Topics in theoretical astrophysics

Abstract

This thesis presents a study of various interesting problems in theoretical astrophysics, including gravitational wave astronomy, gamma ray bursts and cosmology. Chapters 2, 3 and 4 explore prospects for detecting gravitational waves from stellar-mass compact objects spiraling into intermediate-mass black holes with ground-based observatories. It is shown in chapter 2 that if the central body is not a BH but its metric is stationary, axisymmetric, reflection symmetric and asymptotically flat, then the waves will likely be triperiodic, as for a BH. Chapters 3 and 4 show that the evolutions of the waves' three fundamental frequencies and of the complex amplitudes of their spectral components encode (in principle) details of the central body's metric, the energy and angular momentum exchange between the central body and the orbit, and the time-evolving orbital elements. Chapter 5 studies a local readout method to enhance the low frequency sensitivity of detuned signal-recycling interferometers. We provide both the results of improvement in quantum noise and the implementation details in Advanced LIGO. Chapter 6 applies and generalizes causal Wiener filter to data analysis in macroscopic quantum mechanical experiments. With the causal Wiener filter method, we demonstrate that in theory we can put the test masses in the interferometer to its quantum mechanical ground states. Chapter 7 presents some analytical solutions for expanding fireballs, the common theoretical model for gamma ray bursts and soft gamma ray repeaters. We apply our results to SGR 1806-20 and rediscover the mismatch between the model and the afterglow observations. Chapter 8 discusses the reconstruction of the scalar-field potential of the dark energy. We advocate direct reconstruction of the scalar field potential as a way to minimize prior assumptions on the shape, and thus minimize the introduction of bias in the derived potential. Chapter 9 discusses gravitational lensing modifications to cosmic microwave background anisotropies and polarization, produced by a stochastic background of primordial gravitational waves between us and the last scattering surface. Chapter 10 calculates the non-Gaussian covariance of CMB B-modes of polarization.