Modelling gravitational waves from precessing black-hole binaries: Progress, challenges and prospects

The inspiral and merger of two orbiting black holes is among the most promising sources for the first (hopefully imminent) direct detection of gravitational waves (GWs), and measurements of these signals could provide a wealth of information about astrophysics, fundamental physics and cosmology. Detection and measurement require a theoretical description of the GW signals from all possible black-hole-binary configurations, which can include complicated precession effects due to the black-hole spins. Modelling the GW signal from generic precessing binaries is therefore one of the most urgent theoretical challenges facing GW astronomy. This article briefly reviews the phenomenology of generic-binary dynamics and waveforms, and recent advances in modelling them.Comment: Invited review for General Relativity and Gravitatio

Quasi-circular orbits of conformal thin-sandwich puncture binary black holes

I construct initial data for equal-mass irrotational binary black holes using the conformal thin-sandwich puncture (CTSP) approach. I locate quasi-circular orbits using the effective-potential method, and estimate the location of the innermost stable circular orbit (ISCO). The ISCO prediction is consistent with results for conformal thin-sandwich data produced using excision techniques. These results also show that the ISCOs predicted by the effective-potential and ADM-Komar mass-comparison methods agree for conformal thin-sandwich data, just as they did for Bowen-York data.Comment: 7 pages, 1 figure. Added discussion of the Komar mass, and slight modifications for published versio

A method to identify and evaluate the legal and institutional framework for the management of water and land in Asia: the outcome of a study in Southeast Asia and the People’s Republic of China

Water management / Land management / Legal aspects / Environmental policy / China / Laos / Bangladesh / Philippines

Developing a Global Soil Regime

From the 1960s onwards, the global community became more aware of the phenomena of air and water pollution. More recently, the issues of climate change, loss of biodiversity, desertification, drought, and land degradation have become more prominent. While biodiversity loss and climate change have garnered close attention, issues of land degradation and sustainability of soils has attracted less focus in international fora and by national governments. We argue here that soil, as a vital biological and cultural resource, demands attention on the same level as biological diversity and climate change, and that this should be reflected in both international law and in legislation at national level. This article explores the elements that could form the basis of a global instrument for the conservation and sustainable use of soil, and sets out the premise for the community of nations to support the negotiation and drafting of such an instrument. It does so in light of the recent discussion on the introduction of a provision in the United Nations Sustainable Development Goals on the achievement of zero net land degradation, the revision of the World Soil Charter as well as the work of the UN Special Rapporteur on the Right to Food. It also briefly explores other complementary mechanisms that can be used for promoting the sustainable use of soils

Reducing eccentricity in black-hole binary evolutions with initial parameters from post-Newtonian inspiral

Standard choices of quasi-circular orbit parameters for black-hole binary evolutions result in eccentric inspiral. We introduce a conceptually simple method, which is to integrate the post-Newtonian equations of motion through hundreds of orbits, and read off the values of the momenta at the separation at which we wish to start a fully general relativistic numerical evolution. For the particular case of non-spinning equal-mass inspiral with an initial coordinate separation of $D = 11M$ we show that this approach reduces the eccentricity by at least a factor of five to $e < 0.002$ as compared to using standard quasi-circular initial parameters.Comment: 6 pages, 3 figures, 1 tabl

Inferring black-hole orbital dynamics from numerical-relativity gravitational waveforms

Binary-black-hole dynamics cannot be related to the resulting gravitational-wave signal by a constant retarded time. This is due to the non-trivial dynamical spacetime curvature between the source and the signal. In a numerical-relativity simulation there is also some ambiguity in the black-hole dynamics, which depend on the gauge (coordinate) choices used in the numerical solution of Einstein's equations. It has been shown previously that a good approximation to the direction of the binary's time-dependent orbital angular momentum $\mathbf{\hat{L}}(t)$ can be calculated from the gravitational-wave signal. This is done by calculating the direction that maximises the quadrupolar $(\ell=2,|m|=2)$ emission. The direction depends on whether we use the Weyl scalar $\psi_4$ or the gravitational-wave strain $h$, but these directions are nonetheless invariant for a given binary configuration. We treat the $\psi_4$-based direction as a proxy to $\mathbf{\hat{L}}(t)$. We investigate how well the the binary's orbital phase, $\phi_{\rm orb}(t)$, can also be estimated from the signal. For this purpose we define a quantity $\Phi(t)$ that agrees well with $\phi_{\rm orb}(t)$. One application is to studies that involve injections of numerical-relativity waveforms into gravitational-wave detector data.Comment: 12 pages with 10 figure

Is black-hole ringdown a memory of its progenitor?

We have performed an extensive numerical study of coalescing black-hole binaries to understand the gravitational-wave spectrum of quasi-normal modes excited in the merged black hole. Remarkably, we find that the masses and spins of the progenitor are clearly encoded in the mode spectrum of the ringdown signal. Some of the mode amplitudes carry the signature of the binary's mass ratio, while others depend critically on the spins. Simulations of precessing binaries suggest that our results carry over to generic systems. Using Bayesian inference, we demonstrate that it is possible to accurately measure the mass ratio and a proper combination of spins even when the binary is itself invisible to a detector. Using a mapping of the binary masses and spins to the final black hole spin, allows us to further extract the spin components of the progenitor. Our results could have tremendous implications for gravitational astronomy by facilitating novel tests of general relativity using merging black holes.Comment: 5 pages, 3 figures, 1 table, accepted for publication in Physical Review Letter

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

Constraining black-hole spins with gravitational wave observations

The observation of gravitational-wave signals from merging black-hole binaries enables direct measurement of the properties of the black holes. An individual observation allows measurement of the black-hole masses, but only limited information about either the magnitude or orientation of the black hole spins is available, primarily due to the degeneracy between measurements of spin and binary mass ratio. Using the first six black-hole merger observations, we are able to constrain the distribution of black-hole spins. We perform model selection between a set of models with different spin population models combined with a power-law mass distribution to make inferences about the spin distribution. We assume a fixed power-law mass distribution on the black holes, which is supported by the data and provides a realistic distribution of binary mass-ratio. This allows us to accurately account for selection effects due to variations in the signal amplitude with spin magnitude, and provides an improved inference on the spin distribution. We conclude that the first six LIGO and Virgo observations (Abbott et al. 2016a, 2017a,b,c) disfavour highly spinning black holes against low spins by an odds-ratio of 15:1; thus providing strong constraints on spin magnitudes from gravitational-wave observations. Furthermore, we are able to rule out a population of binaries with completely aligned spins, even when the spins of the individual black holes are low, at an odds ratio of 22,000:1, significantly strengthening earlier evidence against aligned spins (Farr et al. 2017). These results provide important information that will aid in our understanding on the formation processes of black-holes