Efficiency and Spectrum of Internal Gamma‐Ray Burst Shocks

Abstract

We present an analysis of the Internal Shock Model of GRBs, where gamma-rays are produced by internal shocks within a relativistic wind. We show that observed GRB characteristics impose stringent constraints on wind and source parameters. We find that a significant fraction, of order 20%, of the wind kinetic energy can be converted to radiation, provided the distribution of Lorentz factors within the wind has a large variance and provided the minimum Lorentz factor is > Γ ± ≈ 10 2.5 L 2/9 52 , where L = 10 52 L 52 erg s −1 is the wind luminosity. For a high, > 10%, efficiency wind, spectral energy breaks in the 0.1 to 1 MeV range are obtained for sources with dynamical time R/c ∼ < 1 ms, suggesting a possible explanation for the observed clustering of spectral break energies in this range. The lower limit Γ ± to wind Lorenz factor and the upper limit ≈ 1(R/10 7 cm) −5/6 MeV to observed break energies are set by Thomson optical depth due to e ± pairs produced by synchrotron photons. Natural consequences of the model are absence of bursts with peak emission energy significantly exceeding 1 MeV, and existence of low luminosity bursts with low, 1 keV to 10 keV, break energies.Subject headings: gamma-rays: bursts -methods: numerical -radiation mechanisms: non-thermal Both the spectrum and temporal dependence of afterglow emission are consistent with synchrotron emission of electrons accelerated to high energy at the shock wave driven by the

Gravitational-Wave Observations May Constrain Gamma-Ray Burst Models: The Case of Gw150914–gbm

“…A more thorough analysis considering pairs and the width of the shells (Guetta et al 2001) yields a stricter limit:…”

On the Generation of Ultra–High‐Energy Cosmic Rays in Gamma‐Ray Bursts: A Reappraisal

“…Although this is not a strict theoretical upper limit (models approaching 100% have been proposed; Lazzati et al 2000), still values derived from observations are so large as to throw doubts on the validity of the present version of internal-shock model. In fact, the maximum efficiency that can be reached with this model is of the order of 20% (Guetta, Spada, & Waxman 2001a), but only under ad hoc assumptions: for random distributions in the wind properties, the efficiency cannot exceed %0.005 (Spada et al 2000). Perfectly efficient models without internal shocks can be conceived (Lazzati et al 2000), but they cannot account for bursts' spectra (Ghisellini et al 2000b).…”

“…The only hope appears to be the production of high-energy neutrinos that must accompany the in situ acceleration of particles; occasionally, in fact, UHECRs will produce pions (and then neutrinos) through collisions with photons in the moderately photon-rich environment provided by the postshock shells. If UHECRs are accelerated at internal shocks, the neutrinos thus produced will arrive at Earth simultaneously with the photons of the burst proper and will have an energy $10 15 eV (Waxman & Bahcall 1997;Guetta, Spada, & Waxman 2001b). If UHECRs are accelerated at external shocks, they will arrive at Earth simultaneously with the photons of the afterglow and will have a higher energy, e10 17 eV (Vietri 1998a(Vietri , 1998b.…”

Neutrinos of Energy∼1016 eVfrom Gamma-Ray Bursts in Pulsar Wind Bubbles

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“…For larger values of 0.2 yr t sd 1 yr, the neutrino flux due to photomeson interaction with the PWB photons will dominate over the one due photomeson interaction with the GRB photons [8], if the GRB has Γ 600 and t v 50 ms. Since larger Γ and t v imply a lower typical synchrotron frequency for the prompt GRB, this may apply to X-ray flashes, if they are indeed GRBs with relatively large Lorentz factors and/or a large variability time, t v [11]. For these events no afterglow emission has been detected and this can be explained considering the fact that for t sd 1 yr the GRB would have a peculiar and short lived afterglow emission.…”