Electron acceleration and synchrotron radiation in decelerating plasmoids

Abstract

An equation is derived to calculate the dynamics of relativistic magnetized plasma which decelerates by sweeping up matter from the ISM. Reduction to the non-radiative and radiative regimes is demonstrated for the general case of a collimated plasmoid whose area increases as a power of distance x from the explosion, and in the specific case of a blast-wave geometry where the area increases quadratically with x. An equation for the evolution of the electron momentum distribution function in the comoving fluid frame is used to calculate the observed synchrotron radiation spectrum. The central uncertainty involves the mechanism for transfering energy from the nonthermal protons to the electrons. The simplest prescription is to assume that a fixed fraction of the comoving proton power is instantaneously transformed into a power-law, "shock"-like electron distribution function. This permits an analytic solution for the case of a relativistic plasmoid with a constant internal magnetic field. Effects of parameter changes are presented. Breaks in the temporal behavior of the primary burst emission and long wavelength afterglows occur on two time scales for external ISM density distributions n ext ∝ x −η . The first, as emphasized by Mészáros & Rees, represents the time when the outflow sweeps up ≈ M th /Γ 0 of material from the ISM, where M th is the mass in the outflow ejecta and Γ 0 is the initial Lorentz factor of the plasmoid. The second represents the time when synchrotron cooling begins strongly to regulate the number of nonthemal electrons that are producing radiation which is observed at a given energy.Results are applied to GRB and blazar variability. The slopes of the time profiles of the X-ray and optical light cuves of the afterglows of GRB 970228 and GRB 970508 are explained by injection of hard electron spectra with indices s < 2 in a deceleration regime near the radiative limit. We also propose that blazar flares are due to the transformation of the directed kinetic energy of the plasmoid when interacting with the external medium, as would occur if relativistic outflows pass through clouds orbiting the central supermassive black hole.

On the multiwavelength emission from gamma ray burst afterglows

“…The exponents are found in the asymptotic regimes of uncooled and cooled electron distributions and are presented in Table 1. The slopes of the synchrotron flux time profiles in the non-radiative regime (see Table 1) coincide with the respective ones presented by Dermer & Chiang (1998). Table 1 shows that SSC flux time profiles are steeper than the respective synchrotron profiles both in the uncooled and cooled regime, for all the magnetic field configurations discussed in Sect.…”

“…(11) for the case of a constant magnetic field. This calculation has already been done by Dermer & Chiang (1998) and thus we can compare our results with theirs. The outline of the comparison can be found in the Appendix (A.3).…”

“…According to the standard model -for a review see Piran (2005), the RBW expands in the circumburst material and, after sweeping some critical amount of mass, it starts to decelerate. At the same time electrons are postulated to energize at the shock front and radiate through synchrotron (Sari et al 1998;Dermer & Chiang 1998) or synchrotron and synchrotron self-compton (SSC) (Chiang & Dermer 1999;Fan et al 2008;Waxman 1997;Panaitescu & Kumar 2000), thus producing the afterglow emission.…”

Baryon Loaded Relativistic Blast Waves in Supernovae

“…Since the swept-up mass is still smaller than the rest mass of the relativistic ejecta, the evolution of the blast wave can neither be described by the rapidly decelerating Blandford & McKee (1976) solution nor by the Sedov-Taylor solution. Dermer & Chiang (1998) and Chiang & Dermer (1999) have considered the emission from a collisionally decelerating blast wave as it transitions from nearly free expansion to the Blandford & McKee (1976) self-similar solution. Huang et al (1999) have discussed the subsequent transition to a Sedov-like phase.…”

The Nature of Microvariability in Blazar 0716+714

“…The flares are presumably produced in shocks formed by colliding inhomogeneities which propagate down the jet with relativistic speeds (Blazejowski et al, 2000). However, present data do not allow us to exclude other possibilities, including production of flares by inhomogeneities flowing through the jets and shocked in the reconfinement regions (Komissarov & Falle, 1997), or collisions of jets with clouds (Dermer & Chiang, 1998).…”