Studying and modelling the complete gravitational-wave signal from precessing black hole binaries

Doctoral thesis English OPEN
Schmidt, Patricia
  • Subject: QB

The coalescence of two stellar mass black holes is regarded as one of the most promising sources\ud for the first gravitational-wave (GW) detection with ground-based detectors. The current\ud detection strategies, however, rely on theoretical knowledge of the gravitational waveforms.\ud It is therefore crucial to obtain an accurate and complete description of the GW signal.\ud This thesis concerns the description of precessing black holes. Misalignment between the\ud orbital angular momentum and the spin angular momenta of the two black holes induces precession,\ud leading to complex dynamics that leaves a direct imprint on the GW. Additionally,\ud the evolution of the binary depends on the mass ratio and both spins spanning a sevendimensional\ud intrinsic parameter space. This makes it difficult to obtain a simple, closed-form\ud description of the waveform through inspiral, merger and ringdown. We are therefore interested\ud in 1) developing a conceptually intuitive framework to systematically model precessing\ud waveforms and 2) exploring the possibility of representing the seven-dimensional parameter\ud space by a lower-dimensional subset.\ud First, we introduce an accelerated frame of reference, which allows us to track the precession\ud of the orbital plane. We then analyse the waveforms in this co-precessing frame resulting\ud in an approximate decoupling between the inspiral and precession dynamics. This leads to\ud the important identification of the inspiral rate of a precessing binary with the inspiral rate\ud of an aligned-spin binary. Based on this decoupling, we develop a general framework to construct\ud precessing waveforms by \twisting up" an aligned-spin waveform with a model for the\ud precession dynamics.\ud In general, precession depends on all seven intrinsic physical parameters, which complicates\ud modelling efforts. However, we find a parameter-reduced representation of the dynamics,\ud which allows us to produce a first closed-form description of the complete waveforms of\ud precessing black-hole binaries within this general and easy-to-grasp fram
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    178 references, page 1 of 18

    2 Preliminaries and framework 5 2.1 Convention and notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 General Relativity in a nutshell . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.3.1 Linearised gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3.2 Interaction of GWs with test masses . . . . . . . . . . . . . . . . . . . 14 2.3.3 The generation of gravitational waves . . . . . . . . . . . . . . . . . . 15 2.3.4 Gravitational-wave sources . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Detecting gravitational waves . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.4.1 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4.2 Searching for GWs: matched ltering . . . . . . . . . . . . . . . . . . 23 2.5 Modelling gravitational waves from coalescing compact binaries . . . . . . . . 25 2.5.1 Post-Newtonian theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.5.2 Numerical Relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.2.1 BAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5.3 Complete waveform models . . . . . . . . . . . . . . . . . . . . . . . . 37

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