The spectral shape of the prompt emissions of gamma-ray bursts (GRBs) is typically expressed by the Band function: smooth joining of two power-law functions for high-energy and low-energy regions. To reveal the origin of the Band function, we revisit the stochastic acceleration model, in which electrons are accelerated via scattering with turbulent waves in the GRB outflow. The balance between the acceleration and synchrotron cooling yields a narrow energy-distribution similar to the Maxwellian distribution. The synchrotron spectrum becomes consistent with the observed hard photon index for the low-energy region. On the other hand, the narrow electron energy distribution contradicts the power-law spectrum for the high-energy region. We consider an evolution of the electron energy distribution to solve this problem. The turbulence and magnetic field induced by a certain hydrodynamical instability gradually decay. According to this evolution, the typical synchrotron photon energy also decreases with time. The time-integrated spectrum forms the power-law shape for the high-energy region. We discuss the required evolutions of the turbulence and magnetic field to produce a typical Band function. Although the decay of the turbulence is highly uncertain, recent numerical simulations for decaying turbulence seem comparatively positive for the stochastic acceleration model. Another condition required to reconcile observations is a much shorter duration of the stochastic acceleration than the dynamical timescale.
Polarization can serve as a probe of the radiation mechanism and magnetic field (MF) configuration in gamma-ray bursts (GRBs). In the case of constant MF, the synchrotron polarization in the prompt phase of GRBs has been widely studied. In this paper, we consider the case of the decaying MF. We calculate the time-averaged and instantaneous synchrotron polarizations in a pulse for different viewing angles and for the large-scale decaying MF model, which can explain the so-called Band spectrum. We find that the on-axis time-averaged polarization degree (PD) in the energy band of 50-500 keV for t…
In the internal shock model for gamma-ray bursts (GRBs), the synchrotron spectrum from the fast cooling electrons in a homogeneous downstream magnetic field (MF) is too soft to produce the low-energy slope of GRB spectra. However the magnetic field may decay downstream with distance from the shock front. Here we show that the synchrotron spectrum becomes harder if electrons undergo synchrotron and inverse-Compton cooling in a decaying MF. To reconcile this with the typical GRB spectrum with low energy slope $νF_ν\proptoν$, it is required that the postshock MF decay time is comparable to the co…
The late afterglow of gamma-ray burst is believed to be due to progressive deceleration of the forward shock wave driven by the gamma-ray burst ejecta propagating in the interstellar medium. We study the dynamic effect of interstellar turbulence on shock wave propagation. It is shown that the shock wave decelerates more quickly than previously assumed without the turbulence. As an observational consequence, an earlier jet break will appear in the light curve of the forward shock wave. The scatter of the jet-corrected energy release for gamma-ray burst, inferred from the jet-break, may be partl…
We examine the possible role of turbulence in feeding the emission of gamma-ray bursts (GRBs). Turbulence may develop in a GRB jet as the result of hydrodynamic or current-driven instabilities. The jet carries dense radiation and the turbulence cascade can be damped by Compton drag, passing kinetic fluid energy to photons through scattering. We identify two regimes of turbulence dissipation: (1) "Viscous" - the turbulence cascade is Compton damped on a scale $\ell_{\rm damp}$ greater than the photon mean free path $\ell_\star$. Then turbulence energy is passed to photons via bulk Comptonizatio…
We analysed all archival data of the low-mass X-ray binary 4U 1636--53 with the Rossi X-ray Timing Explorer (1490 observations). We found a total of 336 type-I X-ray bursts from this source. In the time-resolved spectra of 69 of these bursts, close to the peak of the burst, the best-fitting blackbody radius shows the sharp increase and decrease that is typical of photospheric radius-expansion (PRE) bursts. We found that in 17 of these 69 PRE bursts, after the touchdown point, the blackbody radius increases again quickly after about 1 second, and from then on the radius decreases slightly or it…
We propose a novel model to produce ultrahigh-energy cosmic-rays (UHECRs) in gamma-ray burst jets. After the prompt gamma-ray emission, hydrodynamical turbulence is excited in the GRB jets at or before the afterglow phase. The mildly relativistic turbulence stochastically accelerates protons. The acceleration rate is much slower than the usual first-order shock acceleration rate, but in this case it can be energy-independent. The resultant UHECR spectrum is so hard that the bulk energy is concentrated in the highest energy range, resulting in a moderate requirement for the typical cosmic ray l…
The origin of extended emissions following prompt emissions of short gamma-ray bursts (SGRBs) is in mystery. The long-term activity of the extended emission is responsible for promising electromagnetic counterparts to gravitational waves and, so that it may be a key to uncovering the progenitor of SGRBs. We investigate the early X-ray light curves of 26 SGRBs with known redshifts observed with the X-Ray Telescope aboard the {\it Neil Gehrels Swift Observatory} ({\it Swift}). We find that the exponential temporal decay model is able to describe the extended emissions comprehensively with a rest…
Synchrotron radiation of relativistic electrons is an important radiation mechanism in many astrophysical sources. In the sources where the synchrotron cooling time scale $t_c$ is shorter than the dynamical time scale $t_{dyn}$, electrons are cooled down below the minimum injection energy. It has been believed that such "fast cooling" electrons have an energy distribution $dN_e /dγ_e \propto γ_e^{-2}$, and their synchrotron radiation flux density has a spectral shape $F_ν\propto ν^{-1/2}$. On the other hand, in a transient expanding astrophysical source, such as a gamma-ray burst (GRB), the ma…
Rapid temporal variability has been widely observed in the light curves of gamma-ray bursts (GRBs). One possible mechanism for such variability is related to the relativistic eddies in the jet. In this paper, we include the contribution of the inter-eddy medium together with the eddies to the gamma-ray emission. We show that the gamma-ray emission can either lead or lag behind the observed synchrotron emission, where the latter originates in the inter-eddy medium and provides most of seed photons for producing gamma-ray emission through the inverse-Compton scattering. As a consequence, we argu…
The turbulence in the diffuse intergalactic medium (IGM) plays an important role in various astrophysical processes across cosmic time, but it is very challenging to constrain its statistical properties both observationally and numerically. Via the statistical analysis of turbulence along different sightlines toward a population of fast radio bursts (FRBs), we demonstrate that FRBs provide a unique tool to probe the intergalactic turbulence. We measure the structure function (SF) of dispersion measures (DMs) of FRBs to study the multi-scale electron density fluctuations induced by the intergal…
Freely decaying relativistic force-free turbulence is studied for the first time. We initiate the magnetic field at a short wavelength and simulate its relaxation toward equilibrium on two and three dimensional periodic domains, in both helical and non-helical settings. Force-free turbulent relaxation is found to exhibit an inverse cascade in all settings, and in 3D to have a magnetic energy spectrum consistent with the Kolmogorov $5/3$ power law. 3D relaxations also obey the Taylor hypothesis; they settle promptly into the lowest energy configuration allowed by conservation of the total magne…
We consider a simple model for gamma-ray bursts induced by magnetic reconnection in turbulent media. The magnetic field in a jet is subject to kink instabilities, which distort the regular structure of the spiral magnetic field, drive turbulence, and trigger reconnection. The resulting reconnection takes place in a high Reynolds number medium, where turbulence is further enhanced and in turn accelerates the reconnection process. This boot-strap reconnection gives rise to bursts of reconnection events, through which the free energy of magnetic field is transformed into a gamma-ray burst. The ef…
Gamma ray burst (GRB) time series is a non-stationary time series with all its statistical properties varying with time. Considering that each GRB is a different manifestation of the same stochastic process we studied the time dependent as well as time averaged probability density function (\emph{pdf}) characterizing the underlying stochastic process. The \emph{pdf}s are fitted with Gaussian distribution function and it has been argued that the Gaussian \emph{pdf}s possibly indicate the turbulence origin of GRB. The spectral and temporal evolution of GRBs are also studied through the evolution…
Fast radio bursts (FRBs) are millisecond-duration events thought to originate beyond the Milky Way galaxy. Uncertainty surrounding the burst sources, and their propagation through intervening plasma, has limited their use as cosmological probes. We report on a mildly dispersed (dispersion measure 266.5+-0.1 pc cm^-3), exceptionally intense (120+-30 Jy), linearly polarized, scintillating burst (FRB 150807) that we directly localize to 9 arcmin^2. Based on a low Faraday rotation (12.0+-0.7 rad m^-2), we infer negligible magnetization in the circum-burst plasma and constrain the net magnetization…
In the internal shock model of gamma ray bursts ultrahigh energy muons, pions, neutrons and kaons are likely to be produced in the interactions of shock accelerated relativistic protons with low energy photons (KeV-MeV). These particles subsequently decay to high energy neutrinos/antineutrinos and other secondaries. In the high internal magnetic fields of gamma ray bursts, the ultrahigh energy charged particles ($μ^+$, $π^+$, $K^+$) lose energy significantly due to synchrotron radiations before decaying into secondary high energy neutrinos and antineutrinos. The relativistic neutrons decay to …
We perform 2.5D particle-in-cell simulations of decaying turbulence in the presence of a guide (out-of-plane) background magnetic field. The fluctuating magnetic field initially consists of Fourier modes at low wavenumbers (long wavelengths). With time, the electromagnetic energy is converted to plasma kinetic energy (bulk flow+thermal energy) at the rate per unit volume of ${\pp J}\cdot{\pp E}$ for current density ${\pp J}$ and electric field ${\pp E}$. Such decaying turbulence is well known to evolve toward a state with strongly intermittent plasma current. Here we decompose the electric fie…
We introduce a non-resonant acceleration mechanism arising from the second adiabatic invariant in magnetic turbulence and apply it to study the prompt emission spectra of gamma-ray bursts (GRBs). The mechanism contains both the first- and second-order Fermi acceleration, originating from the interacting turbulent reconnection and dynamo processes. It leads to a hard electron energy distribution up to a cutoff energy at the balance between the acceleration and synchrotron cooling. The sufficient acceleration rate ensures a rapid hardening of any initial energy distribution to a power-law distri…
Turbulence is a vital part of the interstellar medium (ISM) of galaxies, contributing significantly to galaxy energy budgets and acting as a regulator of star formation. Despite this, little is understood about ISM turbulence empirically. In the Milky Way, multiple tracers are used to reconstruct the density- and velocity-fluctuation power spectra over an enormous range of scales, but questions remain on the nature of these fluctuations at the smallest scales. Even less is known about the ISM of distant galaxies, where only a few tracers of turbulence, such as non-thermal broadening of optical…
A time-resolved spectral analysis for a sample of 22 intense, broad GRB pulses from the BATSE GRB sample is presented. We fit the spectra with the Band function and investigate the correlation between the observed flux (F) and the peak energy (E_p) of the $νf_ν$ spectrum in the rising and decaying phases of these pulses. Two kinds of E_p evolution trends, i.e., hard-to-soft (the two-third pulses in our sample) and $E_{\rm p}$-tracing-$F$ (the one-third pulses in our sample) are observed in pulses from different GRBs and even from different pulses of the same burst. No dependence of spectral ev…
Small-scale fluctuating magnetic fields of order $n$G are observed in supernova shocks and galaxy clusters, where its amplification is likely caused by the Biermann battery mechanism. However, these fields cannot be amplified further without the turbulent dynamo, which generates magnetic energy through the stretch-twist-fold (STF) mechanism. Thus, we present here novel three-dimensional magnetohydrodynamic (MHD) simulations of a laser-driven shock propagating into a stratified, multiphase medium, to investigate the post-shock turbulent magnetic field amplification via the turbulent dynamo. The…
Microphysics of weakly magnetized relativistic collisionless shock waves, corroborated by recent high performance numerical simulations, indicate the presence of a microturbulent layer of large magnetic field strength behind the shock front, which must decay beyond some hundreds of skin depths. The present paper discusses the dynamics of such microturbulence, borrowing from these same numerical simulations, and calculates the synchrotron signature of a powerlaw of shock accelerated particles. The decaying microturbulent layer is found to leave distinct signatures in the spectro-temporal evolut…
Conservation of magnetic-helicity fluctuations due to spatial decorrelation of fluxes in decaying MHD turbulence
Research School of Astronomy and Astrophysics, Australian National University（澳大利亚国立大学天文与天体物理研究学院）；Australia’s Climate Simulator (ACCESS-NRI), Australian National University（澳大利亚气候模拟器（ACCESS-NRI），澳大利亚国立大学）；Princeton Center for Theoretical Science（普林斯顿理论科学中心）；Department of Applied Mathematics and Theoretical Physics, University of Cambridge（剑桥大学应用数学与理论物理系）；Gonville & Caius College（冈维尔与凯斯学院）；Canadian Institute for Theoretical Astrophysics, University of Toronto（多伦多大学加拿大理论天体物理研究所）
