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


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

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.


  1. 1

    Abbott, B. P. et al. Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116, 061102 (2016)

    ADS  MathSciNet  CAS  PubMed  Article  Google Scholar 

  2. 2

    Belczynski, K. et al. The effect of metallicity on the detection prospects for gravitational waves. Astrophys. J. 715, L138–L141 (2010)

    ADS  Article  Google Scholar 

  3. 3

    Dominik, M. et al. Double compact objects. III. Gravitational-wave detection rates. Astrophys. J. 806, 263 (2015)

    ADS  Article  Google Scholar 

  4. 4

    Belczynski, K. et al. Compact binary merger rates: comparison with LIGO/Virgo upper limits. Astrophys. J. 819, 108 (2016)

    ADS  Article  Google Scholar 

  5. 5

    Tutukov, A. V. & Yungelson, L. R. The merger rate of neutron star and black hole binaries. Mon. Not. R. Astron. Soc. 260, 675–678 (1993)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Lipunov, V. M., Postnov, K. A. & Prokhorov, M. E. Black holes and gravitational waves: possibilities for simultaneous detection using first-generation laser interferometers. Astron. Lett. 23, 492–497 (1997)

    ADS  Google Scholar 

  7. 7

    Nelemans, G., Yungelson, L. R. & Portegies Zwart, S. F. The gravitational wave signal from the Galactic disk population of binaries containing two compact objects. Astron. Astrophys. 375, 890–898 (2001)

    ADS  Article  Google Scholar 

  8. 8

    Voss, R. & Tauris, T. M. Galactic distribution of merging neutron stars and black holes – prospects for short gamma-ray burst progenitors and LIGO/VIRGO. Mon. Not. R. Astron. Soc. 342, 1169–1184 (2003)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Belczynski, K., Taam, R. E., Kalogera, V., Rasio, F. A. & Bulik, T. On the rarity of double black hole binaries: consequences for gravitational wave detection. Astrophys. J. 662, 504–511 (2007)

    ADS  CAS  Article  Google Scholar 

  10. 10

    Mennekens, N. & Vanbeveren, D. Massive double compact object mergers: gravitational wave sources and r-process element production sites. Astron. Astrophys. 564, A134 (2014)

    ADS  Article  Google Scholar 

  11. 11

    Rodriguez, C. L., Chatterjee, S. & Rasio, F. A. Binary black hole mergers from globular clusters: masses, merger rates, and the impact of stellar evolution. Phys. Rev. D 93, 084029 (2016)

    ADS  Article  CAS  Google Scholar 

  12. 12

    Marchant, P., Langer, N., Podsiadlowski, P., Tauris, T. M. & Moriya, T. J. A new route towards merging massive black holes. Astron. Astrophys. 588, A50 (2016)

    ADS  Article  CAS  Google Scholar 

  13. 13

    de Mink, S. E. & Mandel, I. The chemically homogeneous evolutionary channel for binary black hole mergers: rates and properties of gravitational-wave events detectable by advanced LIGO. Mon. Not. R. Astron. Soc. (2016)

  14. 14

    Eldridge, J. J. & Stanway, E. R. BPASS predictions for Binary Black-Hole Mergers. Preprint at (2016)

  15. 15

    Woosley, S. E. The progenitor of GW150914. Preprint at (2016)

  16. 16

    Belczynski, K., Kalogera, V. & Bulik, T. A comprehensive study of binary compact objects as gravitational wave sources: evolutionary channels, rates, and physical properties. Astrophys. J. 572, 407–431 (2002)

    ADS  Article  Google Scholar 

  17. 17

    Belczynski, K. et al. Compact object modeling with the StarTrack population synthesis code. Astrophys. J. Suppl. Ser. 174, 223–260 (2008)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Fryer, C. L. et al. Compact remnant mass function: dependence on the explosion mechanism and metallicity. Astrophys. J. 749, 91 (2012)

    ADS  Article  Google Scholar 

  19. 19

    Bulik, T., Belczynski, K. & Prestwich, A. IC10 X-1/NGC300 X-1: the very immediate progenitors of BH-BH binaries. Astrophys. J. 730, 140 (2011)

    ADS  Article  Google Scholar 

  20. 20

    Hirschauer, A. S. et al. ALFALFA discovery of the most metal-poor gas-rich galaxy known: AGC 198691. Astrophys. J. 822, 108 (2016)

    ADS  Article  Google Scholar 

  21. 21

    Bulik, T., Gondek-Rosinska, D. & Belczynski, K. Expected masses of merging compact object binaries observed in gravitational waves. Mon. Not. R. Astron. Soc. 352, 1372–1380 (2004)

    ADS  Article  Google Scholar 

  22. 22

    Abbott, B. P. et al. The rate of binary black hole mergers inferred from advanced LIGO observations surrounding GW150914. Preprint at (2016)

  23. 23

    Pavlovskii, K. & Ivanova, N. Mass transfer from giant donors. Mon. Not. R. Astron. Soc. 449, 4415–4427 (2015)

    ADS  Article  Google Scholar 

  24. 24

    Eldridge, J. J., Fraser, M., Smartt, S. J., Maund, J. R. & Crockett, R. M. The death of massive stars – II. Observational constraints on the progenitors of Type Ibc supernovae. Mon. Not. R. Astron. Soc. 436, 774–795 (2013)

    ADS  Article  Google Scholar 

  25. 25

    Gerke, J. R., Kochanek, C. S. & Stanek, K. Z. The search for failed supernovae with the Large Binocular Telescope: first candidates. Mon. Not. R. Astron. Soc. 450, 3289–3305 (2015)

    ADS  Article  Google Scholar 

  26. 26

    Ricker, P. M. & Taam, R. E. The interaction of stellar objects within a common envelope. Astrophys. J. 672, L41–L44 (2008)

    ADS  Article  Google Scholar 

  27. 27

    MacLeod, M. & Ramirez-Ruiz, E. Asymmetric accretion flows within a common envelope. Astrophys. J. 803, 41 (2015)

    ADS  Article  Google Scholar 

  28. 28

    Rogers, T. M., Lin, D. N. C., McElwaine, J. N. & Lau, H. H. B. Internal gravity waves in massive stars: angular momentum transport. Astrophys. J. 772, 21 (2013)

    ADS  Article  CAS  Google Scholar 

  29. 29

    Albrecht, S. et al. The BANANA project. V. Misaligned and precessing stellar rotation axes in CV Velorum. Astrophys. J. 785, 83 (2014)

    ADS  Article  Google Scholar 

  30. 30

    Dominik, M. et al. Double compact objects. I. The significance of the common envelope on merger rates. Astrophys. J. 759, 52 (2012)

    ADS  Article  Google Scholar 

  31. 31

    Xu, X.-J. & Li, X.-D. Erratum: “On the binding energy parameter λ of common envelope evolution” (2010, ApJ, 716, 114). Astrophys. J. 722, 1985–1988 (2010)

    ADS  Article  Google Scholar 

  32. 32

    Belczynski, K., Wiktorowicz, G., Fryer, C. L., Holz, D. E. & Kalogera, V. Missing black holes unveil the supernova explosion mechanism. Astrophys. J. 757, 91 (2012)

    ADS  Article  Google Scholar 

  33. 33

    Hurley, J. R., Pols, O. R. & Tout, C. A. Comprehensive analytic formulae for stellar evolution as a function of mass and metallicity. Mon. Not. R. Astron. Soc. 315, 543–569 (2000)

    ADS  CAS  Article  Google Scholar 

  34. 34

    Vink, J. S. The theory of stellar winds. Astrophys. Space Sci. 336, 163–167 (2011)

    ADS  CAS  Article  Google Scholar 

  35. 35

    Podsiadlowski, P., Joss, P. C. & Hsu, J. J. L. Presupernova evolution in massive interacting binaries. Astrophys. J. 391, 246–264 (1992)

    ADS  Article  Google Scholar 

  36. 36

    Ivanova, N. et al. Common envelope evolution: where we stand and how we can move forward. Astron. Astrophys. Rev. 21, 59 (2013)

    ADS  Article  Google Scholar 

  37. 37

    Hobbs, G., Lorimer, D. R., Lyne, A. G. & Kramer, M. A statistical study of 233 pulsar proper motions. Mon. Not. R. Astron. Soc. 360, 974–992 (2005)

    ADS  Article  Google Scholar 

  38. 38

    Szécsi, D. et al. Low-metallicity massive single stars with rotation. Evolutionary models applicable to I Zwicky 18. Astron. Astrophys. 581, A15 (2015)

    Article  CAS  Google Scholar 

  39. 39

    Sana, H. et al. Binary interaction dominates the evolution of massive stars. Science 337, 444–446 (2012)

    ADS  CAS  PubMed  Article  Google Scholar 

  40. 40

    Bastian, N., Covey, K. R. & Meyer, M. R. A universal stellar initial mass function? A critical look at variations. Annu. Rev. Astron. Astrophys. 48, 339–389 (2010)

    ADS  Article  Google Scholar 

  41. 41

    Dominik, M. et al. Double compact objects. II. Cosmological merger rates. Astrophys. J. 779, 72 (2013)

    ADS  Article  CAS  Google Scholar 

  42. 42

    de Mink, S. E. & Belczynski, K. Merger rates of double neutron stars and stellar origin black holes: the impact of initial conditions on binary evolution predictions. Astrophys. J. 814, 58 (2015)

    ADS  Article  Google Scholar 

  43. 43

    Duchêne, G. & Kraus, A. Stellar multiplicity. Annu. Rev. Astron. Astrophys. 51, 269–310 (2013)

    ADS  Article  CAS  Google Scholar 

  44. 44

    Madau, P. & Dickinson, M. Cosmic star-formation history. Annu. Rev. Astron. Astrophys. 52, 415–486 (2014)

    ADS  Article  Google Scholar 

  45. 45

    Strolger, L.-G. et al. The Hubble Higher z Supernova Search: supernovae to z ≈ 1.6 and constraints on Type Ia progenitor models. Astrophys. J. 613, 200–223 (2004)

    ADS  CAS  Article  Google Scholar 

  46. 46

    Vangioni, E. et al. The impact of star formation and gamma-ray burst rates at high redshift on cosmic chemical evolution and reionization. Mon. Not. R. Astron. Soc. 447, 2575–2587 (2015)

    ADS  CAS  Article  Google Scholar 

  47. 47

    Dvorkin, I., Silk, J., Vangioni, E., Petitjean, P. & Olive, K. A. The origin of dispersion in DLA metallicities. Mon. Not. R. Astron. Soc. 452, L36–L40 (2015)

    ADS  CAS  Article  Google Scholar 

  48. 48

    Almeida, L. A. et al. Discovery of the massive overcontact binary VFTS 352: evidence for enhanced internal mixing. Astrophys. J. 812, 102 (2015)

    ADS  Article  CAS  Google Scholar 

  49. 49

    O’Shaughnessy, R., Kalogera, V. & Belczynski, K. Mapping population synthesis event rates on model parameters. II. Convergence and accuracy of multidimensional fits. Astrophys. J. 667, 1048–1058 (2007)

    ADS  Article  Google Scholar 

  50. 50

    Abbott, B. P. et al. Astrophysical implications of the binary black hole merger GW150914. Astrophys. J. 818, L22 (2016)

    ADS  Article  CAS  Google Scholar 

  51. 51

    Spera, M., Mapelli, M. & Bressan, A. The mass spectrum of compact remnants from the PARSEC stellar evolution tracks. Mon. Not. R. Astron. Soc. 451, 4086–4103 (2015)

    ADS  CAS  Article  Google Scholar 

  52. 52

    Khan, S. et al. Frequency-domain gravitational waves from nonprecessing black-hole binaries. II. A phenomenological model for the advanced detector era. Phys. Rev. D 93, 044007 (2016)

    ADS  Article  CAS  Google Scholar 

  53. 53

    Husa, S. et al. Frequency-domain gravitational waves from nonprecessing black-hole binaries. I. New numerical waveforms and anatomy of the signal. Phys. Rev. D 93, 044006 (2016)

    ADS  Article  CAS  Google Scholar 

  54. 54

    Abbott, B. P. et al. Prospects for observing and localizing gravitational-wave transients with Advanced LIGO and Advanced Virgo. Living Rev. Relativ. 19, 1 (2013)

    ADS  Article  Google Scholar 

  55. 55

    Villante, F. L., Serenelli, A. M., Delahaye, F. & Pinsonneault, M. H. The chemical composition of the sun from helioseismic and solar neutrino data. Astrophys. J. 787, 13 (2014)

    ADS  Article  CAS  Google Scholar 

Download references


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.

Author information




All authors contributed to the analysis and writing of the paper.

Corresponding author

Correspondence to Krzysztof Belczynski.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

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)

Related audio

Reporter Kerri Smith finds out what we know about the black holes that LIGO has spotted.

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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).

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.