Spin it as you like: the (lack of a) measurement of the spin tilt distribution with LIGO-Virgo-KAGRA binary black holes

While much has been learned about black holes by analyzing the latest LVK catalog, GWTC-3, a measurement of the astrophysical distribution of the black hole spin orientations remains elusive. This is usually probed by measuring the cosine of the tilt angle ($\cos\tau$) between each black hole spin and the orbital angular momentum, $\cos\tau=+1$ being perfect alignment. Abbott et al. has modeled the $\cos\tau$ distribution as a mixture of an isotropic component and a Gaussian component with mean fixed at +1 and width measured from the data. We want to verify if the data require the existence of such a peak at $\cos\tau=+1$. We use various alternative models for the astrophysical tilt distribution and measure their parameters using the LVK GWTC-3 catalog. We find that a) Augmenting the LVK model such that the mean $\mu$ of the Gaussian is not fixed at +1 returns results that strongly depend on priors. If we allow $\mu>+1$ then the resulting astrophysical $\cos\tau$ distribution peaks at +1 and looks linear, rather than Gaussian. If we constrain $-1\leq \mu\leq+1$ the Gaussian component peaks at $\mu=0.48^{+0.46}_{-0.99}$ (median and 90% symmetric credible interval). Two other 2-component mixture models yield $\cos\tau$ distributions that either have a broad peak centered at $0.19^{+0.22}_{-0.18}$ or a plateau that spans the range [-0.5, +1], without a clear peak at +1. b) All of the models we considered agree on the fact that there is no excess of black hole tilts at around -1. c) While yielding quite different posteriors, the models considered in this work have Bayesian evidences that are the same within error bars. We conclude that the current dataset is not sufficiently informative to draw any model-independent conclusions on the astrophysical distribution of spin tilts, except that there is no excess of spins with negatively aligned tilts.Comment: 6 pages body + 10 pages appendices. Following Ref suggestion, now includes differential rate plots per unit costilt. Data release on Zenodo linked from Data availability section. Note: the abstract in the metadata is shorter than the paper's due to Arxiv restriction to 1920 character

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

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

Black Hole Formation with an Interacting Vacuum Energy Density

We discuss the gravitational collapse of a spherically symmetric massive core of a star in which the fluid component is interacting with a growing vacuum energy density. The influence of the variable vacuum in the collapsing core is quantified by a phenomenological \beta-parameter as predicted by dimensional arguments and the renormalization group approach. For all reasonable values of this free parameter, we find that the vacuum energy density increases the collapsing time but it cannot prevent the formation of a singular point. However, the nature of the singularity depends on the values of \beta. In the radiation case, a trapped surface is formed for \beta<1/2 whereas for \beta>1/2, a naked singularity is developed. In general, the critical value is \beta=1-2/3(1+\omega), where the \omega-parameter describes the equation of state of the fluid component.Comment: 9 pages, 8 figure