We study the linear stability of a planar interface separating two fluids in relative motion, focusing on the symmetric configuration where the two fluids have the same properties (density, temperature, magnetic field strength, and direction). We consider the most general case with arbitrary sound speed cs, Alfvén speed vA, and magnetic field orientation. For the instability associated with the fast mode, we find that the lower bound of unstable shear velocities is set by the requirement that the projection of the velocity on to the fluidframe wavevector is larger than the projection of the Alfvén speed on to the same direction, i.e. shear should overcome the effect of magnetic tension. In the frame where the two fluids move in opposite directions with equal speed v, the upper bound of unstable velocities corresponds to an effective relativistic Mach number $M_{\rm re}\equiv v/v_{\rm {f}\perp }\sqrt{(1v_{\rm {f}\perp }^2)/(1v^2)} \cos \theta =\sqrt{2}$, where $v_{\rm {f}\perp }=[v_{\rm {A}}^2+c_{\rm s}^2(1v_{\rm {A}}^2)]^{1/2}$ is the fast speed assuming a magnetic field perpendicular to the wavevector (here, all velocities are in units of the speed of light), and θ is the laboratoryframe angle between the flow velocity and the wavevector projection on to the shear interface. Our results have implications for shear flows in the magnetospheres of neutron stars and black holes – both for single objects and for merging binaries – where the Alfvén speed may approach the speed of light.
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ABSTRACT 
Abstract Magnetic reconnection is often invoked as a source of highenergy particles, and in relativistic astrophysical systems it is regarded as a prime candidate for powering fast and bright flares. We present a novel analytical model—supported and benchmarked with largescale threedimensional kinetic particleincell simulations in electron–positron plasmas—that elucidates the physics governing the generation of powerlaw energy spectra in relativistic reconnection. Particles with Lorentz factor
γ ≳ 3σ (here,σ is the magnetization) gain most of their energy in the inflow region, while meandering between the two sides of the reconnection layer. Their acceleration time is , where ${t}_{\mathrm{acc}}\sim \gamma \phantom{\rule{0.25em}{0ex}}{\eta}_{\mathrm{rec}}^{1}{\omega}_{\mathrm{c}}^{1}\simeq 20\phantom{\rule{0.25em}{0ex}}\gamma \phantom{\rule{0.25em}{0ex}}{\omega}_{\mathrm{c}}^{1}$η _{rec}≃ 0.06 is the inflow speed in units of the speed of light andω _{c}=eB _{0}/mc is the gyrofrequency in the upstream magnetic field. They leave the region of active energization aftert _{esc}, when they get captured by one of the outflowing flux ropes of reconnected plasma. We directly measuret _{esc}in our simulations and find thatt _{esc}∼t _{acc}forσ ≳ few. This leads to a universal (i.e.,σ independent) powerlaw spectrum for the particles undergoing active acceleration, and ${\mathit{dN}}_{\mathrm{free}}/d\gamma \propto {\gamma}^{1}$ for the overall particle population. Our results help to shed light on the ubiquitous presence of powerlaw particle and photon spectra in astrophysical nonthermal sources. $\mathit{dN}/d\gamma \propto {\gamma}^{2}$ 
ABSTRACT We perform 2D particleincell simulations of magnetic reconnection in electronion plasmas subject to strong Compton cooling and calculate the Xray spectra produced by this process. The simulations are performed for transrelativistic reconnection with magnetization 1 ≤ σ ≤ 3 (defined as the ratio of magnetic tension to plasma restmass energy density), which is expected in the coronae of accretion discs around black holes. We find that magnetic dissipation proceeds with inefficient energy exchange between the heated ions and the Comptoncooled electrons. As a result, most electrons are kept at a low temperature in Compton equilibrium with radiation, and so thermal Comptonization cannot reach photon energies $\sim 100\,$ keV observed from accreting black holes. Nevertheless, magnetic reconnection efficiently generates $\sim 100\,$ keV photons because of mildly relativistic bulk motions of the plasmoid chain formed in the reconnection layer. Comptonization by the plasmoid motions dominates the radiative output and controls the peak of the radiation spectrum Epk. We find Epk ∼ 40 keV for σ = 1 and Epk ∼ 100 keV for σ = 3. In addition to the Xray peak around 100 keV, the simulations show a nonthermal MeV tail emitted by a nonthermal electron population generated near Xpoints of the reconnection layer. The results are consistent with the typical hard state of accreting black holes. In particular, we find that the spectrum of Cygnus X1 is well explained by electronion reconnection with σ ∼ 3.