The first gravitational-wave source from the isolated evolution of two 40-100 Msun stars

TL;DR

High-precision numerical simulations of the formation of binary black holes via the evolution of isolated binary stars are reported, 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.

Abstract

The merger of two massive 30 Msun black holes has been detected in gravitational waves (1,GW150914). This discovery validates recent predictions (2-4) that massive binary black holes would constitute the first detection. However, previous calculations have not sampled the relevant binary black hole progenitors---massive, low-metallicity binary stars---with sufficient accuracy and input physics to enable robust predictions to better than several orders of magnitude (5-10). Here we report a suite of high-precision numerical simulations of binary black hole formation via the evolution of isolated binary stars, providing a framework to interpret GW150914 and predict the properties of subsequent binary black hole gravitational-wave events. Our models imply that these events form in an environment where the metallicity is less than 10 percent of solar; have initial masses of 40-100 Msun; and interact through mass transfer and a common envelope phase. Their progenitors likely form either at 2 Gyr, or somewhat less likely, at 11 Gyr 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 proposed in this study, with low natal kicks and restricted common envelope evolution, produces 40 times more binary black holes than dynamical formation channels involving globular clusters (11) and is comparable to the rate from homogeneous evolution channels (12-15). Our calculations predict detections of about 1,000 black hole mergers per year with total mass of 20-80 Msun once second generation ground-based gravitational wave observatories reach full sensitivity.

Figures (10)

• Figure 1: Example binary evolution leading to a BH-BH merger similar to GW150914. A massive binary star ($96 + 60{\rm ~M}_{\odot}$) is formed in the distant past ($2$ billion years after Big Bang; $z\sim3.2$) and after five million years of evolution forms a BH-BH system ($37 + 31{\rm ~M}_{\odot}$). For the ensuing $10.3$ billion years this BH-BH system is subject to angular momentum loss, with the orbital separation steadily decreasing, until the black holes coalesce at redshift $z=0.09$. This example binary formed in a low metallicity environment ($Z=3\%{\rm ~Z}_{\odot}$).
• Figure 1: Maximum total mass of BH-BH mergers as a function of metallicity. Binary stars at metallicities lower than $10\%$ solar can form BH-BH mergers more massive than $M_{\rm tot}=64.8{\rm ~M}_{\odot}$. This suggests that GW150914 was formed in a low metallicity environment, assuming it is a product of classical isolated binary evolution. Note that 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. \ref{['fig:ExamplEvol']}).
• Figure 2: Birth times of GW150914-like progenitors across cosmic time. Half of the binaries that form BH-BH mergers detectable in O1 with total redshifted mass in the range $M_{\rm tot,z}=54$--$73{\rm ~M}_{\odot}$ were born within $4.7$ Gyr of the Big Bang (corresponding to $z>1.2$). The birth and merger times of binary from Figure \ref{['fig:ExamplEvol']} is marked; it follows the most typical evolutionary channel for massive BH-BH mergers (BHBH1 in Extended Data Tab. \ref{['tab:EvolChan']}). Note that the merger redshift of GW150914 is $z=0.088$. The bimodal shape of the distribution originates from a combination of the BH-BH delay time distribution with the low-metallicity star formation history (Extended Data Fig. \ref{['fig:Emergence']} for details).
• Figure 2: Emergence of bimodal birth time distribution.a, Black hole binaries follow an intrinsic power-law delay time distribution ($\propto t^{-1}$). The birth time ($t_{\rm birth}=t_{\rm merger}-t_{\rm delay}$) is inverted compared to the delay time distribution, with the spread caused by allowing the merger time ($t_{\rm merger}$) to fall anywhere within the LIGO O1 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 only by low-metallicity stars ($Z<10\%{\rm ~Z}_{\odot}$). The fraction of all stars that form at such low-Z ($F_{\rm Z}$) decreases with cosmic time making low-Z star formation [${\rm ~M}_{\odot}$ Mpc$^{-3}$ yr$^{-1}$] peak at early cosmic time. c, Final birth time distribution for massive BH-BH mergers is a convolution of the intrinsic birth times with the low metallicity star formation rate.
• Figure 3: Comparison of merger rates and masses with LIGO O1 results: for standard (M1), optimistic CE (M2), and pessimistic high BH kicks (M3) models. a, Total redshifted binary merger mass distribution. GW150914 ($70.5{\rm ~M}_{\odot}$: blue square with $90\%$ confidence interval in mass). The blue line shows the fiducial estimate of the sensitivity of the 16 day O1 run. A comparison of the shapes of the blue and red curves suggests that the most likely detections for M1 are BH-BH mergers with mass in the range $25$--$73{\rm ~M}_{\odot}$. NS-NS mergers (first bin) and BH-NS mergers (next five bins) are well below the estimated sensitivity, and thus detections in O1 are not expected. The rate densities are in the detector rest frame. b, Comparison of the LIGO BH-BH rate estimate with our models. The LIGO value of $2$--$400{\rm ~Gpc}^{-3} {\rm ~yr}^{-1}$ ($90\%$ credible range) compares well with our standard and high BH natal kick models. The rate densities are in the source rest frame. Updated version of this figure with the most recent LIGO observations may be found at:www.syntheticuniverse.org/stvsgwo.html