6 Isotropic or beamed outflows?

Computer simulations of compact object mergers and black hole formation can address the fate of the bulk of the matter, but there are some key questions that they cannot yet tackle. In particular, high resolution of the outer layers is needed because even a tiny mass fraction of baryons loading down the outflow severely limits the attainable Lorentz factor - for instance a Poynting flux of 10⁵³ ergs could not accelerate an outflow to $\Gamma \gt 100$ if it had to drag more than $\sim 10^{-4}$ solar masses of baryons with it. Further 2D numerical simulations of the merger and collapse scenarios are under way largely using Newtonian dynamics, and the numerical difficulties are daunting. There may well be a broad spread of Lorentz factors in the outflow - close to the rotation axis $\Gamma$ may be very high; at larger angles away from the axis, there may be an increasing degree of entrainment, with a corresponding decrease in $\Gamma$. Even if the outflow is not narrowly collimated, some beaming is expected because energy would be channeled preferentially along the rotation axis. Moreover, we would expect baryon contamination to be lowest near the axis, because angular momentum flings material away from the axis, and any gravitationally-bound material with low angular momentum falls into the hole. In hypernovae, the envelope is rotating only slowly and thus would not initially have a marked centrifugal funnel; even 10⁵³ ergs would not suffice to blow out more than a narrow cone of the original envelope with a Lorentz factor or more than 100. So in these models the gamma rays would be restricted to a narrow beam, even though outflow with a more moderate Lorentz factor (relevant to the afterglow) could be spread over a wider range of angles. A wide variety of burst phenomenology could be attributable to a standard type of event being viewed from different orientations.

Two further effects render the computational task of simulating jets even more challenging, The first stems from the likelihood that any entrained matter would be a mixture of protons and neutrons (neutrons, being unconstrained by magnetic fields, could also drift into a jet from the denser walls at its boundary). If a streaming velocity builds up between ions and neutrons (i.e. if they have different Lorentz factors in the outflow) then interactions can lead to dissipation even in a steady jet where there are no shocks [6, (Derishev et al. 1999)] A second possibility [24, (Mészáros & Rees 1998b,c)] is that entrained ions in a relativistic jet could become concentrated in dense filaments confined by the magnetic field. As already mentioned, the comoving field strength, even out at 10¹³ cm, is of order 10⁶ G. Trapped filaments of iron-rich thermal, with density up to $10^{19} \, {\rm cm}^{-3}$ and with kT of order a keV, could be confined by such fields. Such filaments must of course have a small volume-filling factor: otherwise they would load down the jet too much. However, in these strong fields the gyroradii would be so small that filaments could survive against thermal conduction and other diffusion processes even if their dimensions (transverse to the field) were less than 100 cm, Such thin filaments can provide a large covering factor even while filling a tiny fraction of the volume. If they were moving relativistically outwards, they could contribute ultra-blueshift spectral features - for instance, K-edges of Fe could be shifted up to hundreds of keV.