Semi-analytical approaches to gravitational radiation froma astrophysical sources

Electromagnetic (EM) astronomical observations have improved the understanding of many astrophysical phenomena, e.g. X-ray binaries, gamma-ray bursts (GRBs) among others. These EM signals are in general incoherent and some information is lost during the propagation. In contrast, gravitational waves (GW) are mostly emitted by the coherent motion of large amounts of matter and can give the additional missing information. However, GWs are rather weak and their detection requires great technological efforts. Since it is expected that the GW signal is smaller than the noise in the detector, the matched-filter technique is usually used for claiming detection and for determining the parameters of the source. This requires knowledge of the physical signal and of the noise, the latter is usually not perfectly known. Numerical-relativity (NR) can provide accurate templates for binary black hole mergers and partially accurate template for binary neutron stars or binary white dwarfs, but currently, simulations are computationally demanding. Semi-analytical approaches to GW can provide solution to this issue. Besides, since they are constructed following basic principles, they provide clear physical interpretations and consistency tests to observational results. This thesis was devoted to the development and study of semi-analytical models of GW radiation from different astrophysical sources. From the basic physics of black holes (BHs), this work introduced the ``helicoidal drift sequence'' (HDS), which describes the dynamics of an inspiraling test particle driven by GW emission on the Kerr spacetime. It was found that the final plunge, after the passage of the innermost stable circular orbit (ISCO), is nearly geodesic and emits less GWs than the amount implied by other semi-analytical approaches. Next, the HDS augmented with the Newtonian center-of-mass point of view, was used here to construct ``test particle'' waveforms in order to model binary black hole (BBH) mergers with comparable mass components. Since this work uses a Kerr ``background'', even in the case of BBHs with spin-less components, the model effectively incorporates frame dragging due to the orbital angular momentum of the system. Test particle waveforms, up to the frequency of the ISCO, were found to be in excellent agreement with the ones of NR simulations. The contribution of the orbital angular momentum of the system to frame dragging was not taken into a account by previous semi-analytical models. This work also studied consistency between EM and GW observations. The recent GW event GW170817, consistent with a binary neutron star (BNS) merger, was associated with the EM counterpart GRB170817-AT 2017gfo. From the GW data, an independent calculation of the localization of the source was made in this work. It was found that the latter localization is consistent with the one inferred from the EM data. On the other hand, the EM counterpart is not consistent when it is compared with the prototype of known GRBs. An alternative scenario, namely the merger of a binary white dwarf, is introduced to explain the EM emission. The recent classification of GRBs and the inferred observed rates were used in this work to compute the detection rate of GWs from BNS, BH-NS and NS-WD systems, by earth-based interferometers. Namely, the inferred detection rate of GWs from BNSs, for design sensitivity (2022+) of LIGO-Virgo detectors is $0.1 - 0.2~yr$^{-1}$, consistent with lower limits of rates found in the literature. In addition, two overlooked astrophysical GW sources were studied: deformed, rotating white dwarf-like objects, called in this work chirping ellipsoids (CELs), and extreme mass-ratio inspirals (EMRIs) composed of a planet-like object and an intermediate-mass BH. It was found that CELs are quasi-monochromactic GW sources and individually detectable by planned space-based missions such as LISA, TianQin and Taiji. Equally important, this work shows that the CEL waveform is practically indistinguishable from the one the aforementioned EMRIs and from the one of non-interacting double white dwarfs (DWDs). In view of this degeneracy, the rates of these sources were estimated and it was found that all the systems have similar rates. The kind of EMRIs studied here do not accumulate the sufficient signal-to-noise ratio to be individually detected by future space-based interferometers, but owing to the fact that they exhibit a rate comparable to DWDs, they are plausible stochastic GW sources. As a consequence of the similarity of the rates of CELs and DWDs, it is expected significant source confusion between them. On the other hand, this work found that the detection degeneracy is not present along the whole lifetime of the systems. Namely, their phase-time evolution become different from some frequency, which in the case of EMRIs is given by the GW frequency when the less massive component is tidally disrupted, and in the case of a DWD by the frequency when Roche-Lobe overflow occurs. Hence, it is possible to break the detection degeneracy. Finally, the question of the post-merger object of BNSs is addressed by means of the laws of energy, angular momentum and baryonic mass conservation. When there is not prompt formation of a BH, it was found that if the total mass of the binary is lower than some discriminant mass, the post-merger compact star does not exhibit bound matter in the form of a disk. This post-merger object can give rise to a new kind of GRB (not yet observed): ultra-short gamma ray flash. If a joint GW and electromagnetic observation of this kind of event takes place, the approach presented here can be used to set a more stringent lower limit on the critical mass of non-rotating neutron stars.