Observation of Gravitational Waves from a Binary Black Hole Merger

The paper reports the first direct detection of gravitational waves—traveling distortions of space—from the merger of two black holes, and asks whether the signal agrees with Einstein’s theory of gravity, general relativity. 14

Earlier observations of energy loss from two orbiting stars had provided indirect evidence for gravitational waves, but the waves had not been directly detected and black hole mergers had not been observed. 234 Direct measurements would allow researchers to test general relativity where gravity is especially strong and objects move rapidly. 34

The authors investigate a signal called GW150914, observed on September 14, 2015, by the two detectors of the Laser Interferometer Gravitational-Wave Observatory, or LIGO. 5 Each detector uses laser light to compare the lengths of two perpendicular arms, which a passing gravitational wave changes differently. 9

The signal grew stronger and its oscillations became faster, as expected when two objects spiral together and merge. 7 The authors argue that black holes are the only known objects compact enough to reach the implied rate of orbit without touching. 8 The fading oscillations after the peak are also consistent with a newly formed black hole settling down. 8

To distinguish a real wave from noise, the authors use one search that compares the data with predicted merger patterns and another that looks more generally for brief signals in both detectors. 1112 They estimate how often unrelated detector noise could mimic a signal by shifting one detector’s data in time and looking for apparent coincidences. 12 Both searches detected GW150914, and investigations found no evidence that it was an instrumental artifact. 1011

By fitting general-relativity models to the signal, the authors also seek to estimate the black holes’ masses, rotations, and distance from Earth. 13 These estimates depend on the models used and include uncertainty from both the data and differences between models. 13

To test general relativity, the authors check whether the early and late parts of the signal give consistent estimates for the final black hole, and whether changes to the theory’s predicted wave pattern are supported by the data. 1415 They also use an assumed alternative model for how gravitational waves travel to constrain the mass of the graviton, a hypothetical particle associated with gravity. 16 The tests found no evidence of disagreement with general relativity for this event; the graviton constraint depends on the assumed propagation model. 141516

The paper does not establish the source’s precise position: with only two detectors observing, it could be located only within a broad region of the sky. 6 The authors also discuss more than one possible way such a black hole pair could form, without identifying which produced this system. 17 They propose expanding the detector network to improve the localization and measurement of future sources. 18

Directly observing gravitational waves—traveling distortions of space—matters because it gives scientists a way to study extreme cosmic events and test general relativity, Einstein’s theory of gravity, where gravity is strong and objects move rapidly. 134

Before this work, observations of energy loss in a pair of orbiting stars had already demonstrated that gravitational waves exist. 3 Measuring the waves’ strength and the timing of their oscillations directly would let researchers study more kinds of systems and test general relativity in strong gravitational fields that change over time. 3

Before this work, astronomers had identified many candidates for black holes—extremely compact objects with strong gravity—using light and other electromagnetic radiation, but had not observed a black hole merger. 26 Gravitational waves offer a way to study the black holes’ inward spiral and merger, as well as how the resulting black hole settles afterward. 356

Astrophysicists also want to understand how black hole pairs form: proposed possibilities include pairs that evolve in isolation and encounters in dense environments. 8 Estimating how often such pairs merge in the nearby universe can constrain predictions about their population, although the estimates depend on assumptions about black hole masses and can remain compatible with a wide range of predictions. 9 The authors also suggest that detecting the combined waves from distant mergers that cannot be distinguished individually could reveal how these systems evolved over the history of the universe. 10

The waves were expected to be extremely weak, so experimenters face the challenge of distinguishing a genuine signal from noise in their instruments and surroundings. 17 Using widely separated detectors helps make that distinction and can also help locate a source on the sky. 7

Directly detecting gravitational waves and identifying their source is difficult because their effects are extremely small, detector noise can produce signal-like events, and the data do not determine every source property precisely. 251314

The Laser Interferometer Gravitational-Wave Observatory (LIGO) uses detectors with two perpendicular, 4-kilometer arms; a passing wave changes their lengths differently, and strain measures that difference relative to an arm’s length. 8 GW150914, the signal observed on September 14, 2015, had a peak strain of only 1.0 × 10⁻²¹. 14

Ground motion, heat-related motion of detector components, and fluctuations in the light used for measurement all create noise that can obscure such a small effect. 910 Using two widely separated detectors helps distinguish a wave from noise local to either site, although the researchers also had to check for disturbances that could affect both sites. 811

Short-lived noise disturbances can produce candidate events, and the noise changes over time and does not follow a simple bell-shaped distribution. 1213 The researchers therefore had to estimate how often noise could produce an event at least as signal-like as a candidate, but they could not switch off gravitational waves to obtain data known to contain only noise. 13 They estimated this noise background by shifting one detector’s data in time so that the same wave could no longer coincide across the detectors; the method works for noise that is uncorrelated between sites. 13 A real signal in one detector could still coincide with noise in the shifted data from the other, making the background estimate conservatively high. 13 For GW150914, investigations found no evidence that instrumental or environmental disturbances caused the signal. 11

Interpreting the source also depends on predicting the waveform, or changing shape of the signal, from black holes spiraling together and merging. 37 Accurate predictions depended on advances in analytical calculations and numerical simulations of gravity. 3 The authors reasoned that the signal implied very massive objects orbiting very close together, leaving black holes as the only known objects compact enough for the observed orbit. 67

Some source properties remained uncertain even after the detection: with only two detectors observing, the area assigned a 90% probability of containing the source covered approximately 600 square degrees of sky. 5 The analysis also only weakly constrained the spin, or rotation, of the smaller black hole. 14

Before this study, gravitational waves—traveling stretches and squeezes of space—had indirect support but no direct detection, and no merger of black holes, objects whose gravity is so strong that light cannot escape, had been observed. 1235

Earlier observations of a binary pulsar—a pair of orbiting objects including a rapidly spinning neutron star that emits pulses—showed energy loss that demonstrated the existence of gravitational waves. 3 But these observations did not directly measure the waves’ amplitude and phase—their strength and position within an oscillation—which could enable new tests of general relativity, Einstein’s theory of gravity, especially in rapidly changing, strong gravitational fields. 13

Scientists had identified many black hole candidates through electromagnetic observations, such as observations of light, and had developed predictions for waves from black hole mergers. 2 Without an observed merger, however, those predictions had not been checked against such an event. 2

The predicted waves were extraordinarily weak, and the initial network of detectors could set bounds on various possible sources but did not directly detect them. 145 A significantly more sensitive generation of detectors had only begun observing in 2015. 4

The paper’s central idea is that tiny waves that stretch and squeeze space, called gravitational waves, can be traced to merging black holes—extremely compact objects—by comparing signals from two distant detectors with Einstein’s theory of gravity and checking whether unwanted disturbances, or noise, could imitate them. 126711

Each detector compares laser light traveling along two perpendicular arms: a passing wave changes the arm lengths differently, changing the light signal. 7 A genuine wave should produce related signals at both sites, and the observed signal arrived at the second detector about seven thousandths of a second after the first, consistent with travel between them. 347

As two orbiting black holes lose energy to gravitational waves, they spiral closer, producing a wave pattern that grows stronger and faster; after they merge, the pattern fades as the new black hole settles. 56 The observed signal follows this sequence and matches the pattern predicted by Einstein’s theory. 156

The authors reasoned that the changing wave rate implied large orbiting masses, while the rapid orbit near the signal’s peak meant the objects had to be very close together. 6 They concluded that, among known objects, only black holes were massive and compact enough to fit. 6

To find the signal, one search compared the data with a large library of predicted patterns from merging objects, while another looked for short-lived signals in both detectors without assuming a particular pattern. 101213 Both searches detected the event, providing checks using different methods. 10

To estimate how often noise could produce a misleading coincidence, the researchers repeatedly shifted one detector’s data in time by more than the possible wave travel time and searched again. 11 These shifted comparisons estimate the noise background when noise at the two sites is uncorrelated. 11 In the predicted-pattern search, the estimated false-alarm rate—the rate at which noise would produce an event at least as convincing—was less than one per 203,000 years. 11114

The researchers also investigated disturbances that could affect both sites and found no significant long-range disturbances or evidence of simultaneous instrumental noise events. 89 Their compactness argument concerns known objects, and their more detailed estimates of the source’s properties depend on models based on Einstein’s theory and include statistical and model-related uncertainties. 615

The paper reports the first direct detection of gravitational waves, or ripples in spacetime, and the first observation of two black holes merging. 12

The signal, named GW150914, was recorded by both detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO), which measure tiny changes in distance caused by gravitational waves. 35 It matches the prediction of general relativity, Einstein’s theory of gravity, for two black holes spiraling together, merging, and settling into one black hole. 12

In the search that used predicted merger signals, the authors estimated that detector noise would produce an event at least as convincing at a rate of less than one per 203,000 years. 789 A separate search that made fewer assumptions about the signal’s shape also detected GW150914, and investigations found no evidence that an instrumental or environmental disturbance caused it. 67

The authors estimate that the original black holes were 36 and 29 times as massive as the Sun, and the final black hole was 62 times as massive. 1 The respective 90% credible ranges are 32–41, 25–33, and 58–66 times the Sun’s mass; each range contains 90% of the probability assigned to that mass by the authors’ analysis. 101112

The merger radiated energy in gravitational waves equivalent to converting 3.0 times the Sun’s mass into energy, with a 90% credible range of 2.5–3.5 times the Sun’s mass. 1

The estimated luminosity distance, a distance measure based on how much the signal has weakened, is 410 million parsecs, with a 90% credible range of 230–570 million parsecs. 1 A parsec is about 3.26 light-years, or the distance light travels in 3.26 years. 1 Because only two detectors were observing, the source could be located only within a broad region of the sky. 4

The authors’ tests found no disagreement with general relativity in the intense gravitational field of the merger. 14 For example, estimates of the final black hole’s mass and rotation made from the early and late parts of the signal agreed. 13 Under an assumption that changes how gravitational waves travel, the authors also set an upper limit on the mass of the graviton, a hypothetical particle associated with gravity. 14

The observation demonstrates that pairs of black holes with masses comparable to those of stars can form and merge within a time comparable to the age of the universe. 1518 The authors discuss proposed formation routes involving isolated pairs or encounters in crowded regions of space, but do not establish which route produced GW150914. 15

Using several models of black-hole masses, the authors estimate that 2–400 such mergers occur each year in the nearby universe in a volume equivalent to a cube one billion parsecs on each side, with volume defined to account for cosmic expansion. 16

The paper also points readers to further results and associated data releases for the event. 17

The paper provides very strong evidence that the researchers directly detected gravitational waves from a black-hole merger, while its estimates and tests remain subject to uncertainty and assumptions. 12327

Gravitational waves are traveling distortions of space, and the Laser Interferometer Gravitational-Wave Observatory (LIGO) uses two widely separated detectors to distinguish a shared signal from local noise. 210 On September 14, 2015, both detectors observed the event called GW150914, with the signal reaching the Hanford detector about 6.9 milliseconds after the Livingston detector. 56 Earlier observations of a binary pulsar had provided evidence for gravitational waves through the system’s energy loss, but the authors identify GW150914 as the first direct detection of the waves themselves. 13

A false-alarm rate estimates how often detector noise would produce an event ranked at least as highly as the observed signal; a lower rate therefore means stronger evidence against noise. 15 In 16 days of coincident observations, a search comparing the data with predicted compact-binary waveforms estimated GW150914’s false-alarm rate at less than one event per 203,000 years. 131420 This rate is an estimate of noise-event frequency, not the probability that GW150914 itself was noise. 1520

A second search, which did not require a specific waveform model, also found GW150914 to be its strongest event. 1618 For its class of signals that increase in frequency over time, this search estimated a false-alarm rate below one per 22,500 years, allowing for its three search classes. 1718 That result supports the detection without depending on the same waveform templates, although its stated rate applies to the increasing-frequency class rather than to signals of every shape. 161819

Both searches estimated their noise backgrounds by repeatedly shifting one detector’s data in time relative to the other’s, a method effective for noise that is not correlated between the detectors. 15 That method alone would not rule out a disturbance shared by both sites, but the authors also investigated environmental and instrumental disturbances and found no evidence that they caused GW150914. 111215

The black-hole merger interpretation is strongly supported by both the signal’s shape and the inferred properties of its source. 189 Its frequency—the number of wave cycles per second—increased as expected when two objects spiral together, and its fading after the peak was consistent with the resulting black hole settling down. 89 The authors argue that the required objects were both massive and compact: two neutron stars, which are compact stellar remnants, would be too light, while a neutron-star–black-hole pair matching the inferred mass pattern would merge at a lower frequency. 9 On that basis, the paper concludes that the observation demonstrates the existence of stellar-mass black holes in pairs and is the first observation of such a pair merging. 1

Using models based on general relativity, Einstein’s theory of gravity, the authors estimate the original black-hole masses at 36 and 29 times the Sun’s mass and the final mass at 62 times the Sun’s mass. 2223 The respective 90% credible intervals are 32–41, 25–33 and 58–66 solar masses. 2122 A 90% credible interval is a range containing 90% of the probability assigned to a parameter by the analysis, given its data and models. 2123 These intervals include statistical uncertainty and uncertainty from averaging results from different waveform models, so the reported masses are estimates rather than exact measurements. 2123

The authors also estimate that energy equivalent to about three solar masses was carried away by gravitational waves. 24 The source’s direction was much less precisely determined because only two detectors were observing at the time. 7

The waveform’s agreement with general relativity supports the theory in a setting with strong gravity and rapidly moving black holes. 430 For example, the final black hole’s mass and spin inferred from the early part of the signal agreed with those inferred independently from the later part, and another test found no evidence of deviations in the inspiral waveform. 2526 These are consistency tests, not proof that general relativity is correct in every circumstance: the paper reports constraints on possible deviations rather than showing that all deviations are impossible. 252627 A further limit on the mass of the hypothetical particle associated with gravitational waves depends on an assumed modification of how the waves propagate, so it is not a model-free measurement of that mass. 27

The event establishes that black-hole pairs can form and merge within a timescale comparable to the age of the universe. 28 It does not establish how this particular pair formed: the paper identifies both isolated binary evolution and interactions in dense environments as possible routes. 28

The observation also constrains how often such mergers occur, but the estimate depends strongly on assumptions about the distribution of black-hole masses. 29 Across the models considered, the authors estimate 2–400 mergers per year per cubic gigaparsec of comoving volume, a volume measure that accounts for the universe’s expansion; a gigaparsec is about 3.26 billion light-years. 29 This wide range leaves the rate poorly determined, and the authors say it excludes only the lowest predictions they considered. 29

The two-detector experiment and independent analyses are appropriate and provide strong support for the first direct detection of gravitational waves from a black-hole merger, although they leave some source properties uncertain. 4112024

Gravitational waves are traveling changes in space, and the researchers looked for the pattern expected when two black holes spiral together, merge, and settle into one. 15

Each of the two widely separated LIGO detectors compared laser light traveling along two perpendicular, four-kilometer arms to measure the tiny difference in arm lengths caused by a passing wave. 7 The event, named GW150914, arrived at the Livingston detector about seven thousandths of a second before it reached Hanford; over about 0.2 seconds, its signal grew stronger and rose from 35 to 150 cycles per second. 235

The researchers checked the instruments and environmental sensors and found no evidence that a disturbance caused the event. 8 During the second containing the signal, measured environmental fluctuations were too small to account for more than 6% of its amplitude. 8

The main searches examined 16 days when both detectors were observing, using two independent methods. 1011 One compared the data with predicted merger waveforms, while the other searched for a shared short-lived signal without requiring a specific waveform. 111314

To estimate how often noise could imitate a signal, the researchers repeatedly shifted one detector’s data in time and counted accidental matches between the detectors. 1216 This method is effective for noise that is uncorrelated between the sites, and the researchers found no evidence of significant shared disturbances or time-correlated instrumental transients. 8912

A false-alarm rate estimates how often noise would produce a candidate ranked at least as convincing as the observed event; a lower rate means stronger evidence against a noise explanation. 12 For GW150914, the waveform-based search estimated a rate below one false alarm per 203,000 years, while the general transient search estimated a rate below one per 22,500 years. 1517

The signal’s changing frequency implied massive objects that had to be close together, and the authors argued that black holes were the only known objects compact enough to produce it. 6 The fading signal was also consistent with a final black hole settling down. 6

To estimate the source’s properties more precisely, the researchers used models based on general relativity and a Bayesian analysis, a statistical method that uses data and models to estimate possible values. 20 A 90% credible interval is a range assigned 90% probability by the analysis given its data and models; the reported intervals include statistical uncertainty and differences among waveform models. 1820 They estimated initial masses of 36 and 29 times the Sun’s mass, with respective 90% credible intervals of 32–41 and 25–33, and a final mass of 62 times the Sun’s mass, with an interval of 58–66; these are masses in the source’s frame. 1819

As a test of general relativity, estimates of the final black hole’s mass and spin, a measure of its rotation, derived from the early and late parts of the signal agreed with each other. 21 The paper reports no evidence of disagreement with general relativity in its tests, which supports the theory under the conditions tested rather than proving it in every situation. 212223

The setup nevertheless had limits: with only two detectors observing, the source could be located only within a large sky region of approximately 600 square degrees at 90% credibility. 4 The spin of the smaller initial black hole was also only weakly constrained, so the observation did not establish every detail of the system. 20

No consequential gap undermines the main conclusion: the paper strongly supports a merger of two black holes, extremely compact objects, as the source of gravitational waves, traveling distortions of space, and it claims neither to rule out every conceivable alternative nor to prove Einstein’s theory of gravity. 141618

Two widely separated instruments of the Laser Interferometer Gravitational-Wave Observatory, or LIGO, detected the event within the time a wave could travel between them. 2 Two kinds of search found it: one compared the data with predicted merger patterns, while the other looked for short-lived signals without requiring a specific pattern. 7

For the search using predicted merger patterns, the estimated false alarm rate—the rate at which detector noise would produce candidates at least as convincing—was less than one per 203,000 years. 810 That rate measures the noise background in this search; it is not itself the probability that the event was something other than a black-hole merger. 810

The background estimate came from repeatedly shifting one detector’s data in time relative to the other’s, a method the authors say is effective when noise at the two sites is uncorrelated. 89 The authors found no significant long-range disturbances or evidence of correlated instrumental transients, supporting that assumption, although the checks cannot establish that every possible shared disturbance was impossible. 56

The signal’s rising frequency—the number of wave cycles per second—suggests orbiting objects spiraling together, and its fading is consistent with a newly formed black hole settling down. 34 From approximate estimates of the masses and required proximity, the authors conclude that black holes are the only known objects compact enough for the inferred orbital motion; that does not exclude every hypothetical unknown object. 4

The estimated masses and final black hole’s properties come from models based on general relativity, Einstein’s theory of gravity, so those estimates do not independently prove the theory. 1213 The reported 90% credible intervals are ranges containing 90% of the estimated probability for a parameter under the analysis, and the authors say they include statistical errors and an allowance obtained by averaging different waveform models. 1112 That allowance does not establish that every conceivable source or modeling uncertainty was covered. 1112

The authors also tested the theory by comparing the final black hole’s mass and spin, or rotation, inferred from earlier and later parts of the signal and by allowing parts of the predicted wave pattern to vary. 1415 They found no evidence of disagreement, which supports consistency in the ways tested but does not prove the theory exact or rule out every alternative theory. 141516

The authors describe formation through isolated binary systems and through interactions in dense environments as possibilities, but they do not establish which produced this particular pair. 17 These limits leave intact the paper’s central conclusion: it reports the first direct detection of gravitational waves, with a signal consistent with a binary black-hole merger. 18

A useful next step proposed by the authors is to expand the network of instruments that detect gravitational waves, which are traveling distortions of space. 16

The signal in this study came from the merger of two black holes, extremely compact objects, and was observed by only two detectors. 237 The source’s position in the sky was estimated mainly from the difference in when the signal reached the two sites. 2

The authors expect additional detectors to improve estimates of where future sources lie and of their properties, such as the masses of merging black holes. 456 These improvements were expected, not demonstrated in this paper. 6