How two detectors made a black-hole merger measurable

On 14 September 2015, two observatories recorded a brief changing signal. Livingston saw it about 6.9 milliseconds before Hanford, according to the released event data (GWOSC data release). The pattern rose in frequency and strength before fading. The collaboration identified it as gravitational radiation from two black holes spiraling together, merging, and leaving a single remnant (discovery paper, published 11 February 2016).

The calibrated strain records a changing relative length. A search tests whether the pattern stands out from noise, and physical models infer the source.

What the interferometers measure

Each Advanced LIGO detector is a laser interferometer with two perpendicular arms, each 4 kilometres long. A laser beam is split and sent down both arms. Mirrors at the ends reflect the light back, and the returning beams are recombined. If the arms change length differently, the light waves return with a changed relative phase. Their combination at the detector then changes.

The measured quantity is expressed as strain, a fractional change in length. In a simplified description, $h\approx\Delta L/L$, where $\Delta L$ is the differential arm-length change and $L$ is the arm length. Gravitational waves stretch one arm while squeezing the other as they pass, so the detector's orientation and the wave's direction affect its response. At the output, interference turns the phase difference into changing light at a photodetector. Calibration maps that optical response to differential strain while accounting for the mirror suspensions and environmental isolation.

Strain is dimensionless because it compares a length change with the arm length. That makes it a relative measure of the detector's response, not a ruler reading for the source. The same strain can arise from sources with different distances and orientations, which is why the detector's small signal must be interpreted with a source model.

At a strain near $10^{-21}$, multiplying by a 4-kilometre arm gives an order-of-magnitude length scale of $4\times10^{-18}\,\mathrm{m}$. That tiny response explains why the instruments need isolation and careful calibration. The scale is approximate because the response depends on wave direction and frequency.

Advanced LIGO's detectors had undergone major upgrades before their first observing run. The collaboration described the interferometers, suspensions, laser systems, isolation and calibration in a separate instrument paper (submitted 11 February 2016).

Why two sites help

One detector can register a disturbance from local vibration, a sensor, or an instrumental glitch. A gravitational wave should also appear at another detector after a delay consistent with travel between the sites. The event was visible at both Hanford and Livingston, with Livingston earlier. Since the sites have different orientations, the signal can have different signs and strengths in their records. For the visual comparison released by the collaboration, one trace is inverted to account for this orientation.

The arrival delay has a geometric meaning: a wavefront reaches separated detectors at slightly different times depending on its direction across Earth. Imagine the line between the observatories as a baseline. The delay depends on how much the wave's direction points along that line, so one measured delay allows a family of sky directions rather than a single point. The two instruments' different orientations add response information, but this timing and response do not determine the source masses.

The shape of a chirp

In the first detector plots, the signal looks like a chirp: its oscillations become faster and its amplitude grows as the event approaches its peak. The frequency swept from about 35 to 250 hertz. That shape fits a pair of orbiting compact objects losing energy through gravitational radiation. As they lose orbital energy, they move closer, orbit faster, and produce waves with a higher frequency. The rising frequency and amplitude are separate features of the changing orbit: one tracks how rapidly cycles pass, while the other tracks the size of the detector's response. A narrow instrumental tone would stay near one frequency. The collaboration showed the chirp in filtered strain before overlaying a predicted waveform (pedagogical analysis, first submitted 5 August 2016).

The three source phases carry different information. During inspiral, the orbit evolves gradually and supports a slow-orbit approximation. Near merger, the objects move quickly in a strong gravitational field, so a fully relativistic description is needed. During ringdown, the remnant's distorted spacetime relaxes through damped modes. The ringdown is a change in the gravitational field, not sound in air or a vibration of a material surface.

What the early chirp measures

In the leading slow-orbit approximation, the frequency and how quickly it rises constrain a particular combination of the component masses, called the chirp mass:

The leading-order chirp mass is $M_c=(m_1m_2)^{3/5}/(m_1+m_2)^{1/5}$.

Here $m_1$ and $m_2$ are the component masses. The product and sum give this combination a different weighting from an ordinary average: the product reflects the pair's joint orbital motion, while the total mass also enters the dynamics. In the slow-orbit model, this combination captures how both masses shape the early rate of frequency increase. Many different mass pairs can share a chirp mass, so measuring this one quantity does not identify either black hole's mass by itself.

The frequency is measured by counting how many wave cycles pass in a given interval. Its rise is visible as those cycles become closer together. A single moment's frequency would provide much less information than this changing sequence. Early in the signal, the observed cycles let the slow-orbit approximation constrain the chirp mass. Near merger, relativistic effects change the waveform, and those later details help distinguish mass pairs that the leading combination leaves unresolved. The inference uses this fuller evolution rather than treating the chirp-mass formula as a direct weighing rule.

How the search weighs a candidate

The collaboration searched by comparing detector records with calculated waveforms, or templates, for compact binaries. A template predicts the strain pattern for a set of source properties. Matched filtering slides predictions across each detector's data and scores their agreement. The searches then compare triggers from the same template at both sites, allowing for a possible arrival-time difference. This method can find a weak signal when it follows a predictable shape.

The score accumulates agreement across many cycles. A template must track both the frequency sweep and the phase, meaning where each oscillation falls in time. A curve can have a similar overall rise yet lose alignment if its predicted cycles drift relative to the data.

The search paper reported a combined signal-to-noise ratio of 24 for GW150914, a false alarm rate below one event in 203,000 years, and significance greater than 5.1 sigma (first submitted 11 February 2016; revised 27 April 2016). In its PyCBC analysis, the background estimate used time offsets between the detector records. These shifts break the same-event correspondence while retaining each instrument's noise, letting accidental coincidences show how often noise can imitate a candidate. The paper also describes GstLAL, which estimates background differently. The quoted false alarm rate is specific to its search analysis. It is not the probability that the black-hole interpretation is false, the cosmic merger rate, or the detectors' observing time.

From the chirp to source-frame masses

The original discovery paper reported source-frame central estimates of about $36\,M_\odot$ and $29\,M_\odot$ for the black holes, about $62\,M_\odot$ for the remnant, and roughly $3M_\odot c^2$ radiated as gravitational-wave energy (discovery paper). The difference between the component-mass total and remnant estimate is roughly the energy radiated, expressed as an equivalent mass. The factor $c^2$ converts that mass unit into energy, which left as gravitational waves rather than ejected matter. The values came from fitting relativistic waveforms to calibrated strain. A likelihood compares proposed source models with the data under the detector-noise description. The analysis reports posterior distributions for source parameters; central values summarize those distributions, while uncertainty ranges show how widely values can vary and still fit the data. They are not exact masses read directly from the signal. Since they are inferred together from one waveform, the masses and radiated energy form a linked account rather than separate measurements. Rounding means their approximate values will not balance exactly.

The measured signal also leaves related source properties correlated. Orbital inclination is the angle between the binary's orbital axis and our line of sight; changing it alters the observed amplitude and polarization pattern. Distance also changes amplitude, with a more distant source appearing weaker. A more distant binary viewed near its orbital axis can therefore resemble a closer binary seen from a less favorable angle. Hanford and Livingston record different projections of the wave's polarizations, which helps constrain the possibilities, but the properties analysis found distance and inclination strongly correlated (properties analysis, published 14 June 2016).

Cosmic expansion stretches the waveform's timescale, making the intervals between cycles longer by the time the signal reaches Earth. The waveform therefore yields redshifted, or detector-frame, masses. If the source redshift is $z$, then $M_{\mathrm{det}}=(1+z)M_{\mathrm{source}}$. Recovering source-frame values requires interpreting the inferred distance through a cosmological redshift. Because distance and inclination are correlated in the amplitude estimate, that conversion carries uncertainty. The detector itself does not weigh either black hole.

Scope of the relativity tests

The collaboration compared the remnant mass and spin inferred separately from low-frequency inspiral and high-frequency post-inspiral portions of the signal. The split was at 132 hertz; the upper band was dominated by merger and ringdown. These frequency bands provide two estimates of the remnant, which agreed within their uncertainties for GW150914. A separate analysis found that the post-peak data were consistent with the least-damped quasinormal mode inferred for the remnant. A quasinormal mode is a characteristic damped oscillation of a perturbed black hole's spacetime. The least-damped mode fades slowest and dominates the late ringdown, so comparing it with the inferred remnant tests a specific part of the relativistic prediction.

These checks found consistency with selected relativistic predictions over the range measured in this event. They do not rule out every alternative theory of gravity, establish a complete version of the black-hole no-hair theorem, or settle what happens at quantum scales. The collaboration's tests paper describes the comparisons (first submitted 11 February 2016).

GW150914 was the first direct detection of gravitational waves and the first observed merger of a binary black-hole system. Earlier observations of a binary pulsar had provided indirect evidence through orbital decay (discovery paper). Astronomers timed the pulsar's regular radio pulses to follow its orbit; the changing orbital period matched the energy loss expected from gravitational radiation. That evidence came from the binary's motion, while LIGO measured the waves themselves as they passed Earth.

Inspecting the released data

Open the GWOSC event release and compare its downloadable strain with the displayed traces. The collaboration filtered the plotted signal to 35-350 hertz and removed narrow spectral lines; it also inverted one trace to account for detector orientation. The bandpass retains oscillations inside the stated range and suppresses frequencies outside it, while line removal targets narrow features. Comparing the two views helps distinguish the measured time series from processing used to make its oscillations easier to see. The release provides a way to inspect the event's timing and waveform shape; source masses require the search and inference methods described in the papers.

Sources

• LIGO Scientific Collaboration and Virgo Collaboration, “Observation of Gravitational Waves from a Binary Black Hole Merger,” Physical Review Letters 116, 061102 (2016), published 11 February 2016. Paper
• LIGO Scientific Collaboration and Virgo Collaboration, “GW150914: First results from the search for binary black hole coalescence with Advanced LIGO,” Physical Review D 93, 122003 (2016), first submitted 11 February 2016, revised 27 April 2016. Paper
• LIGO Scientific Collaboration and Virgo Collaboration, “GW150914: The Advanced LIGO Detectors in the Era of First Discoveries,” Physical Review Letters 116, 131103 (2016), submitted 11 February 2016. Paper
• LIGO Scientific Collaboration and Virgo Collaboration, “Properties of the binary black hole merger GW150914,” Physical Review Letters 116, 241102 (2016), first submitted 11 February 2016, published 14 June 2016. Paper
• LIGO Scientific Collaboration and Virgo Collaboration, “Tests of general relativity with GW150914,” Physical Review Letters 116, 221101 (2016), first submitted 11 February 2016. Paper
• Abbott et al., “The basic physics of the binary black hole merger GW150914,” pedagogical analysis, Annalen der Physik 529, 1600209 (2017), online 4 October 2016, first submitted 5 August 2016, arXiv version revised 24 February 2017. Paper
• Gravitational Wave Open Science Center, GW150914 event page and data release. Event data; dataset DOI