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Electromagnetic Catastrophe in Ultrarelativistic Shocks and the Prompt Emission of Gamma-Ray Bursts  Boris E

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Electromagnetic Catastrophe in Ultrarelativistic Shocks and the Prompt Emission of Gamma-Ray Bursts  Boris E Mon. Not. R. Astron. Soc. 345, 590–600 (2003) Electromagnetic catastrophe in ultrarelativistic shocks and the prompt emission of gamma-ray bursts Boris E. Stern1,2 1Institute for Nuclear Research, Russian Academy of Sciences, Moscow 117312, Russia 2Astro Space Centre of Lebedev Physical Institute, Moscow, Profsoyuznaya 84/32, 117997, Russia Accepted 2003 June 30. Received 2003 June 23; in original form 2003 January 20 Downloaded from https://academic.oup.com/mnras/article/345/2/590/1747042 by guest on 25 September 2021 ABSTRACT It is shown that an ultrarelativistic shock with the Lorentz factor of the order of tens or higher, propagating in a moderately dense interstellar medium (density above ∼1000 cm−3), undergoes a fast dramatic transformation into a highly radiative state. The process leading to this phenomenon resembles the first-order Fermi acceleration with the difference that the energy is transported across the shock front by photons rather than protons. The reflection of the energy flux crossing the shock front in both directions is due to photon–photon pair production and Compton scattering. Such a mechanism initiates a runaway non-linear pair cascade fed directly by the kinetic energy of the shock. Eventually, the cascade feeds back the fluid dynamics, converting the sharp shock front into a smooth velocity gradient and the runaway evolution changes to a quasi-steady-state regime. This effect has been studied numerically using the non- linear large particle Monte Carlo code for the electromagnetic component and a simplified hydrodynamic description of the fluid. The most interesting application of the effect is the phenomenon of gamma-ray bursts (GRBs) where it explains a high radiative efficiency and gives a perspective to explain spectra of GRBs and their time variability. The results predict a phenomenon of ‘GeV bursts’ which arise if the density of the external medium is not sufficiently high to provide a large compactness. Key words: shock waves – methods: numerical – gamma-rays: bursts. other hand, Fermi acceleration has a number of limiting factors in 1 INTRODUCTION available power and radiative efficiency (see Achterberg et al. 2001; Astrophysical objects where we observe – active galactic nuclei Bednarz & Ostrowski 1999). For this reason, Fermi acceleration is (AGN) – or infer – gamma-ray bursts (GRBs), soft gamma-ray re- usually considered as a source of high-energy cosmic rays while the peaters – a relativistic bulk motion demonstrate surprisingly high intensive radiation is traditionally explained in terms of the internal gamma-ray luminosity. In some cases, the energy release in gamma- energy dissipation. rays can be comparable to the total kinetic energy of the bulk motion In this paper, we suggest a highly radiative analogue of Fermi in the source. This implies a very efficient mechanism of the energy acceleration where the main role is played by photons rather than conversion of the bulk motion into hard radiation. It is clear that, by charged particles. A similar idea about the important role of in the case of explosive phenomena such as GRBs, the radiation neutral particles in shocks has been suggested independently in a originates from ultrarelativistic shocks (Cavallo & Rees 1978; Rees very recent paper by Derishev et al. (2003). For a simple illustration, &M´esz´aros1992). This is less certain in the case of AGN jets; the shock and the external medium can be represented as two mirrors however, there exist a large number of works considering shocks as moving with an ultrarelativistic velocity respectively to each other. the main source of AGN jet radiation (for a review, see Kirk 1997). Let ξ s and ξ e be their reflection coefficients (depending on the type We can describe the energy stored in the shock in two ways: as a and the energy of a particle) and let be the Lorentz factor of the total kinetic energy of ejecta and shocked matter or as their internal shock. A photon being elastically reflected head-on from a moving energy. Two different ways of shock energy release are known: the mirror gains a factor of ∼2 in its energy. Thus, the total energy of first-order Fermi acceleration and different mechanisms of internal photons participating in back and forth motion between the mirrors energy dissipation. Fermi acceleration does not require dissipation can be roughly described by the equation as it is fed directly by the kinetic energy of the bulk motion. On the 2 dE/dt = ξsξe − S E/tc (1) where t c is a characteristic time of reflection cycle and S is the E-mail: [email protected] probability of the particle escape. Actually, equation (1) represents C 2003 RAS Ultrarelativistic shocks and GRBs 591 no more than an instructive toy model because a real situation is into a smoother velocity gradient. This transformation removes the essentially non-local (t c is uncertain) and requires an integration radiative divergence; now an upstream photon most probably in- 2 through particle spectra. If ξ sξ e > S, the total energy of particles teracts in the pre-accelerated medium and the energy gain in the will grow exponentially until mirrors decelerate. interaction becomes much less than 2. We should expect the for- In the case of the first-order Fermi acceleration the reflection re- mation of some steady-state regime where the fluid velocity pattern sults from the diffusion of supra-thermal charged particles in the is adjusted in a way to satisfy the energy conservation law. The magnetic field. How will this two-mirror approach look when ap- luminosity at this stage should be close to its ultimate value L ∼ plied to photons? If a soft photon (e.g. of a synchrotron nature) 2 dm/dt where m is the mass of the external matter swept up by interacts only with electrons, the reflection coefficients ξ s and ξ e the shock. are of the order of the Thomson optical depth of each medium (ξ s ∼ Summarizing, we can expect the following evolution: (i) a seed ξ e ∼ τ T, see Section 2). This case does not differ essentially from the radiation due to dissipation of the internal energy; (ii) Compton well-known thermal Comptonization in relativistic regime at elec- boosting and the cascade boosting of the electromagnetic component tron temperature − 1. The photon boosting terminates as soon as in linear exponential regime; (iii) a sharper non-linear evolution Downloaded from https://academic.oup.com/mnras/article/345/2/590/1747042 by guest on 25 September 2021 the photon gains a sufficient energy to interact in the Klein–Nishina when the boosted high-energy component contributes to the soft regime when reflection coefficients decrease. The Compton boost- target photon field; (vi) transformation of the shock front and setting ing is probably not very important by itself, however it could provide up a highly luminous quasi-steady-state regime. The entire event is photons above pair production cut-off and give rise to a new much so dramatic that it deserves the name ‘electromagnetic catastrophe’. more powerful effect. This qualitative illustration is confirmed below at a quantitative The importance of pair production in GRB shocks and AGN jets level. The main tool in this study is the large particle non-linear has been emphasized in many works, for example, by Thompson Monte Carlo (LPMC) code described in Stern et al. (1995). (1997), Ramirez-Ruiz et al. (2001) and Mesz´ aros,´ Ramirez-Ruiz While the mechanism can work in different astrophysical phe- and Rees (2001). Thompson (1997) and Ramirez-Ruiz et al. (2001) nomena, this study is focused on its application to GRBs. Corre- stated that the pair production can enhance the radiation efficiency spondingly, the explored region of parameters represents the pre- of the shock, providing new supra-thermal particles as seeds for vailing view on GRBs (large Lorentz factors, moderately high Fermi acceleration. In this paper, we show that the pair production densities). plays a crucial role in initiating a runaway energy release. In Section 2 we describe the general formulation of the problem, A necessary condition to trigger this process is the existence of a the accepted assumptions and the range of parameters. In Section 3 seed radiation field in the vicinity of the shock. This radiation should we briefly describe the approach to the numerical simulations of the be dense in terms of the photon number, np Rσ T 1, where R is effect. In Section 4 we present the results of simulation runs demon- a characteristic scale. Both np and R correspond to the comoving strating the evolution of the system from a low luminosity initial frame of the shock where photons are approximately isotropic. Such state through the catastrophe to a highly radiative post-catastrophe photons can appear, for example, as the result of an internal energy regime. In Section 5 we extend the range of the phenomenon to lower dissipation and undergo Compton boosting. densities and outline the threshold where the catastrophe is possible Now let a photon of energy ε 1 (hereafter ε is the photon en- at certain assumptions. In Section 6 we describe a phenomenon of ergy in electron mass units) moves upstream across the shock front. GeV bursts, which should arise when the compactness is insufficient Then, interacting with a soft photon, it produces an e+e− pair in to provide optically thick pair loading. Possible associations with unshocked matter (ξ e ∼ 1 in this case). The pair is bound to the existing data are discussed. In Section 7 we discuss various GRB rest frame of the external matter if the e+ and e− Larmor radii do scenarios associated with electromagnetic catastrophe and the issue not exceed the scale characterizing the problem.
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