My dissertation includes two parts: Physics of Gamma-Ray Bursts (GRBs): Gamma-ray bursts are multi-wavelength transients, with both prompt gamma-ray emission and late time afterglow emission observed by telescopes in different wavelengths. I have carried out three investigations to understand GRB prompt emission and afterglow. Chapter 2 develops a new method, namely, "Stepwise Filter Correlation" method, to decompose the variability components in a light curve. After proving its reliability through simulations, we apply this method to 266 bright GRBs and find that the majority of the bursts have clear evidence of superposition of fast and slow variability components. Chapter 3 gives a complete presentation of the analytical approximations for synchrotron self-compton emission for all possible orders of the characteristic synchrotron spectral breaks (nua, nu m, and nuc). We identify a "strong absorption" regime whennua > nuc, and derive the critical condition for this regime. The external shock theory is an elegant theory to model GRB afterglows. It invokes a limit number of model parameters, and has well predicted spectral and temporal properties. Chapter 4 gives a complete reference of all the analytical synchrotron external shock afterglow models by deriving the temporal and spectral indices of all the models in all spectral regimes. This complete reference will serve as a useful tool for afterglow observers to quickly identify relevant models to interpret their data and identify new physics when the models fail.;Milti-messenger signals from double neutron star merger: As the multi-messenger era of astronomy ushers in, the second part of the dissertation studies the possible electromagnetic (EM) and neutrino emission counterparts of double neutron star mergers. Chapter 6 suggests that if double neutron star mergers leave behind a massive magnetar rather than a black hole, the magnetar wind could push the ejecta launched during the merger process, and under certain conditions, accelerates it to a relativistic speed. Such a magnetar-powered ejecta, when interacting with the ambient medium, would develop a bright broad-band afterglow due to external shock synchrotron radiation. We study this physical scenario in detail, and present the predicted X-ray, optical and radio light curves for a range of magnetar and ejecta parameters. Chapter 7 applies the model to interpret one optical transient discovered recently. In chapter 8, we show that protons accelerated in the external shock would interact with photons generated in the dissipating magnetar wind and emit high energy neutrinos and photons. We find that PeV neutrinos could be emitted from the shock front as long as the ejecta could be accelerated to a relativistic speed. These events would contribute to the diffuse Pev neutrino background and sub-Tev gamma-ray background.
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