Electron-positron outflow from black holes and the formation of winds

The collapse of young massive stars or the coalescence of a black holeneutron star binary is expected to give rise to a black hole-torus system. When the torus is strongly magnetized, the black hole produces electron-positron outflow along open magnetic field-lines. Through curvature radiation in gaps, this outflow rapidly develops into a eγ-wind, which is ultra-relativistic and of low comoving density, proposed here as a possible input to GRB fireball models. Here, I discuss some aspects of black holes when exposed to external magnetic fields. For example, black hole-torus systems are a probable outcome of the collapse of young massive stars [28,17] and the coalescence of black hole-neutron star binaries [18], both of which are possible progenitors of cosmological gamma-ray bursts (GRBs). If all black holes are produced by stellar collapse, they should be nearly maximally rotating [1,2]. A surrounding torus or accretion disk is expected to be magnetized by conservation of magnetic flux and linear amplification (cf. [17,15]). A black hole-torus system will have open magnetic field-lines from the horizon to infinity and closed magnetic field-lines between the black hole and the torus [23]. The closed magnetic field-lines mediate Maxwell stresses [24]. This may be seen by way of similarity to pulsar magnetospheres [10]. In a poloidal crosssection, the torus can be identified with a pulsar which rotates at an angular velocity ΩP ∼ ΩH − ΩT , wherein the black hole horizon corresponds to infinity. Then, the inner light-surface [29] corresponds to the pulsar light-cylinder, and a ‘bag’ attached to the torus to the last closed field-line. Here, ΩH and ΩT denote the angular velocities of the black hole and the torus, respectively. The work performed by the Maxwell stresses is commonly attributed to an outgoing Poynting flux emanating from the horizon [3,21]. These Maxwell stresses are likely to be important to the evolution of the torus, and tend to delay accretion onto the black hole. The open magnetic field-lines, on the other hand, enable the black hole to produce an outflow to infinity. Such outflows generate emissions by deceleration against the interstellar medium and through internal shocks. To appear in: Explosive Phenom. Astrophys. Compact Objects, edited by C.-H. Lee, M. Rho, I. Yi & H.K. Lee, AIP Conf. Proc. Here, the outflow along open magnetic field-lines is studied, and found to produce a pair-dominated eγ–wind in combination with curvature radiation. Open field-lines from the horizon to infinity have radiative ingoing boundary conditions at the horizon as seen by zero-angular momentum observers (ZAMOs), and outgoing boundary conditions at infinity. It is well-known that for an outflow to exist, there must be regions in which pairs are created (gaps), somewhere on these open field-lines [3,19,20,4]. The gaps are powered by an electric current I along the field–lines, which is limited by a horizon surface resistivity of 4π, in the presence of a certain potential drop across them. The net particle flow is limited by the black hole luminosity into the gap. The magnetosphere within the gaps is differentially rotating, beyond which the magnetosphere may be force-free and in rigid rotation. Note that, in contrast, the currents along closed magnetic fieldlines are fixed by the angular velocity ΩT of the surrounding matter, where the gaps are most likely residing between the horizon and the inner light surface. Of interest here is the location of the gaps on the open magnetic field-lines and the power dissipated within, as sites of linear acceleration of charged particles and their curvature radiation. A rotating black hole tends to produce electrons and positrons by spontaneous emission along open magnetic field-lines in an effort to evolve to a lower energy state by shedding off its angular momentum. Indeed, in the adiabatic limit, the radiated particles possess a specific angular momentum of at least 2M , whereas the specific angular momentum of the black hole, a, is at most M . In the approximation of an asymptotically uniform magnetic field, e.g., in a Wald-field [27], the emissions at infinity to satisfy a Fermi-Dirac distribution of radiative Landau states, neglecting curvature radiation and magnetic mirror effects. This results from a modification to the Hawking radiation process [25]. This is a highly idealized picture derived in the perturbative limit of small particle densities, which will be modified significantly by curvature radiation and the formation of force-free regions. The spontaneous emission process concerns particles with energy-at-infinity ω below the Fermi-level VF . Here, VF is the energy-at-infinity associated with the particles as seen on a null-generator of the horizon, such as the ZAMO-derivative ξ∂a = ∂t−β∂φ, where β denotes the angular velocity of the sky as seen by ZAMOs. That is,