Studies of the Sunyaev-Zel’dovich (SZ) effect are reaching observational maturity,
and the detailed simulations are required to interpret upcoming data.
In this thesis, we present two approaches for simulating Sunyaev-Zel’dovich
maps. First, we use a hydrodynamical N-body code to generate simulated
maps. On the other hand, we also construct a recipe using semi-analytic
formalism to simulate SZ maps, that is, calculating the SZ anisotropies directly
using results from theoretical models or observations. The latter is
a time-saving method, and the influence of the physical mechanism on the
outputs can be easily seen since the applied models are substitutable. Although
there are many advantages for the semi-analytic method, it is much
less accurate than the N-body simulation. Therefore, we generate the SZ
maps, of size one square degree, with numerical and semi-analytic approaches
and compare them to see in what situations they are similar. We find that
the simulation results of cluster properties are in agreement with theoretical
model. Futhermore, we find out that the flux-limited number counts of
N-body and semi-analytic maps fit surprisingly well. With these results, the
semi-analytic method will be a powerful tool for model testing and to make
predictions for future SZ surveys such as PLANCK, AMiBA, SZA, AMI, etc.Acknowledgements i
Abstract ii
1 Introduction 1
2 preparation 4
2.1 The Sunyaev-Zel’dovich Effect . . . . . . . . . . . . . . . . . . 4
2.2 Background Cosmology . . . . . . . . . . . . . . . . . . . . . . 5
3 Simulation Method and Map-Making Technique 8
3.1 Numerical Method – N-body Simulation . . . . . . . . . . . . 8
3.1.1 Tool and Cosmological Models . . . . . . . . . . . . . . 9
3.1.2 Map-Making Technique . . . . . . . . . . . . . . . . . . 11
3.2 Semi-Analytic Approach . . . . . . . . . . . . . . . . . . . . . 13
3.2.1 The Cluster Spatial Distribution . . . . . . . . . . . . . 13
3.2.2 Cluster Model . . . . . . . . . . . . . . . . . . . . . . . 21
3.2.3 Map-Making from Semi-Analytic Method . . . . . . . . 23
4 Results and Discussion 26
4.1 Tests of N-body Simulation Results and Semi-Analytic Model 26
4.1.1 Cluster Properties . . . . . . . . . . . . . . . . . . . . 27
4.1.2 Flux-Limited Number Counts at Some Specific Redshift 35
4.2 Simulated SZ Maps . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2.1 Comparison of SZ Maps Created by two different Methods
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2.2 Flux-Limited Number Counts from SZ maps . . . . . . 44
5 Conclusions and Future Work 51
5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
