4 The gamma-ray emission mechanism

Well-known arguments connected with opacity, variability timescales and so forth require highly relativistic outflow. Best-guess numbers are Lorentz factors $\Gamma$ in the range 10² to 10³, allowing rapidly-variable emission to occur at radii in the range 10¹⁴ to 10¹⁶ cm s. The entrained baryonic mass would need to be below $10^{-4}\ M_\odot$ to allow these high relativistic expansion speeds.

Because the emitting region must be several powers of ten larger than the compact object that acts as trigger, there is a further physical requirement: the original energy outflowing in a magnetised wind would, after expansion, be transformed into bulk kinetic energy (with associated internal cooling). This energy cannot be efficiently radiated as gamma rays unless it is re-randomised. This requires relativistic shocks. Impact on an external medium would randomise half of the initial energy merely by reducing the expansion Lorentz factor by a factor of 2. Alternatively, there may be internal shocks within the outflow: for instance, if the Lorentz factor in an outflowing wind varied by a factor more than 2, then the shocks that developed when fast material overtakes slower material would be internally relativistic [38, (Rees & Mészáros 1994)].

In an unsteady outflow, if $\Gamma$were to vary by a factor of 2 on a timescale $\delta t$, internal shocks would develop at a distance $\Gamma^2 c \delta t$, and randomise most of the energy. For instance, if $\Gamma$ ranged between 500 and 2000, on a timescale of 1 second, efficient dissipation would occur at $3 \ 10^{16}$ cm s.

There is a general consensus that the longer complex bursts must involve internal shocks, though simple sharp pulses could arise from an external shock interaction (the latter would in effect be the precursor of the afterglow). An external shock moving into a smooth medium would obviously give a burst with a simple time-profile. A blobby external medium could give features, but only if the covering factor of blobs is low, implying modest efficiency. (This issue is discussed by Dermer in his contribution to this meeting).

Even if the bursts were caused by a completely standardised set of objects, their appearance would be likely to depend drastically on orientation relative to the line of sight. Along any given line of sight, the time-structure would be determined partly by the advance of jet material into the external medium, but probably even more by internal shocks within the jet, which themselves depend on the evolution of the torus, from its formation to its eventual swallowing or dispersal.

The radiation processes for the gamma rays are probably no more than synchrotron radiation. This would imply the presence of magnetic fields where the shocks occur. If the outflow from the central trigger is Poynting-dominated, then a field of 10¹⁵ G at (say) 10⁷ cm would imply a comoving field of $10^7 (\Gamma/100)^{-1}$ G out at 10¹³ cm - strong enough to ensure rapid cooling of shocked relativistic electrons. (Note, conversely, that even if magnetic fields were not important near the central trigger, they must be present, with about the same amount of flux that Poynting-dominated models require, at the location of the actual gamma-ray emission.)

We are a long way from modelling what triggers gamma ray bursts. If we had a precise description of the dynamics, along with the baryon content, magnetic field, and Lorentz factor of the outflow, we could maybe predict the gross time-structure. But we could not predict the intensity or spectrum of the emitted radiation - still less answer key questions about the emission in other wavebands - without also having an adequate theory for particle acceleration in relativistic shocks. We need the answers from plasma physicists to the following poorly-understood questions: (i) Do ultra-relativistic shocks yield power laws? The answer probably depends on the ion/positron ratio, and on the relative orientation of the shock front and the magnetic field (e.g. [9, Gallant et al. 1992)]. (ii) In ion-electron plasmas, what fraction of the energy goes into the electrons? (iii) Even if the shocked particles establish a power law, there must be a low-energy break in the spectrum at an energy that is in itself relativistic. But will this energy, for the electrons, be $\Gamma m_{\rm p}c^2$, or (or even, if the positive charges are heavy ions like Fe, $\Gamma m_{\rm Fe} c^2$)? (iv) Can ions be accelerated up to the theoretical maximum where the gyroradius becomes the scale of the system? If so, the burst events could be the origin of the highest energy cosmic rays. (v) Do magnetic fields get amplified in shocks? This is relevant to the magnetic field in the swept-up external matter outside the contact discontinuity, and determines how sharp the external shock actually is.