--- title: Multimessenger Astronomy and Gamma-Ray Bursts draft: false module: Binaries and Gravitational Waves moduleNumber: 9 lessonNumber: 4 order: 904 summary: > Gamma-ray bursts split into two populations: long bursts from the collapse of massive stars and short bursts from merging compact objects. The compactness problem forces the emitting plasma to move at ultra-relativistic speed, beaming the radiation into a narrow jet. The neutron-star merger GW170817 tied a gravitational chirp to a short gamma-ray burst, a radioactive kilonova, and a broadband afterglow, confirming that mergers forge r-process elements. A merger with a measured redshift is a standard siren that reads the Hubble constant from gravitational data alone. topics: [Binaries and Gravitational Waves] sources: - book: Carroll & Ostlie ref: "Ch. 15 §15.4 — Gamma-Ray Bursts" - book: Maoz ref: "Ch. 4 — Stellar Death and Remnants" --- The detection of gravitational waves from merging compact objects opened a channel that carries information no photon can. When a source is seen in gravitational waves and in light, the two messengers jointly determine its distance, its physics, and its chemistry in ways neither could alone. The archetype is the neutron-star merger GW170817, observed across gravitational waves, gamma rays, and the full electromagnetic spectrum. This lesson develops the two classes of gamma-ray burst and their progenitors, the relativistic beaming that the burst energetics demand, the multimessenger anatomy of GW170817 with its kilonova and r-process yield, and the standard-siren measurement of the Hubble constant. ## The two populations of gamma-ray bursts Gamma-ray bursts are brief, intense flashes of gamma rays from cosmological distances, the most luminous electromagnetic events in the universe. Their durations, quantified by $T_{90}$ (the time to accumulate the central ninety percent of the fluence), are bimodal, splitting the population in two at about two seconds. > **Definition (Long and short gamma-ray bursts).** The duration distribution is > bimodal: > - **Long bursts** ($T_{90} \gtrsim 2\ \mathrm{s}$) have softer spectra and occur in > star-forming galaxies. Their progenitors are the core collapse of rapidly > rotating massive stars, the **collapsar** model, and some are accompanied by a > Type Ic supernova. > - **Short bursts** ($T_{90} \lesssim 2\ \mathrm{s}$) have harder spectra and occur > in all galaxy types, including old ellipticals with no recent star formation. > Their progenitors are the mergers of two neutron stars or a neutron star and a > black hole. $$ % caption: The bimodal duration distribution of gamma-ray bursts: a short-hard % population from compact-object mergers below about two seconds and a long-soft % population from massive-star collapse above it. \begin{tikzpicture}[scale=1.0, font=\footnotesize] \definecolor{acc}{HTML}{4A6FA5} \draw[->, black] (0.6,0.6) -- (8.4,0.6) node[right, black!70] {log duration T90}; \draw[->, black] (0.6,0.6) -- (0.6,4.0) node[above, black!70] {number}; % short-burst peak (left) \draw[very thick] (1.0,0.7) .. controls (1.6,2.6) and (2.2,2.6) .. (2.8,0.8); \node[anchor=south] at (1.9,2.5) {short}; % long-burst peak (right, taller) \draw[black, very thick] (4.2,0.7) .. controls (5.2,3.4) and (6.4,3.4) .. (7.4,0.75); \node[black, anchor=south] at (5.8,3.3) {long}; % divide near 2 s \draw[black, densely dotted] (3.5,0.6) -- (3.5,3.4); \node[black, anchor=north] at (3.5,0.55) {two seconds}; \end{tikzpicture} $$ ## The compactness problem and relativistic beaming A gamma-ray burst releases up to $10^{44}$–$10^{47}\ \mathrm{J}$ in gamma rays over seconds, and its rapid variability, on timescales as short as milliseconds, implies a source region no larger than $c\,\delta t \sim 10^{5}\ \mathrm{m}$. Packing that energy of gamma rays into that volume makes the source optically thick to pair production: two gamma-ray photons above the pair threshold produce an electron-positron pair, so the gamma rays cannot escape. Yet a non-thermal gamma-ray spectrum is observed, proving the source is transparent. This is the **compactness problem**. The resolution is bulk relativistic motion. If the emitting plasma moves toward the observer with a large Lorentz factor $\Gamma$, two relativistic effects rescue transparency. The observed photon energies are blueshifted, so in the plasma frame most photons lie below the pair-production threshold; and the causality argument on the source size relaxes, because a shell moving at $\Gamma$ can have a physical radius larger by $\Gamma^2$ than $c\,\delta t$ suggests. Requiring the source to be optically thin forces $$ \Gamma \gtrsim 100. $$ Such a flow is collimated into a narrow jet. Relativistic beaming concentrates the radiation of a source moving at Lorentz factor $\Gamma$ into a forward cone of half-angle $\theta \sim 1/\Gamma$, so an observer sees the burst only if the jet points within that angle. The true rate of bursts exceeds the observed rate by the beaming factor, and the true energy is smaller than the isotropic-equivalent energy by the same factor. $$ % caption: A relativistic jet from a compact merger: bulk motion at Lorentz factor % above one hundred beams the prompt gamma rays into a cone of half-angle one over % Gamma, and the decelerating jet drives the broadband afterglow. \begin{tikzpicture}[scale=1.0, font=\footnotesize] \definecolor{acc}{HTML}{4A6FA5} % central engine \fill[black!70] (1.2,2.2) circle (2.4pt); \node[black, anchor=east] at (1.0,2.2) {engine}; % jet cone \fill[acc!12] (1.2,2.2) -- (6.4,3.3) -- (6.4,1.1) -- cycle; \draw[acc, very thick] (1.2,2.2) -- (6.4,3.3); \draw[acc, very thick] (1.2,2.2) -- (6.4,1.1); \node[acc, anchor=west] at (5.0,2.2) {prompt jet}; % opening angle marker \draw[black, ->] (2.6,2.2) -- (2.6,2.55); \node[black, anchor=west] at (2.65,2.45) {half-angle 1 over Gamma}; % afterglow shell arc \draw[black, densely dashed] (6.7,1.0) arc (-20:20:1.3); \node[black, anchor=west] at (6.9,2.2) {afterglow}; \end{tikzpicture} $$ In the **fireball model** the central engine, a newly formed black hole or magnetar with a hot accretion torus, launches a relativistic outflow. Internal shocks within the variable outflow produce the prompt gamma rays; the external shock, where the jet plows into the surrounding medium and decelerates, produces the longer-lived **afterglow** that fades across X-ray, optical, and radio bands over hours to weeks. ## GW170817: a multimessenger merger On 17 August 2017 the LIGO and Virgo detectors recorded a gravitational-wave chirp lasting about a minute in the sensitive band, with a chirp mass near $1.19\,M_\odot$ and component masses consistent with two neutron stars. The lower masses and the longer, higher-frequency signal distinguished it immediately from the black-hole mergers: neutron stars are lighter and less compact, so their inspiral chirps to higher frequency before merger. This was the first gravitational-wave detection of a binary neutron-star merger. $$ % caption: The GW170817 multimessenger timeline: the gravitational-wave chirp, a % short gamma-ray burst about two seconds later, and the optical and infrared % kilonova hours afterward, followed by the fading broadband afterglow. \begin{tikzpicture}[scale=1.0, font=\footnotesize] \definecolor{acc}{HTML}{4A6FA5} \draw[->, black] (0.5,2.2) -- (8.6,2.2) node[right, black!70] {time (log)}; % events on the timeline \fill[acc] (1.0,2.2) circle (2.2pt); \node[acc, anchor=south] at (1.0,2.45) {GW chirp}; \node[black, anchor=north] at (1.0,1.95) {merger}; \fill[black!70] (3.1,2.2) circle (2pt); \node[black, anchor=south] at (3.1,2.45) {gamma burst}; \node[black, anchor=north] at (3.1,1.95) {plus 1.7 s}; \fill[black!70] (5.3,2.2) circle (2pt); \node[black, anchor=south] at (5.3,2.45) {kilonova}; \node[black, anchor=north] at (5.3,1.95) {hours}; \fill[black!70] (7.3,2.2) circle (2pt); \node[black, anchor=south] at (7.3,2.45) {afterglow}; \node[black, anchor=north] at (7.3,1.95) {days to weeks}; \end{tikzpicture} $$ The sequence of counterparts confirmed the merger picture. - **The short gamma-ray burst.** About $1.7\ \mathrm{s}$ after merger, the Fermi and INTEGRAL satellites recorded a short gamma-ray burst, GRB 170817A, from the same sky region. The near-coincidence directly links short bursts to neutron-star mergers and bounds the speed of gravitational waves to equal the speed of light to about one part in $10^{15}$. - **The kilonova.** Over the following hours to days, an optical and infrared transient, AT2017gfo, appeared in the galaxy NGC 4993 at $40\ \mathrm{Mpc}$. Its luminosity, near $10^{41}\ \mathrm{W}$ at peak, and its rapid reddening matched a **kilonova**: thermal emission powered by the radioactive decay of freshly synthesized heavy nuclei. - **The afterglow.** X-ray and radio emission rose over weeks, the external-shock afterglow of a jet viewed off-axis. ## The r-process in merger ejecta A neutron-star merger ejects a few percent of a solar mass of extremely neutron-rich material, both tidally stripped debris and matter blown from the hot remnant. In this environment the neutron flux is so high that seed nuclei capture neutrons far faster than they can beta-decay, driving matter up to the heaviest elements along a path far from the valley of stability. This is the **rapid neutron-capture** (r-)process, one of the two channels that build elements beyond iron, developed in the [nucleosynthesis lesson](/astrophysics-cosmology/nuclear-astrophysics/advanced-burning-and-neutron-capture-nucleosynthesis). The decay of the newly made radioactive nuclei back toward stability heats the expanding ejecta and powers the kilonova. The heavy r-process elements, particularly the lanthanides, have enormous line opacity, which reddens and prolongs the transient, exactly the behavior AT2017gfo displayed. The inferred ejecta mass and composition imply that neutron-star mergers are a dominant source of the r-process elements in the universe, including much of the gold and the actinides. GW170817 tied a specific nucleosynthetic process to a specific class of astrophysical event through direct observation. ## The standard siren A compact-binary inspiral is a **standard siren**: the gravitational waveform encodes the luminosity distance $d_L$ directly, without any distance-ladder calibration. The strain amplitude scales as $h \propto \mathcal{M}^{5/3} f^{2/3}/d_L$, and because the chirp mass $\mathcal{M}$ is read from the frequency sweep and the frequency $f$ is measured, the observed amplitude yields $d_L$. This is the gravitational analogue of a standard candle, but calibrated by general relativity rather than by astrophysics. The luminosity distance alone does not give the Hubble constant; a redshift is also required. Gravitational waves carry no redshift information, because the waveform is degenerate between mass and redshift. The electromagnetic counterpart supplies it: the kilonova localized GW170817 to NGC 4993, whose recession velocity gives the redshift $z$. Combining the gravitationally measured $d_L$ with the electromagnetically measured $z$ through Hubble's law yields the Hubble constant. > **Worked example.** From GW170817 the gravitational-wave analysis gave a luminosity > distance $d_L \approx 43\ \mathrm{Mpc}$ (with a large uncertainty dominated by the > inclination-distance degeneracy), and the host galaxy NGC 4993 has a Hubble-flow > recession velocity of about $3000\ \mathrm{km\,s^{-1}}$ after correcting for peculiar > motion. At these low redshifts $d_L \approx cz/H_0$, so > $$ > H_0 = \frac{cz}{d_L} \approx \frac{3000\ \mathrm{km\,s^{-1}}}{43\ \mathrm{Mpc}} > \approx 70\ \mathrm{km\,s^{-1}\,Mpc^{-1}}. > $$ > A single event gives a value consistent with both the early- and late-universe > determinations, and a catalog of such sirens promises an independent arbiter of the > [Hubble > tension](/astrophysics-cosmology/cosmology-expansion-and-dynamics/dark-energy-and-the-accelerating-universe). $$ % caption: The standard-siren method: the gravitational waveform fixes the luminosity % distance and the electromagnetic host gives the redshift, so the single point sits % on the Hubble line and its slope reads the Hubble constant. \begin{tikzpicture}[scale=1.0, font=\footnotesize] \definecolor{acc}{HTML}{4A6FA5} \draw[->, black] (0.6,0.6) -- (8.4,0.6) node[right, black!70] {distance from GW}; \draw[->, black] (0.6,0.6) -- (0.6,4.2) node[above, black!70] {recession velocity}; % Hubble line, slope H0 \draw[acc, very thick] (0.8,0.8) -- (7.6,3.9); \node[acc, anchor=south east] at (2.9,2.4) {slope = H0}; % the single siren point with error bars \fill[black!70] (5.0,2.72) circle (2.2pt); \draw[black] (4.5,2.72) -- (5.5,2.72); % distance error \draw[black] (5.0,2.37) -- (5.0,3.07); % velocity error \node[black, anchor=south west] at (5.25,2.95) {GW170817}; % projections \draw[black, densely dotted] (5.0,0.6) -- (5.0,2.72); \draw[black, densely dotted] (0.6,2.72) -- (5.0,2.72); \node[black, anchor=north] at (5.0,0.55) {d from waveform}; \node[black, anchor=east, rotate=90] at (0.5,2.72) {z from host}; \end{tikzpicture} $$ Standard sirens are independent of every rung of the traditional [distance ladder](/astrophysics-cosmology/observational-foundations/the-cosmic-distance-ladder), because they replace the whole chain with a direct measurement from the waveform. As detections accumulate, the statistical precision improves, and a population of a few hundred sirens is expected to measure $H_0$ to the percent level. ## Summary Gamma-ray bursts divide by duration: long bursts ($T_{90} \gtrsim 2\ \mathrm{s}$) come from the collapse of massive rotating stars, short bursts ($T_{90} \lesssim 2\ \mathrm{s}$) from compact-object mergers. The compactness problem, the conflict between the huge gamma-ray energy in a small volume and the observed transparency, forces bulk motion at Lorentz factor $\Gamma \gtrsim 100$, beaming the emission into a jet of half-angle $\sim 1/\Gamma$; internal shocks make the prompt burst and the external shock the afterglow. GW170817 united a neutron-star inspiral chirp, a short gamma-ray burst $1.7\ \mathrm{s}$ later, a radioactively powered kilonova reddened by lanthanide opacity, and a broadband afterglow, confirming that mergers synthesize r-process elements. Because the waveform gives the luminosity distance directly, a merger with an electromagnetically measured redshift is a standard siren, and GW170817 alone read $H_0 \approx 70\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$. [^co-grb]: Carroll & Ostlie, Ch. 15 §15.4 — gamma-ray bursts, the compactness problem, relativistic beaming, and the fireball model. [^maoz-merger]: Maoz, Ch. 4 — compact-object mergers, kilonovae, and r-process nucleosynthesis. [^gw170817]: LIGO Scientific and Virgo Collaborations et al., "Multi-messenger Observations of a Binary Neutron Star Merger," ApJL 848, L12 (2017) — https://arxiv.org/abs/1710.05833.