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Observation of Gravitational Waves from a Binary Black Hole Merger
The LIGO Scientific Collaboration, the Virgo Collaboration
TL;DR
Direct observations of gravitational waves from merging black holes were lacking. Using coincident LIGO observations and interferometric strain measurements, the paper reports a signal matching general relativity, providing the first direct detection of gravitational waves and binary black hole merger.
Problem
Direct observations of black hole mergers and gravitational-wave amplitude and phase were lacking despite theoretical predictions and indirect evidence.
Source: §I · p. 1Method
The study analyzes 16 days of coincident observations from two LIGO interferometers that measure gravitational-wave strain through differential arm-length changes.
Source: §III · p. 3, §V · p. 5Results
The signal matches general relativity and constitutes the first direct detection of gravitational waves and observation of a binary black hole merger.
Source: B. Binary coalescence search · p. 7, §VIII · p. 8Takeaways & Limitations
The observation demonstrates that binary stellar-mass black hole systems exist and can form in nature and merge within a Hubble time.
Source: §VI · p. 8, §VIII · p. 8
Abstract
from arXiv · showhide
On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of $1.0 \times 10^{-21}$. It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 σ. The source lies at a luminosity distance of $410^{+160}_{-180}$ Mpc corresponding to a redshift $z = 0.09^{+0.03}_{-0.04}$. In the source frame, the initial black hole masses are $36^{+5}_{-4} M_\odot$ and $29^{+4}_{-4} M_\odot$, and the final black hole mass is $62^{+4}_{-4} M_\odot$, with $3.0^{+0.5}_{-0.5} M_\odot c^2$ radiated in gravitational waves. All uncertainties define 90% credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.
I. INTRODUCTION
Gravitational waves emerged from general relativity as a prediction whose physical reality and detectability required decades of theoretical and experimental development. GW150914 marked the first direct detection and opened access to strong-field dynamics.
Historical foundations
- 1916: Einstein predicted gravitational waves as transverse strain waves traveling at light speed, generated by changing mass quadrupole moments.Their physical reality remained debated until the 1957 Chapel Hill conference.Source: §I · p. 1
- 1963: Kerr’s solution extended black-hole theory to rotating black holes, while later work established quasinormal modes and relativistic two-body dynamics.Numerical-relativity breakthroughs enabled accurate binary-merger modeling.Source: §I · p. 1
Why direct detection matters
- 1970s onward: Binary-pulsar observations demonstrated gravitational-wave energy loss and motivated direct measurements of amplitude and phase.Direct observations enable tests of general relativity in the dynamic strong-field regime.Source: §I · p. 1
Detection milestone
- GW150914 was the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging into one black hole.The observation also provided access to strong-field, high-velocity spacetime dynamics and nonlinear disturbed-black-hole behavior.Source: §I · pp. 1–2
II. OBSERVATION
LIGO detected GW150914 in both observatories, and its rapidly increasing frequency and amplitude identify a compact binary coalescence. The signal’s timing, significance, and waveform support a binary-black-hole interpretation.
Detection
- September 14, 2015 at 09:50:45 UTC: Hanford and Livingston detected the coincident signal GW150914.Matched-filter searches recovered it as the most significant event in each detector.Source: §II · p. 2
- 24: The combined signal-to-noise ratio for events arriving within the intersite propagation window.The coincidence occurred within the detectors’ 10-ms intersite propagation time.Source: §II · pp. 2–3
Localization
- 600 deg2: With only two detectors observing, the source localization covered approximately this 90% credible-region area.The position was determined primarily from the relative arrival time.Source: §II · p. 3
Waveform interpretation
- 0.2 s: The signal rose in frequency and amplitude through about eight cycles, from 35 to 150 Hz before reaching maximum amplitude.This chirp-like evolution is expected from two orbiting masses losing energy through gravitational radiation.Source: §II · p. 3
- ≈30 M⊙: The inferred chirp mass implied a detector-frame total mass of at least 70 M⊙.That mass and the high orbital frequency made neutron stars or a black-hole–neutron-star system implausible, leaving black holes as the known compact explanation.Source: §II · p. 3
III. DETECTORS
Advanced LIGO converts tiny differential arm-length changes into optical signals using kilometer-scale interferometers and multiple noise-reduction systems. Its improved strain sensitivity enabled observations of distant compact binaries.
Interferometer principle
- 4 km: Each Advanced LIGO arm uses two mirrors as test masses separated by this length.A passing wave produces a differential change ΔL(t) = h(t)L that alters the returning light’s phase.Source: §III · p. 3
Sensitivity enhancements
- 300: Resonant optical cavities in each arm multiply the gravitational-wave effect on the light phase by this factor.Power recycling and signal recycling further build up laser light and optimize signal extraction.Source: §III · pp. 3–4
Optical system
- 1064 nm: Advanced LIGO uses a stabilized Nd:YAG laser wavelength for interferometric readout.The gravitational-wave signal is extracted at the output port using homodyne readout.Source: §III · p. 4
Noise control
- 40 kg: The test masses are fused-silica substrates with low-loss dielectric coatings, suspended by fused-silica fibers.Seismic isolation, low thermal noise, ultrahigh vacuum, and vibration isolation reduce displacement noise.Source: §III · p. 4
Sensitivity
- 3 to 5 times: In the 100–300 Hz band, current LIGO detectors are more sensitive to strain than initial LIGO.Below 60 Hz, the improvement exceeds tenfold; for comparable binary black holes, sensitive volume rises as the cube of strain sensitivity.Source: §III · p. 5
IV. DETECTOR VALIDATION
Extensive validation found no instrumental or environmental explanation for GW150914, supporting its interpretation as a genuine gravitational-wave signal.
Detector state
- Both detectors operated steadily for several hours around GW150914, with typical sensitivity and transient-noise behavior.Source: §IV · p. 5
Environmental checks
- No environmental sensors recorded disturbances evolving like GW150914, and observed fluctuations could explain no more than 6% of its strain amplitude.Tests also found no significant long-range correlated disturbances between the detector sites.Source: §IV · p. 5
Instrumental checks
- No evidence indicated instrumental transients that were temporally correlated between the two detectors.Source: §IV · p. 5
V. SEARCHES
Two independent search strategies recovered GW150914 as an exceptionally significant coincident event. Matched filtering used general-relativistic binary waveforms, while generic searches made minimal waveform assumptions.
Cross-validation
- Two independent search types both detected GW150914: one used relativistic matched-filter templates, while the other targeted generic transient signals.Their detector-noise responses were different and uncorrelated, although both were expected to detect strong binary black-hole mergers.Source: §V · p. 5
Generic transient search
- 4.6σ was the generic transient search significance, with a false alarm rate lower than 1 in 22 500 years after accounting for three search classes.The event was the strongest detected in that entire search.Source: A. Generic transient search · p. 6
Background estimation
- 608 000 years of equivalent background analysis time were generated by repeatedly time-shifting one detector’s data relative to the other.This technique estimates accidental coincidences from uncorrelated instrumental noise.Source: §V · p. 5, B. Binary coalescence search · p. 7
Binary coalescence search
- 5.1σ was the binary coalescence search significance, based on a false alarm rate bounded by 1 in 203 000 years.GW150914’s detection statistic exceeded every background event in its search class.Source: B. Binary coalescence search · p. 7
Background reestimation
- The second most significant event had a false alarm rate of 1 per 2.3 years after GW150914 was removed from the background estimate.Its corresponding Poissonian false alarm probability was 0.02.Source: B. Binary coalescence search · p. 7
VI. SOURCE DISCUSSION
Source modeling interprets GW150914 as a massive binary-black-hole merger and tests the remnant and waveform against general relativity. The results support strong-field predictions while constraining astrophysical merger rates.
Energetics
- 3.0^{+0.5}_{-0.5} M⊙c^2 was radiated in gravitational waves, while the system reached a peak luminosity of 3.6^{+0.5}_{-0.5} × 10^56 erg/s.Source: §VI · p. 7
Relativity tests
- No disagreement was found between remnant mass and spin inferred independently from the early inspiral and late merger stages.The comparison used fitting formulas calibrated to numerical-relativity simulations.Source: §VI · p. 8
- No evidence for violations of general relativity was found when post-Newtonian phase coefficients were allowed to deviate from their nominal values.Source: §VI · p. 8
- λg > 10^13 km constrains the graviton Compton wavelength under a modified dispersion relation, corresponding to mg < 1.2 × 10^-22 eV/c^2.The bound improves Solar System and binary-pulsar limits but not model-dependent galaxy-cluster and weak-lensing bounds.Source: §VI · p. 8
Astrophysical implications
- 2–400 Gpc^-3 yr^-1 is the estimated local merger-rate range across several assumed binary-black-hole mass distributions.Only the lowest predicted event rates are excluded.Source: §VI · p. 8
VII. OUTLOOK
The detector network is being expanded and upgraded to improve sensitivity, increase signal-to-noise ratios, and strengthen localization and multimessenger capabilities.
Future network
- 3 times higher SNR is expected for binaries like GW150914 when Advanced LIGO reaches design sensitivity.Planned improvements include further Advanced LIGO commissioning and additional detectors such as Advanced Virgo and KAGRA.Source: §VII · p. 8
VIII. CONCLUSION
LIGO observed two stellar-mass black holes merging into one, with the waveform matching general relativity through inspiral, merger, and ringdown.
- The detected waveform matches general relativity’s predictions for black-hole inspiral, merger, and the resulting black hole’s ringdown.This agreement identifies the signal as a binary black hole merger and tests gravity in the dynamic strong-field regime.Source: §VIII · p. 8
- The observation demonstrates that binary stellar-mass black hole systems exist.Source: §VIII · p. 8
- This event was the first direct detection of gravitational waves and the first observation of a binary black hole merger.Source: §VIII · p. 8