Distinguishing spin-aligned and isotropic black hole populations with gravitational waves

Abstract

The direct detection of gravitational waves1,2,3,4 from merging binary black holes opens up a window into the environments in which binary black holes form. One signature of such environments is the angular distribution of the black hole spins. Binary systems that formed through dynamical interactions between already-compact objects are expected to have isotropic spin orientations5,6,7,8,9 (that is, the spins of the black holes are randomly oriented with respect to the orbit of the binary system), whereas those that formed from pairs of stars born together are more likely to have spins that are preferentially aligned with the orbit10,11,12,13,14. The best-measured combination of spin parameters3,4 for each of the four likely binary black hole detections GW150914, LVT151012, GW151226 and GW170104 is the ‘effective’ spin. Here we report that, if the magnitudes of the black hole spins are allowed to extend to high values, the effective spins for these systems indicate a 0.015 odds ratio against an aligned angular distribution compared to an isotropic one. When considering the effect of ten additional detections15, this odds ratio decreases to 2.9 × 10−7 against alignment. 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.

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Figure 1: Approximate posteriors on the effective spin χeff for the four likely gravitational wave detections.
Figure 2: Models for the population distribution of χeff, p(χeff).
Figure 3: Odds ratios for our models, p(d | model)/p(d | LI).
Figure 4: Distribution of odds ratios predicted with 10 additional observations.

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Acknowledgements

We thank R. O’Shaughnessy, C. Berry, D. Gerosa and S. Vitale for discussions and comments on this work. W.M.F., S.S., I.M. and A.V. were supported in part by the STFC. M.C.M. acknowledges support of the University of Birmingham Institute for Advanced Study Distinguished Visiting Fellows programme. S.S. and I.M. acknowledge support from the National Science Foundation under grant number NSF PHY11-25915.

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Correspondence to Will M. Farr.

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Reviewer Information Nature thanks I. Bartos and S. Sigurdsson for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Figure 1 Distributions of spin magnitudes.

See equation (1) for the definition of the ‘low’ (blue line), ‘flat’ (green line) and ‘high’ (red line) magnitude distributions. The distributions have mean spins of 0.33, 0.5 and 0.67, and standard deviations of 0.24, 0.29 and 0.24, respectively. Source data

Extended Data Figure 2 Fraction of the binary black hole population that comes from an isotropic distribution under a mixture model.

The blue dotted line shows the flat prior on the fraction fi of binary black holes that come from an isotropic distribution, under the mixture model. The three red lines show the posterior on fi after LIGO O1 and GW170104 with our various assumptions regarding black hole spin magnitudes. The solid line shows the posterior assuming that all black holes have their spin magnitude drawn from the flat distribution. The dashed line assumes the high black hole spin magnitude distribution p(a) = 2a. The dash-dotted line assumes the low distribution p(a) = 2(1 − a). For a wide range of assumptions regarding black hole spin magnitudes, the fraction coming from an isotropic distribution fi peaks at 1. Source data

Extended Data Figure 3 Effect of small spins on the ratio of isotropic and aligned models.

The blue line shows the ratio (plotted as the equivalent σ) between a model in which all systems are from an isotropic distribution and one in which all systems are aligned (σI/A), as a function of the power-law exponent α in equation (3). The top axis shows the mean spin magnitude to which the given value of α corresponds. For mean spin magnitudes of less than about 0.2, we find no evidence for either distribution over the other. Source data

Extended Data Figure 4 Distributions of χeff assuming all merging black holes have equal masses (q = 1) or a 2:1 mass ratio (q = 0.5).

The details of the distribution are sensitive to the mass ratio, but in our analysis the primarily sensitivity is to the changing sign of χeff under the isotropic models. This latter property is unchanged under changing mass ratio. Source data

Extended Data Figure 5 Widths of the 90% credible intervals for χeff for 500 binaries in a simulated detected population.

χeff is better constrained for systems with high χeff and high mass ratio. χsim and qsim are the simulated effective spin and mass ratio, respectively. Source data

Extended Data Table 1 Significance σI/A of the odds ratio between the isotropic and aligned models

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Farr, W., Stevenson, S., Miller, M. et al. Distinguishing spin-aligned and isotropic black hole populations with gravitational waves. Nature 548, 426–429 (2017). https://doi.org/10.1038/nature23453

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