Gamma-ray Burst Spectra Research Articles

GRB Prompt Emission with Anisotropic Electron Distribution

The typical spectrum of the prompt emission of gamma-ray bursts (GRBs) indicates that the electron cooling is suppressed in spite of the strong magnetic field in the standard synchrotron model. Recent particle-in-cell simulations show that the particle acceleration by magnetic reconnection in a magnetically dominated plasma can lead to small pitch angles especially in a low-energy region. Such a small pitch angle prevents electrons from cooling via synchrotron radiation. In this paper, taking into account the effects of the synchrotron cooling and the adiabatic cooling, we numerically calculate the synchrotron spectra with anisotropic electron distributions. If we require a Poynting flux larger than 1050 erg s−1 as the model is motivated by magnetic reconnection, the bulk Lorentz factor of ∼1000 and the electron minimum Lorentz factor of γ min ∼ 104 are required to reproduce the typical GRB spectrum.

Plasma Shock Wave in Gamma-Ray Bursts: Nonlinear Phenomena and Radiative Process

Since gamma-ray bursts (GRBs) are related to extreme explosions in the universe, they provide a unique setup to study various space plasma phenomena. The GRB spectra supply a wide range of information regarding the various nonlinear interactions and associated structures. In this work, we study the generation of shock fronts and their properties in a plasma. Such a plasma shock is the aftereffect of an explosion of which the prompt emission of GRBs are the signatures. The shock fronts are studied analytically by deriving the KdV–Burger’s equation. The solution of the KdV–Burgers equation via the “Cole-Hoff transformation” is studied alongside the usual “hyperbolic-tangent method.” The dynamical properties of the shock solitons are studied further to second our findings and find the stability and any possibility of chaos. The results will help to interpret the stellar plasma properties from data. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">PACS</i> —95.30.Qd, 52.65.-y, 52.35.-g, 52.35.Tc, 52.27.Lw

Resolving the H I in damped Lyman α systems that power star formation.

Reservoirs of dense atomic gas (primarily hydrogen) contain approximately 90 per cent of the neutral gas at a redshift of 3, and contribute to between 2 and 3 per cent of the total baryons in the Universe1-4. These 'damped Lyman α systems'-so called because they absorb Lyman α photons within and from background sources-have been studied for decades, but only through absorption lines present in the spectra of background quasars and γ-ray bursts5-10. Such pencil beams do not constrain the physical extent of the systems. Here we report integral-field spectroscopy of a bright, gravitationally lensed galaxy at a redshift of 2.7 with two foreground damped Lyman α systems. These systems are greater than 238 kiloparsecs squared in extent, with column densities of neutral hydrogen varying by more than an order of magnitude on scales of less than 3 kiloparsecs. The mean column densities are between 1020.46 and 1020.84 centimetres squared and the total masses are greater than 5.5 × 108-1.4 × 109 times the mass of the Sun, showing that they contain the necessary fuel for the next generation of star formation, consistent with relatively massive, low-luminosity primeval galaxies at redshifts greater than 2.

The First Insight-HXMT Gamma-Ray Burst Catalog: The First Four Years

Abstract The Hard X-ray Modulation Telescope (Insight-HXMT) is China’s first X-ray astronomy satellite. It was launched on 2017 June 15. The anticoincidence CsI detectors of the High Energy X-ray telescope (HE) on board Insight-HXMT could serve as an all-sky gamma-ray monitor in about 0.2–3 MeV. In its first four years of operation, Insight-HXMT has detected 322 gamma-ray bursts (GRBs) by the offline search pipeline, including blind search and targeted search. For the GOLDEN sample of Insight-HXMT GRBs, joint analyses were performed with other GRB missions, including the Fermi Gamma-ray Burst Monitor (Fermi/GBM), the Swift Burst Alert Telescope (Swift/BAT), and the Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM). The analyses showed that Insight-HXMT can provide a better constraint on the GRB spectrum at a higher-energy band. The properties of Insight-HXMT GRBs are reported in detail, including their trigger time, duration, spectral parameters, peak fluxes of different timescales, and fluence. This catalog is an official product of the Insight-HXMT GRB team.

Gamma-Ray Burst Prompt Emission Spectrum and E p Evolution Patterns in the ICMART Model

Abstract In this paper, we simulate the prompt emission light curve, spectrum, and E p evolution patterns of gamma-ray bursts (GRBs) within the framework of the Internal-collision-induced Magnetic Reconnection and Turbulence (ICMART) model. We show that this model can produce a Band-shaped spectrum, whose parameters (E p, α, β) could follow the typical distribution of GRB observations, as long as the magnetic field and the electron acceleration process in the emission region are under appropriate conditions. On the other hand, we show that for one ICMART event, E p evolution is always a hard-to-soft pattern. However, a GRB light curve is usually composed of multiple ICMART events that are fundamentally driven by the erratic activity of the GRB central engine. In this case, we find that if one individual broad pulse in the GRB light curve is composed of multiple ICMART events, the overall E p evolution could be disguised as an intensity-tracking pattern. Therefore, mixed E p evolution patterns can coexist in the same burst, with a variety of combined patterns. Our results support the ICMART model as a competitive model to explain the main properties of GRB prompt emission. The possible challenges faced by the ICMART model are also discussed in detail.

Capabilities of the GAMMA-400 gamma-ray telescope to detect gamma-ray bursts from lateral directions

• The GAMMA-400 gamma-ray telescope performance for lateral aperture. • Detection of GRB from the lateral aperture in the energy range from ∼ 10 to ∼ 100 MeV. • The problem of connection between high- and low-energy gamma-ray emissions of GRBs. The currently developing space-based gamma-ray telescope GAMMA-400 will measure the gamma-ray and electron + positron fluxes using the main top-down aperture in the energy range from ∼ 20 MeV to several TeV in a highly elliptic orbit (without shading the telescope by the Earth and outside the radiation belts) continuously for a long time. The instrument will provide fundamentally new data on discrete gamma-ray sources, gamma-ray bursts (GRBs), sources and propagation of Galactic cosmic rays and signatures of dark matter due to its unique angular and energy resolutions in the wide energy range. The gamma-ray telescope consists of the anticoincidence system (AC), the converter-tracker (C), the time-of-flight system (S1 and S2), the position-sensitive and electromagnetic calorimeters (CC1 and CC2), scintillation detectors (S3 and S4) located above and behind the CC2 calorimeter and lateral detectors (LD) located around the CC2 calorimeter. In this paper, the capabilities of the GAMMA-400 gamma-ray telescope to measure fluxes of GRBs from lateral directions of CC2 are analyzed using Monte-Carlo simulations. The analysis is based on off-line second-level trigger construction using signals from S3, CC2, S4 and LD detectors. For checking the numerical algorithm the data from space-based GBM and LAT instruments of the Fermi experiment are used, namely, three long bursts: GRB 080916C, GRB 090902B, GRB 090926A and one short burst GRB 090510A. The obtained results allow us to conclude that from lateral directions the GAMMA-400 space-based gamma-ray telescope will reliably measure the spectra of bright GRBs in the energy range from ∼ 10 to ∼ 100 MeV with the on-axis effective area of about 0.13 m 2 for each of the four sides of CC2 and total field of view of about 6 sr.

A connection between spectral sharpness and energies as well as flux in fermi gamma-ray bursts

ABSTRACT We revisit the sharpness angle (θ) under the peak or break of gamma-ray burst (GRB) spectra with the best peak flux P and time-integrated F spectral data provided by the Fermi GBM Burst Catalogue. We compute the sharpness angles of best-fit model spectra and check some interesting relations between θ and physics quantities. It is found that (i) a positive correlations between θ and the observed fluence as well as the isotropic radiated energy holds among GRBs, especially for the F spectra; (ii) when checking the correlation between θ and energy flux a weaker anti-correlation holds among GRBs and a tighter anti-correlation holds within GRBs, especially in single pulses. Our results further show that the spectral shape is related to the energy and flux by cross-checking other measures of spectral curvature. The correlated relationship between spectral sharpness and energy flux can be well explained as a thermal origin for GRB prompt emission: A large entropy around the peak of the light curve makes the photosphere approach the saturation radius, resulting in an intense emission with a narrow spectrum; as the entropy decreases, the photosphere deviates from the saturation radius, resulting in weaker emission with a broader spectrum.

The photosphere emission spectrum of hybrid relativistic outflow for gamma-ray bursts

ABSTRACT The photospheric emission in the prompt phase is the natural prediction of the original fireball model for gamma-ray burst (GRB) due to the large optical depth (τ &amp;gt; 1) at the base of the outflow, which is supported by the quasi-thermal components detected in several Fermi GRBs. However, which radiation mechanism (photosphere or synchrotron) dominates in most GRB spectra is still under hot debate. The shape of the observed photosphere spectrum from a pure hot fireball or a pure Poynting-flux-dominated outflow has been investigated before. In this work, we further study the photosphere spectrum from a hybrid outflow containing both a thermal component and a magnetic component with moderate magnetization (σ0 = LP/LTh ∼ 1 − 10), by invoking the probability photosphere model. The high-energy spectrum from such a hybrid outflow is a power law rather than an exponential cutoff, which is compatible with the observed Band function in a great amount of GRBs. Also, the distribution of the low-energy indices (corresponding to the peak-flux spectra) is found to be quite consistent with the statistical result for the peak-flux spectra of GRBs best-fitted by the Band function, with similar angular profiles of structured jet in our previous works. Finally, the observed distribution of the high-energy indices can be well understood after considering the different magnetic acceleration (due to magnetic reconnection and kink instability) and the angular profiles of dimensionless entropy with the narrower core.

Probing the physical properties of the intergalactic medium using blazars

ABSTRACT We use Swift blazar spectra to estimate the key intergalactic medium (IGM) properties of hydrogen column density ($\mathit {N}\small {\rm HXIGM}$), metallicity, and temperature over a redshift range of 0.03 ≤ z ≤ 4.7, using a collisional ionization equilibrium model for the ionized plasma. We adopted a conservative approach to the blazar continuum model given its intrinsic variability and use a range of power-law models. We subjected our results to a number of tests and found that the $\mathit {N}\small {\rm HXIGM}$ parameter was robust with respect to individual exposure data and co-added spectra for each source, and between Swift and XMM–Newton source data. We also found no relation between $\mathit {N}\small {\rm HXIGM}$ and variations in source flux or intrinsic power laws. Though some objects may have a bulk Comptonization component that could mimic absorption, it did not alter our overall results. The $\mathit {N}\small {\rm HXIGM}$ from the combined blazar sample scales as (1 + z)1.8 ± 0.2. The mean hydrogen density at z = 0 is n0 = (3.2 ± 0.5) × 10−7 cm−3. The mean IGM temperature over the full redshift range is log(T/K) =6.1 ± 0.1, and the mean metallicity is [X/H] = −1.62 ± 0.04(Z ∼ 0.02). When combining with the results with a gamma-ray burst (GRB) sample, we find the results are consistent over an extended redshift range of 0.03 ≤ z ≤ 6.3. Using our model for blazars and GRBs, we conclude that the IGM contributes substantially to the total absorption seen in both blazar and GRB spectra.

Synchrotron self-Compton radiation from magnetically dominated turbulent plasmas in relativistic jets

ABSTRACT Relativistic jets launched by rotating black holes are powerful emitters of non-thermal radiation. Extraction of the rotational energy via electromagnetic stresses produces magnetically dominated jets, which may become turbulent. Studies of magnetically dominated plasma turbulence from first principles show that most of the accelerated particles have small pitch angles, i.e. the particle velocity is nearly aligned with the local magnetic field. We examine synchrotron self-Compton radiation from anisotropic particles in the fast cooling regime. The small pitch angles reduce the synchrotron cooling rate and promote the role of inverse Compton (IC) cooling, which can occur in two different regimes. In the Thomson regime, both synchrotron and IC components have soft spectra, νFν ∝ ν1/2. In the Klein–Nishina regime, synchrotron radiation has a hard spectrum, typically νFν ∝ ν, over a broad range of frequencies. Our results have implications for the modelling of BL Lacertae objects (BL Lacs) and gamma-ray bursts (GRBs). BL Lacs produce soft synchrotron and IC spectra, as expected when Klein–Nishina effects are minor. The observed synchrotron and IC luminosities are typically comparable, which indicates a moderate anisotropy with pitch angles θ ≳ 0.1. Rare orphan gamma-ray flares may be produced when θ ≪ 0.1. The hard spectra of GRBs may be consistent with synchrotron radiation when the emitting particles are IC cooling in the Klein–Nishina regime, as expected for pitch angles θ ∼ 0.1. Blazar and GRB spectra can be explained by turbulent jets with a similar electron plasma magnetization parameter, σe ∼ 104, which for electron–proton plasmas corresponds to an overall magnetization σ = (me/mp)σe ∼ 10.

A marginally fast-cooling proton–synchrotron model for prompt GRBs

ABSTRACTA small fraction of gamma-ray bursts (GRBs) with available data down to soft X-rays (∼0.5 keV) has been shown to feature a spectral break in the low-energy part (∼1–10 keV) of their prompt emission spectrum. The overall spectral shape is consistent with optically thin synchrotron emission from a population of particles that have cooled on a time-scale comparable to the dynamic time to energies that are still much higher than their rest-mass energy (marginally fast cooling regime). We consider a hadronic scenario and investigate if the prompt emission of these GRBs can originate from relativistic protons that radiate synchrotron in the marginally fast cooling regime. Using semi-analytical methods, we derive the source parameters, such as magnetic field strength and proton luminosity, and calculate the high-energy neutrino emission expected in this scenario. We also investigate how the emission of secondary pairs produced by photopion interactions and γγ pair production affect the broad-band photon spectrum. We support our findings with detailed numerical calculations. Strong modification of the photon spectrum below the break energy due to the synchrotron emission of secondary pairs is found, unless the bulk Lorentz factor is very large (Γ ≳ 103). Moreover, this scenario predicts unreasonably high Poynting luminosities because of the strong magnetic fields (106–107 G) that are necessary for the incomplete proton cooling. Our results strongly disfavour marginally fast cooling protons as an explanation of the low-energy spectral break in the prompt GRB spectra.

The variable absorption in the X-ray spectrum of GRB 190114C

Gamma-ray burst (GRB) 190114C was a bright burst that occurred in the local Universe (z = 0.425). It was the first GRB ever detected at teraelectronvolt (TeV) energies, and this was thanks to MAGIC. We characterize the ambient medium properties of the host galaxy through the study of the absorbing X-ray column density. Using a combination of Swift, XMM-Newton, and NuSTAR observations, we find that the GRB X-ray spectrum is characterized by a high column density that is well in excess of the expected Milky Way value and decreases, by a factor of ∼2, around ∼105 s. Such a variability is not common in GRBs. The most straightforward interpretation of the variability in terms of the photoionization of the ambient medium is not able to account for the decrease at such late times, when the source flux is less intense. Instead, we interpret the decrease as due to a clumped absorber, denser along the line of sight and surrounded by lower-density gas. After the detection at TeV energies of GRB 190114C, two other GRBs were promptly detected. These two also have high intrinsic column density values, and there are hints for a decrease in their column densities as well. We speculate that a high local column density might be a common ingredient of TeV-detected GRBs.

Temporal evolution of prompt GRB polarization

ABSTRACT The dominant radiation mechanism that produces the prompt emission in gamma-ray bursts (GRBs) remains a major open question. Spectral information alone has proven insufficient in elucidating its nature. Time-resolved linear polarization has the potential to distinguish between popular emission mechanisms, e.g. synchrotron radiation from electrons with a power-law energy distribution or inverse Compton scattering of soft seed thermal photons, which can yield the typical GRB spectrum but produce different levels of polarization. Furthermore, it can be used to learn about the outflow’s composition (i.e. whether it is kinetic-energy-dominated or Poynting-flux-dominated) and angular structure. For synchrotron emission, it is a powerful probe of the magnetic field geometry. Here, we consider synchrotron emission from a thin ultrarelativistic outflow, with bulk Lorentz factor Γ(R) = Γ0(R/R0)−m/2 ≫ 1, that radiates a Band-function spectrum in a single (multiple) pulse(s) over a range of radii, R0 ≤ R ≤ R0 + ΔR. Pulse profiles and polarization evolution at a given energy are presented for a coasting (m = 0) and accelerating (m = −2/3) thin spherical shell and for different viewing angles for a top-hat jet with sharp as well as smooth edges in emissivity. Four different magnetic field configurations are considered, such as a locally ordered field coherent over angular scales θB ≳ 1/Γ, a tangled field (B⊥) in the plane transverse to the radial direction, an ordered field (B∥) aligned in the radial direction, and a globally ordered toroidal field (Btor). All field configurations produce distinct polarization evolution with single (for B⊥ and B∥) and double (for Btor) 90○ changes in the polarization position angle.

Probing the physical properties of the intergalactic medium using gamma-ray bursts

ABSTRACT We use gamma-ray burst (GRB) spectra total continuum absorption to estimate the key intergalactic medium (IGM) properties of hydrogen column density ($\mathit {N}_{\mathrm{HXIGM}}$), metallicity, temperature, and ionization parameter over a redshift range of 1.6 ≤ z ≤ 6.3, using photoionization equilibrium (PIE) and collisional ionization equilibrium (CIE) models for the ionized plasma. We use more realistic host metallicity, dust corrected where available, in generating the host absorption model, assuming that the host intrinsic hydrogen column density is equal to the measured ionization corrected intrinsic neutral column from UV spectra (${\it N}_{\mathrm{H}\,{\small I,IC}}$). We find that the IGM property results are similar, regardless of whether the model assumes all PIE or CIE. The $\mathit {N}_{\mathrm{HXIGM}}$ scales as (1 + z)1.0–1.9, with equivalent hydrogen mean density at z = 0 of $n_0 = 1.8^{+1.5}_{-1.2} \times 10^{-7}$ cm−3. The metallicity ranges from $\sim 0.1\, \mathrm{Z}_{\odot }$ at redshift z ∼ 2 to $\sim 0.001\, \mathrm{Z}_{\odot }$ at redshift z &amp;gt; 4. The PIE model implies a less rapid decline in average metallicity with redshift compared to CIE. Under CIE, the temperature ranges between 5.0 &amp;lt; log (T/K) &amp;lt; 7.1. For PIE the ionization parameter ranges between 0.1 &amp;lt; log (ξ) &amp;lt; 2.9. Using our model, we conclude that the IGM contributes substantially to the total absorption seen in GRB spectra and that this contribution rises with redshift, explaining why the hydrogen column density inferred from X-rays is substantially in excess of the intrinsic host contribution measured in UV.

A comprehensive view of blackbody components in the X-ray spectra of GRBs

Abstract A small fraction of gamma-ray bursts (GRBs) exhibit blackbody emission in the X-ray spectra, the origin of which is debated. In order to gain a more complete understanding of this phenomenon, we present a search for blackbody components in 116 GRBs with known redshifts observed by Swift X-ray telescope (XRT). A time-resolved spectral analysis is carried out and the significance of the blackbody is assessed with respect to an absorbed power-law model. We report nine new detections and confirm the previously reported blackbody in GRB 171205A. Together with our previous results, there are a total of 19 GRBs with significant blackbody emission in a sample of 199 GRBs observed by Swift over 13 yr. The detections include one short GRB and two low-luminosity GRBs. We estimate fireball parameters from the blackbody components and note that the blackbody luminosity is correlated with the temperature and inferred Lorentz factor. There is a large spread in the properties of the blackbody components and the light curves, which points to different origins for the emission. In about a third of the GRBs, the blackbody is clearly associated with late prompt emission from the jet. The rest of the sample includes cases that are fully consistent with the expectations from a cocoon, as well cases that may be explained by high-latitude emission or more energetic cocoons. These results indicate that thermal emission is associated with all parts of the jet.

The localization method of GECAM and simulation analysis

Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) is scheduled to launch in late 2020. It will monitor the whole sky for gamma-ray transients, such as Gamma-Ray Bursts (GRBs) and high-energy electromagnetic counterpart of gravitational wave events. One of the key scientific capabilities of GECAM is to localize the GRB. In this study, we established a ground localization method for GECAM by simultaneously fitting the spectrum and location of GRB. In addition, with the instrument response and in-flight background simulated using the current GECAM mass model, we examined the localization capability of GECAM. As a result, we derived the relationship between localization accuracy and different parameters of the GRB, such as brightness, spectral hardness, and burst duration. Moreover, for typical brightness (flux $10^{-6}$ erg$\\,$s$^{-1}$$\\,$cm$^{-2}$ in 10–1000 keV energy range with duration of 10 s) spectrum of medium hardness, the localization accuracy was observed at about 0.6$^\\circ$ (1-$\\sigma$ statistical error). We also performed localization for two special bursts: (1) the suspected high-energy counterpart of the Fast Radio Burst (FRB 131104) with the GECAM localization error approximately 5$^{\\circ}$ and (2) the gamma-ray electromagnetic counterpart (GRB 170817A) of the first binary neutron star merger gravitational wave event GW170817, with GECAM localization error of about 10$^{\\circ}$.

Spectral Diversities of Gamma-Ray Bursts in High-energy Bands: Hints from Turbulent Cascade

Abstract We statistically examine the gamma-ray burst (GRB) photon indices obtained by the Fermi-GBM and Fermi-LAT observations and compare the LAT GRB photon indices to the GBM GRB photon indices. We apply the jitter radiation to explain the GRB spectral diversities in the high-energy bands. In our model, the jitter radiative spectral index is determined by the spectral index of the turbulence. We classify GRBs into three classes depending on the shape of the GRB high-energy spectrum when we compare the GBM and LAT detections: the GRB spectrum is concave (GRBs turn out to be softer and are labeled as S-GRBs), the GRB spectrum is convex (GRBs turn out to be harder and are labeled as H-GRBs), and the GRBs have no strong spectral changes (labeled as N-GRBs). A universal Kolmogorov index 7/3 in the turbulent cascade is consistent with the photon index of the N-GRBs. The S-GRB spectra can be explained by the turbulent cascade due to the kinetic magnetic reconnection with the spectral index range of the turbulence from 8/3 to 3.0. The H-GRB spectra originate from the inverse turbulent cascade with the spectral index range of the turbulence from 2.0 to 3.5 that occurred during the large lengthscale magnetic reconnection. Thus, the GRB radiative spectra are diversified because the turbulent cascade modifies the turbulent energy spectrum. More observational samples are expected in the future to further identify our suggestions.

Looking for MACHOs in the spectra of fast radio bursts

ABSTRACT We explore a novel search strategy for dark matter in the form of massive compact halo objects (MACHOs) such as primordial black holes or dense mini-haloes in the mass range from $10^{-4}\, \mathrm{M}_{\odot }$ to $0.1\, \mathrm{M}_{\odot }$. These objects can gravitationally lens the signal of fast radio bursts (FRBs), producing a characteristic interference pattern in the frequency spectrum, similar to the previously studied femtolensing signal in gamma-ray burst spectra. Unlike traditional searches using microlensing, FRB lensing will probe the abundance of MACHOs at cosmological distance scales (∼Gpc) rather than just their distribution in the neighbourhood of the Milky Way. The method is thus particularly relevant for dark mini-haloes, which may be inaccessible to microlensing due to their finite spatial extent or tidal disruption in galaxies. We find that the main complication in FRB lensing will be interstellar scintillation in the FRB’s host galaxy and in the Milky Way. Scintillation is difficult to quantify because it heavily depends on turbulence in the interstellar medium, which is poorly understood. We show that, nevertheless, for realistic scintillation parameters, FRB lensing can set competitive limits on compact dark matter object, and we back our findings with explicit simulations.

A Spectral Analysis of Fermi-LLE Gamma-Ray Bursts

Abstract The prompt emission of gamma-ray bursts remains mysterious since the mechanism is difficult to understand even though there are many more observations with the development of detection technology. Most of the gamma-ray bursts spectra show the Band shape, which consists of the low-energy spectral index α, the high-energy spectral index β, the peak energy E p , and the normalization of the spectrum. We present a systematic analysis of the spectral properties of 36 gamma-ray bursts (GRBs), which were detected by the Gamma-ray Burst Monitor (GBM) and simultaneously were also observed by the Large Area Telescope (LAT) and the LAT Low Energy (LLE) detector on the Fermi satellite. We performed a detailed time-resolved spectral analysis for all of the bursts in our sample. We found that the time-resolved spectrum at peak flux can be well fitted by the empirical Band function for each burst in our sample. Moreover, the evolution patterns of α and E p have been carried for statistical analysis and the parameter correlations have been obtained such as E p –F, α–F, and E p –α, all of them are presented by performing a detailed time-resolved spectral analysis. We also demonstrated that the two strong positive correlations α–F and E p –α for some bursts originate from nonphysical selection effects through simulation.

Adiabatic and Radiative Cooling of Relativistic Electrons Applied to Synchrotron Spectra and Light Curves of Gamma-Ray Burst Pulses

Abstract We investigate the adiabatic and radiative (synchrotron and inverse-Compton) cooling of relativistic electrons whose injected or initial distribution with energy is a power law. Analytical and numerical results are presented for the cooling-tail and the cooled-injected distribution that develop below and above the typical energy of injected electrons, for the evolution of the peak energy E p of the synchrotron emission spectrum. The pulse shape resulting from an episode of electron injection is also analyzed. The synchrotron emission calculated numerically is compared with the spectrum and shape of Gamma-ray burst (GRB) pulses. Both adiabatic and radiative cooling processes lead to a softening of the pulse spectrum, and both types of cooling processes lead to pulses peaking earlier and lasting shorter at higher energy, quantitatively consistent with observations. For adiabatic-dominated electron cooling, a power-law injection rate R i suffices to explain the observed power-law GRB low-energy spectra. Synchrotron-dominated cooling leads to power-law cooling-tails that yield the synchrotron standard slope α = −3/2 provided that R i ∼ B 2, which is exactly the expectation if the magnetic field is a constant fraction of the post-shock energy density. Increasing (decreasing) R i and decreasing (increasing) B(t) lead to harder (softer, respectively) slopes α than the standard value and to nonpower-law (curved) cooling-tails. Inverse-Compton cooling yields four values for the slope α but, as for synchrotron, other R i or B histories yield a wider range of slopes and curved low-energy spectra. Feedback between the power-law segments that develop below and above the typical injected electron leads to a synchrotron spectrum with many breaks.