Beyond the Bowen-York extrinsic curvature for spinning black holes

It is well-known that Bowen-York initial data contain spurious radiation. Although this ``junk'' radiation has been seen to be small for non-spinning black-hole binaries in circular orbit, its magnitude increases when the black holes are given spin. It is possible to reduce the spurious radiation by applying the puncture approach to multiple Kerr black holes, as we demonstrate for examples of head-on collisions of equal-mass black-hole binaries.Comment: 10 pages, 2 figures, submitted to special "New Frontiers in Numerical Relativity" issue of Classical and Quantum Gravit

The implications of a changing climate on agricultural land classification in England and Wales

The agricultural land classification (ALC) of England and Wales is a formal method of assessing the quality of agricultural land and guiding future land use. It assesses several soil, site and climate criteria and classifies land according to whichever is the most limiting. A common approach is required for calculating the necessary agroclimatic parameters over time in order to determine the effects of changes in the climate on land grading. In the present paper, climatic parameters required by the ALC classification have been re-calculated from a range of primary climate data, available from the Meteorological Office's UKCP09 historical dataset, provided as 5 km rasters for every month from 1914 to 2000. Thirty-year averages of the various agroclimatic properties were created for 1921–50, 1931–60, 1941–70, 1951–80, 1961–90 and 1971–2000. Soil records from the National Soil Inventory on a 5 km grid across England and Wales were used to determine the required soil and site parameters for determining ALC grade. Over the 80-year period it was shown that the overall climate was coolest during 1951–80. However, the area of land estimated in retrospect as ‘best and most versatile (BMV) land’ (Grades 1, 2 and 3a) probably peaked in the 1951–80 period as the cooler climate resulted in fewer droughty soils, more than offsetting the land which was downgraded by the climate being too cold. Overall there has been little change in the proportions of ALC grades among the six periods once all 10 factors (climate, gradient, flooding, texture, depth, stoniness, chemical, soil wetness, droughtiness and erosion) are taken into account. This is because it is rare for changes in climate variables all to point in the same direction in terms of ALC. Thus, a reduction in rainfall could result in higher grades in wetter areas but lead to lower classification in drier areas

Bowen-York trumpet data and black-hole simulations

The most popular method to construct initial data for black-hole-binary simulations is the puncture method, in which compactified wormholes are given linear and angular momentum via the Bowen-York extrinsic curvature. When these data are evolved, they quickly approach a ``trumpet'' topology, suggesting that it would be preferable to use data that are in trumpet form from the outset. To achieve this, we extend the puncture method to allow the construction of Bowen-York trumpets, including an outline of an existence and uniqueness proof of the solutions. We construct boosted, spinning and binary Bowen-York puncture trumpets using a single-domain pseudospectral elliptic solver, and evolve the binary data and compare with standard wormhole-data results. We also show that for boosted trumpets the black-hole mass can be prescribed {\it a priori}, without recourse to the iterative procedure that is necessary for wormhole data.Comment: 15 pages, 14 figures. Published versio

Modeling the gravitational wave signature of neutron star black hole coalescences: PhenomNSBH

Accurate gravitational-wave (GW) signal models exist for black-hole binary (BBH) and neutron-star binary (BNS) systems, which are consistent with all of the published GW observations to date. Detections of a third class of compact-binary systems, neutron-star-black-hole (NSBH) binaries, have not yet been confirmed, but are eagerly awaited in the near future. For NSBH systems, GW models do not exist across the viable parameter space of signals. In this work we present the frequency-domain phenomenological model, PhenomNSBH, for GWs produced by NSBH systems with mass ratios from equal-mass up to 15, spin on the black hole up to a dimensionless spin of $|\chi|=0.5$, and tidal deformabilities ranging from 0 (the BBH limit) to 5000. We extend previous work on a phenomenological amplitude model for NSBH systems to produce an amplitude model that is parameterized by a single tidal deformability parameter. This amplitude model is combined with an analytic phase model describing tidal corrections. The resulting approximant is accurate enough to be used to measure the properties of NSBH systems for signal-to-noise ratios (SNRs) up to 50, and is compared to publicly-available NSBH numerical-relativity simulations and hybrid waveforms constructed from numerical-relativity simulations and tidal inspiral approximants. For most signals observed by second-generation ground-based detectors within this SNR limit, it will be difficult to use the GW signal alone to distinguish single NSBH systems from either BNSs or BBHs, and therefore to unambiguously identify an NSBH system

Conformal thin-sandwich puncture initial data for boosted black holes

We apply the puncture approach to conformal thin-sandwich black-hole initial data. We solve numerically the conformal thin-sandwich puncture (CTSP) equations for a single black hole with non-zero linear momentum. We show that conformally flat solutions for a boosted black hole have the same maximum gravitational radiation content as the corresponding Bowen-York solution in the conformal transverse-traceless decomposition. We find that the physical properties of these data are independent of the free slicing parameter.Comment: 12 pages, 11 figure

BSSN in Spherical Symmetry

The BSSN (Baumgarte-Shapiro-Shibata-Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal--Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth--order finite difference implementation of the equations.Comment: This is the final version to be published in CQG. It contains much more information and detail than the original versio

Total recoil: the maximum kick from nonspinning black-hole binary inspiral

When unequal-mass black holes merge, the final black hole receives a ``kick'' due to the asymmetric loss of linear momentum in the gravitational radiation emitted during the merger. The magnitude of this kick has important astrophysical consequences. Recent breakthroughs in numerical relativity allow us to perform the largest parameter study undertaken to date in numerical simulations of binary black hole inspirals. We study non-spinning black-hole binaries with mass ratios from $q=M_1/M_2=1$ to $q =0.25$ ($\eta = q/(1 + q)^2$ from 0.25 to 0.16). We accurately calculate the velocity of the kick to within 6%, and the final spin of the black holes to within 2%. A maximum kick of $175.2\pm11$ km s$^{-1}$ is achieved for $\eta = 0.195 \pm 0.005$.Comment: 4 pages, 4 figures. Version accepted by PR

Supermassive recoil velocities for binary black-hole mergers with antialigned spins

Recent calculations of the recoil velocity in binary black hole mergers have found the kick velocity to be of the order of a few hundred km/s in the case of non-spinning binaries and about $500$km/s in the case of spinning configurations, and have lead to predictions of a maximum kick of up to $1300$km/s. We test these predictions and demonstrate that kick velocities of at least $2500$km/s are possible for equal-mass binaries with anti-aligned spins in the orbital plane. Kicks of that magnitude are likely to have significant repercussions for models of black-hole formation, the population of intergalactic black holes and the structure of host galaxies.Comment: Final version, published by Phys. Rev. Lett.; title changed according to suggestion of PRL; note added after preparation of manuscrip

Homogeneity and Heterogeneity: two approaches for designing spatial sound

My research explores the process for designing and reproducing spatial sound through two personal sound-design projects: Pilate (2006) and Metamorphosis42 (2009). Located within the context of design, it explores two modes for spatial sound composition, which at its heart contemplates the potential for the phenomenon of the sound experience to guide the design and reproduction of spatial sound using electroacoustic techniques. The intent is to convey an approach to sound design, by combining the concepts with the tools and techniques used in sound composition, to create an impression of space that is perceived by the listener. This process has enabled me to draw a distinction in approach between my projects, based on the concepts, tools and techniques I apply in the act of making, to guide my work. In emphasising the sound space relation, the notions of the ‘homogeneous’ and the ‘heterogeneous’ emerge. I apply these terms in my research, to embody the essence of a compositional methodology, explored through an analysis of my projects and by engaging with a process of reflection and listening. On this basis, my research suggests that the notion of the ‘homogeneous’ builds on the physical relations of sound and space through an experience of sound within space. If our experience of sound in a real-world scenario can be considered coherent, then, in the context of a sound design process, my research proposes that a ‘homogeneous’ approach to sound composition seeks to faithfully reproduce the perceptually coherent sounding qualities observed in the real-world. This approach is predicated on the fact that the sensations of sound are the result of vibrating materials. The displacement, which occurs at the material surface, creates a pressure wave that moves through the atmosphere interacting with other materials within the environment. As a consequence, the pressure waves that reach our ears come from all directions, not just one and the physical qualities of the materials the pressure wave interacts with – their size, shape and density, for example, directly influence how sound is perceived. The notion of the ‘heterogeneous’ builds on the internal relation of sound and space - the space within sound, and how the physical and imagined qualities of space are interchangeable which conveys a dynamic and complex sense of space. A quality of this approach is that sound is suspended in its own time and space through a poetic re-imagination - an interior space in which sound is decoupled from its physical source. As François Bayle (2007, p.241) writes, ‘a sound from a transducer is like no other’. I interpret this as a way to think about the reproduced sound, which sits beyond the physical. I use the term ‘re-imagination’ to emphasise that the listener is not passive, but instead an active body engaged in this contemplation of sound. On this basis, the heterogeneous is not one singular homogeneous image bound entirely by the physical nature of the source. Instead, it is an affective experience that is bound to our senses and our emotions, reaching our ears through a patchwork of sounds that collide in space and time creating a transformation that occurs at the boundaries of perception

Exploring black hole superkicks

Recent calculations of the recoil velocity in black-hole binary mergers have found kick velocities of $\approx2500$km/s for equal-mass binaries with anti-aligned initial spins in the orbital plane. In general the dynamics of spinning black holes can be extremely complicated and are difficult to analyze and understand. In contrast, the ``superkick'' configuration is an example with a high degree of symmetry that also exhibits exciting physics. We exploit the simplicity of this ``test case'' to study more closely the role of spin in black-hole recoil and find that: the recoil is with good accuracy proportional to the difference between the $(l = 2, m = \pm 2)$ modes of $\Psi_4$, the major contribution to the recoil occurs within $30M$ before and after the merger, and that this is after the time at which a standard post-Newtonian treatment breaks down. We also discuss consequences of the $(l = 2, m = \pm 2)$ asymmetry in the gravitational wave signal for the angular dependence of the SNR and the mismatch of the gravitational wave signals corresponding to the north and south poles