Point source transfer function (PST)

The approximation of a linear PST allows us to construct a filtered mapping of any extended signal by convolving the true signal with the PST. This is used as a transfer function that modifies the original astrophysical signal on the sky into the filtered source. The total sum of the transfer function is expected to be zero, however, due to uneven weights in different part of the sky, when the polynomial baselines are applied to the time streams the sum is not strictly zero.

The data reduction method is tuned to filter out any low frequency noise. This limits the recovering of the full extent of the astrophysical source, which itself is thereby heavily filtered. Therefore, there is a partial loss of the source flux. This is demonstrated in Figure 3.6 using a simulation of an extended astrophysical signal. The scales upto which the signal can be recovered optimally depends on various factors including the size of the array, separation between the bolometer channels, and the radius of scan pattern. If the extent of the source signal is larger than the array size then the large scale source signal would be partially or fully lost. It is also important to note that the only case where the full extent of the signal can be fully recovered rests only for the sources which are smaller than the minimum separation between the channels. That is, the source is small enough that it does not produce any correlation between neighbouring channels. It must be noted that the time scale filtering that occurs in data reduction process does not relate to spatial filters on one-to-one level. But a Fourier transform of the PST helps us see that the filters in spatial scales behave effectively as a spatial scale band pass filter. Figure 3.7 show the Fourier transform amplitude of the PST for all APEX-SZ clusters.

3.6 Summary

The APEX-SZ experiment, data and analysis are introduced in this chapter. For a sample of nearly 40 galaxy clusters, the APEX-SZ collaboration has observed these targets in SZ, X-ray and lensing. A sub-sample of clusters forming a complete sample with a well-defined selection criteria is constructed. This sub-sample is an X-ray selected sample. The lensing mass measurements of these clusters are provided by Klein et al. (in preparation). The APEX-SZ observations of these targets have been reduced and final data products can be used further to extract the integrated Comptonization. This makes it possible to measure cross-correlation between lensing mass and the integrated Compton parameter, where the Comptonization can be obtained from APEX-SZ.

3.6 Summary

For this, an accurate measurement of the integrated Compton parameter from filtered the APEX-SZ data products is required. A measurement of this quantity has been done for APEX-SZ data processed through the MATLAB version of pipeline and is given by Bender et al. (2016). However, that work dealt with scaling between X-ray observables and SZ observable using various literature estimated X-ray observables. In this work, the global observable measured from the BoA pipeline is used for finally measuring the mass-observable scaling relations. The purpose is multi-fold as this provides independent measurements of the Y parameter, which is useful as a consistency check between both the pipelines, and a homogeneous re-estimation of Y using some knowledge from the lensing analysis (that is analysed in a homogeneous manner) is useful for controlling for any systematic effect and inferring the underlying relations more accurately. The actual method used for extracting the cluster observables from BoA data products and the results from such is described in detail in Chapter 4.

C H A P T E R

4

Methods: measuring integrated

Comptonization from APEX-SZ

Overview

The determination of an optimal method, in the sense that the extended Comptonization is both accurate and as precise as possible, to model the integrated SZ signal (YSZ) in the filtered APEX-SZ maps is the key focus of this chapter. The primary goal is to have an unbiased modelling of the SZ signal of galaxy clusters from APEX-SZ bolometer measurements in the presence of the strong filtering processes described in Chapter 3. By making use of a number of mock reduced APEX-SZ cluster maps, two methods of fitting the maps are discussed, namely: a) a Fourier domain fitting, where the fit of a model to data is performed in the 2-D spatial frequency space; b) Radial binning method, wherein the model and data are averaged into radial bins from the cluster centre before fitting. The quantitative analysis of the recovered parameters from mock simulations is used to find the optimal fitting routine to apply to all cluster dataset.

In Section 4.1, the motivation for exploring and testing different methods for extracting information on the SZ signal from APEX-SZ observations is elaborated. Following this in Section 4.2, all the necessary set-ups that would be used in this Chapter to fit models to data are established. The basic tools are introduced and parametric models, describing the ICM distribution and established in previous literature, are discussed. A quantitative and qualitative analysis of the two fitting methods are discussed in detail. The results from different modelling choices are discussed in Section 4.3. The conclusions and discussion based on the results are presented in the final section 4.4.

4.1 Motivation

Towards the aim of studying scaling properties of the intra-cluster gas medium pressure with total galaxy cluster mass, this Chapter will deal with the methodologies required for measuring the total SZ signal from APEX-SZ filtered images for the full sample of targeted clusters. Due to the strong filtering process of the data analysis described in Chapter 3, the filtered maps have attenuated astrophysical signal. In addition to the attenuation, the point source transfer function of the telescope

Chapter 4 Methods: measuring integrated Comptonization from APEX-SZ

optics and data reduction introduce correlations in the image noise.

It is imperative to employ a fitting method that is capable of extracting an unbiased estimate of the integrated Compton signal (often denoted by Compton-Y or integrated Comptonization) from the filtered APEX-SZ co-added images. To set up the appropriate apparatus for measuring the integrated Comptonization, parametric models for the ICM pressure are used to simulate the APEX-SZ filtered images and each apparatus is rigorously tested on them. Two methods of fitting a parametric pressure profile to the APEX-SZ data are considered.