Determining the population properties of spinning black holes

There are at least two formation scenarios consistent with the first gravitational-wave observations of binary black hole mergers. In field models, black hole binaries are formed from stellar binaries that may undergo common envelope evolution. In dynamic models, black hole binaries are formed through capture events in globular clusters. Both classes of models are subject to significant theoretical uncertainties. Nonetheless, the conventional wisdom holds that the distribution of spin orientations of dynamically merging black holes is nearly isotropic while field-model black holes prefer to spin in alignment with the orbital angular momentum. We present a framework in which observations of black hole mergers can be used to measure ensemble properties of black hole spin such as the typical black hole spin misalignment. We show how to obtain constraints on population hyperparameters using minimal assumptions so that the results are not strongly dependent on the uncertain physics of formation models. These data-driven constraints will facilitate tests of theoretical models and help determine the formation history of binary black holes using information encoded in their observed spins. We demonstrate that the ensemble properties of binary detections can be used to search for and characterize the properties of two distinct populations of black hole mergers.Comment: 10 pages, 5 figures, 1 table. Minor revisions, published in PR

Growing Pains: Understanding the Impact of Likelihood Uncertainty on Hierarchical Bayesian Inference for Gravitational-Wave Astronomy

Observations of gravitational waves emitted by merging compact binaries have provided tantalising hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems, (mass, spin, distance) used to extract these inferences about the Universe are subject to large uncertainties. The current method of performing these analyses requires performing many Monte Carlo integrals to marginalise over the uncertainty in the properties of the individual binaries and the survey selection bias. These Monte Carlo integrals are subject to fundamental statistical uncertainties. Previous treatments of this statistical uncertainty has focused on ensuring the precision of the inferred inference is unaffected, however, these works have neglected the question of whether sufficient accuracy can also be achieved. In this work, we provide a practical exploration of the impact of uncertainty in our analyses and provide a suggested framework for verifying that astrophysical inferences made with the gravitational-wave transient catalogue are accurate. Applying our framework to models used by the LIGO-Virgo-Kagra collaboration, we find that Monte Carlo uncertainty in estimating the survey selection bias is the limiting factor in our ability to probe narrow populations model and this will rapidly grow more problematic as the size of the observed population increases.Comment: 8 pages, 6 figure

Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.Comment: 12 pages, 7 figure

Parallelized Inference for Gravitational-Wave Astronomy

Bayesian inference is the workhorse of gravitational-wave astronomy, for example, determining the mass and spins of merging black holes, revealing the neutron star equation of state, and unveiling the population properties of compact binaries. The science enabled by these inferences comes with a computational cost that can limit the questions we are able to answer. This cost is expected to grow. As detectors improve, the detection rate will go up, allowing less time to analyze each event. Improvement in low-frequency sensitivity will yield longer signals, increasing the number of computations per event. The growing number of entries in the transient catalog will drive up the cost of population studies. While Bayesian inference calculations are not entirely parallelizable, key components are embarrassingly parallel: calculating the gravitational waveform and evaluating the likelihood function. Graphical processor units (GPUs) are adept at such parallel calculations. We report on progress porting gravitational-wave inference calculations to GPUs. Using a single code - which takes advantage of GPU architecture if it is available - we compare computation times using modern GPUs (NVIDIA P100) and CPUs (Intel Gold 6140). We demonstrate speed-ups of $\sim 50 \times$ for compact binary coalescence gravitational waveform generation and likelihood evaluation and more than $100\times$ for population inference within the lifetime of current detectors. Further improvement is likely with continued development. Our python-based code is publicly available and can be used without familiarity with the parallel computing platform, CUDA.Comment: 5 pages, 4 figures, submitted to PRD, code can be found at https://github.com/ColmTalbot/gwpopulation https://github.com/ColmTalbot/GPUCBC https://github.com/ADACS-Australia/ADACS-SS18A-RSmith Add demonstration of improvement in BNS spi

Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used, and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We find that the difference in our inference when using different PSD estimation techniques is larger than the predicted statistical uncertainty

Searching for structure in the binary black hole spin distribution

The spins of black holes in merging binaries can reveal information related to the formation and evolution of these systems through their gravitational wave emission. Combining events to infer the astrophysical distribution of black hole spins allows us to determine the relative contribution from different formation scenarios to the population. Many previous works have modeled spin population distributions using parametric models. While these are valuable approaches when the observed population is small, they make strong assumptions about the shape of the underlying distribution and are highly susceptible to biases due to mismodeling. The results obtained with such parametric models are only valid if the allowed shape of the distribution is well-motivated (i.e. for astrophysical reasons). In this work, we relax these prior assumptions and model the spin distributions using a more data-driven approach, modeling these distributions with flexible cubic spline interpolants in order to allow for capturing structures that the parametric models cannot. We find that adding this flexibility to the model substantially increases the uncertainty in the inferred distributions, but find a general trend for lower support at high spin magnitude and a spin tilt distribution consistent with isotropic orientations. We infer that 62 - 87% of black holes have spin magnitudes less than a = 0.5, and 27- 50% of black holes exhibit negative $\chi_{\rm eff}$. Using the inferred $\chi_{\rm eff}$ distribution, we place a conservative upper limit of 37% for the contribution of hierarchical mergers to the astrophysical BBH population. Additionally, we find that artifacts from unconverged Monte Carlo integrals in the likelihood can manifest as spurious peaks and structures in inferred distributions, mandating the use of a sufficient number of samples when using Monte Carlo integration for population inference.Comment: 15 pages, 14 figure