摘 要
我們提出對相對論性電子的時變與非時變再加速模型（re-acceleration model），來解釋在Coma星系團（galaxy cluster）所觀測到的無線電暈（radio halo）與硬X射線過剩（hard X-ray excess）的形成。在我們的模型中，我們假設相對論性電子是由星系團合併時造成的衝擊波（shock wave）所產生，然後再由隨之而來的強烈紊流繼續再加速。在我們的模型中，我們也一併考慮衝擊波的馬赫數對形成無線電暈與硬X射線過剩的影響。我們的模型可以重現Coma星系團中無線電暈的所有觀測特徵。特別是spectral index分佈中的中心平坦部分，我們的模型是最先能重現這個觀測的模型。在逆康普頓散射（inverse Compton scattering）的假設下，我們的模型所得到的硬X射線過剩也與觀測相當一致。我們也發現衝擊波的馬赫數約在1.6-2才能得到與在Coma星系團中的無線電暈與硬X射線過剩的觀測值吻合的結果。
如果形成無線電暈的相對論性電子在產生後沒有被再加速，由於各種能量損耗機制的作用（主要為同步輻射與對宇宙背景輻射光子的逆康普頓作用），這些電子約略在一億年內會將其能量損耗殆盡。相對的，無線電暈的壽命也約略是一億年。在我們提出的相對論性電子的時變與非時變再加速模型中，得到於Coma星系團中的無線電暈的"年齡"約為十億年。所以如果這些相對論性電子在產生後繼續被紊流再加速，則這些無線電暈的壽命應約略為十億年的數量級。另一個形成無線電暈的理論為次電子模型（secondary electron model）。在此理論中，形成無線電暈的相對論性電子是由宇宙射線質子與在星系團中的熱離子發生破壞性碰撞所產生。而研究發現，在星系團中的宇宙射線質子要經過與宇宙壽命相當的時間才能脫逃出星系團。所以，如果無線電暈是由次電子所產生，則其壽命也應與宇宙壽命相當。我們建構了一個無線電暈數量密度的演化模型，並研究無線電暈壽命為一億年、十億年與宇宙壽命時，其現今在星系團中應有的比例。與觀測結果比較，我們發現，只有當其壽命為十億年時，所得到的結果才較符合觀測值。因此我們推論，形成無線電暈的相對論性電子必須被再加速才能維持無線電暈十幾或幾十億年的壽命；而我們的研究結果也顯示，次電子應該不是形成無線電暈的主要來源。
最後我們提出一個方法，來計算在星系團內非等熱分佈對SZ效應的實際影響。非等熱分佈對SZ效應的影響通常都以兩種近似的方法來計算。一種是先計算放射比重溫度（emission-weighted temperature）再以此溫度作等熱分佈假設；另一種是計算非等熱的康普頓y參數（Compton y-parameter）。我們以所提出的方法來計算有cooling flow和無cooling flow的非等熱星系團的SZ效應，再與兩種近似方法所得的結果比較。我們也研究在非等熱星系團中，兩種近似方法對估計哈伯常數所造成的誤差。

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.

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