The physics of gamma-ray bursts

Gamma-ray bursts (GRB’s), short and intense pulses of low-energy $\gamma$ rays, have fascinated astronomers and astrophysicists since their unexpected discovery in the late sixties. During the last decade, several space missions—BATSE (Burst and Transient Source Experiment) on the Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer)—together with ground-based optical, infrared, and radio observatories have revolutionized our understanding of GRB’s, showing that they are cosmological, that they are accompanied by long-lasting afterglows, and that they are associated with core-collapse supernovae. At the same time a theoretical understanding has emerged in the form of the fireball internal-external shocks model. According to this model GRB’s are produced when the kinetic energy of an ultrarelativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circumburst matter. This model has had numerous successful predictions, like the predictions of the afterglow itself, of jet breaks in the afterglow light curve, and of the optical flash that accompanies the GRB’s. This review focuses on the current theoretical understanding of the physical processes believed to take place in GRB’s.

Figure 1

Distribution of the observed values of the break energy $(\tilde{\alpha }-\tilde{\beta })E_0$ in a sample of bright bursts observed by BATSE: From 316. Solid line, the whole sample; dashed line, a subset of the data.

Figure 2

The hardness-duration correlation for BATSE bursts. HR is the ratio of fluence between BATSE channels 3 and 2. ⊞, short bursts; 엯, long bursts; solid line, a regression line for the whole sample; dotted lines, the regressions lines for the short and long samples, respectively. From 319.

Figure 3

(Color in online edition) The light curve of GRB 920627. The total duration of the burst is $52\sec$, while typical pulses are $0.8\sec$ wide. Two quiescent periods lasting $\sim 10\sec$ are marked by horizontal solid bold lines.

Figure 4

(Color in online edition) Pulses within γ-ray bursts: right, the pulse width distribution; left, the distribution of intervals between pulses. From 263.

Figure 5

Venn diagram of the distribution of 47 afterglows observed in different wavelengths between 1997 and 2001. From a talk given by D. Frail at the Sackler GRB Workshop, Harvard, May 2001.

Figure 6

The distribution of x-ray fluxes $(2–10\mathrm{keV})$ at $t=11\mathrm{h}$ after the GRB in 21 afterglows observed by BeppoSAX.The sample includes all the fast observations performed by BeppoSAX on GRB’s from January 1997 to October 1999. No x-ray afterglow was detected in GRB 990217 to the limiting instrumental sensitivity of ${10}^{-13}\mathrm{erg}{\mathrm{cm}}^{-2}{\sec }^{-1}$, $6\mathrm{h}$ after the burst. In the case of GRB 970111 a candidate was detected, but evidence of fading behavior is marginal, so both cases are considered as upper limits (indicated by the arrow). From 303.

Figure 7

(Color in online edition) The fraction of bursts with optical afterglow above three limiting magnitudes as a function of time (compared to the total number of bursts with optical afterglow).

Figure 8

Optical light curves of GRB 990510. A fit for the observed optical light curves is obtained with ${\alpha }_1=0.82\pm 0.02$, ${\alpha }_2=2.18\pm 0.05$ and $t_{*}=1.2\pm 0.08\text{days}$. From 154.

Figure 9

Light curves of the radio afterglow of GRB 970508 at 4.86 and $1.43\mathrm{GHz}$, compared with the predictions of the adiabatic fireball model. From 99.

Figure 10

(Color in online edition) Comparison of the peak magnitudes of GRB supernovae with those of local type-Ib/Ic supernovae. Left, solid cumulative histogram for those GRB’s with a believable detection of a supernova bump; dotted histogram, the brightness of all other claimed GRB supernova peaks or reported upper limits. Right, solid histogram for those local Ibc supernovae for which the supernova was observed before peak; all others were discovered after peak. The faintest GRB-supernova nondetection (010921) probes only the top $\sim 40\text{th}$ percentile of local type-Ib/Ic supernovae. It is clear that the current GRB-supernovae population may have revealed only the tip of the iceberg; plausibly, then, supernovae could accompany all long-duration GRB’s. From 32.

Figure 11

Evolution of the GRB 030329/SN2004dh spectrum from April $1.13\mathrm{UT}$ ($2.64\text{days}$ after the burst) to April $8.13\mathrm{UT}$ ($6.94\text{days}$ after the burst). The early spectra consist of a power-law continuum $(F_{\nu }\propto {\nu }^{-0.9})$ with narrow emission lines originating from HII regions within the host galaxy at redshift $z=0.168$. Spectra taken after April 5 show the development of broad peaks characteristic of a supernova. From 389.

Figure 12

Observed and predicted light curve at $8.6\mathrm{Ghz}$ light curves of GRB 990510. The different behaviors of the optical and radio light curves after the jet break are clearly seen. From 154.

Figure 13

(Color in online edition) Histogram of GRB energies $\left(E_{\gamma }\right)$ with three equal logarithmic spacings per decade. The histogram shows a narrow distribution of GRB energies about the standard energy $E_{\gamma }=1.33\times {10}^{51}\mathrm{ergs}$, with an error of $\sigma =0.07\mathrm{dex}$. The observed burst-to-burst rms spread is $0.35\mathrm{dex}$ (a factor of 2.23) about this value. Bands of 1, 2, and $5\sigma$ about the standard energy are shown. There are five identifiable outliers, which lie more than $5\sigma$ from the mean. However, there is currently no basis other than discrepant energy to exclude these bursts from the sample. From 33.

Figure 14

(Color in online edition) GRB energy release vs redshift. Bands of 1, 2, and $5\sigma$ about the mean energy $E_{\gamma }=1.33\times {10}^{51}\mathrm{ergs}$ are shown. Star symbols: trajectories of five GRB’s with no known spectroscopic redshift. While the energies of GRB 980329 and GRB 000630 could be consistent with the standard value at redshifts beyond $z\sim 1.5$, the energies of GRB 980326 and GRB 980519 were consistent at no redshift. From 33.

Figure 15

(Color in online edition) Observed pulse from an instantaneous flash from a spherical relativistic thin shell moving relativistically and emitting with a power law ${\nu }^{-0.6}$.

Figure 16

Different possible broadband synchrotron spectra from a relativistic blast wave, which accelerates the electrons to a power-law distribution of energies. Thin solid line: asymptotic power-law segments and their points of intersection, where the break frequencies ${\nu }_b$ and the corresponding flux densities $F_{{\nu }_b,\mathrm{ext}}$ are defined. The different PLS’s are labeled A through H, while the different break frequencies are labeled 1–11. The temporal scalings of the power-law segments and the break frequencies, for an ISM $(k=0)$ or stellar wind $(k=2)$ environment, are indicated by the arrows. The different spectra are labeled 1–5, from top to bottom. The relevant spectrum is determined by the ordering of the break frequencies. The top two panels (spectra 1 and 2) correspond to slow cooling $({\nu }_m<{\nu }_c)$. Spectrum 1 applies when ${\nu }_{sa}<{\nu }_m$, while spectrum 2 applies when ${\nu }_m<{\nu }_{sa}<{\nu }_c$. The two bottom panels (spectra 4 and 5) correspond to fast cooling $({\nu }_c<{\nu }_m)$. Spectrum 5 applies when ${\nu }_{sa}<{\nu }_c$, and spectrum 4 applies when ${\nu }_c<{\nu }_{sa}<{\nu }_m$. Spectrum 3 (middle panel) applies when ${\nu }_{sa}>{\nu }_m,{\nu }_c$, in which case the relative ordering of ${\nu }_c$ and ${\nu }_m$ is unimportant (i.e., spectrum 3 may apply both to slow cooling or fast cooling). From 139.

Figure 17

(Color in online edition) Polarization from a uniform magnetic field (following 129). The circle marks the angle where the matter moves at an angle ${\Gamma }^{-1}$ from the observer. Note that the polarization is maximal along the line perpendicular to the uniform field, but it vanishes in the other direction near the ${\Gamma }^{-1}$ circle.

Figure 18

(Color in online edition) Polarization from a random magnetic field in the plane of the shock. The solid circle marks the angle where the matter moves at an angle ${\Gamma }^{-1}$ from the observer. Polarization may arise if we view a part of a jet (dashed line), or if the emission is dominated by hot spot (dash-dotted regions), or if there is an overall gradient of the emissivity as would arise in the standard jet model. From 268.

Figure 19

(Color in online edition) Time integrated polarization (solid lines) and the efficiency (dashed lines) as a function of ${\theta }_{\mathit{obs}}\Gamma$; (a) for two different values and (b) for two other different values of ${\theta }_j$ for a random magnetic field.

Figure 20

Different time scales from a relativistic expanding shell in terms of the arrival times $\left(t_i\right)$ of various photons: $t_{\mathit{ang}}=t_D-t_A$, $t_R=t_C-t_A$ and $t_{\Delta }=t_B-t_A$.

Figure 21

(Color in online edition) The internal shocks model (from 359). Faster shells collide with slower ones and produce the observed $\gamma$ rays. The variability time scale is $L∕c$, while the total duration of the burst is $\Delta ∕c$. From 359.

Figure 22

(Color in online edition) The clumpy ISM model. Note the small covering factor and the resulting “geometrical” inefficiency. From 359.

Figure 23

(Color in online edition) The shotgun model. The inner engine emits narrow “bullets” that collide with the ISM. From 359.

Figure 24

The Lorentz factor $\Gamma$, the density $\rho$, and the pressure $p$ in the shocks. There are four regions: the ISM (region 1), the shocked ISM (region 2), the shocked shell (region 3), and the unshocked shell (region 4), which are separated by the forward shock (FS), the contact discontinuity (CD), and the reverse shock (RS). From 189.

Figure 25

(Color in online edition) Light curves resulting from a Gaussian $(\Delta R∕R=0.1)$ overdense region in the ISM. The different thick lines are for maximal overdensities of 40 (dashed-dot), 5 (dashed), and 2 (solid). The thin line is the light curve for a constant ISM density. The inset depicts the ratio of the mass, $M\left(R\right)$ over the mass of an ISM (without the overdense region), $M_{ISM}\left(R\right)$. From 264.

Figure 26

(Color in online edition) A relativistic jet at the last time step of the simulation: (left) 3D view of the jet. The outer surface represents the shock front, while the two inner faces show the proper number density (lower face) and proper emissivity (upper face) in a logarithmic color scale. (Right) 2D “slice” along the jet axis, showing the velocity field on top of a linear color map of the laboratory frame density. From 132.

Figure 27

(Color in online edition) Hydrodynamic simulation of a jet: (a) radius $R$; (b) Lorentz factor $\Gamma -1$; (c) opening angle $\theta$ of the jet as a function of the laboratory frame time in days. From 132.

Figure 28

Light curves of an inhomogeneous jet observed from different angles. From the top, ${\theta }_o=0.5°$, 1°, 2°, 4°, 8°, 16°. The break time is related only to the observer angle: $t_b\propto {\theta }_o^2$. The dashed line is the on-axis light curve of an homogeneous jet with an opening angle $2{\theta }_o$ and an energy per unit solid angle $\epsilon \left({\theta }_o\right)$. The blowup is the time range between $4\mathrm{h}$ and $1\text{month}$, when most of the optical observations are performed. Comparing the solid and dashed lines for a fixed ${\theta }_o$, it is apparent that one can hardly distinguish the two models by fitting the afterglow data. From 340.

Figure 29

Light curves for structured jets (initially $ϵ\propto {\theta }^{-a}$ and $\Gamma \propto {\theta }^{-b}$), for models 1 and 2, in the optical $(\nu =5\times {10}^{14}\mathrm{Hz})$, for a jet core angle ${\theta }_c=0.02$, viewing angles ${\theta }_{\mathrm{obs}}=0.01$, 0.03, 0.05, 0.1, 0.2, 0.3, 0.5, $p=2.5$, ${ϵ}_e={ϵ}_B=0.1$, $n=1{\mathrm{cm}}^{-3}$, ${\Gamma }_0={10}^3$, and ${ϵ}_0$ was chosen so that the total energy of the jet would be ${10}^{52}\mathrm{ergs}$ (GK). A power law of $t^{-p}$ is added in some of the panels for comparison. From 131.

Figure 30

Polarization geometry from observer’s viewpoint: (a) Shape of the emitting region: dashed line, physical extent of the jet; solid lines, viewable region $1∕\gamma$. The observed radiation arises from the gray-shaded region. In each frame, the percentage of polarization is given at the top right and the initial size of the jet relative to $1∕\gamma$ is given on the left. The frames are scaled so that the size of the jet is unity. (b) Observed and theoretical polarization light curves for three possible offsets of the observer relative to the jet axis. Observational data for GRB 990510 is marked by crosses $(\times )$, assuming $t_{\mathrm{\text{jet}}}=1.2\text{days}$. The upper limit for GRB 990123 is given by a triangle, assuming $t_{\mathrm{\text{jet}}}=2.1\text{days}$. From 360.

Figure 31

(Color in online edition) Schematic afterglow light curve. While the bursts differ before the jet break (due to different opening angles, the light curves coincide after the break when the energy per unit solid angle is a constant.

Figure 32

(Color in online edition) Orphan afterglows: Left vertical scale, number of observed orphan afterglows per square degree; right vertical scale, in the entire sky, in a single exposure, as a function of the limiting magnitude for detection. Thick lines are for model A with three different sets of parameters: solid line, our “canonical” normalization $F_0=0.003\mu \mathrm{Jy}$, $z_{\mathit{\text{peak}}}=1$, ${\theta }_j=0.1$. The gray area around this line corresponds to an uncertainty by a factor of 5 in this normalization. Dashed-dotted line, our most optimistic model with a relatively small ${\theta }_j=0.05$ and a large $F_0=0.015\mu \mathrm{Jy}$. Dotted line, the same as our “canonical” model, except for $z_{\mathit{\text{peak}}}=2$. Thin lines are for model B: solid line, our “optimistic” parameters; dashed line is for our “canonical” parameters. Both models are similar for the “optimistic” parameters, but model B predicts slightly more orphan afterglows than model A for the “canonical” parameters. From 266.

Figure 33

Afterglow from a GRB ejecta decelerating in a wind of a Wolf-Rayet progenitor, where $\dot{M}=2\times {10}^{-5}{M}_{☉}{\mathrm{yr}}^{-1}$ and $w={10}^3\mathrm{km}{\mathrm{s}}^{-1}$. The burst has an isotropic energy $E={10}^{53}\mathrm{ergs}$ and a thin ejecta shell with kinetic energy $E={10}^{53}\mathrm{ergs}$ and a Lorentz factor $\Gamma =200$: dashed curves, prediction of the standard model that neglects the impact of the radiation front; solid curves, actual behavior. Two extreme cases are displayed in the figure: $\eta =0$ (adiabatic blast wave) and $\eta =1$ (radiative blast wave). Four zones are marked: $\mathrm{I}—R<R_{\mathit{\text{gap}}}$ (the gap is opened); $\mathrm{II}—R_{\mathit{\text{gap}}}<R<R_{\mathit{acc}}$ (the gap is closed and the ejecta sweeps the relativistically preaccelerated $e^{\pm }$-loaded ambient medium); $\mathrm{III}—R_{\mathit{acc}}<R<R_{\mathit{\text{load}}}$ ($e^{\pm }$-loaded ambient medium with ${\Gamma }_{\mathit{\text{ambient}}}\approx 1$); and $\mathrm{IV}—R>R_{\mathit{\text{load}}}$ (pair-free ambient medium with ${\Gamma }_{\mathit{\text{ambient}}}\approx 1$). The radii are measured in units of $R_{\mathit{acc}}\approx {10}^{16}\mathrm{cm}$. Top panel, dissipation rate. Bottom panel, synchrotron peak frequency (assuming ${ϵ}_B=0.1$) in units of $m_e{c}^2∕h$. From 19.