Multi-Messenger Astronomy with GW170817

On 17 August 2017 the same event was heard and seen. For about a hundred seconds the LIGO and Virgo interferometers registered a rising "chirp" — the gravitational-wave signature of two neutron stars spiralling together — and 1.7 seconds after the waveform ended, gamma-ray satellites caught a short burst from the same patch of sky. Within half a day telescopes on six continents found a fading point of light in the galaxy NGC 4993, forty megaparsecs away. GW170817 is the founding event of multi-messenger astronomy: a single astrophysical catastrophe read simultaneously through the spin-2 metric perturbation of general relativity and across the electromagnetic spectrum. The physics packed into this one coincidence is extraordinary. The long, clean inspiral fixed the chirp mass to better than a percent, confirming two neutron-star-mass bodies. The near-simultaneous arrival of gravity and light over 130 million light-years bounded the speed of gravitational waves to fifteen decimal places, executing a wholesale cull of modified-gravity theories. The gravitational-wave amplitude served as a self-calibrating standard siren, delivering the Hubble constant with no cosmic distance ladder. The late-inspiral phase carried the fingerprint of tidal deformation, constraining the equation of state of matter denser than an atomic nucleus. And the kilonova AT 2017gfo, reddening from blue to infrared over days, caught r-process nucleosynthesis in the act — the cosmic forge of gold and platinum. One event, four fields: relativity, cosmology, nuclear physics, and the origin of the heavy elements.

Key takeaways

GW170817 was the first binary neutron star merger seen in gravitational waves — LIGO and Virgo, 17 August 2017 — a chirp lasting about 100 s and roughly 3000 cycles in the detector band.
About 1.74 s after the merger, Fermi-GBM and INTEGRAL detected the short gamma-ray burst GRB 170817A from the same sky region, and hours later the kilonova AT 2017gfo was localized to NGC 4993 at about 40 Mpc.
The long inspiral pins the chirp mass $\mathcal{M}\approx 1.188\,M_\odot$ , the single best-measured parameter, through the quadrupole-driven chirp rate.
Joint GW–gamma timing over 40 Mpc bounds the propagation speed of gravity, $|v_{\mathrm{gw}}/c-1|\lesssim 10^{-15}$ , killing broad classes of dark-energy and modified-gravity models.
As a standard siren the event gives $H_0\approx 70\;\mathrm{km\,s^{-1}\,Mpc^{-1}}$ , independent of the Cepheid/supernova distance ladder.
Tidal deformability from the late inspiral bounds the neutron-star equation of state ( $\tilde\Lambda\lesssim 800$ ), and the kilonova confirms mergers as an r-process site.
Key idea: A single inspiral–merger event radiates two distinct messengers — gravitational waves from the spin-2 metric perturbation and electromagnetic radiation from neutron-rich ejecta — whose joint detection cross-correlates the dynamical spacetime (mass, distance, tidal structure) with the emergent astrophysics (gamma-ray burst, kilonova, nucleosynthesis), each constraining what the other cannot.

The core insight

A single inspiral–merger event radiates two distinct messengers — gravitational waves carried by the spin-2 metric perturbation and electromagnetic radiation from shocked, neutron-rich ejecta — whose joint detection cross-correlates the dynamical spacetime (mass, distance, tidal structure) with the emergent astrophysics (gamma-ray burst, kilonova, nucleosynthesis), each constraining what the other cannot.

Where this lives today

GW170817 opened a program that is now routine and expanding. The LIGO–Virgo–KAGRA network, in its O4 run, issues public gravitational-wave alerts within minutes so that robotic telescopes, satellites, and neutrino observatories can chase counterparts in real time — the low-latency localization and early-warning pipelines are direct descendants of the 2017 follow-up. The standard-siren method is being scaled up: each well-localized merger with an identified host adds an independent $H_0$ estimate, and "dark siren" methods use galaxy catalogues when no unique host is found, aiming to arbitrate the tension between the local distance-ladder value ( $\sim 73$ ) and the CMB-inferred value ( $\sim 67$ ) with shared systematics of neither. Nuclear physicists fold each new tidal-deformability measurement into equation-of-state inference alongside NICER's X-ray radii. And the next generation — the Einstein Telescope and Cosmic Explorer on the ground, LISA in space — will reach neutron-star mergers to cosmological distances, while kilonova r-process yields are now written into galactic chemical-evolution models. The single event of 17 August 2017 has become an observing strategy.

The physical picture

Picture two neutron stars — each about one and a third solar masses packed into a ball the size of a city — whirling around each other. Their changing mass quadrupole radiates gravitational waves, and the energy carried off drains the orbit, so the separation shrinks and the orbital frequency climbs. The detectors record this as a signal of rising pitch and rising loudness: the chirp. Because neutron stars are so much lighter than the stellar-mass black holes of earlier detections, the binary crawls through the audio band for over a minute, sweeping some three thousand cycles from roughly 24 Hz up through the few hundred hertz where the detectors still had useful sensitivity; merger itself lies near 2 kHz, above the band that contributed appreciable signal-to-noise in O2 — an enormous number of wave crests over which the waveform's phase is measured, and with it the masses. The first figure shows the chirp itself and the one relation that reads the masses off it.

Figure

The chirp of GW170817: two neutron stars of chirp mass ℳ = 1.188 M⊙ sweep from about 24 Hz through the detector band in roughly 100 s and about 3000 cycles, both frequency and strain amplitude rising toward merger, with amplitude h ∝ ℳ^5/3 f^2/3 / d_L

When the stars finally touch, a fireball of neutron-rich matter is flung outward. Free neutrons rain onto seed nuclei in the rapid-neutron-capture (r-process), building the lanthanides, gold, and platinum; the decay of those fresh isotopes heats the expanding cloud, which glows as a kilonova — blue at first, reddening over days as lanthanide opacity takes over — while a relativistic jet punches out and makes the short gamma-ray burst. The second figure is the part that tests fundamental physics: two messengers, one racecourse. Gravity and light left NGC 4993 together, ran the same forty megaparsecs, and finished within a couple of seconds of each other after 130 million years — a photo finish that pins the speed of gravity to the speed of light.

Figure

Two messengers, one race over about 40 Mpc (roughly 1.3×10⁸ light-years): the gravitational wave and the gamma-ray flash cross the same path and arrive within Δt ≈ 1.74 s of each other after a travel time D/c ≈ 4×10¹⁵ s, forcing their fractional speed difference (v_gw − c)/c below about 10⁻¹⁵

The core equations

The whole of GW170817's inspiral physics flows from one master quantity: the chirp mass, the particular combination of the two component masses that governs the leading-order rate at which the orbit decays. It is the parameter the phase of the waveform measures most directly.

\mathcal{M} = \frac{(m_1 m_2)^{3/5}}{(m_1+m_2)^{1/5}} \approx 1.188\,M_\odot \qquad (1)

where: $\mathcal{M}$ — chirp mass, the mass combination that controls the inspiral rate; $m_1, m_2$ — the two neutron-star masses, each in roughly $1.17$ – $1.60\,M_\odot$ for GW170817; $M_\odot$ — solar mass, $1.989\times10^{30}\,\mathrm{kg}$ . Reading: for near-equal masses $\mathcal{M}\approx m\,2^{-1/5}$ , so $\mathcal{M}=1.188\,M_\odot$ implies each star $\approx 1.36\,M_\odot$ and total $\approx 2.74\,M_\odot$ — squarely neutron-star territory. Energy balance between the orbit's shrinking binding energy and the power carried off by gravitational waves turns $\mathcal{M}$ into a prediction for how fast the frequency sweeps upward. This chirp rate is the quadrupole formula wearing observational clothes.

\frac{\mathrm{d}f_{\mathrm{gw}}}{\mathrm{d}t} = \frac{96}{5}\,\pi^{8/3}\left(\frac{G\mathcal{M}}{c^3}\right)^{5/3} f_{\mathrm{gw}}^{11/3} \qquad (2)

where: $f_{\mathrm{gw}}$ — gravitational-wave frequency, twice the orbital frequency; $G$ — Newton's constant; $c$ — speed of light; $\mathrm{d}f_{\mathrm{gw}}/\mathrm{d}t$ — rate the frequency rises as the orbit decays. Reading: measuring $f$ and $\dot f$ anywhere on the chirp fixes $\mathcal{M}$ ; the steep $f^{11/3}$ makes the sweep accelerate violently, so the chirp ends in a fraction of a second after lingering for a minute and a half. The strain the detectors actually record ties the intrinsic source to its distance. General relativity fixes how loud a source of given chirp mass must be at a given luminosity distance — no external calibration — which is what makes a binary inspiral a standard siren.

h \sim \frac{1}{d_L}\,\frac{(G\mathcal{M})^{5/3}}{c^4}\,(\pi f_{\mathrm{gw}})^{2/3} \qquad (3)

where: $h$ — characteristic strain amplitude; $d_L$ — luminosity distance to the source; the omitted $O(1)$ factor depends on the inclination $\iota$ and detector orientation. Reading: $\mathcal{M}$ and $f$ come from the phase, so the measured amplitude yields $d_L$ directly — the one distance–inclination degeneracy is broken by the three-detector polarization content. With a self-calibrated distance in hand and a redshift from the host galaxy, the low-redshift Hubble law delivers the expansion rate — cosmology with no distance ladder.

H_0 = \frac{c\,z_{\mathrm{host}}}{d_L} \approx 70^{+12}_{-8}\;\mathrm{km\,s^{-1}\,Mpc^{-1}} \qquad (4)

where: $H_0$ — present-day Hubble constant; $z_{\mathrm{host}}$ — redshift of NGC 4993 after peculiar-velocity correction; $d_L$ — luminosity distance from the GW amplitude, $\approx 43.8\,\mathrm{Mpc}$ . Reading: the wide error bar is a single-siren result; a population of sirens shrinks it toward arbitrating the $H_0$ tension with independent systematics. Comparing when gravity and light arrive after crossing the same enormous baseline turns the coincidence into a precision test of the propagation speed of gravitational waves.

\left|\frac{v_{\mathrm{gw}}-c}{c}\right| \lesssim \frac{c\,\Delta t}{D} \sim 10^{-15} \qquad (5)

where: $v_{\mathrm{gw}}$ — propagation speed of gravitational waves; $\Delta t$ — allowed propagation-time difference (conservatively a few seconds); $D\approx 40\,\mathrm{Mpc}\approx 1.2\times10^{24}\,\mathrm{m}$ . Reading: the tiny bound comes from the vast denominator $D/c\approx 4\times10^{15}\,\mathrm{s}$ , not from any sub-second timing miracle — the baseline does the work. The very last cycles before merger carry the imprint of each star's finite size: tidal fields raise a quadrupole bulge that speeds the inspiral and advances the phase, encoded in the dimensionless tidal deformability.

\lambda_i = \frac{2}{3}\,k_2\,R_i^5,\qquad \Lambda_i = \frac{\lambda_i\,c^{10}}{(G m_i)^5} \qquad (6)

where: $\lambda_i$ — dimensional tidal deformability of star $i$ (induced quadrupole per unit tidal field); $k_2$ — second tidal Love number, an equation-of-state-dependent coefficient; $R_i$ — stellar radius; $\Lambda_i$ — dimensionless deformability entering the waveform phase. Reading: the steep $R^5$ makes $\Lambda$ a sensitive radius gauge, so the measured phase shift bounds neutron-star radii and the pressure–density relation of cold dense matter.

Derivation AChirp mass from the measured frequency evolution

The goal is to show that the leading-order inspiral chirp translates directly into the chirp mass — the single most precisely determined parameter of GW170817 — and to see why. We start from the quadrupole-driven chirp rate, in which all dependence on the individual masses has already collapsed into $\mathcal{M}$ , separate variables, and integrate forward to the formal coalescence time. The result is an explicit frequency-versus-time law whose shape is fixed entirely by $\mathcal{M}$ , so that fitting the ~3000-cycle sweep of GW170817 pins the chirp mass to under a percent while the individual masses remain far more uncertain.

Step 1. Begin from energy balance. The Newtonian binding energy of a circular orbit of separation $r$ is $E=-Gm_1m_2/2r$ , and the quadrupole luminosity of that orbit is $L_{\mathrm{gw}}=\tfrac{32}{5}(G/c^5)\mu^2 r^4\Omega^6$ with reduced mass $\mu$ and $\Omega^2=G(m_1+m_2)/r^3$ from Kepler. Setting $\mathrm{d}E/\mathrm{d}t=-L_{\mathrm{gw}}$ and trading $r$ for $f_{\mathrm{gw}}=\Omega/\pi$ collapses every mass factor into $\mathcal{M}$ , giving the chirp ODE $\dot f = \tfrac{96}{5}\pi^{8/3}(G\mathcal{M}/c^3)^{5/3} f^{11/3}$ . Why: this is the crucial simplification — the two masses enter the leading inspiral only through the single combination $\mathcal{M}$ , so that is what the phase measures.

Step 2. Separate variables. Writing $f^{-11/3}\,\mathrm{d}f = \tfrac{96}{5}\pi^{8/3}(G\mathcal{M}/c^3)^{5/3}\,\mathrm{d}t$ isolates all frequency dependence on the left and the constants on the right. The antiderivative of $f^{-11/3}$ is $-\tfrac{3}{8}f^{-8/3}$ . Why: the power-law ODE is exactly integrable at leading post-Newtonian order, so the whole chirp is one closed-form curve rather than a numerical solution.

Step 3. Integrate to coalescence. Carrying out both integrals from time $t$ (frequency $f$ ) to the formal coalescence time $t_c$ (where $f\to\infty$ for point particles) gives $f^{-8/3}(t)=\tfrac{256}{5}\pi^{8/3}(G\mathcal{M}/c^3)^{5/3}(t_c-t)$ . Why: $t_c$ is just the integration constant; only the time remaining to merger, $t_c-t$ , appears, which is what makes the law universal in shape.

Step 4. Solve for frequency. Inverting gives the boxed chirp law

f_{\mathrm{gw}}(t)=\frac{1}{\pi}\left(\frac{5}{256}\,\frac{1}{t_c-t}\right)^{3/8}\left(\frac{G\mathcal{M}}{c^3}\right)^{-5/8}.

Measuring $f(t)$ and its slope over the chirp fixes $\mathcal{M}$ ; for GW170817 the fit yields $\mathcal{M}\approx 1.188\,M_\odot$ . Why: the entire curve pivots on one number, so thousands of cycles of data over-determine $\mathcal{M}$ while leaving the mass ratio (a higher-order effect) loose. *The $96/5$ coefficient and $-3/8$ exponent are standard leading-order post-Newtonian results, and integrating from $f=24\,\mathrm{Hz}$ with $\mathcal{M}=1.188\,M_\odot$ gives $t_c-t\approx 101\,\mathrm{s}$ , matching the observed in-band duration.*

Go deeper · Derivation B · 2 minSpeed of gravity from joint gravitational-wave and gamma-ray timing

Derivation BSpeed of gravity from joint gravitational-wave and gamma-ray timing

The goal is to convert the ~1.7 s gamma-ray delay into a bound on the fractional difference between the propagation speeds of gravitational waves and light, and to be explicit about where the astonishing precision comes from. Two signals leave the source separated by an unknown intrinsic astrophysical delay and then travel the same distance at possibly different speeds; the observed lag mixes both effects. We write the arrival-time relation, linearize the propagation term, bracket the intrinsic delay from jet physics, and divide by the vast travel time — showing that it is the 40-megaparsec baseline, not the small delay, that delivers the $10^{-15}$ bound.

Step 1. Write the arrival-time relation. If the gamma rays are emitted an intrinsic time $\delta t_{\mathrm{int}}$ after the GW merger and both signals cross distance $D$ , the observed lag is $\Delta t_{\mathrm{obs}}=\delta t_{\mathrm{int}}+D(1/v_{\mathrm{gw}}-1/c)$ , with $\Delta t_{\mathrm{obs}}\approx 1.74\,\mathrm{s}$ . Why: the measured lag is not purely a propagation effect — it contains an emission offset we do not independently know, and honesty about that is the whole subtlety.

Step 2. Linearize the propagation term. For $|v_{\mathrm{gw}}-c|\ll c$ , $D(1/v_{\mathrm{gw}}-1/c)\approx -(D/c)(\Delta v/c)$ with $\Delta v\equiv v_{\mathrm{gw}}-c$ and $D/c\approx 4\times10^{15}\,\mathrm{s}$ . Why: this exposes the enormous lever arm $D/c$ that multiplies the fractional speed difference — a tiny $\Delta v/c$ produces a measurable time shift only because $D/c$ is so large.

Step 3. Bracket the intrinsic delay. Jet-launch physics motivates $0\le\delta t_{\mathrm{int}}\le 10\,\mathrm{s}$ : the central engine plausibly needs up to several seconds to launch and break the jet out, and it is very unlikely the gamma rays preceded the merger. Why: we cannot measure $\delta t_{\mathrm{int}}$ , so we replace it with a defensible physical range and propagate that ignorance into the bound.

Step 4. Solve for the speed difference. Rearranging, $\Delta v/c=-(c/D)(\Delta t_{\mathrm{obs}}-\delta t_{\mathrm{int}})$ , and pushing the assumed range of $\delta t_{\mathrm{int}}$ through the prefactor $c/D\approx 2.4\times10^{-16}\,\mathrm{s^{-1}}$ gives the boxed interval

-3\times10^{-15}\;\le\;\frac{v_{\mathrm{gw}}-c}{c}\;\le\;+7\times10^{-16},

i.e. $|\Delta v/c|\lesssim 10^{-15}$ . Why: even a generous ten-second uncertainty in emission, divided by four thousand trillion seconds of travel, still forces gravity and light to agree to fifteen decimal places. *The 90% limits $-3\times10^{-15}$ and $+7\times10^{-16}$ follow from $\Delta t_{\mathrm{obs}}=1.74\,\mathrm{s}$ , $D/c=4.1\times10^{15}\,\mathrm{s}$ , and the 10 s emission bracket.*

Go deeper · Derivation C · 2 minThe standard siren — luminosity distance from strain, and the Hubble constant

Derivation CThe standard siren — luminosity distance from strain, and the Hubble constant

The goal is to explain why a gravitational-wave inspiral is a self-calibrating distance indicator and how that yields the Hubble constant with no rung of the cosmic distance ladder. The core is that general relativity fixes the strain amplitude in terms of the intrinsic parameters and the luminosity distance alone; because those parameters are read from the phase, the amplitude is a direct distance readout. We isolate the amplitude scaling, note what the phase supplies, resolve the degeneracy that limits the method, and close with the Hubble law applied to NGC 4993.

Step 1. Isolate the amplitude scaling. The measured strain obeys $h\propto (G\mathcal{M})^{5/3}(\pi f)^{2/3}/(c^4 d_L)$ , so once $\mathcal{M}$ and $f$ are known the amplitude depends on distance and geometry only. Why: unlike a supernova, whose intrinsic brightness must be calibrated against nearer standard candles, the inspiral's intrinsic loudness is fixed by general relativity itself.

Step 2. Use what the phase gives for free. The chirp mass $\mathcal{M}$ and instantaneous frequency $f$ come from the phase evolution (previous derivation), which is measured over thousands of cycles and is essentially independent of the amplitude. Why: separating "how loud it should be" (phase-determined) from "how loud it looks" (measured amplitude) is exactly what converts a strain into a distance.

Step 3. Resolve the inclination degeneracy. The amplitude also depends on the orbital inclination $\iota$ through a factor like $(1+\cos^2\iota)/2$ for the plus polarization, so a single detector confuses a near-face-on distant source with an edge-on nearer one; the relative amplitudes and phases across the three-detector network (plus the electromagnetic identification of the host) break the degeneracy. Why: this is the practical limit on siren distances, and it is why a three-site network and an EM counterpart matter so much for GW170817.

Step 4. Apply the Hubble law. With $d_L\approx 43.8\,\mathrm{Mpc}$ from the strain and the host recession velocity $c\,z_{\mathrm{host}}\approx 3000\,\mathrm{km\,s^{-1}}$ (NGC 4993, peculiar-velocity corrected), the low-redshift law gives

H_0=\frac{c\,z_{\mathrm{host}}}{d_L}\approx 70^{+12}_{-8}\;\mathrm{km\,s^{-1}\,Mpc^{-1}}.

Why: no Cepheids, no Type Ia supernovae, no ladder — a single geometric distance plus a redshift measures the expansion rate, with independent systematics from every other method. *Using $d_L=43.8\,\mathrm{Mpc}$ and $c\,z\approx 3017\,\mathrm{km\,s^{-1}}$ gives $H_0\approx 69\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ , inside the quoted $70^{+12}_{-8}$ .*

Limiting cases

GW170817 stresses several distinct physical regimes at once; the key extracted quantities and their limiting interpretations follow.

Case	Result	Meaning
Newtonian / leading-PN inspiral	$f_{\mathrm{gw}}\propto \mathcal{M}^{-5/8}(t_c-t)^{-3/8}$	The early chirp is quadrupole-driven; the chirp mass $\mathcal{M}\approx 1.188\,M_\odot$ is the best-measured parameter, fixed by the phase.
Tidal (finite-size) regime	$\Psi_{\mathrm{tidal}}\sim \tilde\Lambda\,(\pi f)^{5/3}$	Near merger, finite-size deformation advances the phase at 5PN order; $\tilde\Lambda\lesssim 800$ (90% credible) disfavours the stiffest equations of state.
Propagation / speed-of-gravity limit	$\left\|c_{\mathrm{gw}}/c-1\right\|\lesssim 10^{-15}$	Long-baseline GW–gamma timing bounds Lorentz violation and anomalous GW dispersion to extraordinary precision.
Cosmological / standard-siren limit	$H_0=cz/d_L\big\|_{z\to 0}\approx 70\;\mathrm{km\,s^{-1}\,Mpc^{-1}}$	At low redshift the Hubble law connects the GW luminosity distance to the host redshift, giving a ladder-free $H_0$ .
Equal-mass point-particle limit	$\mathcal{M}\to m\,2^{-1/5}$ , mass ratio unmeasured	The leading chirp fixes $\mathcal{M}$ tightly but leaves $m_1/m_2$ loose; splitting the masses needs higher-order phase terms.

Common trapthe 1.7-second lag is not a stopwatch on the speed of gravity

The tempting misread is that gamma rays arriving 1.74 s after the merger directly measures how much slower gravity travels than light. It does not. That lag is dominated by unknown astrophysical emission delays — the time for the central engine to launch a relativistic jet and for the jet to break out of the surrounding ejecta — which are of order seconds all by themselves. The stringent $10^{-15}$ bound does not come from the smallness of 1.74 s; it comes from dividing a conservatively bracketed emission delay by the colossal travel time $D/c\approx 4\times10^{15}\,\mathrm{s}$ over 40 Mpc. It is the length of the racecourse, not the closeness of the finish, that does the work. Quote the delay as evidence of coincidence; quote the baseline as the source of precision.

Worked examples

1 · Why the chirp lasted about 100 seconds (fully worked)

GW170817 entered the LIGO band near $f_{\mathrm{gw}}=24\,\mathrm{Hz}$ with chirp mass $\mathcal{M}=1.188\,M_\odot$ . Estimate how long the inspiral spent in band before merger, and compare with a heavy binary-black-hole chirp.

Step 1. Invert the chirp law for the time to coalescence. From Derivation 1, $t_c-t=\tfrac{5}{256}\,(G\mathcal{M}/c^3)^{-5/3}\,(\pi f_{\mathrm{gw}})^{-8/3}$ . Use $G M_\odot/c^3=4.925\times10^{-6}\,\mathrm{s}$ , so $G\mathcal{M}/c^3=1.188\times 4.925\times10^{-6}=\mathbf{5.85\times10^{-6}\,\mathrm{s}}$ .

Step 2. Evaluate the two factors. $(G\mathcal{M}/c^3)^{-5/3}=(5.85\times10^{-6})^{-5/3}=5.3\times10^{8}$ , and with $\pi f=\pi(24)=75.4$ , $(\pi f)^{-8/3}=9.85\times10^{-6}$ .

Step 3. Multiply. $t_c-t=\tfrac{5}{256}\times(5.3\times10^{8})\times(9.85\times10^{-6})=0.01953\times 5.2\times10^{3}=\mathbf{101\,s}$ . This matches the observed ~100 s in-band duration, over which the phase accumulates roughly 3000 gravitational-wave cycles.

Step 4. Compare with a heavy black-hole binary. Because $t_c-t\propto \mathcal{M}^{-5/3}$ , a GW150914-like binary with $\mathcal{M}\approx 30\,M_\odot$ inspirals faster by a factor $(30/1.188)^{5/3}\approx 200$ , spending well under a second in band. The light neutron stars are what make the waveform long, clean, and precisely measurable — 100 s versus a fraction of a second.

2 · The speed-of-gravity bound (fully worked)

Take the observed lag $\Delta t\approx 1.74\,\mathrm{s}$ and source distance $D\approx 40\,\mathrm{Mpc}$ . Estimate the fractional bound on the GW speed.

Step 1. Travel time over the baseline. With $1\,\mathrm{Mpc}=3.086\times10^{22}\,\mathrm{m}$ , $D=40\times3.086\times10^{22}=1.23\times10^{24}\,\mathrm{m}$ , so $D/c=1.23\times10^{24}/2.998\times10^{8}=\mathbf{4.1\times10^{15}\,\mathrm{s}}$ (about 130 million years).

Step 2. Divide the lag by the travel time. Taking $\Delta t\approx 1.74\,\mathrm{s}$ as an order-of-magnitude cap on any propagation difference, $\Delta v/c\sim \Delta t/(D/c)=1.74/4.1\times10^{15}=\mathbf{4.2\times10^{-16}}$ .

Step 3. Bracket the emission delay. Allowing the gamma rays to be emitted up to 10 s after the merger, $\Delta v/c=-(c/D)(\Delta t-\delta t_{\mathrm{int}})$ ranges over roughly $[-3\times10^{-15},+7\times10^{-16}]$ , i.e. $|v_{\mathrm{gw}}/c-1|\lesssim 10^{-15}$ . This single measurement excludes broad classes of modified-gravity theories (many Horndeski and dark-energy models) that predicted $c_{\mathrm{gw}}\ne c$ .

3 · The standard-siren Hubble constant (worked)

Given the GW luminosity distance $d_L\approx 43.8\,\mathrm{Mpc}$ and the peculiar-velocity-corrected recession velocity $c\,z_{\mathrm{host}}\approx 3017\,\mathrm{km\,s^{-1}}$ for NGC 4993, estimate $H_0$ .

Step 1. Apply the low-redshift Hubble law, $H_0=cz_{\mathrm{host}}/d_L$ , valid because $z\approx 0.01\ll 1$ so higher-order cosmological corrections are negligible.

Step 2. Plug in: $H_0=3017\,\mathrm{km\,s^{-1}}/43.8\,\mathrm{Mpc}=\mathbf{69\;km\,s^{-1}\,Mpc^{-1}}$ , consistent with the published $70^{+12}_{-8}$ . No Cepheids or supernovae entered — the distance came straight from the strain, so the systematics are independent of the traditional ladder. The broad error bar is set by the inclination degeneracy and the host's peculiar velocity, both shrinking with a larger siren population.

Physics of the portrait

The idea that a gravitational-wave chirp could be a self-calibrating cosmic distance marker — the conceptual seed of GW170817's standard-siren cosmology — was sown by one theorist a full three decades before the event.

Origins · 1 minBernard Schutz and how this was discovered

Bernard Schutz

b. 1946 · gravitational-wave astronomy and the standard-siren method

Bernard F. Schutz is an American-British physicist whose reach spans both the pedagogy and the practice of gravitational-wave science. His textbook A First Course in General Relativity (1985) taught the linearized-radiation and quadrupole machinery on which this article rests to a generation of students. But his signature contribution to GW170817 is older and sharper: in a 1986 Nature paper he showed that a compact-binary inspiral is a standard siren — because general relativity fixes the strain amplitude in terms of the chirp mass and luminosity distance, the distance can be read directly off the waveform, and combined with a host-galaxy redshift it measures the Hubble constant with no cosmic distance ladder. That single insight is exactly what the LIGO/Virgo/EM collaborations executed in 2017. As founding director of the Albert Einstein Institute in Potsdam and a leader of the GEO600 and LIGO data efforts, Schutz also helped build the pipelines that turned his proposal into a measured number — the bridge from the field equations to the standard siren.

History

1916

— Einstein derives gravitational waves from the linearized field equations

1963

— Freeman Dyson and others note that neutron-star binaries could be detectable GW sources

1986

— Schutz shows a compact-binary "standard siren" can measure the Hubble constant

2015

— LIGO makes the first direct detection, GW150914, from a binary black hole

2017

— GW170817: first binary neutron star merger, seen jointly in gravitational waves, gamma rays, and light

Going further

Texts. Misner, Thorne and Wheeler, Gravitation, ch. 36 (generation of gravitational waves) · Wald, General Relativity, §4.4 (linearized radiation) · Schutz, A First Course in General Relativity, ch. 9 · Carroll, Spacetime and Geometry, ch. 7 · Hartle, Gravity, ch. 16 · Maggiore, Gravitational Waves Vol. 1, ch. 4 (inspiral and chirp).

Primary sources. Abbott et al. (LIGO/Virgo), "GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral", Phys. Rev. Lett. 119, 161101 (2017) · "Multi-messenger Observations of a Binary Neutron Star Merger", Astrophys. J. Lett. 848, L12 (2017) · "Gravitational Waves and Gamma-Rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A", Astrophys. J. Lett. 848, L13 (2017) · "A gravitational-wave standard siren measurement of the Hubble constant", Nature 551, 85 (2017) · Schutz, "Determining the Hubble constant from gravitational wave observations", Nature 323, 310 (1986). All numbers are standard published values for GW170817: chirp mass $\mathcal{M}\approx 1.188\,M_\odot$ , luminosity distance $\approx 43.8\,\mathrm{Mpc}$ (host NGC 4993 at $\approx 40\,\mathrm{Mpc}$ ), GW–gamma lag $\approx 1.74\,\mathrm{s}$ , $H_0\approx 70^{+12}_{-8}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ , $\tilde\Lambda\lesssim 800$ , and $E_{\mathrm{rad}}\gtrsim 0.025\,M_\odot c^2$ . Key checks: the chirp-rate coefficient $96/5$ and the $f^{11/3}$ scaling follow from the quadrupole formula; integrating from $f=24\,\mathrm{Hz}$ with $\mathcal{M}=1.188\,M_\odot$ gives $\sim 101\,\mathrm{s}$ in-band time; the travel time $D/c\approx 4\times10^{15}\,\mathrm{s}$ for 40 Mpc yields the speed bound $|\Delta v/c|\lesssim 10^{-15}$ .

Prerequisites. Quadrupole Formula · Gravitational Wave Equation · Plus and Cross Polarizations · Transverse-Traceless Gauge. Leads to. Isaacson Stress-Energy of Gravitational Waves · Multipole Expansion of Gravitational Radiation.

Ask the tutor: Ask me to walk through any single thread — the chirp-mass fit, the speed-of-gravity bound, the standard-siren $H_0$ , or the tidal-deformability constraint — and we will rebuild the numbers of GW170817 from the equations up.

Why did the GW170817 chirp last about 100 seconds when a black-hole chirp of comparable era lasts a fraction of a second?

The in-band inspiral time scales steeply with chirp mass: $t_c-t\propto\mathcal{M}^{-5/3}f^{-8/3}$ . Neutron stars have $\mathcal{M}\approx 1.2\,M_\odot$ , far smaller than the roughly $30\,M_\odot$ chirp mass of GW150914's black holes, so the binary inspirals through the audio band about two hundred times more slowly — roughly 100 s and some 3000 cycles rather than a fraction of a second. More cycles means the phase is sampled far more finely, which is exactly why the neutron-star chirp mass is measured to better than a percent: the long, clean chirp is a gift for precision.

Does the 1.7-second gamma-ray lag mean gravity is slightly slower than light?

No. The lag is dominated by astrophysical emission delays — the central engine needs time to launch a relativistic jet and for it to break out through the merger ejecta, and those processes take of order seconds by themselves. The speed-of-gravity bound does not come from the lag being small; it comes from dividing a conservatively bracketed emission delay by the enormous travel time $D/c\approx 4\times10^{15}\,\mathrm{s}$ over 40 Mpc. That gives $|v_{\mathrm{gw}}/c-1|\lesssim 10^{-15}$ . The long baseline, not the short delay, is what makes the constraint one of the tightest in all of physics.

How can a single event measure the Hubble constant with no cosmic distance ladder?

The gravitational-wave strain amplitude scales as $\mathcal{M}^{5/3}f^{2/3}/d_L$ , and both $\mathcal{M}$ and $f$ are read directly from the chirp phase. General relativity therefore fixes the luminosity distance $d_L$ from the measured amplitude with no external calibration — the source is a "standard siren." Identifying the host NGC 4993 supplies the redshift, and the Hubble law $H_0=cz/d_L$ yields the expansion rate. Because no Cepheids or Type Ia supernovae enter, the systematics are independent of the traditional ladder — which is what makes sirens so valuable for the $H_0$ tension.

What is a kilonova, and why does it redden from blue to infrared over days?

A kilonova is the thermal glow of neutron-rich material ejected in the merger, powered by the radioactive decay of freshly synthesized r-process nuclei rather than by nickel-56 as in a supernova. Early on, lighter r-process elements dominate and the ejecta is relatively transparent, giving a blue transient. Within a day or two the lanthanides — with their enormous line opacity — take over, trapping the light and shifting the emission to the red and near-infrared. Watching AT 2017gfo fade from blue to infrared over about a week was direct evidence that both light and heavy r-process components were produced, confirming mergers as a forge of gold, platinum, and the lanthanides.

How does the inspiral waveform constrain the neutron-star equation of state?

Each star's gravity raises a tidal bulge on its companion; the induced mass quadrupole is characterized by the tidal deformability $\Lambda\propto k_2(Rc^2/Gm)^5$ . That bulge advances the gravitational-wave phase, formally a 5PN effect that only matters in the last cycles. Because $\Lambda$ depends on the fifth power of the radius, measuring the phase shift is a sensitive probe of compactness. For GW170817 the bound $\tilde\Lambda\lesssim 800$ disfavours the stiffest equations of state and implies neutron-star radii of order 11–13 km, constraining the pressure of matter above nuclear saturation density.

Why did GW170817 eliminate so many modified-gravity and dark-energy theories?

Many alternatives to general relativity — large parts of the Horndeski and beyond-Horndeski families invoked to explain cosmic acceleration — predict that gravitational waves propagate at a speed different from light, often by amounts far larger than $10^{-15}$ . The joint GW–gamma timing showed $c_{\mathrm{gw}}=c$ to fifteen decimal places, which is fatal to any theory whose extra gravitational degrees of freedom shift the tensor-wave speed. Whole swaths of parameter space that had been viable dark-energy models the day before the announcement were excluded the day after — one astrophysical coincidence acting as a precision laboratory for fundamental theory.

Was GW170817 seen by all three detectors, and why did that matter?

Yes — the two LIGO interferometers (Hanford and Livingston) and Virgo near Pisa were all operating. Virgo's response was in fact nearly a null, and that near-non-detection was crucial: combined with the arrival-time differences across the three sites, it triangulated the source to about 28 square degrees, small enough for telescopes to tile and search. A single detector cannot localize a source on the sky or cleanly separate distance from inclination. The three-site network supplied both the localization that enabled the electromagnetic follow-up and the polarization information that tightened the luminosity distance — the twin ingredients behind the multi-messenger and standard-siren results.