Towards models of gravitational waveforms from generic binaries II: Modelling precession effects with a single effective precession parameter

Gravitational waves (GWs) emitted by generic black-hole binaries show a rich structure that directly reflects the complex dynamics introduced by the precession of the orbital plane, which poses a real challenge to the development of generic waveform models. Recent progress in modelling these signals relies on an approximate decoupling between the non-precessing secular inspiral and a precession-induced rotation. However, the latter depends in general on all physical parameters of the binary which makes modelling efforts as well as understanding parameter-estimation prospects prohibitively complex. Here we show that the dominant precession effects can be captured by a reduced set of spin parameters. Specifically, we introduce a single \emph{effective precession spin} parameter, $\chi_p$, which is defined from the spin components that lie in the orbital plane at some (arbitrary) instant during the inspiral. We test the efficacy of this parameter by considering binary inspiral configurations specified by the physical parameters of a corresponding non-precessing-binary configuration (total mass, mass ratio, and spin components (anti-)parallel to the orbital angular momentum), plus the effective precession spin applied to the larger black hole. We show that for an overwhelming majority of random precessing configurations, the precession dynamics during the inspiral are well approximated by our equivalent configurations. Our results suggest that in the comparable-mass regime waveform models with only three spin parameters faithfully represent generic waveforms, which has practical implications for the prospects of GW searches, parameter estimation and the numerical exploration of the precessing-binary parameter space.Comment: 19 pages, 15 figures. Modified discussio

Tracking the precession of compact binaries from their gravitational-wave signal

We present a simple method to track the precession of a black-hole-binary system, using only information from the gravitational-wave (GW) signal. Our method consists of locating the frame from which the magnitude of the $(\ell=2,|m|=2)$ modes is maximized, which we denote the "quadrupole-aligned" frame. We demonstrate the efficacy of this method when applied to waveforms from numerical simulations. In the test case of an equal-mass nonspinning binary, our method locates the direction of the orbital angular momentum to within $(\Delta \theta, \Delta \phi) = (0.05^{\circ},0.2^{\circ})$. We then apply the method to a $q = M_2/M_1 = 3$ binary that exhibits significant precession. In general a spinning binary's orbital angular momentum $\mathbf{L}$ is \emph{not} orthogonal to the orbital plane. Evidence that our method locates the direction of $\mathbf{L}$ rather than the normal of the orbital plane is provided by comparison with post-Newtonian (PN) results. Also, we observe that it accurately reproduces similar higher-mode amplitudes to a comparable non-spinning (and therefore non-precessing) binary, and that the frequency of the $(\ell=2,|m|=2)$ modes is consistent with the "total frequency" of the binary's motion. The simple form of the quadrupole-aligned waveform will be useful in attempts to analytically model the inspiral-merger-ringdown (IMR) signal of precessing binaries, and in standardizing the representation of waveforms for studies of accuracy and consistency of source modelling efforts, both numerical and analytical.Comment: 11 pages, 12 figures, 1 tabl

What should religious education aim to achieve?: An investigation into the purpose of religious education in the public sphere

This thesis is concerned with the question of what religious education should aim to achieve in the public sphere, and from that comes an interest in what is it that the teacher of religious education should aim to do. My enquiry is located, theoretically as well as conceptually, in the sphere of education. It is an educational study into religious education and situated in what can be termed a ‘Continental construction’ of educational research. I identify that since the inception of religious education in public schools in England, persistent assumptions have been made about both religion and education. I show how this has led, in my view, to conceptualisations of religious education which have been, and continue to be, incomplete. The central chapters of my thesis consider first religion and then education. This allows me to introduce my theoretical base, which is especially but not exclusively drawn from the work of Simone Weil and Hannah Arendt. I develop an argument suggesting that by also understanding religion existentially as faith, rather than as only belief or practice, will open new ways of considering the role of religious education in the public sphere. This is alongside an argument I develop with Arendt for education being conceptualised as bringing the child to action rather than to reason. This thesis argues for a broader understanding of religion, and therefore what it means to live a religious life, in religious education than has previously been considered. I bring this broader way of understanding what it means to live a religious life together with my argument for conceptualising education as bringing the child to action. This enables me to make a new proposal for what religious education should aim to achieve in the public sphere

Degeneracy between mass and spin in black-hole-binary waveforms

We explore the degeneracy between mass and spin in gravitational waveforms emitted by black-hole binary coalescences. We focus on spin-aligned waveforms and obtain our results using phenomenological models that were tuned to numerical-relativity simulations. A degeneracy is known for low-mass binaries (particularly neutron-star binaries), where gravitational-wave detectors are sensitive to only the inspiral phase, and the waveform can be modelled by post-Newtonian theory. Here, we consider black-hole binaries, where detectors will also be sensitive to the merger and ringdown, and demonstrate that the degeneracy persists across a broad mass range. At low masses, the degeneracy is between mass ratio and total spin, with chirp mass accurately determined. At higher masses, the degeneracy persists but is not so clearly characterised by constant chirp mass as the merger and ringdown become more significant. We consider the importance of this degeneracy both for performing searches (including searches where only non-spinning templates are used) and in parameter extraction from observed systems. We compare observational capabilities between the early (~2015) and final (2018 onwards) versions of the Advanced LIGO detector.Comment: 11 pages, 9 figure

Towards models of gravitational waveforms from generic binaries: A simple approximate mapping between precessing and non-precessing inspiral signals

One of the greatest theoretical challenges in the build-up to the era of second-generation gravitational-wave detectors is the modeling of generic binary waveforms. We introduce an approximation that has the potential to significantly simplify this problem. We show that generic precessing-binary inspiral waveforms (covering a seven-dimensional space of intrinsic parameters) can be mapped to a two-dimensional space of non-precessing binaries, characterized by the mass ratio and a single effective total spin. The mapping consists of a time-dependent rotation of the waveforms into the quadrupole-aligned frame, and is extremely accurate (matches $> 0.99$ with parameter biases in the total spin of $\Delta \chi \leq 0.04$), even in the case of transitional precession. In addition, we demonstrate a simple method to construct hybrid post-Newtonian--numerical-relativity precessing-binary waveforms in the quadrupole-aligned frame, and provide evidence that our approximate mapping can be used all the way to the merger. Finally, based on these results, we outline a general proposal for the construction of generic waveform models, which will be the focus of future work.Comment: 16 pages, 11 figures, 2 tables; replaced to match published version; journal ref. adde

Simple Model of Complete Precessing Black-Hole-Binary Gravitational Waveforms

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger, and ringdown, is one of the most pressing theoretical problems in the buildup to the era of GW astronomy. We present the first such model in the frequency domain, PhenomP, which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary’s mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying nonprecessing-binary model. The nonprecessing-binary waveforms are then twisted up with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, χp. All other parameters (total mass, sky location, orientation and polarization, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model’s fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations—although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modeling in the advanced-detector era

Simple model of complete precessing black-hole-binary gravitational waveforms

The construction of a model of the gravitational-wave (GW) signal from generic configurations of spinning-black-hole binaries, through inspiral, merger, and ringdown, is one of the most pressing theoretical problems in the buildup to the era of GW astronomy. We present the first such model in the frequency domain, PhenomP, which captures the basic phenomenology of the seven-dimensional parameter space of binary configurations with only three key physical parameters. Two of these (the binary’s mass ratio and an effective total spin parallel to the orbital angular momentum, which determines the inspiral rate) define an underlying nonprecessing-binary model. The nonprecessing-binary waveforms are then twisted up with approximate expressions for the precessional motion, which require only one additional physical parameter, an effective precession spin, χp. All other parameters (total mass, sky location, orientation and polarization, and initial phase) can be specified trivially. The model is constructed in the frequency domain, which will be essential for efficient GW searches and source measurements. We have tested the model’s fidelity for GW applications by comparison against hybrid post-Newtonian-numerical-relativity waveforms at a variety of configurations—although we did not use these numerical simulations in the construction of the model. Our model can be used to develop GW searches, to study the implications for astrophysical measurements, and as a simple conceptual framework to form the basis of generic-binary waveform modeling in the advanced-detector era

Clinical information needs and access for clinical healthcare staff in Highland health and social care service.

Background: Clinical information is required by all clinical healthcare staff to promote better patient care and safety. The information needed, sources, formats and accessibility varies from one staff member to another according to factors such as experience, specialty, location and searching skills. This study aims to identify clinical information needs and related access of NHS Highland staff. Methods: A survey was developed in Survey Monkey using the COM-B model as a theoretical framework. COM-B relates behaviour to capability, opportunity and motivation. Survey questions were based on clinical information needs, where, why, when and how staff accessed clinical information. The survey was distributed, with management approval, to all staff in the Highland Health and Social Care Service via NHS email with two reminders sent at weekly intervals. Participants had the option to take part in a follow up, more in depth audio-recorded interview or focus group. Quantitative data will be analysed using descriptive statistics in SPSS version 21; qualitative data will be analysed using a thematic and content approach. Results and analysis: The study will report the resource types and forms of clinical information and access used by staff, highlighting their views. It will also explore healthcare professionals' experiences on the clinical information they search in terms of robustness, timeliness and clinical usefulness for patient care and safety. Conclusion: As this is an in-process research, the conclusion will be added after data analysis, interpretation and discussion considering behavioural aspects by inspecting capabilities, opportunities and motivation of all research participants

Gravitational waves: search results, data analysis and parameter estimation

The Amaldi 10 Parallel Session C2 on gravitational wave (GW) search results, data analysis and parameter estimation included three lively sessions of lectures by 13 presenters, and 34 posters. The talks and posters covered a huge range of material, including results and analysis techniques for ground-based GW detectors, targeting anticipated signals from different astrophysical sources: compact binary inspiral, merger and ringdown; GW bursts from intermediate mass binary black hole mergers, cosmic string cusps, core-collapse supernovae, and other unmodeled sources; continuous waves from spinning neutron stars; and a stochastic GW background. There was considerable emphasis on Bayesian techniques for estimating the parameters of coalescing compact binary systems from the gravitational waveforms extracted from the data from the advanced detector network. This included methods to distinguish deviations of the signals from what is expected in the context of General Relativity