  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.
