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Register a new userExplosive X-point collapse in relativistic magnetically-dominated plasma
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Authors
Maxim Lyutikov
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The extreme properties of the gamma ray flares in the Crab Nebula present a clear challenge to our ideas on the nature of particle acceleration in relativistic astrophysical plasma. It seems highly unlikely that standard mechanisms of stochastic type are at work here and hence the attention of theorists has switched to linear acceleration in magnetic reconnection events. In this series of papers, we attempt to develop a theory of explosive magnetic reconnection in highly-magnetized relativistic plasma which can explain the extreme parameters of the Crab flares. In the first paper, we focus on the properties of the X-point collapse. Using analytical and numerical methods (fluid and particle-in-cell simulations) we extend Syrovatskys classical model of such collapse to the relativistic regime. We find that the collapse can lead to the reconnection rate approaching the speed of light on macroscopic scales. During the collapse, the plasma particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $sigma$. For sufficiently high magnetizations and vanishing guide field, the non-thermal particle spectrum consists of two components: a low-energy population with soft spectrum, that dominates the number census; and a high-energy population with hard spectrum, that possesses all the properties needed to explain the Crab flares.
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Magnetic energy around compact objects often dominates over plasma rest mass, and its dissipation can power the object luminosity. We describe a dissipation mechanism which works faster than magnetic reconnection. The mechanism involves two strong Alfven waves with anti-aligned magnetic fields $boldsymbol{B}_1$ and $boldsymbol{B}_2$ that propagate in opposite directions along background magnetic field $boldsymbol{B}_0$ and collide. The collision forms a thin current sheet perpendicular to $boldsymbol{B}_0$, which absorbs the incoming waves. The current sheet is sustained by electric field $boldsymbol{E}$ breaking the magnetohydrodynamic condition $E<B$ and accelerating particles to high energies. We demonstrate this mechanism with kinetic plasma simulations using a simple setup of two symmetric plane waves with amplitude $A=B_1/B_0=B_2/B_0$ propagating in a uniform $boldsymbol{B}_0$. The mechanism is activated when $A>1/2$. It dissipates a large fraction of the wave energy, $f=(2A-1)/A^2$, reaching $100%$ when $A=1$. The plane geometry allows one to see the dissipation process in a one-dimensional simulation. We also perform two-dimensional simulations, enabling spontaneous breaking of the plane symmetry by the tearing instability of the current sheet. At moderate $A$ of main interest the tearing instability is suppressed. Dissipation transitions to normal, slower, magnetic reconnection at $Agg 1$. The fast dissipation described in this paper may occur in various objects with perturbed magnetic fields, including magnetars, jets from accreting black holes, and pulsar wind nebulae.
Relativistic jets launched by rotating black holes are powerful emitters of non-thermal radiation. Extraction of the rotational energy via electromagnetic stresses produces magnetically-dominated jets, which may become turbulent. Studies of magnetically-dominated plasma turbulence from first principles show that most of the accelerated particles have small pitch angles, i.e. the particle velocity is nearly aligned with the local magnetic field. We examine synchrotron-self-Compton radiation from anisotropic particles in the fast cooling regime. The small pitch angles reduce the synchrotron cooling rate and promote the role of inverse Compton (IC) cooling, which can occur in two different regimes. In the Thomson regime, both synchrotron and IC components have soft spectra, $ u F_ upropto u^{1/2}$. In the Klein-Nishina regime, synchrotron radiation has a hard spectrum, typically $ u F_ upropto u$, over a broad range of frequencies. Our results have implications for the modelling of BL Lacs and Gamma-Ray Bursts (GRBs). BL Lacs produce soft synchrotron and IC spectra, as expected when Klein-Nishina effects are minor. The observed synchrotron and IC luminosities are typically comparable, which indicates a moderate anisotropy with pitch angles $thetagtrsim0.1$. Rare orphan gamma-ray flares may be produced when $thetall0.1$. The hard spectra of GRBs may be consistent with synchrotron radiation when the emitting particles are IC cooling in the Klein-Nishina regime, as expected for pitch angles $thetasim0.1$. Blazar and GRB spectra can be explained by turbulent jets with a similar electron plasma magnetisation parameter, $sigma_{rm e}sim10^4$, which for electron-proton plasmas corresponds to an overall magnetisation $sigma=(m_{rm e}/m_{rm p})sigma_{rm e}sim10$.
We perform two-dimensional particle-in-cell simulations of reconnection in magnetically dominated electron-positron plasmas subject to strong Compton cooling. We vary the magnetization $sigmagg1$, defined as the ratio of magnetic tension to plasma inertia, and the strength of cooling losses. Magnetic reconnection under such conditions can operate in magnetically dominated coronae around accreting black holes, which produce hard X-rays through Comptonization of seed soft photons. We find that the particle energy spectrum is dominated by a peak at mildly relativistic energies, which results from bulk motions of cooled plasmoids. The peak has a quasi-Maxwellian shape with an effective temperature of $sim 100$ keV, which depends only weakly on the flow magnetization and the strength of radiative cooling. The mean bulk energy of the reconnected plasma is roughly independent of $sigma$, whereas the variance is larger for higher magnetizations. The spectra also display a high-energy tail, which receives $sim 25$% of the dissipated reconnection power for $sigma=10$ and $sim 40$% for $sigma=40$. We complement our particle-in-cell studies with a Monte-Carlo simulation of the transfer of seed soft photons through the reconnection layer, and find the escaping X-ray spectrum. The simulation demonstrates that Comptonization is dominated by the bulk motions in the chain of Compton-cooled plasmoids and, for $sigmasim 10$, yields a spectrum consistent with the typical hard state of accreting black holes.
Magnetic reconnection in strongly magnetized astrophysical plasma environments is believed to be the primary process for fast energy release and particle energization. Currently there is strong interest in relativistic magnetic reconnection, in that it may provide a new explanation for high-energy particle acceleration and radiation in strongly magnetized astrophysical systems. We review recent advances in particle acceleration and reconnection physics in the magnetically-dominated regime. More discussion is focused on the physics of particle acceleration, power-law formation as well as the reconnection rate problem. In addition, we provide an outlook for studying reconnection acceleration mechanisms and kinetic physics in the next step.
Recent observations and theoretical work on gamma-ray bursts (GRBs) favor the central engine model of a Kerr black hole (BH) surrounded by a magnetized neutrino-dominated accretion flow (NDAF). The magnetic coupling between the BH and disk through a large-scale closed magnetic field exerts a torque on the disk, and transports the rotational energy from the BH to the disk. We investigate the properties of the NDAF with this magnetic torque. For a rapid spinning BH, the magnetic torque transfers enormous rotational energy from BH into the inner disk. There are two consequences: (i) the luminosity of neutrino annihilation is greatly augmented; (ii) the disk becomes thermally and viscously unstable in the inner region, and behaves S-Shape of the surface density versus accretion rate. It turns out that magnetically torqued NDAF can be invoked to interpret the variability of gamma-ray luminosity. In addition, we discuss the possibility of restarting the central engine to produce the X-ray flares with required energy.
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