightness are averaged using inverse-variance weighting based on the rms of each detector's processed and relative-gain-scaled time-ordered data.

Small corrections must be applied to the pointing information in the timestream to ensure that pointing errors are suitably small compared to the size of the SPT beams. The largest pointing errors of the SPT are attributed to thermal gradients across the telescope support structure. These pointing errors are corrected from 20 arcsec rms to better than 8 arcsec rms by using an offline model which incorporates information from thermal and linear displacement sensors on the telescope structure and observations of H ii regions. The astrometry of the pointing model is tied to the PMN and SUMSS catalogs (Wright et al. 1994; Mauch et al. 2003) and is accurate to 10 arcsec in the final maps. The main-lobe beams in the final maps are well approximated by two-dimensional elliptical Gaussians with average FWHM of 1.5, 1.2, and 1.1 arcmin for 95, 150, and 225 GHz. As the beams include the effects of pointing variations and the timestream filtering, they are larger than expected from the diffraction of the central 8 m diameter region of primary mirror illuminated by the SPT-SZ optics (see Padin et al. 2008).

The optimal choice for the source template is unclear for SZ clusters, so we explore three basic profiles, all motivated by some guess at the underlying three-dimensional pressure profile of clusters: a modified version of the Navarro–Frenk–White (NFW; Navarro et al. 1996, 1997) model as suggested in Nagai et al. (2007), numerically integrated along the line of sight to produce a model for the SZ surface brightness; a Gaussian profile; and a β-model with β between 2/3 and 4/3, which can be analytically integrated to yield the SZ surface brightness. The three models proved almost indistinguishable in terms of detecting the highly significant clusters presented in this work. The results in Section 3 are based on a spherical β-model with β = 1. The SZ surface brightness profile using a β-model is given by

$$\begin{equation} \Delta {T_{\rm SZ}}(\theta) = \Delta T_{0}(1 + \theta ^2/{\rm \theta ^2_{\rm core}})^{(1\hbox{--}3\beta)/2}, \end{equation} \tag{ 2 }$$

where θ is the angular distance from the line of sight through the center of the cluster, θ_core is the (angular) core radius, and ΔT₀ is the peak signal. We choose to fix β and vary θ_core, as these two parameters are highly degenerate in the fit, given the current depth and resolution of our observations. The model is truncated at 10 × θ_core. We have explored the dependence on the scale size, parameterized as θ_core in the range from 025 to 35 in 025 steps, and generated a matched filter of each case.

The timestream filtering described in Section 2.3.3 affects the expected shape of the cluster signal in our maps. To account for this effect, we convolve the source templates with a spatial filter intended to represent the map-domain version of our timestream filtering before including the source templates in the matched filter for cluster detection. (The source templates are also convolved with the instrument beam). The spatial filter used in this work is simply a high-pass in the R.A. direction, with a cutoff on roughly half-degree scales. Simulations of the timestream filtering have shown this to be an accurate representation of the effect of our timestream polynomial removal. We do not attempt to include the effects of our common-mode subtraction, which predominantly affects modes that will be heavily de-weighted in the matched filter by the inclusion of the primary CMB as a noise term.

In addition to the SZ signal from massive clusters, SPT maps contain primary CMB, instrument and atmospheric noise, point sources, and an unresolved SZ background. For cluster detection, all of these are noise sources. The covariance matrix used to create the optimal matched filter can be expressed as the sum, N = N_CMB + N_noise + N_PS + N_SZ, of these components. The point-source covariance only includes the unresolved source background; point sources bright enough to be detected in our maps are treated separately as discussed below.

The signal covariance of the primary CMB and undetected point sources is estimated analytically from the best-fit WMAP5 CMB power spectrum (Nolta et al. 2009) and the Borys et al. (2003) model for dusty point sources. We assume that the contribution of faint radio sources to the background source covariance is negligible. We assume a spectral index of 2.7 to extend the dusty source counts to 150 GHz. The power spectrum of this source count distribution is estimated with the formalism in White & Majumdar (2004). The SZ background covariance is estimated from the simulations described in Shaw et al. (2008).

A different approach is taken for the bright point sources in the map. Any bright sources left in our map will cause ringing in the maps due to the matched filter used, which can give spurious high significance decrements in their vicinity. We take advantage of the fact that these sources show up as bright spots in our maps, while any SZ cluster will be a decrement at 150 GHz. We filter the 150 GHz map using a simple matched filter assuming isotropic noise and no signal filtering, and we flag every positive source above 5σ in the filtered map, totaling 47 sources in the ∼40 deg² BCS5h30 field. (Note that this number differs from the number of sources detected in a preliminary map and masked in the timestream processing. The mapmaking, source flagging, and timestream processing loop was not iterated over.) All pixels within a radius of four times the beam FWHM of the locations of these sources are set to a DC level defined to be the average of the pixels just outside the mask radius. To avoid any edge effects from the masking procedure, pixels within 8' of a masked source are flagged and excluded from later cluster finding. This technique proved adequate to avoid false detections of decrements near bright positive sources.

The instrumental and atmospheric noise properties of the maps are estimated using the two-dimensional power spectrum of jackknife noise maps (Sayers et al. 2009; Halverson et al. 2009). Under the assumption of stationarity in the map basis, the noise covariance matrix $\tilde{N}_{\rm noise}$ is diagonal in the Fourier domain and equal to the noise power spectrum. We construct an individual jackknife map by multiplying one half of the individual observations (selected randomly) by −1 then coadding the full set of observations. We repeat this process n > m times (where m is the number of individual observations), computing the two-dimensional spatial power spectrum for each individual jackknife map. The mean of these power spectra is our estimate of $\tilde{N}_{\rm noise}$.

The significance of a detection is estimated using the standard deviation of the filtered map pixels while excluding regions around bright point sources. As the integration time per pixel is a weak function of elevation, the scatter is estimated independently for each 15 band in elevation. The coverage of the selected region is uniform in azimuth. We define detection significance as the ratio of the peak of the candidate decrement divided by the rms at the appropriate elevation.

As discussed in Section 2.3.4, the absolute pointing of the SPT maps from which cluster candidates are extracted is accurate to roughly 10 arcsec, as measured using sources in the PMN and SUMSS catalogs. However, the locations of the cluster candidates reported in Table 1 will not necessarily line up with the centers of the cluster optical or X-ray emission to that level of precision, because the different observations are sensitive to different combinations of physical properties of the cluster. Such a separation is particularly likely in extended systems and systems that have undergone recent mergers, such as SPT-CL 0517-5430/RXCJ0516.6-5430 (Zhang et al. 2006). The position of the brightest cluster galaxy, the peak of the X-ray emission (which is proportional to electron column density squared), and the center of the SZ emission (which is linearly proportional to electron column density and is smoothed by the matched filter used for detection) can be offset by many times the positional uncertainty in any of the three measurements.

Figure 2 shows a minimally filtered version of the 150 GHz image in Figure 1, and it clearly shows the offset between the center of the diffuse SZ emission and the deepest part of the SZ decrement. The extent of the deepest part of the SZ decrement is ∼1', and it is detected as a separate feature at 2–3σ in this version of the 150 GHz map, indicating that the ∼07 offset between the SZ centroid and the deepest part of the decrement is statistically significant. The X-ray emission should be strongly peaked in this deepest part of the decrement, and indeed this is where the reported REFLEX position is located.

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