What is the approximate luminosity distance of the gravitational wave event GW150914?

The approximate luminosity distance of gravitational-wave event GW150914 was 1.3 billion light-years.

LIGO detected GW150914 on September 14, 2015, when ripples in spacetime reached its two observatories in Louisiana and Washington. The signal came from the merger of two black holes roughly 1.3 billion light-years away. Technically, the original analysis estimated a luminosity distance of about 410 megaparsecs, with substantial uncertainty.

The event was not seen as ordinary light from a host galaxy. Instead, LIGO inferred its distance from the measured strength and shape of the gravitational-wave signal, combined with general-relativistic models of the merging black holes. The uncertainty was large because gravitational-wave amplitude depends partly on the system's orientation relative to Earth.

GW150914's signal lasted about 0.2 seconds and rose from roughly 35 to 250 hertz. The merging black holes had masses of about 36 and 29 Suns; the final black hole was about 62 solar masses, with the equivalent of roughly three Suns radiated as gravitational-wave energy.