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The Physics of Gamma-Ray Bursts

Tsvi Piran

arXiv:astro-ph/0405503v1astro-ph

TL;DR

GRB theory requires a framework for explaining prompt emission and afterglows. This review examines the fireball internal-external shocks model and its associated physical processes, emphasizing its account of afterglows and related observables.

  • Problem

    The physical processes underlying GRBs and their afterglows require a coherent theoretical framework.

    Source: §2 · p. 68

  • Method

    The review focuses on the fireball internal-external shocks model and the physical processes it proposes for GRBs and afterglows.

    Source: §I · pp. 5–6

  • Results

    The review presents the afterglow as a single entity within the GRB framework.

    Source: B. The Afterglow · p. 17

  • Takeaways & Limitations

    The fireball internal-external shocks model provides the review’s organizing framework for interpreting GRB emission and afterglows.

    Source: §I · pp. 5–6

Abstract

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Gamma-Ray Bursts (GRBs), 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 Compton Gamma-Ray Observatory, BeppoSAX and now HETE II (High-Energy Transient Explorer), together with ground optical, infrared and radio observatories have revolutionized our understanding of GRBs 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 GRBs are produced when the kinetic energy of an ultra-relativistic flow is dissipated in internal collisions. The afterglow arises when the flow is slowed down by shocks with the surrounding circum-burst matter. This model has numerous successful predictions like the prediction of the afterglow itself, the prediction of jet breaks in the afterglow light curve and of an optical flash that accompanies the GRBs themselves. In this review I focus on theoretical aspects and on physical processes believed to take place in GRBs.

X. Open Questions and Future Prospects … 2. Temporal Structure

This section examines GRB prompt-emission spectra and temporal structure within the fireball internal–external-shocks framework, covering optical flashes, nonthermal spectra, variability, pulse structure, and luminosity correlations. It also considers unresolved spectral issues, evidence about the inner engine, observational selection effects, and temporal power spectra in long and short bursts.

I. INTRODUCTION

  • The fireball model attributes GRBs to internal dissipation in an ultra-relativistic flow and afterglows to external shocks in the circum-burst medium.The inner engine remains indirectly constrained, while energetic and timescale requirements suggest catastrophic collapse or neutron-star merger scenarios.Source: §I · pp. 5–6

II. OBSERVATIONS

  • The review organizes observations around prompt emission, afterglows, and GRB rates, locations, and host-galaxy properties.The observational review is explicitly brief and directs readers to other reviews for comprehensive coverage.Source: §II · pp. 6–7

A. Prompt Emission

  • Optical flashes were observed simultaneously with γ-ray emission in three cases.Prompt emission can also include lower-energy X-rays, optical light, and radio emission, although longer-wavelength signals are harder to detect.Source: A. Prompt Emission · p. 7

1. Spectrum

  • The prompt spectrum is nonthermal, peaks at a few hundred keV, and often has a high-energy tail extending to GeV energies.The Band function provides an excellent fit to most observed spectra despite lacking a particular theoretical prediction for their shape; X-ray flashes show that the apparent low-energy cutoff reflects BATSE sensitivity [189].Source: §1 · pp. 7–8
  • Observed spectral distributions peak near 250 keV, but BATSE selection effects leave the existence of a hard-GRB cutoff unresolved.BATSE was less sensitive to bursts emitting mainly in the MeV range, so harder populations with comparable total power cannot be ruled out [55, 166, 221, 313].Source: §1 · p. 8
  • The narrow hardness distribution remains puzzling: its observational reality and physical origin are uncertain, while a narrow distribution extending to high redshift would require intrinsic hardness to increase with redshift.Evidence exists for correlations involving E_p, peak flux, isotropic-equivalent energy, and redshift, but their consistency depends on bursts’ intrinsic luminosity dominating distance effects.Source: §1 · p. 9
  • High-energy emission can extend from 100 MeV to 18 GeV, sometimes delayed by more than an hour, while GRB 941017 showed a distinct tail to 200 MeV.For GRB 941017, the high-energy component appeared 10–20 seconds after onset, remained roughly constant through 200 seconds, and later contained 50 times more energy than the 30keV–2MeV band.Source: §1 · pp. 9–10
  • Low-energy spectral slopes remain problematic: some analyses find slopes steeper than synchrotron limits, whereas all HETE bursts fall within 1/3 to -1/2, leaving detector resolution as a possible explanation.The issue may require a future spectrometer with better low-energy resolution because BATSE and HETE use NaI detectors with poor low-energy resolution.Source: §1 · p. 10

2. Temporal Structure

  • GRB durations span less than 0.01 sec to more than 100 sec, variability can be over 10^4 times faster than burst duration, and millisecond structure occurs in some long bursts.Source: §2 · pp. 10–11
  • Variability and spectral lag correlate with luminosity, allowing luminosity estimates without known redshifts; pulse intervals and widths are approximately log-normal but include quiescent gaps.The average pulse interval is 1.3sec versus a 1sec average pulse width, and pulse widths correlate with the preceding interval.Source: §2 · pp. 11–12
  • Individual pulses are typically FRED-shaped, evolve from hard to soft, show delayed and broader low-energy emission, and obey hardness-, width-symmetry-, and intensity-related correlations.The average pulse rise-to-decay ratio is 1:3, and pulse width scales approximately as E^-0.4.Source: §2 · p. 11
  • Long-burst light curves have power density spectra with a ∼−5/3 power-law slope and a sharp break at 1Hz.The temporal behavior can be analyzed using the traditional Fourier transform method.Source: §2 · p. 12
  • Short bursts (T < 2sec) are more difficult to analyze because their durations approach the detectors’ limiting resolution.The reported results so far concern long bursts.Source: §2 · p. 12
  • Approximately 66% of short bursts are variable with δt/T < 0.1, and these variable bursts consist of multiple subpulses.Their variability is therefore observed despite the resolution-related analysis difficulty.Source: §2 · p. 12

3. Populations … 1. The X-ray afterglow

This section reviews GRB populations and multiwavelength afterglows, covering distinctions between long and short bursts, X-ray flashes, prompt polarization and optical flashes, and the emergence and properties of X-ray, optical, and radio counterparts. It also addresses the limited characterization of short-burst afterglows and the debated significance of reported X-ray line features.

3. Populations

  • Short bursts differ from long bursts in hardness and spatial distribution: they are typically harder, lack soft short events, and have higher ⟨V/Vmax⟩ values, although detector sensitivity complicates the interpretation.Guetta and Piran report ⟨V/Vmax⟩long = 0.282 and ⟨V/Vmax⟩long = 0.390, implying the observed short-burst population is nearer on average, while shorter triggering windows are less sensitive to short bursts.Source: §3 · pp. 12–13
  • Afterglows had been detected only from long bursts, and the sole well-localized short hard burst lacked an X-ray afterglow at least 100–300 times as intense as comparable long-burst afterglows, leaving short-burst properties unknown.Because host and redshift identification depends on afterglow detection, the distribution, progenitors, and environments of short bursts remained unconstrained.Source: §3 · p. 13
  • X-ray flashes have GRB-like temporal durations but softer spectra, form a continuous extension of GRB distributions, occur at roughly half the GRB frequency, and have detected afterglows.BeppoSAX observations found 32 XRFs versus 54 GRBs above the stated threshold; XRF 020903 had an optical afterglow at z = 0.25 with a possible supernova signal, and XRF 030723 also showed an afterglow.Source: §3 · pp. 13–14

4. Polarization

  • A reported 80% ± 20% linear polarization for GRB 021206 rejected the no-polarization hypothesis at 5.7σ, but methodological criticism and a reanalysis yielding an approximately 4% upper limit leave the result highly uncertain.The constant-polarization fit was consistent with the observations only at a 5% probability level, and the authors did not clearly resolve the methodological criticism.Source: §4 · pp. 14–15

5. Prompt Optical Flashes

  • ROTSE detected a 9th-magnitude optical flash concurrent with GRB 990123, whose peak did not coincide with the gamma-ray peak, suggesting the optical emission was not simply the gamma-ray low-energy tail.The snapshots began 40 seconds after the trigger, and the second snapshot at 60 seconds recorded the 9th-magnitude flash.Source: §5 · p. 15
  • An optical signal from GRB 021004 was detected 193 seconds after the trigger, only 93 seconds after its 100-second burst activity ended.Source: §5 · p. 15
  • Prompt optical flashes were detected rapidly, including a 14.67-magnitude signal 105 seconds after GRB 021211, while searches for other bursts mostly produced upper limits.The reported upper limits were consistent with recent detections around 15th magnitude, suggesting more rapid discoveries could follow.Source: §5 · pp. 15–16

6. The GRB-Afterglow Transition - Observations

  • The GRB-to-afterglow transition appears as a sharp hardness change several dozen seconds after the burst, long soft tails, and spectra inconsistent with simply extrapolating the X-ray afterglow backward to the gamma-rays.The observations support internal and external shocks producing the prompt and afterglow phenomena through different effects.Source: §6 · p. 16

B. The Afterglow

  • X-ray, optical, and radio afterglows established GRB counterparts: BeppoSAX first detected GRB 970228’s X-ray afterglow, its position enabled optical identification, and radio emission followed for GRB 970508.More than forty X-ray afterglows had been observed, about half with optical and radio afterglows, enabling host-galaxy identifications and redshift measurements from 0.16 to 4.5.Source: B. The Afterglow · p. 16

1. The X-ray afterglow

  • X-ray afterglows are the first and strongest but shortest afterglow signal, apparently beginning during the GRB, with hours-later light curves generally extrapolating to late prompt emission.Their overall energy is generally a few percent of the GRB energy, while beaming-corrected luminosity is approximately constant with a dispersion of only a factor of 2.Source: §1 · p. 17
  • The X-ray afterglow follows fν(t) ∝ ν−βt−α with α ∼1.4 and β ∼0.9, while its 1–10 keV flux 11 hours after the burst is 5 × 10−13 ergs/cm−2 sec with σfx ≈0.43 ± 0.1.The normalized flux distribution is relatively narrow, and optical-afterglow bursts are on average 5 times brighter in X-rays than dark bursts.Source: §1 · p. 17
  • X-ray lines were reported in seven GRBs, typically around 10 hours after the burst with luminosities of about 10^44–10^45 ergs/sec and fluence near 10^49 ergs, but their statistical significance remains contested.The detections were reported at only 2–5 σ, and some analyses argued that none was statistically significant.Source: §1 · pp. 17–18

2. Optical and IR afterglow … 3. GRB rates and the isotropic luminosity function

This section examines multiwavelength afterglows, dark bursts, and GRB host galaxies, focusing on their emission properties, environments, and cosmological distribution. It also considers GRB rates and luminosity functions, including beaming, redshift evolution, and the model dependence and observational uncertainties affecting their estimates.

2. Optical and IR afterglow

  • About 50% of well-localized GRBs show optical/IR afterglows, which typically fade as t^-α with α ≈1.2; many later steepen achromatically with α ≈2.Rapid HETE II localization enabled an almost complete light curve from 193 seconds after GRB021004. Late red bumps, especially in GRB 030329 [167, 395], are interpreted as underlying supernovae, and varying polarization reaches a few to ten percent [27, 61, 62, 145, 346, 441].Source: §2 · pp. 18–19

4. Radio afterglow

  • Radio afterglows occur in about 50% of well-localized bursts, with typical peak fluxes near 2 mJy; their observations directly establish relativistic expansion and enable late-time energy estimates.Scintillation measurements inferred an emitting-region size of approximately 10^17 cm for GRB 970508, providing the first direct proof of relativistic expansion; years-late radio emission permits calorimetry after the relativistic-to-Newtonian transition.Source: §4 · pp. 20–21

1. Hosts

  • By early 2004, host galaxies were identified for all but one or two bursts, resolving the no-host problem; they are faint, with median R ≈25 and some near R ≈29.GRBs are located within host galaxies, and some evidence indicates hosts are bluer with higher star-formation rates than average galaxies.Source: §1 · pp. 21–22
  • GRB host galaxies have typical magnitudes and redshifts, while GRB-host offsets follow the host light distribution, whose light is roughly proportional to star-formation density.Source: §1 · p. 22
  • GRB hosts show active star formation and at most moderate metallicity, with Lyman alpha emission reported whenever suitable searches were conducted, distinguishing them from most Lyman break galaxies.Only about 1/4 of Lyman break galaxies show Lyman alpha emission.Source: §1 · pp. 22–23

2. The Spatial Distribution

  • BATSE’s uniform sky distribution indicates that GRBs are not associated with the Galaxy or nearby local structure, although short-burst samples show possible angular clustering.The short-burst two-point correlation exhibits a ∼2σ deviation from isotropy on 2°−4° scales, potentially reflecting proximity, repetition, or a distinct population.Source: §2 · p. 23

3. GRB rates and the isotropic luminosity function

  • The wide luminosity function weakly constrains GRB rates from BATSE peak fluxes, while short-burst estimates remain uncertain because of detector sensitivity and unknown spatial distribution.Short bursts have ⟨V/Vmax⟩ around 0.5 versus around 0.32 for long bursts, implying that observed short bursts are nearer.Source: §3 · pp. 24–25
  • Guetta et al. [153] infer a typical isotropic luminosity L∗ = 1.1 × 10^51 ergs/sec, slopes α = −0.6 and β = −2, and local rate ρ0 = 0.44 Gpc−1 yr−1.These canonical estimates carry roughly a factor-of-two uncertainty in typical luminosity and local rate.Source: §3 · p. 25
  • Short GRBs have ⟨V/Vmax⟩=0.354 and an estimated local rate of 0.075Gpc−3yr−1, about half the long-GRB rate, with comparable isotropic peak luminosities.These estimates assume short GRBs follow the star-formation rate.Source: §3 · p. 25
  • An alternative calculation finds ⟨V/Vmax⟩=0.390 and a local rate of 1.7Gpc−3yr−1, about four times the long-GRB rate, because observed short GRBs are nearer.This result is attributed to Guetta and Piran.Source: §3 · p. 25
  • The corrected peak luminosity is much more narrowly distributed than the isotropic peak luminosity, with Lpeak(θ2/2) ∼const.; beaming increases the implied rate by a factor f −1.Source: §3 · pp. 25–26
  • Direct redshift-distribution inference remains limited by unclear observational biases and the need for a homogeneous sample; luminosity evolution would imply narrower collimation at earlier times.The dependence of these features on redshift is also difficult to reconcile with their apparent dependence on the inner engine.Source: §3 · p. 26
  • Redshift-based luminosity estimators indicate that GRB rates increase backward in time even beyond z > 10, luminosity evolves as (1+z)1.4±0.5, and hardness correlates strongly with luminosity.These findings use the Fenimore and Ramirez-Ruiz sample and are reported by Lloyd-Ronning et al..Source: §3 · p. 26

4. Association with Supernovae · D. Energetics

This section examines the association between long GRBs and core-collapse supernovae alongside the energetics of GRBs. It covers observational evidence, beaming-corrected and kinetic-energy estimates, and the uncertainties and constraints affecting interpretations of the total energy output.

4. Association with Supernovae

  • SN 1998bw associated with GRB 980425 was unusually powerful, while the burst had an isotropic-equivalent energy of ~10^48 ergs, several orders below a typical GRB.The supernova’s high velocity and kinetic energy contrasted with the unusually weak, smooth GRB 980425.Source: §4 · pp. 26–27
  • Late red bumps in several GRB afterglows are generally interpreted as underlying supernovae, but current nondetections probe only the brightest ~40th-percentile of local Type Ib/Ic supernovae.This limited sensitivity leaves open the possibility that supernovae accompany all GRBs.Source: §4 · pp. 27–28
  • GRB 030329’s SN 2003dh signature provided a final conclusive link between long GRBs and supernovae, with a contemporaneous SN-like bump and spectrum.The bump appeared six days after the burst, and the result argued against a delayed Supranova interpretation.Source: §4 · p. 28

D. Energetics

  • Direct redshift measurements replaced population-level luminosity-function estimates with burst-specific energies inferred from fluence and redshift under an isotropic-emission assumption.The first measured-redshift burst, GRB 970508, had an energy around 10^51 ergs.Source: D. Energetics · p. 29
  • Eγ,iso reached 3.4×10^54 ergs for GRB 990123 and varied by about three orders of magnitude, motivating beaming corrections Eγ ≡ (θ^2/2)Eγ,iso.The effective emission angle θ can be estimated from the afterglow break time.Source: D. Energetics · p. 29
  • Beaming-corrected γ-ray energies are typically around 10^51 ergs, with ∼0.35 dex variance—three orders of magnitude below isotropic-equivalent variance.Bloom et al. report Eγ = 1.33×10^51 h−2 65 erg; the constancy combines prompt γ-ray flux with the afterglow-inferred jet opening angle.Source: D. Energetics · p. 30
  • The γ-ray energy may not equal total engine energy because unknown radiative efficiency and angular inhomogeneities affect E_tot = ϵ−1Eγ = ϵ−1(θ2/2)Eγ,iso.Early GRB 021004 afterglow observations indicate significant angular variability in the relativistic ejecta.Source: D. Energetics · p. 30
  • Afterglow kinetic-energy estimates suggest either Ēγ ≈3 Ēk,θ or comparable beamed energies, while late-time radio calorimetry yields comparable total-energy values.The kinetic energy is less sensitive to angular variability because it is measured at a smaller Lorentz factor.Source: D. Energetics · pp. 30–31
  • Universal structured-jet interpretations make beams wider, reduce the inferred GRB rate, increase inferred energies, and require E(θ) ∝θ−2.Guetta et al. estimate a structured-to-uniform energy factor of ∼7, but the viewing-angle distribution is inconsistent with the simplest geometric prediction.Source: D. Energetics · pp. 30–31
  • Orphan-afterglow searches provide weak optical constraints, whereas radio surveys find nine candidates and imply a lower limit f_b−1 > 90 if all are GRB-associated.Narrower beams produce more GRBs but lower-energy, harder-to-detect radio afterglows; the latter effect dominates.Source: D. Energetics · p. 31
  • X-ray orphan limits make the energy of matter at Lorentz factor ∼40 at most comparable to that of material at a few hundred, while optical limits remain insufficient.Radio observations already constrain the overall energy output, but these observations do not constrain gravitational radiation, neutrinos, cosmic rays, or very-high-energy photons.Source: D. Energetics · p. 32

III. THE GLOBAL PICTURE - GENERALLY ACCEPTED INGREDIENTS … C. Relativistic Beaming and the Patchy Shell Model

This section outlines the generally accepted physical ingredients of GRB models, including ultra-relativistic motion, shock dissipation, synchrotron emission, beaming, compact-object engines, and massive-star associations. It then examines how relativistic beaming and the patchy-shell model shape observations, inferred properties, variability, and afterglow fluctuations.

III. THE GLOBAL PICTURE - GENERALLY ACCEPTED INGREDIENTS

  • Independent radio scintillation and low-frequency self-absorption estimates place the afterglow at ∼1017cm two weeks after the burst, implying relativistic expansion.The optical flash of GRB 990123 was interpreted as evidence for Γ ∼100, while another estimate found 1000 ± 100; these interpretations are model dependent.Source: §III · p. 33
  • GRB models generally attribute prompt emission to internal dissipation and afterglows to external shocks, with synchrotron radiation from shock-accelerated electrons as the standard emission mechanism.Internal shocks are supported for most bursts, although some models disagree; synchrotron predictions broadly agree with afterglow observations and polarization measurements but face slope inconsistencies.Source: §III · pp. 33–34
  • Afterglow breaks are interpreted as jet breaks from sideways beaming and spreading, or alternatively as viewing-angle effects in structured jets; both imply beaming, lower true energy, and higher event rates than isotropic estimates.The two interpretations yield different estimates of the overall rate and GRB energies.Source: §III · p. 34
  • Beaming-corrected GRB energies are ∼1051ergs, indicating a compact-object engine, while host-galaxy environments, light distributions, supernova bumps, and SN 1999bw/GRB 980425 and SN 2003dh/GRB 030329 associations link long GRBs to massive-star collapse.The inner engine remains unresolved, and much less is known about short GRBs.Source: §III · pp. 34–35

A. Compactness and relativistic motion

  • Γ ≳ 100 is required to make a typical cosmological GRB source optically thin, resolving the compactness problem caused by γ-ray pair production.Naively, the pair-production optical depth is τ_e± ∼1015; relativistic motion reduces the optical depth, and for α ∼2 one needs Γ >∼100.Source: A. Compactness and relativistic motion · pp. 35–36

B. Relativistic time effects

  • For Γ ≫ 1, emission from a relativistic shell arrives on an observer-time scale set by R/2cΓ^2, while angular delays produce a late-time decay t^−(2−α).Emission outside the beaming angle contributes delayed radiation; a decelerating source introduces a numerical factor of order eight relative to constant-velocity motion during the afterglow.Source: B. Relativistic time effects · pp. 36–37

C. Relativistic Beaming and the Patchy Shell Model

  • Relativistic beaming limits a GRB observer to a region of size R/Γ, so local shell conditions may differ from the true average conditions of the burst.As the flow decelerates, the visible fraction grows until Γ ≈ θ^−1, where θ is the jet’s angular size.Source: C. Relativistic Beaming and the Patchy… · pp. 37–38
  • Different viewing angles can yield different prompt light curves and apparent burst strengths, while afterglows converge as observers see the same angular regions.This predicts larger early-time than late-time fluctuations and biases emission estimates toward bursts whose hot spots point toward the observer.Source: C. Relativistic Beaming and the Patchy… · p. 38
  • Angular patchiness produces variability that weakens as deceleration enlarges the observed region, and simulations fit GRB 021004’s fluctuations and correlated polarization changes.A consistent angular hot-spot pattern can preserve patchiness across shells, whereas summing unrelated shell hot spots may erase it.Source: C. Relativistic Beaming and the Patchy… · p. 38

V. PHYSICAL PROCESSES … 1. Frequency and Power

This section examines synchrotron emission from shock-accelerated particles as a likely source of GRB prompt radiation, developing the underlying relativistic-shock and particle-acceleration physics. It also reviews polarization, cooling, variability, and pulse-shape constraints on the synchrotron emission model.

V. PHYSICAL PROCESSES

  • Prompt emission most likely arises from synchrotron radiation by particles accelerated in collisionless shocks, although a simple synchrotron spectrum does not fit every burst [321, 16].The relevant ingredients include particle acceleration, magnetic-field amplification, synchrotron emission, and potentially inverse Compton emission.Source: §V · p. 39

A. Relativistic Shocks

  • Relativistic shocks compress matter by a factor Γ, generate downstream internal energy of order Γ^2n_1m_pc^2, and convert ordered kinetic energy into comparable random energy.Downstream random velocities are ultra-relativistic, and these conservation-law jump conditions are expected to apply to collisionless shocks.Source: A. Relativistic Shocks · p. 39
  • The shock energy fractions ǫ_e and ǫ_B are commonly treated as constant, but this assumption cannot reproduce the observed prompt spectrum [68].This motivates models in which the equipartition parameters depend on physical conditions within the shocked matter.Source: A. Relativistic Shocks · p. 40

B. Particle Acceleration

  • In relativistic shocks, the first crossing can yield energy gain of order Γ_sh, whereas subsequent cycles give ⟨E_f/E_i⟩≈2.Repeated crossings produce the power-law acceleration spectrum, with magnetic irregularities scattering particles across the shock.Source: B. Particle Acceleration · p. 41
  • Relativistic diffusive shock acceleration yields a robust electron power law with p ≈2.2−2.3 for Γ_sh ≫1, consistent with GRB and afterglow spectra.The result assumes highly turbulent downstream conditions; weaker turbulence can produce a much steeper spectrum, while mildly relativistic internal shocks may differ.Source: B. Particle Acceleration · p. 42
  • Synchrotron losses limit acceleration; under the stated conditions, the corresponding particle Lorentz factor is of order 10^8 for Γ_sh = 100 and B = 1 Gauss.The estimate compares radiation losses with energy gain and assumes an acceleration time equal to the Larmor time.Source: B. Particle Acceleration · p. 42
  • The synchrotron cooling time is equated with the Larmor time up to a numerical factor likely of order unity.This factor modifies the equality rather than changing the underlying timescale identification.Source: B. Particle Acceleration · p. 42

C. Synchrotron

  • Polarization observations in GRB afterglows and one prompt-emission case support synchrotron emission, although inverse Compton radiation can also be polarized.Synchrotron radiation is presented as important in both GRBs and their afterglows.Source: C. Synchrotron · p. 43

1. Frequency and Power

  • At a fixed observed frequency, the synchrotron cooling time is independent of the shock’s electron energy distribution, provided electrons with the required γe exist.The cooling time is therefore described as “universal” under this condition.Source: §1 · pp. 43–44
  • Synchrotron cooling scales as tsyn(ν) ∝ν^-1/2, close to the observed δT ∝ν^-0.4, and sets a lower limit on GRB variability times.A burst cannot contain intensity spikes shorter than its cooling time.Source: §1 · p. 44
  • A fast-rise, slow-decay pulse could reflect rapid shock heating followed by cooling, but reasonable parameters give decays that are too short and long cooling causes adiabatic losses.These problems make synchrotron cooling alone unlikely to explain GRB pulse shapes.Source: §1 · p. 44

2. The Optically thin Synchrotron Spectrum · 3. Synchrotron Self-Absorption · D. Inverse Compton

This section examines synchrotron and inverse Compton processes in GRB prompt emission and afterglows, focusing on how electron distributions, cooling, self-absorption, and the Compton parameter shape spectra and radiative efficiency. It covers optically thin and self-absorbed emission, including fast- and slow-cooling regimes and associated observational limitations.

2. The Optically thin Synchrotron Spectrum

  • For a power-law electron distribution with index p and minimum Lorentz factor γe,min, the typical synchrotron frequency is νm ≡ νsyn(γe,min), while p > 2 prevents divergent high-energy content.The upper energy cutoff mainly affects the distant high-frequency tail for p > 2, not the peak flux or peak energy.Source: §2 · pp. 44–45
  • If only a fraction ξe of electrons is accelerated, the typical Lorentz factor increases by ξe^-1 while the emitted flux gains a multiplicative factor ξe.Pair formation similarly changes how the electron energy is shared and modifies the spectrum.Source: §2 · p. 45
  • The low-frequency optically thin spectrum is universally Fν ∝ ν1/3, but about one-fifth of bursts show steeper slopes below the synchrotron line of death.HETE spectra do not show this problem, while it may reflect BATSE’s low-energy resolution; efficient GRB emission otherwise requires fast cooling, predicting Fν ∝ ν−1/2.Source: §2 · pp. 45–46
  • Fast cooling (γe,c < γe,min) gives νc < νm, with Fν ∝ ν1/3 below νc and Fν ∝ ν−1/2 between νc and νm.The peak flux is at νc, while the peak of νFν is at νm.Source: §2 · pp. 46–47
  • Slow cooling (γe,c > γe,min) leaves most electrons uncooled, with Fν ∝ ν1/3 up to νm and Fν ∝ ν−p/2 above νc.Here the peak flux is at νm, whereas the peak energy emitted is at νc.Source: §2 · p. 47
  • A Gaussian electron distribution produces a ν1/3 low-frequency spectrum but a sharp exponential high-frequency cutoff, and without a high-energy tail it fails to fit most observed GRB spectra.The expected external-shock evolution can transition from fast to slow cooling during the afterglow.Source: §2 · p. 48
  • Optically thin synchrotron spectra can fit several observed GRB spectra when a Gaussian electron distribution includes a high-energy tail whose form depends on the electron power-law index [401, 402].The resulting spectrum contains a ν1/3 component and an additional high-energy tail; it may fit a small subgroup with a NHE.Source: §2 · p. 48

3. Synchrotron Self-Absorption

  • Self-absorption steepens the low-energy synchrotron spectrum to ν5/2 or ν2, depending on whether the emitting electrons lie within the self-absorption range or contribute through their low-energy tail.For fast cooling, an inhomogeneous electron distribution produces an intermediate range νsa < ν < νsa′ with Fν ∝ν11/8.Source: §3 · p. 49
  • Self-absorption is usually irrelevant during the GRB, but extreme conditions can move its frequency into low X-rays and explain steep low-energy spectra in some bursts.Those conditions require optical thickness to synchrotron radiation while remaining optically thin to Thomson scattering and pair creation.Source: §3 · pp. 49–50
  • Self-absorption occurs regularly in afterglows, typically in radio emission, whereas the expected fast-cooling self-absorbed spectrum in the early radio afterglow had not yet been observed.The fast-cooling case corresponds to νc < νm and involves electrons with different cooling states behind the shock.Source: §3 · pp. 49–50

D. Inverse Compton

  • Inverse Compton is negligible when Y < 1, but for Y > 1 it upscatters a large fraction of synchrotron photons and carries a large fraction of the cooling-electron energy.Its direct contribution to observed spectra can be limited when the IC photons lie far beyond the observed energy range, although it still changes the cooling and energy budget.Source: D. Inverse Compton · p. 50
  • For Y > 1, inverse Compton scattering can add a GeV–TeV component, accelerate cooling by a factor Y, and reduce synchrotron radiative efficiency by the same factor.The upscattered component is typically near γ^2 times ∼100 KeV photons; even when it is outside the observed range, inverse Compton still affects cooling and energy partition.Source: D. Inverse Compton · p. 51

E. Quasi-Thermal Comptonization … 1. General Considerations

This section examines physical mechanisms underlying GRB prompt emission and polarization, focusing on quasi-thermal Comptonization, pair production, and relativistic emission processes. It also distinguishes internal-shock prompt variability from external-shock afterglow emission and considers the geometric and arrival-time effects shaping observable signals.

E. Quasi-Thermal Comptonization

  • Quasi-thermal Comptonization uses pair-loaded internal shocks, with self-absorbed synchrotron photons serving as seeds for inverse-Compton emission.The emitting region has optical depth of order unity, becomes optically thick to synchrotron radiation, and produces copious pairs.Source: E. Quasi-Thermal Comptonization · p. 51
  • The pairs act as a thermostat, yielding a 30-300kev effective temperature range and a flat spectrum Fν ∝ν0 that evolves as pair creation lowers the temperature.The spectrum extends between hνsaΓ and kT′Γ, while the temperature decreases during the burst.Source: E. Quasi-Thermal Comptonization · pp. 51–52

F. Polarization from Relativistically Moving Sources

  • Polarization is obtained by integrating local electron Stokes parameters over the emitting region, with relativistic transformations altering photon and polarization directions.The resulting global polarization can differ substantially from the local value because radiation is emitted by relativistically moving regions.Source: F. Polarization from Relativistically… · p. 52
  • Even 100% local polarization can reduce to 70% globally, while synchrotron emission reaches 75% locally for 2 < p < 3 and inverse Compton can approach 100%.For α = 1, integration gives about 45% overall polarization, while exact fast-cooling values with p = 2.5 give about 50% [134, 275].Source: F. Polarization from Relativistically… · pp. 52–53
  • Random magnetic fields can produce net polarization when jet geometry or emission structure breaks spherical symmetry, including off-axis viewing, bright patches, or angle-dependent jets.For planar random fields, the polarization pattern is radial and cancels under complete symmetry; broken symmetry permits a net signal.Source: F. Polarization from Relativistically… · pp. 53–54
  • Large polarization is physically expected mainly for jets with 1 ≲ θjΓ < a few, while polarization above 40% comes with sharply reduced radiative efficiency.For θjΓ = 0.5, 1, 2, 4, the probabilities of polarization above 30% with efficiency above 0.1 are 0.68, 0.41, 0.2, and 0.08, respectively.Source: F. Polarization from Relativistically… · pp. 54–55

VI. THE GRB AND THE PROMPT EMISSION

  • The GRB and its afterglow are introduced as phenomena arising from dissipation of energy.This subsection begins the discussion of the GRB and prompt-emission theory.Source: §VI · p. 55
  • Internal shocks produce GRBs, while subsequent external shocks dissipate remaining energy and generate smooth, long-lasting afterglow emission.Because internal shocks dissipate only part of the kinetic energy, the model requires following external shocks.Source: §VI · pp. 55–56

1. General Considerations

  • External shocks cannot produce variable bursts because angular and radial arrival-time scales satisfy t∆/c ≤ R/cΓ^2 ≈ tR ≈ tang, smoothing the emission.For a spreading shell, ∆ ≈ R/cΓ^2, so external shocks produce only smooth bursts.Source: §1 · p. 56
  • Internal shocks occur at Rs ≈ LΓ^2, where tang ≈ tR ≈ L/c < t∆, allowing variability on the source timescale.The observed duration T = t∆ reflects the inner engine’s active period, whereas δt reflects source variability L/c.Source: §1 · p. 57
  • The observed burst duration reflects the inner engine’s activity duration, while the variability timescale reflects its intrinsic variability.This distinction follows because internal shocks continue while the source remains active, with T = t∆ and δt tied to L/c.Source: §1 · p. 57
  • Numerical simulations show that internal-shock time scales and the source’s temporal behavior are reproduced in the observed light curve on an almost one-to-one basis.The simulations preserve both characteristic timescales and the source temporal pattern.Source: §1 · p. 57

2. Caveats and Complications … 1. Hydrodynamics

This section examines caveats and complications in GRB internal-shock models, focusing on alternative variability mechanisms, efficiency, light-curve timing, and relativistic shock hydrodynamics. It considers how Lorentz-factor variability, shell spacing and spreading, and reverse-shock regimes shape energy conversion, pulse structure, and thermalization.

2. Caveats and Complications

  • Clumpy external media yield a covering factor δt/T ≪1, making γ-ray conversion efficiency potentially below 10^-2 for typical variable bursts.The inferred clump size and shock radius are d ≈cΓδt and R ≈cTΓ^2, respectively.Source: §2 · pp. 57–58

3. External Shocks on a Clumpy Medium sec:Clumpy

  • External shocks on a clumpy, inhomogeneous medium are discussed for δt/T ∼10−2; the result is marginal at 50% modulation and insufficient for δt/T ∼10−3 or ∼100% modulation.Millisecond variability has been observed in many long GRBs.Source: §3 · p. 58

4. The Shot-Gun Model

  • The shot-gun model uses multiple narrow bullets whose emission or deceleration sets pulse widths, while engine activity sets burst duration and pulse intervals without explaining their correlation.The bullets are assumed not to spread and to decelerate rapidly in dense circumburst matter.Source: §4 · p. 59

5. Relativistic Turbulence

  • Relativistic turbulence can generate variability after external deceleration, with Γs ≈ΓbΓp, but it leaves pulse-interval correlations and late-time pulse spreading unresolved.Because the process is not described by regular shocks, some preceding shock-based arguments do not apply.Source: §5 · p. 59

1. Hydrodynamics of Internal Shocks

  • Internal shocks require Rint < Rext, imposing upper limits on the initial Lorentz factor of a few thousands; excessive Γ causes external shocks to occur first.The shocks are mildly relativistic, with strength determined by the shells’ relative Lorentz factors.Source: §1 · pp. 60–61

2. The Efficiency of Internal Shocks

  • Efficient internal-shock conversion requires substantial velocity contrast, Γr ≫Γs, together with comparable shell masses, mr ≈ms.The merged shell’s internal energy represents the kinetic-energy difference before and after collision.Source: §2 · p. 61
  • Internal-shock efficiency increases with broad Lorentz-factor distributions, reaching unity when typical fluctuations are about a factor of 10 and roughly 20% radiation conversion in simulations.Not all generated internal energy is radiated: weak electron coupling leaves proton thermal energy to return to kinetic energy through adiabatic cooling.Source: §2 · pp. 61–62
  • About 60% overall efficiency is possible even with ϵe = 0.1 when shell Lorentz factors vary between 10 and 10^4, through repeated collisions.Kobayashi and Sari [195] obtain greater emission from subsequent collisions than from the first collision alone.Source: §2 · p. 62

3. Light Curves from Internal Shocks

  • Pulse widths and separations share the shell-ejection interval, naturally producing their similarity and observed correlations, while more than 80% of efficient collisions follow two timing scenarios.Equal-energy shells preserve the Δt-δt correlation, whereas equal-mass shells shorten pulses by a factor of a and can erase that correlation.Source: §3 · pp. 62–63

1. Hydrodynamics

  • A relativistic shell entering cold matter forms forward and reverse shocks separated by a contact discontinuity; their energy partition depends on density contrast and shock regime.When n4/n1 > Γ2, the reverse shock is Newtonian and forward-shock conversion dominates; after expansion lowers the contrast, both shocks become relativistic and thermalize comparable energy.Source: §1 · p. 64
  • The treatment assumes isotropic-equivalent energy and neglects angular structure on scales larger than Γ−1, while distinguishing shell width ∆ and expansion state.For non-spreading shells, the larger possible shock radius is used; the discussion generally adopts the spreading-shell relation.Source: §1 · pp. 65, 67
  • Initially the reverse shock is Newtonian and extracts negligible energy, but half the shell’s kinetic energy becomes thermal after collecting external mass M/Γ.The shell initially acts together before substantial dissipation begins.Source: §1 · pp. 65–66
  • If the reverse shock becomes relativistic before RΓ, RΓ no longer marks energy dissipation, which instead occurs at r∆ during one efficient shell-crossing.For RN > RΓ, dissipation occurs while the shocks are Newtonian; for RN < RΓ, the reverse shock becomes relativistic.Source: §1 · p. 66
  • With typical parameters, ξ is near unity, so the effective energy-extraction radius is the characteristic location where the relevant radii converge.In the expanding-shell case, ξ = 1 at R∆ = RΓ = RN when ξ0 > 1, and the reverse shock becomes mildly relativistic as extraction becomes efficient.Source: §1 · p. 67
  • Shell expansion decreases ξ; if ξ0 ≪ 1, the shell remains insufficiently expanded, yet a relativistic reverse shock still extracts energy at R∆.In this regime, effective extraction occurs at R∆ for all initial ξ0 values.Source: §1 · p. 67

2. Synchrotron Spectrum from External Shocks · D. The Transition from Internal Shocks to External Shocks · E. Prompt Polarization

The external-shock synchrotron spectrum depends strongly on shock conditions and magnetic-field evolution, with the reverse shock potentially producing a late-prompt optical flash. For long bursts, external-shock afterglow emission can overlap internal shocks, while tentative prompt-polarization interpretations remain uncertain.

2. Synchrotron Spectrum from External Shocks

  • Shock compression alone yields εB ≪1, so turbulent instabilities are invoked to raise magnetic fields toward equipartition in both forward and reverse shocks.The reverse-shock field is especially uncertain: pure flux freezing may leave εB far below equipartition, while instabilities could produce εB →1.Source: §2 · p. 68
  • Early forward-shock emission spans low γ-rays to X-rays, but its cooling regime depends sensitively on parameters such as Γ.For canonical parameters, νm < νc, whereas slightly larger Γ can reverse this inequality and produce fast cooling.Source: §2 · p. 69
  • The reverse shock emits at lower characteristic energy than the forward shock, usually in the infrared or optical, and can produce a powerful optical flash coincident with the late GRB.Its electrons are generally in the slow-cooling regime, and the reverse shock exists only briefly before becoming a rarefaction wave.Source: §2 · p. 69

D. The Transition from Internal Shocks to External Shocks

  • External shocks begin near Rext ∼10^16 cm, and in long bursts the afterglow starts while internal shocks are still active.The overlap condition is Rext/Γ^2 ≤ T = ∆/c, with typical engine timescales of ∼50 sec for long bursts and ∼0.5 sec for short bursts.Source: D. The Transition from Internal Shocks… · p. 70
  • During this overlap, forward-shock afterglow emission peaks in high X-rays, contributes to γ-rays, and produces a transition from a hard to softer, smoother signal.Some observational evidence for this transition was reported.Source: D. The Transition from Internal Shocks… · p. 70

E. Prompt Polarization

  • The claimed high linear polarization of GRB 021206 was interpreted as evidence for synchrotron emission, uniform magnetic fields, or Poynting-flux dominance, but the data analysis is uncertain.Coburn and Boggs, Lyutikov et al., Granot, and others proposed these implications, while alternative interpretations include inverse Compton emission [211, 71].Source: E. Prompt Polarization · p. 70
  • Random magnetic fields can yield nearly uniform-field polarization for narrow edge-viewed jets, so polarization alone does not establish synchrotron emission or Poynting-flux dominance.High polarization should occur in almost every burst for uniform fields but only rarely for random fields; further burst data are needed, though unlikely soon.Source: E. Prompt Polarization · p. 70

VII. THE AFTERGLOW … C. Light Curves for the early radiative phase

This section examines afterglow light curves from the standard adiabatic evolution of relativistic ejecta and extends the dynamics to an early radiative phase. It covers the resulting piecewise spectral behavior, including fast- and slow-cooling regimes and the evolution of the synchrotron break frequencies.

VII. THE AFTERGLOW

  • The afterglow starts at R_ext as ejecta energy transfers to the shocked external medium, initially possibly affecting shock hydrodynamics through radiation losses before becoming adiabatic.For long bursts, this energy transfer occurs while the burst is still ongoing.Source: §VII · p. 71

A. Relativistic Blast Waves and the Blandford-McKee solution

  • The Blandford–McKee solution models an adiabatic ultra-relativistic blast wave with Γ ≫1, including ambient density profiles ρ = ρ0(R/R0)^−k and conical geometries.For a double-sided jet, the solid angle is Ω ≈ 2πθ^2; the k = 2 case is relevant to progenitor winds.Source: A. Relativistic Blast Waves and the… · pp. 71–72
  • The adiabatic approximation applies for most of the afterglow, but the first hour—or first day for k = 2—may be radiative or partially radiative when ǫ_e ≈1.Analytic self-similar solutions describe the radiative phase, including cases with continuous energy injection from the central engine.Source: A. Relativistic Blast Waves and the… · pp. 73–74

B. Light Curves for the ”Standard” Adiabatic Synchrotron Model

  • The standard synchrotron light curve is obtained from the time evolution of Fν,max and the break frequencies νc, νm, and νsa, treating fast- and slow-cooling cases separately.The calculation uses the Blandford–McKee dynamics and exact integration over its profile for the numerical factors.Source: B. Light Curves for the ”Standard”… · pp. 74–75
  • The peak flux remains constant while moving to lower frequencies, with fast cooling at early times, slow cooling at late times, and transition when νc = νm.The transition is determined by the crossing of the cooling and typical synchrotron frequencies.Source: B. Light Curves for the ”Standard”… · p. 75
  • Below the self-absorption frequency νsa, optically thick synchrotron emission follows Fν ∝ ν^2 in slow cooling, while fast-cooling emission is controlled by the τν ∼1 emitting layer.In fast cooling, the effective emitting location shifts from the back of the shocked shell toward the shock as frequency decreases.Source: B. Light Curves for the ”Standard”… · p. 75
  • The model gives Fν ∝ ν^2 for ν < ν_ac and Fν ∝ ν^11/8 for ν_ac < ν < ν_sa, with fast- and slow-cooling results summarized separately.These results are valid only for p > 2 and γ_max much higher than γ_min; if p < 2, γ_max plays a critical role.Source: B. Light Curves for the ”Standard”… · p. 76
  • Integrating the full Blandford–McKee shocked-fluid volume smooths the spectrum and light curve near break frequencies while preserving asymptotic slopes away from them.A simple integration procedure is discussed following, and detailed numerical smooth-spectrum treatments are described by Granot and Sari and [148].Source: B. Light Curves for the ”Standard”… · p. 76
  • The standard solution assumes adiabaticity, although long-term energy losses can alter the hydrodynamics and require evolving the energy in the dynamical equations [290].The model also includes cases involving wind propagation and jet breaks in its summarized light-curve tables.Source: B. Light Curves for the ”Standard”… · p. 76

C. Light Curves for the early radiative phase

  • When ǫ_e is near unity, the first few afterglow hours can be radiative, with significant kinetic-energy loss and dynamics satisfying E ∝ Γ and Γ ≅ (R/L)^−3.The radiative-to-adiabatic transition occurs when losses become negligible; radiative emission requires ν_c below ν_m, with ν_c = ν_m at t_rad [376].Source: C. Light Curves for the early… · p. 77

D. Light Curve During the Newtonian transition … 2. The light curve with a variable density or energy

This section develops a light-curve formalism spanning the Newtonian Sedov–Taylor and relativistic Blandford–McKee phases, including wind-like environments and slowly varying density or energy. It examines how refreshed and reverse shocks, density drops, overdense regions, and self-similar emission structure affect observable re-brightening and model validity.

D. Light Curve During the Newtonian transition

  • In the Newtonian Sedov-Taylor phase, ν_m ∝t^-3, while the late-time light curve enables calorimetric estimates of afterglow energy and searches for orphan radio afterglows.The radio flux is relatively large and varies over several months.Source: D. Light Curve During the Newtonian… · p. 78

E. Generalizations: I. Winds

  • For a wind profile n(R) ∝R^-k, high initial density lowers the cooling frequency, which then increases with time unlike the constant-density case.Cooling-regime transitions differ, and the cooling frequency may initially lie below the synchrotron self-absorption frequency; wind and constant-density light curves can nevertheless look similar when ν_m, ν_c < ν.Source: E. Generalizations: I. Winds · pp. 78–79

F. Generalizations: II. Energy injection and refreshed shocks

  • Refreshed shocks occur when slower matter catches up; adding such matter changes the canonical decay slope and produces a slower light-curve decay.The reverse shock is always mildly relativistic.Source: F. Generalizations: II. Energy… · pp. 79–80

G. Generalizations: III. Inhomogeneous density profiles

  • Inhomogeneous circumburst density can be modeled numerically or analytically by representing the light curve as emission from instantaneous BM solutions with distinct external densities.This framework addresses the variable afterglow light curve observed in GRB 021004.Source: G. Generalizations: III. Inhomogeneous… · p. 80

1. The light curve of a BM solution

  • For a self-similar BM profile, integrating equal-arrival-time emission yields a finite pulse whose radiation is concentrated within ∼R/Γ^2 behind the shock front.The pulse-shape function g_β depends on the shell’s radial and angular structure, while A_ν depends on shock-front conditions along the line of sight.Source: §1 · p. 81
  • The BM formalism describes emission within each power-law spectral segment and can be matched across segments to calculate the complete blast-wave light curve.It relates blast-wave variables, observer time, break frequencies, external density, energy, collected mass, and spectral factors.Source: §1 · p. 82

2. The light curve with a variable density or energy

  • Variable-density or variable-energy light curves are approximated by integrating emission from instantaneous BM solutions, provided variations are not too rapid.For density changes, the approximation relaxes over ΔR ≈ R(2^(1/(4−k)) − 1) and requires variations broader than this scale.Source: §2 · p. 82
  • After a sharp density drop, adiabatic cooling initially dominates, emission near R ≈ R_d later prevails, and the new forward shock eventually becomes dominant.The approximation includes emission before the drop and from the new forward shock but omits emission during adiabatic cooling.Source: §2 · p. 83
  • Even a mild overdense region with maximal over-density 2 affects the light curve for a long duration, mainly because of angular spreading, with duration depending strongly on over-density.The example considers a Gaussian overdensity with ΔR/R = 0.1 in an interstellar medium.Source: §2 · p. 83
  • The variable-density treatment is limited to slowly varying, low-contrast profiles because strong reverse shocks reduce Γ_sh, suppress flux, and constrain re-brightening steepness.Since observed flux scales roughly as n^1/2, a significant re-brightening requires a large density contrast that instead produces a strong reverse shock and delayed emission.Source: §2 · p. 83
  • The same approximation applies to blast-wave energy variations, including refreshed shocks, but it misses the resulting reverse shock while enabling simple light-curve calculations for a specified energy profile.Spherically symmetric energy variations can arise when inner shells arrive from the source and refresh the blast wave.Source: §2 · p. 84

H. Generalizations: IV. Jets · I. Generalizations: V. Angular Dependent Jets and the Structured Jet Model

These sections examine how jet geometry, hydrodynamic evolution, observing conditions, and angular structure shape afterglow jet breaks and light curves. They assess the implications of realistic lateral spreading and structured-jet models for predicted observational behavior.

H. Generalizations: IV. Jets

  • When Γ ∼ θ^-1, reduced beaming produces an on-axis jet break and allows off-axis observers to detect an orphan afterglow.The transition occurs as Γ^-1 exceeds the original jet opening angle θ.Source: H. Generalizations: IV. Jets · p. 84
  • Jet-break predictions are model-dependent: sideways-expansion assumptions can yield simultaneous breaks, or two distinct breaks when beaming changes before hydrodynamic spreading.Different analytic and semi-analytic models predict different break sharpness, durations, and changes in the temporal decay index.Source: H. Generalizations: IV. Jets · p. 86
  • 2D simulations show that realistic jets spread sideways less, have egg-shaped shock fronts, and increase their opening angle much more slowly than simple models predict.Matter at the sides moves sideways more slowly and is less luminous than the jet front, while most radiation remains within the initial opening angle.Source: H. Generalizations: IV. Jets · pp. 86–87
  • Emission-weighted quantities remain near the jet front and axis, whereas density-weighted quantities are lower because much shocked matter resides in the slower side regions.This mismatch demonstrates that the emitting material and the bulk shocked matter occupy dynamically different parts of the jet.Source: H. Generalizations: IV. Jets · p. 87
  • Because jetted-afterglow light curves depend strongly on jet hydrodynamics, realistic hydrodynamic models are essential for reliable predictions.The large differences between simple dynamical assumptions and 2D simulations motivate calculating light curves from realistic jet evolution.Source: H. Generalizations: IV. Jets · p. 87
  • For ν > νm(tjet), jets produce an achromatic break, whereas radio frequencies show a gradual change at tjet and stronger steepening when νm crosses the observing band.The break is sharper and slightly earlier for on-axis than off-axis observers; after the break, α = 2.85 for p = 2.5.Source: H. Generalizations: IV. Jets · pp. 87–88

I. Generalizations: V. Angular Dependent Jets and the Structured Jet Model

  • Structured jets average angular structure at later times as decreasing Γ widens the visible region and mixing averages the ejecta.In the standard structured-jet interpretation, all bursts share a fixed angular structure and the break reflects the viewing angle.Source: §I · p. 88
  • A structured jet viewed at θo remains comparable to the pre-break light curve until Γ^-1(0) = θo, after which declining energy per solid angle produces a break.The model interprets the luminosity distribution as a viewing-angle distribution with P(θo)dθo ∝ sin θodθo, but current observations are somewhat inconsistent and remain inconclusive because of biases.Source: §I · p. 89
  • Models with and without angular mixing have similar light curves, indicating that widening of the viewing angle dominates physical averaging; constant-energy, variable-Γ profiles can lack observed jet breaks.For (a, b) = (2, 2) and (2, 0), breaks occur when Γ(θo) ∼ θo^-1, but predicted slope changes and pre-break flattening are not supported by observations.Source: §I · p. 90
  • A reduced 1-D hydrodynamic model reproduces the light curves of more detailed approximations, with model 1 favored at early times and model 2 at late times.The analysis concludes that full numerical simulations are required for a complete angular-dependent-jet solution.Source: §I · p. 90

J. Afterglow Polarization - a tool that distinguished between the different jet models … 1. Pre-acceleration

This section examines afterglow polarization and orphan afterglows as probes of jet geometry and beaming, including their observational signatures and search strategies. It also considers prompt-radiation pre-acceleration, which alters the surrounding medium and external-shock deceleration.

J. Afterglow Polarization - a tool that distinguished between the different jet models

  • Three polarization peaks are predicted for an off-axis uniform jet, with the central peak’s position angle rotated by 90°; structured jets instead differ sharply and show no polarization-angle jumps.Structured-jet polarization is expected to reach around 20% near the jet break, when θobs ∼ Γ^-1.Source: J. Afterglow Polarization - a tool… · p. 91
  • Patchy-shell hot spots predict correlated light-curve and polarization fluctuations, with later bumps decreasing in amplitude and polarization-direction jumps being random, sharp, and accompanied by changes in polarization amount.For angular fluctuation scale θf, the first light-curve bump occurs when Γ^-1 ∼ θf.Source: J. Afterglow Polarization - a tool… · pp. 91–92

K. Orphan Afterglows

  • Orphan afterglows become detectable outside the jet opening angle when Γ^-1 reaches the observer’s viewing angle, with larger angles producing weaker and softer emission.X-ray orphan afterglows may appear hours to a few days after the burst, optical afterglows brighter than 25th magnitude can persist for a week within roughly 10° of the jet axis, and late radio emission may be visible at all viewing angles.Source: K. Orphan Afterglows · p. 92

1. Optical Orphan Afterglow

  • The constant-energy interpretation makes the post-jet-break optical afterglow light curve universal, yielding a fixed detectable θmax(z, m) independent of θj when θj < θmax.The maximal flux is independent of jet opening angle, θj, but declines rapidly as the observer moves off-axis.Source: §1 · p. 93
  • Optical orphan-afterglow detection rates increase with limiting magnitude, while shallow, wide surveys provide the highest rate per square degree per hour, provided the limit is not fainter than ~23rd magnitude.Optimistic estimates predict 15 SDSS detections and 35 detections for a dedicated 2m telescope operating for one year, but candidate identification remains difficult.Source: §1 · p. 94

2. Radio Orphan Afterglow

  • Radio orphan afterglows become isotropic after the Newtonian transition, so their observed rate directly measures GRB beaming; nondetection instead supplies a lower limit on beaming.The radio flux is expected to be around 1 mJy at roughly three months, and nine candidates above 6 mJy were found but could be radio-loud AGNs.Source: §2 · pp. 95–96

L. Generalizations: VI. Additional Physical Processes

  • The review identifies prompt-radiation pre-acceleration and neutron decay as additional physical processes that can influence observed GRB afterglows.This part develops the pre-acceleration process.Source: L. Generalizations: VI. Additional… · p. 96

1. Pre-acceleration

  • When η exceeds ηload ≈20−30, runaway e± loading begins; above ηacc = 100−150 the medium accelerates, and at ηgap ≈3 × 10^3 it opens a gap ahead of the ejecta.The radiation front’s interaction with ambient electrons can amplify backscattering through pair production, despite the medium’s small optical depth.Source: §1 · pp. 96–97
  • Radiation preacceleration creates a cavity in which the ejecta moves freely until R = Rgap, where it begins sweeping the medium with a small relative Lorentz factor.This demonstrates how γ-rays modify the standard external-shock interaction.Source: §1 · p. 98
  • When Rext < Rgap, effective deceleration begins only at Rgap; the ambient Lorentz factor then approaches unity by Racc ≈ 3Rgap as Γambient = (R/Racc)−6.For Rext > Rgap, this delayed-deceleration effect is not important.Source: §1 · p. 98
  • After the delay, the ejecta abruptly encounters substantial ambient material, resembling a collision with a wall and generating a sharp pulse.The pulse is associated with the rapid fall of Γambient as the preaccelerated medium is encountered.Source: §1 · p. 98
  • Preacceleration generally requires a dense circumburst environment and a large initial Lorentz factor, as expected around Wolf-Rayet progenitors.Otherwise Rgap becomes too large and deceleration occurs after the gap has closed.Source: §1 · p. 98
  • Observational limits on prompt emission constrain the ambient interstellar-medium density in the modeled preacceleration scenario.The supplied passage reports a density constraint but its upper-bound units are truncated.Source: §1 · p. 98

2. Neutron decoupling and decay … C. Cosmic Rays and Ultra High Energy Cosmic Rays

This section examines neutron decoupling, particle acceleration, and the production and propagation of high-energy photons, neutrinos, and cosmic rays in GRBs. It also considers attenuation and cooling conditions, GZK-related effects, and unresolved observational evidence.

2. Neutron decoupling and decay

  • Neutron decay modifies afterglow evolution through freely coasting neutrons, with outcomes determined by whether R_decay is below or above R_ext.For R_decay < R_ext, decay products mix with protons without significantly changing evolution beyond adding energy; low Γ_n can instead produce a delayed shock.Source: §2 · p. 99
  • Γ_n ≈ Γ_0 neutron decay can produce an early triple interaction and brightening at a few seconds, when decay products interact ahead of the proton shell.The interaction occurs at radii of a few times R_decay, with an observed time of approximately a few seconds divided by Γ_n/300.Source: §2 · p. 99
  • Inelastic proton-neutron collisions during internal shocks can produce 10 GeV ν_μ and 5 GeV ν_e, with fluxes potentially yielding approximately 7 events per year in km^3 detectors.Associated GeV photons are expected but are unlikely to be detectable.Source: §2 · p. 99

A. TeV γ-rays

  • SSC emission can create secondary high-energy components from a few hundred GeV in internal shocks to approximately 100 TeV in the early afterglow.Reverse-shock emission can yield approximately 100 MeV SSC photons, while these components may be comparable to or larger than prompt GRB γ-ray fluxes and can be simultaneous with the burst.Source: A. TeV γ-rays · p. 100
  • High-energy photon production may also arise from proton acceleration and photo-pion cascades, producing photons from 10 MeV to 100 GeV or up to 300 GeV.Photons above 1 TeV can be strongly attenuated by pair production with intergalactic near-infrared radiation, while secondary delayed GeV emission may be deflected by weak intergalactic magnetic fields.Source: A. TeV γ-rays · pp. 100–101

B. Neutrinos

  • GRBs could be detectable sources of high-energy neutrinos with energies ranging from 10^14 eV to 10^17 eV, produced by internal or external shocks.Internal shocks produce a significant flux of approximately 10^14 eV neutrinos.Source: B. Neutrinos · pp. 101–102
  • GRB jets and shocks can produce neutrinos from TeV to 10^17eV through interactions involving stellar-shell, pulsar-wind-bubble, and afterglow photons.The Supranova channel may yield 10^16eV neutrinos at a comparable detection rate to internal-shock proton interactions with gamma rays.Source: B. Neutrinos · p. 102

C. Cosmic Rays and Ultra High Energy Cosmic Rays

  • GRB internal and reverse shocks can accelerate protons to 10^20eV, and comparable gamma-ray and UHECR energy outputs would make GRBs potential sources of the highest-energy cosmic rays.The lower-energy fireball component was several orders of magnitude below the observed supernova-remnant cosmic-ray flux and was therefore unimportant.Source: C. Cosmic Rays and Ultra High Energy… · pp. 102–103
  • Above the GZK energy, CMBR interactions attenuate UHECRs, so 10^20eV protons travel only several tens of Mpc and must originate from relatively nearby sources.Because GRBs are transient and UHECRs are deflected and delayed by intergalactic magnetic fields, direct GRB-arrival associations are not expected.Source: C. Cosmic Rays and Ultra High Energy… · p. 103
  • If GRBs produce UHECRs, the spectrum should break at the GZK energy, with cosmological sources below it but only local sources within several dozen Mpc above it.A possible break has been suggested, but the observational situation remains unclear and likely requires the Auger detector for resolution.Source: C. Cosmic Rays and Ultra High Energy… · p. 103

D. Gravitational Radiation … B. The Pulsar Model

This section examines gravitational-wave emission from GRBs and the compact-object engines that may power them, including accretion-powered black holes and magnetized pulsar-like alternatives. It considers contributions from mergers, collapsars, supranovae, and prompt jets, with some signals potentially detectable while direct GRB radiation is generally weak.

D. Gravitational Radiation

  • GRB-associated gravitational waves may arise indirectly from compact-object formation or directly during jet acceleration, but the direct pulse is weak and perpendicular to the GRB signal.A GRB pointed away from Earth may still produce an orphan afterglow; the nearest burst in the adopted rate estimate would be approximately 0.1 Mpc, while a burst directed toward us would be approximately 450 Mpc away.Source: D. Gravitational Radiation · pp. 103–104

1. Gravitational Radiation from Neutron Star Mergers

  • If neutron-star mergers produce short GRBs at a high rate, one merger event per year could fall within LIGO II sensitivity and be marginally detectable by LIGO I, although its burst points away from us.Merger searches use chirping templates, and coincidence with a GRB could lower the required signal-to-noise ratio and improve effective detector sensitivity; statistical directional searches have also been proposed [196], [97].Source: §1 · p. 104

2. Gravitational Radiation from Collapsars

  • Collapsar radiation is dominated by black-hole lowest normal modes, with typical frequency 20c^3/GM and efficiency of a few × 10^-4, beyond LIGO II detection at 1 Gpc, [397].The collapsar model involves massive-star core collapse to a black hole surrounded by a thick accretion disk.Source: §2 · p. 105

3. Gravitational Radiation from Supranova

  • The supranova model predicts an initial supernova gravitational-wave signal weeks or months before the GRB and a second collapse signal coincident with it [426].Because the first collapse precedes the GRB substantially, its gravitational waves are not temporally correlated with the burst.Source: §3 · p. 105

4. Gravitational Radiation from the GRB

  • The direct GRB signal has h ≈ .5·10^-25 at f_max ≈100 Hz and is far below planned-detector sensitivity, although some engine models predict 10^53 ergs near a few hundred Hz [417, 418].Those enhanced signals arise from instabilities that break axial symmetry in a black-hole–accretion-torus system and fall within the LIGO/VIRGO frequency range.Source: §4 · p. 107
  • GRBs are among the most powerful burst sources of gravitational waves in the Universe.Source: §4 · p. 107

IX. MODELS OF INNER ENGINES

  • The inner engine must produce ultrarelativistic, collimated flows and multiple activity timescales, ruling out a single explosive release and favoring accretion onto a newborn black hole.The proposed disk has mass ∼0.1m⊙ and accompanies black-hole formation.Source: §IX · p. 108

A. Black hole accretion

  • Black-hole accretion models associate long bursts with Collapsars and short bursts with NS-NS or NS-BH mergers because disk size and feeding determine duration.Source: A. Black hole accretion · pp. 108–109

B. The Pulsar Model

  • Pulsar-like mechanisms for rapidly rotating, highly magnetized sources require magnetic fields of order 10^15G and produce relativistic Poynting-flux-dominated flows that couple through plasma instability to observed γ-rays.Source: B. The Pulsar Model · p. 109

C. Rotating black holes and the Blandford Znajek mechanism … X. OPEN QUESTIONS AND FUTURE PROSPECTS

This section reviews GRB central-engine scenarios, including black-hole extraction, collapsars, supranovae, and compact-object mergers, and considers their connections to long and short GRBs. It also examines unresolved issues in relativistic-wind mechanisms, prompt and afterglow emission, progenitors, jet structure, and population properties, alongside prospects for neutrino and gravitational-wave tests.

C. Rotating black holes and the Blandford Znajek mechanism

  • The Blandford–Znajek mechanism may extract a rotating black hole’s energy through magnetic fields engulfing the black-hole–torus system, but its relativistic-MHD treatment is beyond this review.The review refers readers to recent extensive discussions, including Lee et al..Source: C. Rotating black holes and the… · p. 110

D. The Collapsar Model

  • In the Collapsar model, a rapidly rotating star above 30M⊙ collapses to a black hole with an accretion disk and axial funnel, whose accretion powers a jet that penetrates the envelope and produces a long GRB.The disk is around 0.1 M⊙, accretes over several dozen seconds, and can power the burst through neutrino annihilation [242] or the Blandford-Znajek mechanism; jet propagation through the stellar mantle is the model’s distinctive ingredient.Source: D. The Collapsar Model · pp. 110–111
  • Collapsar simulations find stellar-mantle collimation from initial half-angles up to 20° to roughly 5°, with terminal Lorentz factors around 150 and possible thermal precursors at breakout.More than 80% of the jet’s total energy is initially internal, and instabilities can generate Lorentz-factor variability needed for internal shocks.Source: D. The Collapsar Model · p. 111

E. The Supranova Model

  • The Supranova model separates a supernova from a later neutron-star collapse by weeks or months, but GRB 030329 with SN 2003dh is incompatible with it and long-lived 50 sec disks may be inefficient.A pulsar wind can create a magnetized propagation medium, amplify afterglow magnetic fields, and explain EGRET emission through inverse Compton scattering, although its density may be too high for spherical models.Source: E. The Supranova Model · p. 112

F. Merging neutron stars

  • Neutron-star or neutron-star–black-hole mergers form black-hole–accretion-disk systems and are candidate inner engines specifically for short GRBs, driven by gravitational-radiation-induced orbital decay.This evolutionary pathway is exemplified by the binary pulsar PSR 1913+16.Source: F. Merging neutron stars · p. 113
  • Neutron-star mergers produce black hole–accretion-disk systems with disks of order 0.1M⊙ and release ∼5 × 10^53ergs, though most energy emerges as neutrinos and gravitational waves.The available energy could power a GRB, but the relativistic wind mechanism is unresolved; neutrino annihilation may be insufficient because many neutrinos are swallowed by the black hole.Source: F. Merging neutron stars · p. 114

X. OPEN QUESTIONS AND FUTURE PROSPECTS

  • The afterglow is well understood: observations across wavelengths broadly fit a slowing relativistic flow with synchrotron emission, and the flow is collimated.New observations can still require refinements such as refreshed shocks, patchy shells, or variable external densities.Source: §X · pp. 114–115
  • Key afterglow questions concern X-ray-line energy requirements, distinguishing GHOSTs from OTGRBs, and determining whether short GRBs possess afterglows and suitable environments.Orphan-afterglow searches could test collimated jets and constrain GRB rates, while image resolution and polarization could probe jet geometry and synchrotron emission.Source: §X · p. 115
  • Prompt-emission physics remains less clear: internal shocks explain temporal structure, but the observed spectrum may require modifying simple synchrotron emission.Open issues include narrow Ep distributions, luminosity-related correlations, redshift correlations, and the microphysics of collisionless shocks, particle acceleration, and magnetic-field generation.Source: §X · p. 116
  • GRB population properties remain unresolved, including the luminosity function, redshift-dependent rate, relation to star formation, and the connection between XRFs and GRBs.Improved spectral resolution and observations at higher γ-ray energies could provide additional constraints, while the XRF–GRB continuum must be reconciled with the narrow Ep distribution.Source: §X · p. 116
  • Ultra-high-energy neutrinos could test proton acceleration to ultra-high energies in GRBs and thereby assess whether GRBs produce ultra-high-energy cosmic rays.MeV-neutrino fluxes would be too weak to detect from cosmological distances.Source: §X · pp. 116–117
  • Gravitational radiation could directly probe inner-engine activity and identify merger events, while similarities among GRBs, microquasars, and AGNs may reveal common accretion-powered engines.All three systems accelerate collimated relativistic flows and appear to involve accretion onto black holes.Source: §X · p. 117
  • Long GRBs have substantial observational evidence linking them to core-collapse supernovae, while short-GRB progenitors lack direct or indirect evidence.The supernova association constrains the inner engine of long GRBs, but the corresponding situation for short GRBs remains unclear.Source: §X · p. 117
  • Most inner-engine models invoke a black-hole–torus system powered by neutrino annihilation or electromagnetic extraction, including Blandford–Znajek variants.Proposed electromagnetic mechanisms include magnetic turbulence in the accretion disk, disk–black-hole–magnetic-field interaction, and pulsar-like activity.Source: §X · p. 117
  • Key unresolved questions concern whether the ultrarelativistic flow is baryonic or Poynting-dominated, and how it is accelerated, collimated, and varied.The model must explain the variability required for internal shocks and the different observed timescales, but direct inner-engine observations are unavailable.Source: §X · p. 117

Figures · Tables

This section compiles figures and tables covering observational signatures of GRBs and fireball-model predictions. It organizes visual and tabular treatments of variability, afterglows, jets, polarization, radiation processes, and temporal and spectral behavior across different regimes and environments.

Figures

  • GRB 920627 lasted 52 sec, with typical 0.8-sec pulses and two quiescent intervals of approximately 10 sec.Source: Figure 2 · p. 139, Figures · p. 139
  • The GRB 990510 optical light curve fit gives α1 = 0.82 ± 0.02, α2 = 2.18 ± 0.05, and t∗ = 1.2 ± 0.08 days.Source: Figure 7 · p. 141, Figures · p. 141
  • GRB-SN comparisons indicate that observed GRB-SNe may represent only the bright tail of local Type Ib/Ic supernovae, plausibly accompanying all long-duration GRBs [33].The faintest GRB-SN non-detection probes only approximately the top 40th percentile of local Type Ib/Ic SNe.Source: Figure 10 · p. 143, Figures · p. 143
  • The GRB 030329/SN2004dh spectra evolve from a power-law continuum with narrow host-galaxy HII-region lines at z = 0.168 to broad supernova-like peaks.Source: Figure 11 · p. 144, Figures · p. 144
  • The GRB energy histogram centers on Eγ = 1.33·10^51 ergs with σ = 0.07 dex and a burst-to-burst rms spread of 0.35 dex, while five bursts are more than 5σ outliers.The figure states that discrepant energy alone does not justify excluding the outliers.Source: Figure 12 · p. 144, Figures · p. 145
  • The model figures depict internal shocks from faster shells colliding with slower ones, forward and reverse shocks in four regions, and synchrotron spectra determined by break-frequency ordering.They also show polarization from ordered or structured magnetic fields and jet light curves varying with viewing angle and environment.Source: Figure 19 · p. 148, Figures · pp. 148–149, Figure 22 · p. 149
  • The figures show that homogeneous and structured-jet light curves can be difficult to distinguish observationally, while post-break afterglows converge when energy per solid angle is constant.The comparison focuses on optical observations from roughly 4 hours to 1 month and on differing opening angles before the jet break.Source: Figures · pp. 153–154
  • The figures also depict polarization from different observer offsets and radiation-front effects across adiabatic and radiative blast-wave regimes.The radiation-front example marks four propagation zones and contrasts standard predictions that neglect the front with the actual behavior.Source: Figures · pp. 154, 156
  • Orphan-afterglow predictions are similar for optimistic parameters, whereas model B predicts slightly more events than model A for canonical parameters.The figure varies normalization, peak redshift, and jet opening angle; model A’s canonical normalization is F0 = 0.003 µJy, while its optimistic case uses θj = 0.05 and F0 = 0.015 µJy.Source: Figures · p. 155, Figure 32 · p. 155

Tables

  • The tables compile α and β prescriptions for fast and slow cooling in constant-density media, winds, jets, multiple frequency bands, electron indices 1 < p < 2, and post-jet-break evolution.Separate entries address optical/X-ray and radio frequencies in wind profiles, with table ordering tied to light-curve evolution at fixed high or low observed frequency.Source: Table I · p. 156, Table II · p. 156, Table III · p. 157

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