Gamma-Ray Burst fireballs: a neutron component constrains internal shock models

The most favored model to produce the radiation of GRBs calls for internal shocks within a relativistic outflow of plasma, produced by accretion onto newly born few solar masses black hole. This would produce a neutron rich fireball (Beloborodov 2003, astro-ph/0210522). We investigate the possibility that neutrons, decaying sizably before and during the GRBs phase, heat the protons to relativistic internal velocities via two stream instabilities. Depending on the initial fireball parameters, this can lead to a substantial reduction of the internal shock efficiency or even to their complete suppression. We find that for standard initial radii, luminosities and entropy per baryon an effective proton heating can be still present with a neutron-proton ratio equal unity. Fireball dynamics and decoupling We consider a fireball with a baryon component made by a mixture of protons and neutrons (ions may be present as well). The fireball, generated at rest with a large internal energy is accelerated by radiation pressure to relativistic speeds. Initially, the neutrons and protons are coupled and, even if the neutrons cannot feel the radiation pressure, are accelerated at the same rate of protons. If the entropy-per-baryon is large enough, however, the neutrons decouple from the protons before the acceleration stage is completed. This happens (e.g. Bahcall & Meszaros, 2000, PRL, 85, 7) if: η ≥ ηmin = [ Lσπ 4πmp c3 r0 (ξ +1) ]1/4 (1) where ξ is the neutron richness, i.e. the ratio of neutron to proton density and R0 the size of the fireball release area. After the decoupling radius (Rdec in the figures), the protons continue to be accelerated up to their saturation radius (Γp ∝ R; T ∝ R−1; Rs in the figures) and, in the absence of a neutron component, enter the coasting phase in which their bulk Lorentz factor is constant and their temperature drops adiabatically as R−2/3. This stage lasts until the internal shocks set in (RIS in the figures). The presence of a neutron component does not influence this evolution in itself, since protons and neutrons do not interact at low densities (after the decoupling). However, the neutrons β-decay into protons on-fly, and the decayed neutrons make a plasma of slower protons. Through the two-stream instability (see e.g. Beloborodov 2003, ApJ, 585, L19), these slower protons interact with the original faster ones, heating and decelerating them. This interaction takes place continuously from the moment of the decoupling up to the separation radius (Rsep in the figures), at which the shell of protons overtakes completely that of neutrons. In the second phase of the acceleration of protons and in the coasting phase, therefore, the internal energy of the proton shell (and therefore its temperature) is controlled by two competing effects: an adiabatic term which tends to decrease their temperature, and a heating term, due to the interaction of the proton shell with the decayed neutrons.