The Probable Connection Between Relativistic Shock Acceleration and Gamma Ray Bursts

ATel #4; R. Lieu (Department of Physics, University of Alabama, Huntsville, AL 35899)
on 6 Jan 1998; 06:11 UT
Credential Certification: rutledge@rosat.mpe-garching.mpg.de

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The recent detection of delayed Gamma ray burst (GRB) afterglows at longer wavelengths (van Paradijs et al 1997, Piro et al 1997, Bond 1997, Frail and Kulkarni 1997, Halpern et al 1997) supports strongly the notion that GRBs are produced at relativistic cosmological shocks (Pacynski 1986, Goodman 1986, Rees and Meszaros 1992). The current understanding is that these shocks are ultra-relativistic, with an upstream Lorentz factor Gamma ~300, and radiate the gamma rays as the shock accelerated electrons emit by the synchrotron or inverse-Compton process (Waxman 1997).

A non-thermal origin of the GRB requires acceleration of electrons to energies comparable to those of the UHE cosmic rays. As already pointed out by Vietri (1995 and 1997), it is well known that diffusive acceleration at non-relativistic shocks is not rapid enough to produce such particles, which are at the top end of the cosmic ray spectrum (i.e. ~10^{20} eV). This same author also correctly noted that an earlier paper (Quenby and Lieu 1989) recognized for the first time an enhancement in the acceleration rate when a shock becomes relativistic. The effect, which may either be viewed in terms of a higher rate or a shorter time to reach a given particle energy when compared with conventional shocks, scales as Gamma^2, meaning that for Gamma ~300 acceleration can in principle be ~10^5 times faster. The production of gamma rays and UHE cosmic rays can therefore be achieved simultaneously at the sites of GRBs.

The original application of Quenby and Lieu (1989) was to termination shocks in AGN jets, and the value of Gamma assumed in that paper was ~3. Obviously since the Lorentz boosting scales as Gamma^2 the effect is far more important in GRBs. It is entirely reasonable to expect such a powerful mechanism to dominate other acceleration/energization process, and to easily overcome any complicating factors. For example, while our result was obtained assuming a parallel shock, the presence of a shock obliquity (i.e. a finite angle between the upstream flow vector and the upstream magnetic field) does not affect the basic physics (Lieu et al 1992). Even in the case of a perpendicular shock where the problem of returning particles upstream is most acute, the dense environment of the expanding GRB shells ensures sufficient turbulence to confine particles to within the shock vicinity by scattering.

I conclude with a simple heuristic way of appreciating why relativistic shocks are such efficient accelerators by drawing an analogy with the inverse Compton process. The upstream cosmic ray particles are likened to the laboratory photons, while scatterers downstream of a relativistic shock are likened to the fast electrons. An elastic collision in the frame of a scatterer returns a quantum to the original (laboratory) frame with an energy gain of Gamma^2. This is especially so for relativistic shocks, where anisotropies in the particle distributions favor backward scattering events. Acceleration in this kind of environment are more appropriately classified as a zeroth-order Fermi process.

References

• Bond, H.E. 1997, IAUC # 6654
• Frail, D.A. & Kulkarni, S.R. 1997, IAUC # 6662
• Goodman, J. 1986, ApJ, 308, L47.
• Halpern, J. et al 1997, IAUC # 6788
• Lieu, R., Quenby, J.J. & Naidu, K. 1992, ApJ, 421, 211.
• Quenby, J.J. & Lieu, R. 1989, Nature, 342, 654.
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• Rees, M. & Meszaros, P. 1992, MNRAS, 258, 41P.
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