Using spin to understand the formation of LIGO's black holes

With the detection of four candidate binary black hole (BBH) mergers by the Advanced LIGO detectors thus far, it is becoming possible to constrain the properties of the BBH merger population in order to better understand the formation of these systems. Black hole (BH) spin orientations are one of the cleanest discriminators of formation history, with BHs in dynamically formed binaries in dense stellar environments expected to have spins distributed isotropically, in contrast to isolated populations where stellar evolution is expected to induce BH spins preferentially aligned with the orbital angular momentum. In this work we propose a simple, model-agnostic approach to characterizing the spin properties of LIGO's BBH population. Using measurements of the effective spin of the binaries, which is LIGO's best constrained spin parameter, we introduce a simple parameter to quantify the fraction of the population that is isotropically distributed, regardless of the spin magnitude distribution of the population. Once the orientation characteristics of the population have been determined, we show how measurements of effective spin can be used to directly constrain the underlying BH spin magnitude distribution. Although we find that the majority of the current effective spin measurements are too small to be informative, with LIGO's four BBH candidates we find a slight preference for an underlying population with aligned spins over one with isotropic spins (with an odds ratio of 1.1). We argue that it will be possible to distinguish symmetric and anti-symmetric populations at high confidence with tens of additional detections, although mixed populations may take significantly more detections to disentangle. We also derive preliminary spin magnitude distributions for LIGO's black holes, under the assumption of aligned or isotropic populations

Statistical Gravitational Waveform Models: What to Simulate Next?

Models of gravitational waveforms play a critical role in detecting and characterizing the gravitational waves (GWs) from compact binary coalescences. Waveforms from numerical relativity (NR), while highly accurate, are too computationally expensive to produce to be directly used with Bayesian parameter estimation tools like Markov-chain-Monte-Carlo and nested sampling. We propose a Gaussian process regression (GPR) method to generate accurate reduced-order-model waveforms based only on existing accurate (e.g. NR) simulations. Using a training set of simulated waveforms, our GPR approach produces interpolated waveforms along with uncertainties across the parameter space. As a proof of concept, we use a training set of IMRPhenomD waveforms to build a GPR model in the 2-d parameter space of mass ratio $q$ and equal-and-aligned spin $\chi_1=\chi_2$. Using a regular, equally-spaced grid of 120 IMRPhenomD training waveforms in $q\in[1,3]$ and $\chi_1 \in [-0.5,0.5]$, the GPR mean approximates IMRPhenomD in this space to mismatches below $4.3\times 10^{-5}$. Our approach can alternatively use training waveforms directly from numerical relativity. Beyond interpolation of waveforms, we also present a greedy algorithm that utilizes the errors provided by our GPR model to optimize the placement of future simulations. In a fiducial test case we find that using the greedy algorithm to iteratively add simulations achieves GPR errors that are $\sim 1$ order of magnitude lower than the errors from using Latin-hypercube or square training grids

Cover Your Basis: Comprehensive Data-Driven Characterization of the Binary Black Hole Population

We introduce the first complete non-parametric model for the astrophysical distribution of the binary black hole (BBH) population. Constructed from basis splines, we use these models to conduct the most comprehensive data-driven investigation of the BBH population to date, simultaneously fitting non-parametric models for the BBH mass ratio, spin magnitude and misalignment, and redshift distributions. With GWTC-3, we report the same features previously recovered with similarly flexible models of the mass distribution, most notably the peaks in merger rates at primary masses of ${\sim}10\,M_\odot$ and ${\sim}35\,M_\odot$. Our model reports a suppressed merger rate at low primary masses and a mass ratio distribution consistent with a power law. We infer a distribution for primary spin misalignments that peaks away from alignment, supporting conclusions of recent work. We find broad agreement with the previous inferences of the spin magnitude distribution: the majority of BBH spins are small ($a<0.5$), the distribution peaks at $a\sim0.2$, and there is mild support for a non-spinning subpopulation, which may be resolved with larger catalogs. With a modulated power law describing the BBH merger rate's evolution in redshift, we see hints of the rate evolution either flattening or decreasing at $z\sim0.2-0.5$, but the full distribution remains entirely consistent with a monotonically increasing power law. We conclude with a discussion of the astrophysical context of our new findings and how non-parametric methods in gravitational-wave population inference are uniquely poised to complement to the parametric approach as we enter the data-rich era of gravitational-wave astronomy.Comment: 20 pages, 12 figure, 3 table

Comparing the impact of management on public and private nurses in Bangladesh

Purpose The purpose of this paper is to use conservation of resources (COR) theory as a lens for comparing the impact of line management on Bangladeshi public and private nurses’ perception of work harassment, well-being and turnover intentions where Anglo-American and European management models have been super-imposed on an existing different culture. Design/methodology/approach Survey data were collected from 317 Bangladeshi nurses’ (131 from the public sector and 186 from the private sector). Structural equation modelling was used for analysis. Findings High work harassment was associated with low-being, and together with management practices, it explained approximately a quarter of private sector nurses’ well-being. In total, management, work harassment and employee well-being explained approximately a third of the turnover intentions of public sector nurses, whereas only work harassment explained approximately a third of private sector nurses’ turnover intentions. The findings suggest a differential impact of management on work harassment across the public and private sector. Research limitations/implications Cross-sectional data are susceptible to common method bias. A common latent factor was included, and several items that were explained by common method variance were controlled. Further, the findings are limited by the sample size from one sector and the use of only one developing country. Practical implications It is a waste of resources to transplant Anglo-American and European management models to developing countries without understanding the impact on nurses’ outcomes. Originality/value Anglo-American and European management models are not easily transferable to the Bangladesh context probably because of the impact of ties and corruption. Line management is a positive resource that builds employee well-being for public sector employees only

Distinguishing Spin-Aligned and Isotropic Black Hole Populations With Gravitational Waves

The first direct detections of gravitational waves from merging binary black holes open a unique window into the binary black hole formation environment. One promising environmental signature is the angular distribution of the black hole spins; systems formed through dynamical interactions among already-compact objects are expected to have isotropic spin orientations whereas binaries formed from pairs of stars born together are more likely to have spins preferentially aligned with the binary orbital angular momentum. We consider existing gravitational wave measurements of the binary effective spin, the best-measured combination of spin parameters, in the four likely binary black hole detections GW150914, LVT151012, GW151226, and GW170104. If binary black hole spin magnitudes extend to high values we show that the data exhibit a $2.4\sigma$ ($0.015$ odds ratio) preference for an isotropic angular distribution over an aligned one. By considering the effect of 10 additional detections, we show that such an augmented data set would enable in most cases a preference stronger than $5\sigma$ ($2.9 \times 10^{-7}$ odds ratio). The existing preference for either an isotropic spin distribution or low spin magnitudes for the observed systems will be confirmed (or overturned) confidently in the near future.Comment: 32 pages, 9 figures, code and document at https://github.com/farr/AlignedVersusIsoSpin/ ; updated to use custom LaTeX class to include figures in PD