WARPLAB

What am I looking at?

What you are looking at

Two black holes spiral together, merge and ring down, and this module follows that from five sides. Chirp and sound turns the masses and distance into the strain that reaches Earth and lets you hear it; 3D merger flies round GW150914 on a to-scale sheet of spacetime; Detector shows a LIGO interferometer that lights up only while the wave passes. Fit real data lines your masses up against the real GW150914 signal from both LIGO sites, and Catalogue lists every published event with each value explained. Without 3D or with reduced motion, the merger comes in six still steps instead. Guided tours, above the tabs, walk through real events in four or five narrated stops each, from Greatest hits to Virgo's discoveries; each stop loads its event into the chirp, the 3D merger and the catalogue.

Controls

On this device:

Mouse

  • Click a tab to switch: Chirp and sound, 3D merger, Detector, Fit real data, Catalogue.
  • Chirp: drag Mass 1, Mass 2 and Distance. Play chirp plays the sound; Set GW150914 puts the first detection back.
  • 3D merger: drag to rotate, scroll to zoom, right-drag to pan. Options holds the camera views, the surface and the layers.
  • 3D merger: drag along the time strip to scrub. Speed picks real time or a slow motion; the corner button goes full screen.
  • Detector: Play, or drag Time in the pass. Fit: drag the two masses, then Reveal published values to compare.
  • Catalogue: click an event, click a column heading to sort (again to reverse), click any value to see what it means.
  • Guided tours: click Guided tours, pick a tour, then Next, Back or Exit tour on the card. The link in the address bar opens the same stop.

Keyboard

  • Tab reaches the tab row. Left and Right arrows, Home and End switch tabs.
  • Sliders take the arrow keys, one step at a time (the chirp's masses about 2.5%, the fit's 1 M☉, distance 10 Mpc); Home and End jump to the ends.
  • Enter or Space presses a button: Play chirp, Play and Pause, Set GW150914, the views and layers.
  • 3D merger: the time strip is a slider, so the arrows scrub and pause the merger. The camera takes no keys: pick Orbit, Top, Edge-on, Close or Against sky under Options.
  • Esc leaves full screen, or closes the Options menu.
  • Catalogue: the list is one Tab stop. Up and Down, Home and End move the selection; Tab on to the values, Enter opens each explanation.
  • Guided tours: Left and Right arrows move between stops anywhere outside a slider, a tab row or the catalogue list.
  • H or ? opens this panel. Esc closes it.
Other devices

Touch

  • Tap a tab. On a phone the five tabs wrap onto two rows.
  • Drag any slider with one finger: the masses, the distance, the time in the pass.
  • 3D merger: one finger rotates, pinch zooms, two fingers pan. Options opens the views and layers.
  • Full screen fills the phone. The same button or the browser's Back returns to the page.
  • Catalogue: tap an event, then tap any value. On a phone the selected event sits above the list.
  • Guided tours: tap Guided tours and a tour, then swipe the card left for the next stop and right for the one before.

Headset and AR

  • On a headset, Enter VR stands you on the sheet with the binary ahead and a detector beside you; View in AR puts a 1:25 model on a table. iPhone and iPad show a note instead.
  • Point a controller or your hand at the panel. Pull the trigger or pinch to press.
  • Panel: m₁ and m₂ up or down 4 M☉ (8 to 64 M☉), Pause, Restart and GW150914 masses. It reads out the phase, the frequency and the LIGO arm change.
  • VR: aim at the floor and press to teleport; the right stick turns 30° at a time. Exit VR is on the panel.
  • AR on a headset: point at the ring on a table or the floor and press to place. Place again, Smaller and Bigger are on the panel.
  • AR on a phone: tap to place, drag one finger to move it, pinch two fingers to resize. Exit AR sits at the top.
  • The first session in VR and in AR opens a short intro that teaches these controls step by step; Controls on the panel opens it again.

Glossary

Solar mass (M☉)
The mass of our Sun, about 2 × 10³⁰ kg. Black holes and neutron stars are weighed in it.
Why it matters GW150914's black holes weighed 36 and 29 Suns, each packed inside a horizon about 200 km across.
Mass 1 and mass 2
The masses of the two bodies before they merge. In the chirp tab they are as the detector sees them, and the model ignores redshift. In the catalogue and the fit they are source-frame masses, as the bodies would weigh where they are; in the catalogue, mass 1 is the heavier.
Why it matters Heavier binaries merge sooner and at a lower frequency, so their chirp is shorter and deeper.
Distance
Luminosity distance to the source, in megaparsecs. 1 Mpc is about 3.26 million light-years, so GW150914's 410 Mpc (the 2016 paper) is about 1.3 billion light-years. The strain falls as 1/distance: twice as far, half the strain.
Why it matters In the chirp tab distance changes only how loud the signal is, never its shape.
Chirp mass
The mass combination 𝓜 = (m₁m₂)^(3/5) / (m₁ + m₂)^(1/5). It sets how fast the frequency sweeps up during the inspiral. For 36 + 29 M☉ it is 28.1 M☉.
Why it matters The signal pins it down far better than either mass: in the fit, pairs with nearly the same chirp mass fit almost equally well.
Total mass
Mass 1 plus mass 2. It sets where the inspiral ends and how high the merger frequency gets: the heavier the pair, the lower the pitch at the end. In the catalogue, the median of the sum is not exactly the sum of the two medians.
Final mass
The mass of the single black hole left after the merger. It is always less than mass 1 plus mass 2: GW150914 went from 36 + 29 to 62 M☉. The chirp tab works it out from the two masses with fits to simulations of non-spinning black holes.
Why it matters The gap between the two is the mass that left as gravitational waves.
Energy radiated
Mass turned into gravitational waves, by E = mc². GW150914 radiated about 3 M☉, most of it in its last few orbits.
Why it matters At its peak that was more power than all the stars in the visible universe give off as light.
Remnant spin
How fast the final black hole spins, as a share of the most a black hole of its mass can spin (0 to 1). GW150914's remnant spins at 0.67. Most of it comes from the orbit: the two holes' circling becomes the remnant's rotation.
Why it matters Mass and spin together set the ringdown's pitch.
Effective spin
The mass-weighted spin of the two bodies along the orbital axis, from −1 to +1. Positive means spinning with the orbit, negative against it; near 0 the spins are small or tilted into the orbital plane. GW150914 reads −0.04.
Why it matters Spins aligned with the orbit let the pair circle longer before merging; the chirp model and the fit's templates leave spin out.
Redshift
The expanding universe stretched the wave by a factor 1 + z on its way here. That lowers every frequency, so at the detector the binary looks (1 + z) times heavier than it is. GW150914 has z ≈ 0.1, so the fit stretches its template masses by 1.1.
Why it matters It is why the catalogue's source-frame masses and the chirp tab's detector masses do not compare one to one.
Time to merger
In the chirp tab, how long the signal takes from 20 Hz, where the detectors start to hear it, to its peak. In 3D, real seconds to the end of the plunge: negative before it, positive after. It scales as 𝓜^(−5/3): lighter binaries stay in band much longer.
Why it matters GW150914 lasts under a second from 20 Hz; two neutron stars take minutes.
Cycles from 20 Hz
How many full wave cycles the signal goes through from 20 Hz to the merger. Each cycle is half an orbit, since every orbit sends out two crests.
Why it matters Searches add the signal up cycle by cycle, so a faint signal with many cycles can still rise out of the noise.
Frequency
How many wave crests pass per second, in Hz. It is twice the orbital frequency and rises as the orbit shrinks. In the chirp plot it is the white line, read on the right-hand axis.
Heard frequency
Play chirp plays the signal at real speed, with every frequency ×4: two octaves up. "Heard at" is the pitch that comes out of the speaker. Loudness is scaled so the merger plays at full volume.
Why it matters The signal starts at 20 Hz, too low for a phone speaker to play.
Strain h
How much the wave stretches and squeezes space, as a fraction of length. The plot shows h₊, the plus polarisation at Earth, for a binary seen face-on. GW150914 peaks near 10⁻²¹.
Why it matters 10⁻²¹ of the distance from the Earth to the Sun is about one atom's width.
Ringdown
After the merger, the single misshapen black hole rings like a struck bell at one frequency, and the ringing dies away in a few milliseconds. The readout is that frequency, set by the remnant's mass and spin.
Why it matters GW150914's 62 M☉ remnant at spin 0.67 rings at about 272 Hz: that pitch alone gives away its mass and spin.
Phases
The 3D readout's stage. Inspiral: the orbit shrinks from 30 Hz. Merger: a plunge of about 4 ms. Ringdown: one black hole rings. Settled: one quiet black hole until the loop restarts. Merger and ringdown are approximate.
Separation
The distance between the two black holes' centres in km, from Kepler's law at the current frequency. Once they merge it reads as one black hole.
Why it matters Sizes are to scale with it: at 30 Hz GW150914's holes are about 1000 km apart, each about 100 km in radius.
Orbital speed
How fast the two black holes move relative to each other, as a share of light speed: v = (πGMf)^(1/3) / c. About 0.31 at 30 Hz, past half near the merger.
Playback
How many times slower than real the 3D view runs. The default speed stretches the inspiral from 30 Hz, a fraction of a second in reality, to about 16 s. Speed switches between Real and two slow motions, the second four times slower.
Display scaling
What is drawn bigger than life. In 3D, sizes, separation, wavelength and wave speed are to scale with each other, and only the wave height is drawn about 10²⁰ times larger. In the detector the arms move with the strain ×10²⁰, the light is drawn as a share of its peak, and time runs 40 times slower.
Why it matters Drawn to true scale, the waves and the arms would not move a single pixel.
Dark fringe
LIGO sets its output where the two returning laser beams meet out of step and cancel, so with no wave no light reaches the photodetector. A passing wave makes one arm longer and the other shorter, the beams stop cancelling, and light leaks out.
Why it matters On a dark output any light at all is the signal, instead of a tiny change on a bright background.
Arm change
How far each 4 km arm (3995 m) moves: hL/2, one arm longer and the other shorter. At GW150914's peak that is about 4.5 × 10⁻¹⁸ m, 1/370 of a proton's width. In VR and AR it is the arm change of the detector standing in the scene.
Why it matters No instrument had measured a length change this small before LIGO.
Light out
The share of the laser power that reaches the photodetector: P/P₀ = sin²(φ/2), where φ = 4πhL/λ is the beams' phase difference and λ = 1064 nm. Zero with no strain, growing as h². At GW150914's true peak it is of order 10⁻²¹ of the laser power.
Why it matters Growing as h² makes a bare Michelson nearly blind, so real LIGO holds its output a hair off dark.
Whitened data
The real strain each LIGO site recorded, with each frequency divided by its noise level, then filtered to 35–350 Hz. A quarter of a second, 1024 samples per second, around GW150914.
Why it matters Raw strain is swamped by low-frequency noise far larger than the signal; whitened, the chirp shows by eye.
σ of noise
The unit of the fit's vertical axis: one standard deviation of the whitened noise. 1 is a typical noise wiggle; GW150914 climbs to several σ near the merger.
Template
The predicted signal for one pair of masses: IMRPhenomD from PyCBC, non-spinning, one for each pair of whole source-frame masses from 24 to 44 M☉. Each is redshifted by 1 + z = 1.1 and whitened the same way as the data. The fit picks arrival time, amplitude and phase per detector; you pick the masses.
Match
How much of the data the template explains, over both detectors: √(explained power / data power), from 0 to 1.
Why it matters Noise is in the data, never in the template, so even the right masses stay below 1.
Residual
Data minus template, drawn under each detector. The readout is the share of the data's power left over, which equals 1 − match². Smaller is a better fit, but the noise keeps it above zero.
Livingston ahead
How many milliseconds earlier the fitted template sits in Livingston than in Hanford. The fit lets each detector's arrival time move within ±10 ms, about the light travel time between the two sites. GW150914 reached Livingston about 7 ms first.
Why it matters The gap and its sign narrow down where in the sky the wave came from.
GPS time
Seconds since midnight UTC on 6 January 1980, counted without leap seconds, so it now runs 18 s ahead of UTC. Detectors stamp their data with it. GW150914 arrived at 1126259462.4.
Type
Two black holes, a neutron star and a black hole, or two neutron stars. Read here from the masses: a body under 3 M☉ counts as a neutron star, a heavier one as a black hole. A rule of thumb, not the release's own label.
Signal-to-noise ratio
How loud the signal stood above the noise, across the detector network. Searches start to trust a signal around 8 to 10. GW150914 reads 26 in GWTC-2.1.
Why it matters The louder the signal, the tighter the ranges on its masses and distance.
False alarm rate
How often detector noise alone would make a signal at least this loud, per year. Smaller is more convincing.
Why it matters For GW150914 the 2016 paper put it at less than once in 200,000 years.
Probability it is real (p_astro)
The probability, from 0 to 1, that the signal came from space rather than from detector noise. Recent releases list an event as a detection above 0.5.
90% credible interval
Each value is a median with a small + and − after it. The analysis gives a 90% chance that the true value lies between median − minus and median + plus: 34.6 +4.4 −2.6 M☉ means 32.0 to 39.0 M☉.
Why it matters A single number hides how unsure the measurement is; many events' ranges overlap.
Release
The catalogue release the values come from, such as GWTC-2.1 or GWTC-3. Later releases re-analyse earlier events, so values shift: the chirp tab uses the 2016 paper (36 + 29 M☉ at 410 Mpc), the catalogue GWTC-2.1 (34.6 + 30.0 M☉ at 470 Mpc).
Strain axis (×10ⁿ)
The strain plots label their axis in a power of ten picked from the peak. Under h (×10⁻²¹), a tick at 1 means h = 10⁻²¹.
Post-Newtonian (2PN)
Newton's gravity plus Einstein's corrections in powers of v/c, here up to (v/c)⁴. The model uses it for the inspiral; merger and ringdown are a smooth bridge to the final black hole's ringing, not a numerical-relativity fit.
Stretched and squeezed
The two colours on the 3D sheet mark where the passing wave stretches space and where it squeezes it. Stretching one way comes with squeezing across it, and the two swap every half cycle.
Test ring
A ring of free particles standing across the wave's path, a layer in the 3D view. As the wave passes it turns into an ellipse one way, then the other.
Why it matters That stretch-and-squeeze is exactly what moves LIGO's mirrors.
Lensing
The black holes bend the light of the stars behind them, so the sky warps around them. Turn it on under Layers and look with the Against sky view.
Detector network (H1, L1, V1)
The detectors that saw an event: LIGO Hanford (H1) and LIGO Livingston (L1) in the United States, Virgo (V1) near Pisa, and KAGRA (K1) in Japan. A tour's Virgo stops show them as chips, Virgo highlighted.
Why it matters Arrival times at three or more sites place a source on the sky: Virgo shrank GW170814's patch from 1160 to 60 square degrees.

All help and questions

Gravitational-wave chirp

Two black holes spiral in and merge. Change their masses, hear the chirp, fit them to real LIGO data and browse every detected event.

Short stories through real events, four or five stops each.

Heard ×4 (two octaves up), at real speed

The first detection: 36 + 29 M☉ at 410 Mpc.
Peak strain at Earth
2.3 × 10-21
Chirp mass
28.1 M☉
From 20 Hz to merger
0.75 s
Cycles from 20 Hz
23
Ringdown
275 Hz
Final black hole
61.9 M☉

Display scaling. Plot: the real strain at Earth (h₊, binary seen face-on), drawn in units of 10⁻²¹. Audio: real speed, every frequency ×4 (two octaves up) so phone speakers can play it; loudness scaled so the merger is full volume.

Masses are as seen at the detector; the model ignores redshift. Inspiral: post-Newtonian to 2PN. Merger and ringdown: a smooth bridge to the final black hole's ringing, not a numerical-relativity fit.

Sources

Physics benchmarks

  • Time to coalescence scales as 𝓜^(−5/3) f^(−8/3): τ = (5/256)(G𝓜/c³)^(−5/3)(πf)^(−8/3) at leading order, and the generated waveform follows it within the post-Newtonian corrections.
  • Frequency rises by the 2PN post-Newtonian formula: df/dt = (96/5)π^(8/3)(G𝓜/c³)^(5/3) f^(11/3) [1 + corrections in v², v³ and v⁴].
  • With GW150914's parameters (36 + 29 M☉ at 410 Mpc), the strain h peaks at order 10⁻²¹ and falls as 1/distance.
  • A Michelson on the dark fringe gives P/P₀ = sin²(2πhL/λ): zero with no strain, rising as h². With the model's GW150914 strain each LIGO arm (3995 m) moves about 4.5 × 10⁻¹⁸ m at the peak, and the drawing exaggerates the strain by 10²⁰.
  • The catalogue reproduces GWTC-2.1 for GW150914: m₁ = 34.6 (+4.4 −2.6) M☉, m₂ = 30.0 (+2.9 −4.6) M☉, chirp mass 27.9 (+1.7 −1.5) M☉, distance 470 (+140 −160) Mpc; and for every event the chirp mass computed from the m₁ and m₂ medians falls inside its 90% credible interval (allowing for the published rounding).
  • Fitted to the real whitened Hanford and Livingston strain, the bank's best template gives a GW150914 chirp mass inside the GWTC-2.1 90% interval (27.9 +1.7 −1.5 M☉).
  • The model's phase agrees with PyCBC: at GW150914's masses its match with LALSuite's 2PN TaylorT4 is above 0.999 over the inspiral from 30 Hz, and with IMRPhenomD above 0.95 over the whole signal.
  • The 3D view uses one length scale and one time scale: at 30 Hz the wavelength is about 10 times the separation and v/c ≈ 0.31; the 62 M☉ remnant with spin 0.67 rings at ≈ 272 Hz with Q ≈ 3.17 (Berti, Cardoso and Will fit).

A release ships only when these checks pass.