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Student Number 88242001
Author Ping-Hung Kuo()
Author's Email Address No Public.
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Department Graduate Institute of Astronomy
Year 2003
Semester 1
Degree Ph.D.
Type of Document Doctoral Dissertation
Language English
Title Relativistic Electrons and
the Sunyaev-Zel'dovich Effect
in Galaxy Clusters
Date of Defense 2004-01-09
Page Count 126
Keyword
  • galaxy clusters
  • non-thermal emission
  • relativistic electrons
  • the SZ effect
  • Abstract We investigate theoretical models for the radio halo and hard X-ray (HXR)
    excess in the Coma galaxy cluster. Time-independent and time-dependent
    re-acceleration models for relativistic electrons have been carried out to
    study the formation of the radio halo and HXR excess. In these models, the
    relativistic electrons are injected by merger shocks and re-accelerated by
    ensuing violent turbulence. The effects of different Mach numbers of the merger
    shocks on the radio and HXR excess emission are also investigated. We adopt 6
    uG as the central magnetic field and reproduce the observed radio spectra
    via the synchrotron emission. We also obtain a central "plateau" in the radio
    spectral-index distribution, which have been observed in radio emission
    distribution. Our models can also produce the observed HXR excess emission via
    the inverse Compton scattering of the cosmic microwave background photons. We
    find that only the merger shocks with Mach numbers around 1.6--2 can produce
    results in agreement with both the radio and HXR emission in the Coma cluster.
    We also investigate the evolution and number distribution of radio halos in
    galaxy clusters. Without re-acceleration or regeneration, the relativistic
    electrons responsible for the diffuse radio emission will lose their energy via
    inverse-Compton and synchrotron losses in a rather short time, and radio halos
    will have lifetimes ~ 0.1 Gyr. Radio halos could last for ~ Gyr if a
    significant level of re-acceleration is involved. The lifetimes of radio halos
    would be comparable with the cosmological time if the radio-emitting electrons
    are mainly the secondary electrons generated by pion decay following
    proton-proton collisions between cosmic-ray protons and the thermal
    intra-cluster medium within the galaxy clusters. Adopting both observational
    and theoretical constraints for the formation of radio halos, we calculate the
    formation rates and the comoving number density of radio halos in the
    hierarchical clustering scheme. Comparing with observations, we find that the
    lifetimes of radio halos are ~ Gyr. Our results indicate that a
    significant level of re-acceleration is necessary for the observed radio halos
    and the secondary electrons may not be a dominant origin for radio halos.
    We have proposed a method to calculate the real effect of non-isothermality on
    the Sunyaev-Zel'dovich effect (SZE). The non-isothermal effect is
    conventionally approximated by an emission-weighted temperature with the
    isothermal assumption or only considered the influence of the non-isothermal
    Compton y-parameter. We have compared the calculated SZE with those estimated
    by these two approximative methods for non-isothermal clusters with and without
    cooling flows. Two temperature profiles, the hybrid model and polytropic model,
    are considered for the clusters without cooling flows. For investigating the
    effect of cooling flows on the SZE, the A1835 cluster is taken for example.
    Temperature profiles in galaxy clusters strongly affect the SZE and
    consequently the estimated values of the Hubble constant. Different profiles
    result in very different error ranges for estimating the Hubble constant,
    ~ -3%--+10% for the hybrid model and ~ -10%--+40% for the
    polytropic model. Specially, the effect of cooling flows on determining the
    value of the Hubble constant is dramatic, ~ +45% for A1835, when the
    isothermal emission-weighted temperature is adopted.
    Table of Content Contents
    1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 1
    1.1 X-ray Galaxy Clusters . . . . . . . . . . . . . . . . . . . 1
    1.1.1 Temperature Distribution and Dynamical State of Coma . . . 1
    1.2 Non-thermal Emission from Galaxy Clusters . . . . . . . . . 9
    1.3 Observational Properties of Radio Halos . . . . . . . . . . 15
    1.4 Observational Features of Coma C . . . . . . . . . . . . . . 16
    2 Formation of Radio Halos . . . . . . . . . . . . . . . . . . . 22
    2.1 Particle Acceleration Models . . . . . . . . . . . . . . . . 26
    2.2 Injection and Evolution of the Electron Spectrum . . . . . . 29
    2.3 Distribution of Magnetic Fields in Coma . . . . . . .. . . . 30
    2.4 Modeling Procedure . . . . . . . . . . . . . . . . . . . . . 33
    2.5 Model Results for Coma C . . . . . . . . . . . . . . . . . . 34
    2.5.1 Time-Independent Re-Acceleration . . . . . . . . . . . . . 34
    2.5.2 Time-Dependent Re-Acceleration . . . . . . . . . . . . . . 41
    2.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 45
    2.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . 50
    3 Cosmological Evolution of Radio Halos . . . . . . . . . . . . 52
    3.1 Formation Criteria . . . . . . . . . . . . . . . . . . . . . 54
    3.2 Formulation . . . . . . . . . . . . . . . . . .. . . . . . . 56
    3.2.1 Formation Rates . . . . . . . . . . . . . . .. . . . . . . 56
    3.2.2 Cumulative Comoving Number Density . . . . . . . . . . . . 57
    3.3 Results and Comparisons with Observations . . .. . . . . . . 59
    3.4 Discussion and Summary . . . . . . . . . . . . . . . . . . . 69
    4 The Sunyaev-Zel'dovich Effect . . . . . . . . . .. . . . . . . 76
    4.1 Determining Cosmological Parameters . . . . . .. . . . . . . 79
    4.1.1 Hubble Constant . . . . . . . . . . . . . . .. . . . . . . 81
    4.1.2 Cluster Gas-Mass Fraction . . . . . . . . . .. . . . . . . 83
    4.1.3 Cluster Peculiar Velocities . . . . . . . . .. . . . . . . 86
    4.2 Non-thermal SZ Effect . . . . . . . . . . . . . . . . . . . 88
    5 Non-Isothermality on the SZ Effect . . . . . . . . . . . . . . 92
    5.1 Thermal Sunyaev-Zel'dovich Effect . . . . . . . . . . . .. . 93
    5.1.1 Isothermal Electron Population . . . . . . . . . . . . . . 93
    5.1.2 Non-Isothermal Electron Population . . . . . . . . . . . . 95
    5.2 Approximation for the Non-Isothermal Effect . . . . . . . . .96
    5.2.1 Isothermal Emission-Weighted Temperature . . . . . . . . . 96
    5.2.2 Non-Isothermal Compton y-parameter . . . . . . . . . . . . 96
    5.3 Sunyaev-Zel'dovich Effect for Non-Isothermal Clusters . . . . 97
    5.3.1 Clusters Without Cooling Flows . . . . . . . . . . . . . . 97
    5.3.2 Clusters with Cooling Flows . . . . . . . . . . . . . . . .101
    5.4 Estimation of the Hubble Constant . . . . . . . . . . . . . .105
    5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .109
    6 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . .115
    A List of Papers . . . . . . . . . . . . . . . . . . . . . . . . 126
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