The Prompt Emission from Gamma Ray Bursts

Overview

Gamma-ray bursts (GRBs) are the most luminous electromagnetic events in the Universe since the Big Bang. They occur at cosmological distances, with an average redshift of around z ≈ 3 and examples beyond z = 6, yet for a few seconds they can outshine everything else in the gamma-ray sky.

This project was a directed reading (PA4440 Advanced Study Topic) completed during the fourth year of an MPhys in Physics with Astrophysics at the University of Leicester, supervised by Dr Richard Willingale. The aim was to review the theories that attempt to explain the prompt emission — the gamma-rays that arrive first — and to assess how well each stands up against the observational evidence.

The problem

The energy involved is extraordinary. Assuming the emission is isotropic, a GRB can release up to around 10⁴⁷ J within a few seconds. For comparison, the rest-mass energy of the Sun is about 1.8 × 10⁴⁷ J (E = mc²), and a GRB can emit more energy in ten seconds than the Sun will radiate over its entire ten-billion-year lifetime.

The physical mechanism behind such an outburst is not fully understood. Any successful model must explain:

• Huge energy output released over very short timescales.
• Two apparent populations: short bursts (roughly under 2 seconds) and long bursts (over 2 seconds).
• Variability down to the millisecond scale, implying a very compact source.
• Non-thermal spectra that are well described empirically by the Band function but lack a clear theoretical origin.
• A luminosity so high that the radiation must be relativistically beamed, with Lorentz factors above 100, to avoid the compactness problem.

A short history

• Vela satellites (1960s): GRBs were discovered by US satellites built to detect gamma-ray pulses from nuclear weapons tests in space. The findings were published by Klebesadel and colleagues in 1973.
• CGRO / BATSE (1991–2000): thousands of bursts showed an isotropic sky distribution, casting doubt on a Galactic origin. The V/V_max test and the log N – log P distribution indicated a cosmological population.
• BeppoSAX (1996): the first X-ray afterglows allowed accurate positions, optical follow-up and redshift measurements, confirming cosmological distances and opening the “afterglow era”.
• Swift (2004) and Fermi/GLAST (launched 11 June 2008): a new generation of missions with better localisation and broader energy coverage. A burst detected in April 2009 and followed up with ESO’s Very Large Telescope was measured at a redshift of 8.2, making it the most distant known object at the time.

Generally accepted ingredients

Despite open questions, nearly all current models share several features:

1. Relativistic motion with a Lorentz factor Γ > 100, needed to overcome the compactness problem. Relativistic beaming means we see only a fraction of the source.
2. Dissipation of the energy of the relativistic flow, most likely through collisionless shocks.
3. Synchrotron radiation from relativistic electrons accelerated in those shocks. This agrees reasonably well with afterglow observations, but there are concerns about whether it fully explains the prompt spectra.
4. Jets and collimation, supported by achromatic “jet breaks” in afterglow light curves. Beaming reduces the true energy to around 10⁵¹ erg, comparable to a supernova.
5. A compact object — a black hole or neutron star — as the central engine, most likely formed in the same event.

Possible engines

• Long bursts: the collapse of a massive star (a collapsar or hypernova), producing a black hole and accretion disc. This is supported by the association of long GRBs with core-collapse supernovae and with star-forming regions.
• Short bursts: the merger of compact binaries such as neutron star–neutron star or neutron star–black hole systems. Direct evidence for short-burst progenitors was still lacking at the time of this project.

Physical processes studied

• Synchrotron radiation: derivation from the equations of motion of a charged particle in a magnetic field, leading to a power-law spectrum for a power-law electron distribution.
• Cooling breaks: fast-cooling and slow-cooling regimes and the resulting broken power-law spectra.
• Fermi acceleration: second-order acceleration (energy gain proportional to β²) and the more efficient first-order mechanism at shocks (energy gain of about 4β/3 per cycle), which naturally produces a power-law particle distribution.
• Synchrotron self-absorption, Compton scattering and inverse Compton scattering, including the limits imposed by the Klein–Nishina regime.
• Blackbody components: evidence that a power law plus a black body can fit time-resolved BATSE spectra.

Theories for the prompt emission

Fireball model (Rees and Mészáros; reviewed by Piran)

A large amount of energy is released into a compact region, forming an opaque photon–lepton fireball that expands relativistically. In the internal–external shocks picture:

• Internal shocks between shells of ejecta moving at different speeds produce the prompt gamma-rays, so the light curve reflects the activity of the inner engine.
• External shocks between the outflow and the surrounding medium produce the longer-lived afterglow.

The model explains the temporal structure well and is the most widely used framework, but internal shocks convert only a fraction of kinetic energy into radiation, and a simple synchrotron spectrum does not fit every burst.

Fireshell model (Ruffini and collaborators)

This model assumes that all GRBs originate from gravitational collapse to a black hole. An electron–positron plasma created by vacuum polarisation expands as an optically thick “fireshell”. It is described by only two parameters: the total plasma energy and the baryon loading, B.

The emission splits into a proper GRB (P-GRB), released when the shell becomes transparent, and an afterglow phase as the baryons interact with the circumburst medium. Short bursts divide into “genuine” short GRBs (very low baryon loading, B < 10^-5) and “fake” short GRBs (a very low-density environment). The model also connects naturally to the Amati relation between peak energy and isotropic-equivalent energy (E_p ∝ E_iso^~0.5). It is one of the few attempts to describe the whole GRB phenomenon in one framework.

Cannonball model (Dar, and Heinz and Begelman)

The central engine fires a series of narrow, non-spreading “bullets” that are quickly decelerated by dense circumburst matter. Pulse widths are set by the slowing-down time, and the burst duration by how long the engine keeps emitting bullets.

Assessment

• The afterglow is reasonably well understood; the prompt emission is not.
• Within the internal shocks picture, the temporal structure is reasonably understood, but the origin of the observed spectrum remains unclear and simple synchrotron emission probably needs modifying.
• The link between long GRBs and core-collapse supernovae points clearly to the engine of long bursts, but there is no direct or indirect evidence about the progenitors of short bursts.
• How the flow is accelerated and collimated, and what sets its variability, remain poorly constrained because the inner engine cannot be observed directly.
• Open observational questions include the GRB luminosity function, the burst rate as a function of redshift, and how closely GRBs trace star formation.

Teaching outputs

As well as the literature review, the project required the design of teaching materials.

Six-lecture course outline

1. Introduction, history, energetics, distribution and the short/long split.
2. Observational constraints, prompt emission and light curves.
3. Non-thermal spectra, power laws, synchrotron radiation, Fermi acceleration, cooling breaks and inverse Compton scattering.
4. The fireball model: compactness problem, internal shocks, efficiency and Sedov analysis.
5. The fireshell and cannonball models, the Amati relation and the B parameter.
6. Future prospects, models and missions, including GLAST/Fermi.

40-minute lecture

Delivered on 14 May 2009, covering the history of GRB observations, their observed properties, the generally accepted ingredients, the main prompt emission models and their physical processes, and open questions for future research.

Suggested problems

1. Energy calculation: estimate the energy needed to “evaporate” the Sun, convert fluence to isotropic energy at the mean GRB redshift, and compare with the Eddington luminosity.
2. Source distribution: show that a homogeneous distribution gives a log N – log F slope of −3/2.
3. Synchrotron radiation: derive the equations of motion, the cyclotron frequency and the power-law spectrum from a power-law electron distribution.
4. Fermi acceleration: derive the mean energy gain for second-order and first-order acceleration and the resulting energy after n collisions.

My role

I carried out the full project: gathering and critically reading the literature, writing detailed notes on each work studied, deriving the key physical results, and designing and delivering the lecture and problem set under the supervision of Dr Richard Willingale.

Key sources

• Piran, T. (2004). The physics of gamma-ray bursts. Reviews of Modern Physics, 76(4), 1143–1210.
• Mészáros, P. (2002). Theories of gamma-ray bursts. Annual Review of Astronomy and Astrophysics, 40, 137–169.
• Rybicki, G.B. and Lightman, A.P. (1979). Radiative Processes in Astrophysics. Wiley.
• Band, D. et al. (1993). BATSE observations of gamma-ray burst spectra. I. Spectral diversity. Astrophysical Journal, 413, 281.
• Klebesadel, R. et al. (1973). Observations of gamma-ray bursts of cosmic origin. Astrophysical Journal, 182, L85.
• Meegan, C.A. et al. (1992). Spatial distribution of gamma-ray bursts observed by BATSE. Nature, 355, 143.
• Bianco, C.L. et al. (2007–2008). Papers on the fireshell model and the canonical GRB scenario (arXiv:0712.0495, 0804.2816, 0804.2818).
• Dar, A. et al. (2006). Fireball and cannonball models of gamma-ray bursts confront observations. Chinese Journal of Astronomy and Astrophysics, 6, suppl. 1, 301–314.

Keywords

Gamma-ray bursts; GRB; prompt emission; relativistic astrophysics; fireball model; fireshell model; cannonball model; synchrotron radiation; inverse Compton; Fermi acceleration; internal shocks; BATSE; Swift; Fermi; MPhys; University of Leicester.