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Register a new userPhysics of relativistic shocks
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Added by
Mikhail V. Medvedev
Publication date
2009
fields
Physics
and research's language is
English
Authors
Mikhail V. Medvedev
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Relativistic shocks are usually thought to occur in violent astrophysical explosions. These collisionless shocks are mediated by a plasma kinetic streaming instability, often loosely referred to as the Weibel instability, which generates strong magnetic fields from scratch very efficiently. In this review paper we discuss the shock micro-physics and present a recent model of pre-conditioning of an initially unmagnetized upstream region via the cosmic-ray-driven Weibel-type instability.
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We develop a comprehensive theoretical model of relativistic collisionless pair shocks mediated by the current filamentation instability. We notably characterize the noninertial frame in which this instability is of a mostly magnetic nature, and describe at a microscopic level the deceleration and heating of the incoming background plasma through its collisionless interaction with the electromagnetic turbulence. Our model compares well to large-scale 2D3V PIC simulations, and provides an important touchstone for the phenomenology of such plasma systems.
Relativistic astrophysical collisionless shocks represent outstanding dissipation agents of the huge power of relativistic outflows produced by accreting black holes, core collapsed supernovae and other objects into multi-messenger radiation (cosmic rays, neutrinos, electromagnetic radiation). This article provides a theoretical discussion of the fundamental physical ingredients of these extreme phenomena. In the context of weakly magnetized shocks, in particular, it is shown how the filamentation type instabilities, which develop in the precursor of pair dominated or electron-ion shocks, provide the seeds for the scattering of high energy particles as well as the agent which preheats and slows down the incoming precursor plasma. This analytical discussion is completed with a mesoscopic, non-linear model of particle acceleration in relativistic shocks based on Monte Carlo techniques. This Monte Carlo model uses a semi-phenomenological description of particle scattering which allows it to calculate the back-reaction of accelerated particles on the shock structure on length and momentum scales which are currently beyond the range of microscopic particle-in-cell (PIC) simulations.
In this first paper of a series dedicated to the microphysics of unmagnetized, relativistic collisionless pair shocks, we discuss the physics of the Weibel-type transverse current filamentation instability (CFI) that develops in the shock precursor, through the interaction of an ultrarelativistic suprathermal particle beam with the background plasma. We introduce in particular the notion of Weibel frame, or scattering center frame, in which the microturbulence is of mostly magnetic nature. We calculate the properties of this frame, using first a kinetic formulation of the linear phase of the instability, relying on Maxwell-Juttner distribution functions, then using a quasistatic model of the nonlinear stage of the instability. Both methods show that: (i) the Weibel frame moves at subrelativistic velocities relative to the background plasma, therefore at relativistic velocities relative to the shock front; (ii) the velocity of the Weibel frame relative to the background plasma scales with $xi_{rm b}$, i.e., the pressure of the suprathermal particle beam in units of the momentum flux density incoming into the shock; and (iii), the Weibel frame moves slightly less fast than the background plasma relative to the shock front. Our theoretical results are found to be in satisfactory agreement with the measurements carried out in dedicated large-scale 2D3V PIC simulations.
In this third paper of a series, we discuss the physics of the population of accelerated particles in the precursor of an unmagnetized, relativistic collisionless pair shock. In particular, we provide a theoretical estimate of their scattering length $l_{scatt}(p)$ in the self-generated electromagnetic turbulence, as well as an estimate of their distribution function. We obtain $l_{scatt}(p) simeq (gamma_p /epsilon_B)(p/gamma_{infty} mc)^2 (c/omega_p)$, with p the particle momentum in the rest frame of the shock front, $epsilon_B$ the strength parameter of the microturbulence, $gamma_p$ the Lorentz factor of the background plasma relative to the shock front and $gamma_{infty}$ its asymptotic value outside the precursor. We compare this scattering length to large-scale PIC simulations and find good agreement for the various dependencies.
The physics of instabilities in the precursor of relativistic collisionless shocks is of broad importance in high energy astrophysics, because these instabilities build up the shock, control the particle acceleration process and generate the magnetic fields in which the accelerated particles radiate. Two crucial parameters control the micro-physics of these shocks: the magnetization of the ambient medium and the Lorentz factor of the shock front; as of today, much of this parameter space remains to be explored. In the present paper, we report on a new instability upstream of electron-positron relativistic shocks and we argue that this instability shapes the micro-physics at moderate magnetization levels and/or large Lorentz factors. This instability is seeded by the electric current carried by the accelerated particles in the shock precursor as they gyrate around the background magnetic field. The compensation current induced in the background plasma leads to an unstable configuration, with the appearance of charge neutral filaments carrying a current of the same polarity, oriented along the perpendicular current. This ``current-driven filamentation instability grows faster than any other instability studied so far upstream of relativistic shocks, with a growth rate comparable to the plasma frequency. Furthermore, the compensation of the current is associated with a slow-down of the ambient plasma as it penetrates the shock precursor (as viewed in the shock rest frame). This slow-down of the plasma implies that the ``current driven filamentation instability can grow for any value of the shock Lorentz factor, provided the magnetization sigma <~ 10^{-2}. We argue that this instability explains the results of recent particle-in-cell simulations in the mildly magnetized regime.
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