---
title: "Read the GW150914 paper from the traces to the masses"
description: "Which parts of the discovery paper establish the signal, its significance and its source properties?"
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Astronomy · Cosmology · Gravity

# Read the GW150914 paper from the traces to the masses

Sandbox Physics · 2026-10-24

Which parts of the discovery paper establish the signal, its significance and its source properties?

1. Read the filtered strain
2. Separate measured traces from waveforms
3. Inspect the noise comparison
4. Interpret the reported source parameters

Use the discovery paper, arXiv:1602.03837v1, Figures 1–4 and Table I.

## Figure 1 begins with calibrated and filtered measurements

Open “Observation of Gravitational Waves from a Binary Black Hole Merger”, arXiv:1602.03837v1, published as Physical Review Letters 116, 061102. Keep Figure 1, Figure 2, Figure 3, Figure 4 and Table I beside you. They address different questions. The time traces show what the observatories measured; the search comparison asks how readily noise can imitate it; the parameter table describes the source inferred under waveform and astrophysical assumptions.

Start with the top row of Figure 1. The left column is Hanford, labelled H1, and the right column is Livingston, L1. The horizontal axis is time relative to 14 September 2015 at 09:50:45 UTC. The vertical quantity is gravitational-wave strain after calibration. The caption says these display traces pass through a 35–350 hertz bandpass, with additional filters removing strong instrumental lines. Calibration converts the instrument output into strain; filtering selects the frequencies shown.

Livingston received the signal first. For the visual overlay, Hanford is shifted by about 6.9 milliseconds and its sign is reversed to account for the different detector orientations. The overlay compares the same event as seen by two instruments. Read that transformation before comparing peaks. Then look at the bottom row: the bright feature rises in frequency as time advances. This is the chirp in a time-frequency display.

Sources: [1]

## The middle rows distinguish reconstructions from residuals

Figure 1’s second row contains inferred signal waveforms. A numerical-relativity waveform is drawn as a solid line. Shaded regions represent two reconstruction approaches, one based on binary-black-hole waveforms and another assembled from flexible wavelets, which are short oscillating functions localized in time. The caption identifies the shaded regions as 90% credible regions. They describe uncertainty within the reconstruction procedures.

The third row shows residuals: the filtered measured trace after subtracting the filtered numerical waveform. A residual resembling ordinary noise is a useful check that the proposed signal describes the visible structure. A good-looking subtraction alone does not give the detection’s false-alarm rate. That question needs the search and its noise background. Keep the visual agreement here separate from the statistical comparison in Figure 4.

Sources: [1]

## Figure 2 and Equation 1 connect the chirp with a mass scale

Figure 2 shows an inferred waveform over its full bandwidth, without the display filtering used in Figure 1. The black-hole images are numerical models. The lower panel gives effective orbital separation and relative speed derived from the binary description. These panels help interpret the waveform physically; their separations are model quantities inferred from the wave, so they should not be read as independently photographed positions.

Equation 1 gives an approximate way to obtain the chirp mass from the low-frequency inspiral. The two masses are m-one and m-two; their combination is the chirp mass. The observed gravitational-wave frequency is f, its increase per second is f-dot, G is the gravitational constant and c is the speed of light. Use a smoothly estimated frequency evolution, not a derivative taken between two noisy sample points. The relation describes the leading inspiral approximation for a nearly circular binary.

The paper uses this estimate to obtain a chirp mass of about 30 solar masses in the detector frame. That already indicates an unusually massive, compact pair. Near merger, higher-order and strong-gravity effects matter, and the full analysis uses relativistic waveforms. Treat Equation 1 as a route to the mass scale and a physical explanation of the rising pitch.

Sources: [1] [3]

## Figure 3 explains which frequencies carry useful information

Figure 3 combines an instrument diagram, site information and strain noise as a function of frequency. The noise curves show that LIGO’s sensitivity varies with frequency. Tall narrow peaks mark instrumental spectral lines. Frequencies with large noise contribute less useful information than a quiet band containing the same signal amplitude. Template matching therefore gives each frequency a weight according to the detector noise.

A template is a predicted waveform for a chosen binary. Matched filtering compares many templates with the data, weighting the comparison by the measured frequency-dependent noise. A signal-to-noise ratio summarizes the strength of the match. It is not the probability that the signal is real. The collaboration also checks whether an apparent match distributes its power across frequencies as the waveform predicts, since a short instrumental glitch can otherwise score highly.

Sources: [1] [2]

## Figure 4 asks how often noise earns a similar score

Figure 4 plots candidate events and an estimated background against the search detection statistic. The left panel concerns a generic transient search; the right concerns the binary-coalescence search. Each search has its own ranking procedure, so the two horizontal scales are not interchangeable. Look for GW150914’s score relative to the noise tail within its own panel.

The background comes from artificial time shifts between the two detectors. The shifts exceed the intersite propagation time, breaking true shared signals while retaining many accidental noise pairings. This procedure depends on understanding detector noise and possible correlations. It also incorporates the search process that selected a candidate. A false-alarm rate below one event per 203,000 years in the matched-filter analysis measures the rarity of a noise event at least this highly ranked under that procedure.

That number is a rate, not the posterior probability that the source is a binary black hole. Notice also that the caption discusses GW150914 paired with noise after time shifting. Those pairings can contribute to an estimated background. The different curves and quoted significances must be read with the search definitions in the main text.

Sources: [1] [4]

## Table I reports inferred source properties

Table I lists medians and 90% credible intervals for source parameters. The primary and secondary masses are approximately 36 and 29 solar masses, and the remnant about 62 solar masses. Read the asymmetric upper and lower uncertainties in the table. These are inferences from the signal using waveform models, with the table explaining how model differences enter the uncertainties.

The table gives source-frame masses. Cosmic expansion stretches the signal’s time scale before it reaches Earth. Detector-frame masses are consequently larger by one plus the source redshift. The approximate 30-solar-mass chirp estimate earlier in the paper belongs to that detector frame. A difference between the two frames is therefore expected. The reported redshift also assumes a cosmological model to connect luminosity distance with redshift.

Sources: [1]

## Carry the questions to the next paper

For the next gravitational-wave result, first identify the measured quantity and any display filtering. Mark which curves are data, reconstructed signals and physical models. Check the noise weighting, candidate ranking and background estimate. Then read the parameter table’s uncertainty convention, waveform assumptions and source-versus-detector frame. These questions let the figure sequence do its job: establish a shared signal, measure its rarity among noise events and learn which source most plausibly produced it.

Sources: [1]

## Sources and reading notes

1. [LIGO Scientific Collaboration & Virgo Collaboration (2016), Observation of Gravitational Waves from a Binary Black Hole Merger](https://arxiv.org/abs/1602.03837v1)

   Read Figure 1 with its filtering and alignment caption, Equation 1, Figures 2–4 and Table I.

2. [LIGO Scientific Collaboration (2016), GW150914: The Advanced LIGO Detectors in the Era of First Discoveries](https://dcc.ligo.org/LIGO-P1500237/public)

   The four-kilometre interferometers, optical layout, isolation and frequency-dependent detector noise.

3. [LIGO Scientific Collaboration & Virgo Collaboration, The basic physics of the binary black hole merger GW150914](https://dcc.ligo.org/LIGO-P1600161/public)

   The inspiral frequency increase, chirp mass and compactness argument, with the limits of leading-order estimates.

4. [LIGO Scientific Collaboration, How do we know GW150914 was real?](https://ligo.org/science-summaries/GW150914Detchar/)

   Instrumental and environmental checks, auxiliary channels and the empirically estimated noise background.

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