Gravitational-Wave Background From The Ultralight Bosons And Orbital Dynamics Of Post-Newtonian Compact Binaries

Gravitational wave astronomy is an important research frontier today.Currently,relevant research mainly targets the transient gravitational waves（GWs）generated by the merger of compact binaries,and the stochastic gravitational wave background（SGWB）formed by incoherent superpositions of discrete GW signals.Our work focuses on the latter,and we consider the SGWB formed by a particular type of GW source–those resulting from black hole（BH）superradiance of ultralight boson dark matter（ULDM）.In the first part of this thesis,we present the theoretical predictions and observation prospects of this SGWB signal.The second part studies the chaotic dynamics of compact binary orbits,in preparation for further research on the SGWB from binaries.In the first part,we assume that cosmological dark matter consists of ultralight bosons described by a massive scalar field.When surrounding a Kerr BH,such a scalar field can extract some of the rotational energy of the BH under certain conditions,and consequently form a boson cloud around the BH.This phenomenon is known as BH superradiance.The boson cloud thus formed has a nonvanishing mass quadrupole moment,so it emits GWs.This GW signal has already become an important detection method for ultralight bosons.In this thesis,we consider the SGWB sourced by superradiance of stellar-mass BHs.Based on the BH population model of isolated stars and the line-of-sight integration approach,we predict the anisotropic signal（angular power spectrum）of this SGWB for the first time.Our results show that anisotropies of the SGWB sourced by boson clouds depend on cosmic matter density fluctuations,so this signal provides a new probe of large-scale structure of the Universe.In the theory of BH superradiance,stellar-mass BHs correspond to an ultralight boson mass range of about 10^-14 to 10^-11 e V,for which the GW signals fall within the sensitive band of terrestrial GW detectors such as LIGO.Our theoretical prediction shows that for some range of model parameters,the angular power spectrum signal above can reach the current observational upper limit given by LIGO.It indicates that current GW detection experiments are already able to put strong constraints on the ULDM.In addition,we consider the shot noise caused by the finite spatial resolution of the detector and predict the signal-to-noise ratio of this anisotropy signal based on the designed sensitivity of LIGO.In the second part of the thesis,we propose an extended phase-space symplectic-like integrator to study the orbital dynamics of compact stars in the post-Newtonian Lagrange framework.The post-Newtonian inspiral phase of the binaries is another major contribution to SGWB.Because of the precession and chaotic nonlinear effects affected by the post-Newtonian term of the strong gravitational field,the orbits of binaries become complicated rather than the general spectrum,and the traditional explicit algorithm cannot keep the conserved quantity of the system for a long time.As a geometric algorithm,symplectic algorithm can keep the relative conserved quantity of the system for a long time.We apply our algorithm to Lagrangian exact equations of motion,which retain all post-Newtonian higher-order terms compared to the approximate equations of motion.The Runge-Kutta method,the implicit mid-point symplectic algorithm and the Gauss Runge-Kutta method are compared.Our algorithm keeps the total energy and other motion integral of the system close to the mechanical accuracy.Because of its good computational performance,it is used to study whether the initial orbital eccentricity and spin angle parameter distribution can affect orbit chaos.The numerical results show that the influence of the initial angular momentum direction on the chaotic orbit is stochastic,and high orbital eccentricity is more likely to cause chaos.Such dynamics will be further used to construct SGWB in future research.