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The magnetorotational instability (MRI) plays a crucial role in regulating the accretion efficiency in astrophysical accretion discs. In low-luminosity discs around black holes, such as Sgr A* and M87, Coulomb collisions are infrequent, making the MRI physics effectively collisionless. The collisionless MRI gives rise to kinetic plasma effects that can potentially affect its dynamic and thermodynamic properties. We present 2D and 3D particle-in-cell (PIC) plasma simulations of the collisionless MRI in stratified discs using shearing boxes with net vertical field. We use pair plasmas, with initial β = 100 and concentrate on subrelativistic plasma temperatures (kBT ≲ mc2). Our 2D and 3D runs show disc expansion, particle and magnetic field outflows, and a dynamo-like process. They also produce magnetic pressure dominated discs with (Maxwell stress dominated) viscosity parameter α ∼ 0.5–1. By the end of the simulations, the dynamo-like magnetic field tends to dominate the magnetic energy and the viscosity in the discs. Our 2D and 3D runs produce fairly similar results, and are also consistent with previous 3D MHD (magnetohydrodynamic) simulations. Our simulations also show non-thermal particle acceleration, approximately characterized by power-law tails with temperature-dependent spectral indices − p. For temperatures $k_\mathrm{ B}T \sim 0.05-0.3\, mc^2$, we find p ≈ 2.2–1.9. The maximum accelerated particle energy depends on the scale separation between MHD and Larmor-scale plasma phenomena in a way consistent with previous PIC results of magnetic reconnection-driven acceleration. Our study constitutes a first step towards modelling from first principles potentially observable stratified MRI effects in low-luminosity accretion discs around black holes.

 

We study a relativistic collisionless electron–positron shock propagating into an unmagnetized ambient medium using 2D particle-in-cell simulations of unprecedented duration and size. The shock generates intermittent magnetic structures of increasingly larger size as the simulation progresses. Toward the end of our simulation, at around 26,000 plasma times, the magnetic coherence scale approachesλ∼ 100 plasma skin depths, both ahead and behind the shock front. We anticipate a continued growth ofλbeyond the time span of our simulation, as long as the shock accelerates particles to increasingly higher energies. The post-shock field is concentrated in localized patches, which maintain a local magnetic energy fractionε_B∼ 0.1. Particles randomly sampling the downstream fields spend most of their time in low field regions (ε_B≪ 0.1) but emit a large fraction of the synchrotron power in the localized patches with strong fields (ε_B∼ 0.1). Our results have important implications for models of gamma-ray burst afterglows.

 

Some of the most energetic pulsars exhibit rotation-modulatedγ-ray emission in the 0.1–100 GeV band. The luminosity of this emission is typically 0.1%–10% of the pulsar spin-down power (γ-ray efficiency), implying that a significant fraction of the available electromagnetic energy is dissipated in the magnetosphere and reradiated as high-energy photons. To investigate this phenomenon we model a pulsar magnetosphere using 3D particle-in-cell simulations with strong synchrotron cooling. We particularly focus on the dynamics of the equatorial current sheet where magnetic reconnection and energy dissipation take place. Our simulations demonstrate that a fraction of the spin-down power dissipated in the magnetospheric current sheet is controlled by the rate of magnetic reconnection at microphysical plasma scales and only depends on the pulsar inclination angle. We demonstrate that the maximum energy and the distribution function of accelerated pairs is controlled by the available magnetic energy per particle near the current sheet, the magnetization parameter. The shape and the extent of the plasma distribution is imprinted in the observed synchrotron emission, in particular, in the peak and the cutoff of the observed spectrum. We study how the strength of synchrotron cooling affects the observed variety of spectral shapes. Our conclusions naturally explain why pulsars with higher spin-down power have wider spectral shapes and, as a result, lowerγ-ray efficiency.

 

Using the field–particle correlation technique, we examine the particle energization in a three-dimensional (one spatial dimension and two velocity dimensions; 1D-2V) continuum Vlasov–Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field–particle correlation technique with the high-fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons arising from the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov–Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field–particle correlation technique to spacecraft measurements of collisionless shocks.