The first gravitational-wave source from the isolated evolution of two stars in the 40–100 solar mass range

Abstract

The merger of two massive (about 30 solar masses) black holes has been detected in gravitational waves1. This discovery validates recent predictions2,3,4 that massive binary black holes would constitute the first detection. Previous calculations, however, have not sampled the relevant binary-black-hole progenitors—massive, low-metallicity binary stars—with sufficient accuracy nor included sufficiently realistic physics to enable robust predictions to better than several orders of magnitude5,6,7,8,9,10. Here we report high-precision numerical simulations of the formation of binary black holes via the evolution of isolated binary stars, providing a framework within which to interpret the first gravitational-wave source, GW150914, and to predict the properties of subsequent binary-black-hole gravitational-wave events. Our models imply that these events form in an environment in which the metallicity is less than ten per cent of solar metallicity, and involve stars with initial masses of 40–100 solar masses that interact through mass transfer and a common-envelope phase. These progenitor stars probably formed either about 2 billion years or, with a smaller probability, 11 billion years after the Big Bang. Most binary black holes form without supernova explosions, and their spins are nearly unchanged since birth, but do not have to be parallel. The classical field formation of binary black holes we propose, with low natal kicks (the velocity of the black hole at birth) and restricted common-envelope evolution, produces approximately 40 times more binary-black-holes mergers than do dynamical formation channels involving globular clusters11; our predicted detection rate of these mergers is comparable to that from homogeneous evolution channels12,13,14,15. Our calculations predict detections of about 1,000 black-hole mergers per year with total masses of 20–80 solar masses once second-generation ground-based gravitational-wave observatories reach full sensitivity.

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Figure 1: Example binary evolution leading to a BH–BH merger similar to GW150914.
Figure 2: Birth times of GW150914-like progenitors across cosmic time.
Figure 3: Comparison of merger rates and masses with O1 LIGO results.

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Acknowledgements

We are indebted to G. Wiktorowicz, W. Gladysz and K. Piszczek for their help with population synthesis calculations, and to H.-Y. Chen and Z. Doctor for their help with our LIGO/Virgo rate calculations. We thank the thousands of Universe@home users that have provided their personal computers for our simulations. We also thank the Hannover GW group for letting us use their ATLAS supercomputer. K.B. acknowledges support from the NCN grant Sonata Bis 2 (DEC-2012/07/E/ST9/01360). D.E.H. was supported by NSF CAREER grant PHY-1151836. D.E.H. also acknowledges support from the Kavli Institute for Cosmological Physics at the University of Chicago through NSF grant PHY-1125897 as well as an endowment from the Kavli Foundation. T.B. acknowledges support from the NCN grant Harmonia 6 (UMO-2014/14/M/ST9/00707). R.O’S. was supported by NSF grant PHY-1505629.

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Correspondence to Krzysztof Belczynski.

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Reviewer Information Nature thanks M. Cantiello and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Figure 1 Maximum total mass of BH–BH mergers as a function of metallicity.

Binary stars at metallicities Z < 0.1Z can form BH–BH mergers that are more massive than Mtot = 64.8M. This suggests that GW150914 was formed in a low-metallicity environment, assuming it is a product of classical isolated binary evolution. The total binary-maximum BH–BH mass is not a simple sum of maximum BH masses resulting from single stellar evolution; this is a result of mass loss during the RLOF and CE evolution phases in the formation of massive BH–BH mergers (Fig. 1).

Extended Data Figure 2 Emergence of a bimodal birth-time distribution.

a, BH binaries follow an intrinsic power-law delay-time distribution (proportional to t−1). The birth time (tbirth = tmerger − tdelay) is inverted compared to the delay-time distribution (blue line), with the spread caused by allowing the merger time (tmerger) to fall anywhere within the O1 LIGO horizon: z = 0–0.7; this generates a peak corresponding to BH–BH progenitors born late with short delay times. b, Massive BH–BH binaries are formed by only low-metallicity stars (Z < 0.10Z). The fraction of all stars that form at such low Z (FZ) decreases with cosmic time, making low-Z star formation (in units of M Mpc−3 yr1) peak at early cosmic time. sfr, star-formation rate. c, The final birth-time distribution for massive BH–BH mergers is a convolution of the intrinsic birth times and the low-metallicity star-formation rate.

Extended Data Figure 3 Predicted distribution of BH–BH merger mass ratios.

dRdet/dq is the contribution to the detection rate, Rdet, from binaries within a given 0.02 bin in mass ratio, q. Standard model (M1) detector-frame mass ratio is shown. BH–BH binaries prefer mass ratios of q 0.7, with a prominent peak near comparable-mass systems. GW150914, with (90% credible range) and a total redshifted mass of Mtot,z = 70.5M, falls within the expected region.

Extended Data Figure 4 Source-frame merger-rate density for BH–BH binaries as a function of redshift.

The red line shows the results from our standard model (M1); in this model, massive BHs do not get natal kicks. A sequence of models with increasing BH natal kicks (models M6, M5, M4, M3) is shown. The rate density decreases with increasing natal kick strength described by a Maxwellian distribution with a one-dimensional root mean square deviation of σ. The local merger-rate density (z < 0.1) changes from 218 Gpc−3 yr−1 (M1) to 63 Gpc−3 yr−1 (M6), 25 Gpc−3 yr−1 (M5), 11 Gpc−3 yr−1 (M4) and 6.6 Gpc−3 yr−1 (M3). The LIGO estimate (2–400 Gpc−3 yr−1) encompasses all of these models. We mark the O1 LIGO detection horizon (z = 0.7; see Extended Data Fig. 7).

Extended Data Figure 5 BH mass as a function of initial star mass, for a range of metallicities.

These results show calculations for single star evolution with no binary interactions. Our updated models of BH formation show a general increase of BH mass with initial progenitor star mass. There is strong dependence of BH mass on the chemical composition of the progenitor. For example, the maximum BH mass increases from 10M–15M for high-metallicity progenitors (Z = 1.5Z–1Z) to 94M for low-metallicity progenitors (Z = 0.005Z). The formation of a single 30M BH requires a metallicity of Z ≤ 0.25Z. ZAMS, zero-ago main sequence.

Extended Data Figure 6 Mean-metallicity evolution of the Universe with redshift.

It is assumed that at each redshift the metallicity distribution is log-normal with a standard deviation of σ = 0.5 dex. The blue line denotes the mean-metallicity evolution adopted in previous studies. The new relation generates more low-metallicity stars at all redshifts. We mark the line above which we can make predictions (log(Z/Z) = −2.3, Z = 0.02; ref. 55) based on actual evolutionary stellar models adopted in our calculations. Below this line we assume that stars produce BH–BH mergers in the same way as in the case of our lowest available model.

Extended Data Figure 7 Horizon redshift for the first advanced LIGO observational run (O1).

Horizon is given as a function of the total redshifted binary merger mass (assuming equal-mass mergers). For the highest-mass mergers found in our simulations (Mtot,z = 240M), the horizon redshift is zhor = 0.7. For GW150914 (Mtot,z = 70.5M), the horizon redshift is zhor = 0.36.

Extended Data Table 1 Formation channels of massive BH–BH mergers (M1)

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Belczynski, K., Holz, D., Bulik, T. et al. The first gravitational-wave source from the isolated evolution of two stars in the 40–100 solar mass range. Nature 534, 512–515 (2016). https://doi.org/10.1038/nature18322

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