Magnetic accelerations of relativistic jets Serguei Komissarov University

Magnetic accelerations of relativistic jets. Serguei Komissarov University of Leeds UK N. Vlahakis (Athens) A. Konigl (Chicago) M. Barkov (Moscow) Y. Granot (Hertfordshire) A. Spitkovsky (Princeton)

Plan 1. Introduction. 2. Standard model: Steady-state axisymmetric jets. • Relativistic regime versus non-relativistic one; • Thermal mechanism versus magnetic one; • Problems of the standard magnetic model; 3. Alternatives to the standard model; 4. Impulsive acceleration; 5. Conclusions.

Introduction: Magnetic paradigm of relativistic jets • Jets are accelerated magnetically; • Energy is transported to large distances without losses in the form of Poynting flux; • Then it is converted into the kinetic energy of plasma (can also be transported without losses); • Then it is dissipated at shocks and converted into radiation.

Key difference between acceleration of relativistic and non-relativistic steady-state flows Non-relativistic: most of the acceleration is in the sub-sonic (sub-magnetosonic) regime. Relativistic: most of the acceleration is in the super-sonic (super-magnetosonic) regime.

• Non-relativistic gasdynamics Kinetic energy ~ thermal energy at the sonic point ! • Non-relativistic cold MHD Kinetic energy ~ magnetic energy at the magneto-sonic point !

• Relativistic gasdynamics only ! Kinetic energy << thermal energy at the sonic point !

• Relativistic cold MHD - magnetic field in the fluid frame High Lorentz factor at the magnetosonic point ! However, (kinetic energy) << (magnetic energy) at the sonic point !

So what ? The key difference between thermal and magnetic acceleration mechanisms of steady-state flows in relativistic supersonic regime Thermal : fast, robust, and efficient. Magnetic: slow, delicate, and less efficient.

• Thermal acceleration mechanism (conical flow) Mass conservation: A v~c Rj Energy conservation: Bernoulli equation: from Bernoulli eq. Very fast acceleration ! z

• Ideal MHD acceleration mechanism (conical flow) A Rj Mass conservation: Energy conservation: Bernoulli equation: from Bernoulli eq. No acceleration ! v~c

Another explanation: v~c Volume of the fluid element: Its magnetic field: Its magnetic energy: Thus, the magnetic energy is preserved !

v • Ideal MHD acceleration mechanism Non-conical flows ( toroidal magnetic field): v v d. R R Consider the flow between two close flux surfaces, Mass conservation: Energy conservation: Bernoulli equation: from Bernoulli eq. A

should decrease for acceleration ! In a conical flow is constant (no acceleration). Curved stream lines? d. R 0 z 0 v Try d. R R z is still constant (no acceleration) !

Try where . Now and decreases if . Further from the axis a stream-lines is faster it moves away from it with z - the geometric condition of acceleration. equidistant here concentrated towards the axis here Can this condition be satisfied? In any case there has to be a communication across the jet - the causal connectivity condition !

Summary of recent numerical and theoretical results Komissarov et al. (2009), Lyubarsky (2009) • Freely expanding (unconfined) flows quickly loose causal connectivity, become conical and stop accelerating; • Externally confined jets with and accelerate if a < 2; remain causally connected The Lorentz factor grows as until ~one half of the magnetic energy is converted into the kinetic one. (Not particularly efficient still !? ) • If a > 2 jets still loose causal connectivity and stop accelerating.

Terminal Lorentz factor and opening angle Causal connectivity condition: Jet half opening angle Mach angle Upper limit on Lorentz factor (full conversion of magnetic energy ) Efficient conversion implies OK for AGN jets. For GRBs with G~1000 this gives the opening angle !

Another problem: The model predict almost purely toroidal magnetic field. 3 C 120 This is in conflict with the observations of AGN jets! Marscher et al. (2004)

Alternatives to the “standard model” • Tangled magnetic field (Heinz & Begelman 2000) (result of a current-driven instability? ) If , where a, b are constant then the magnetic field behaves as an ultra-relativistic gas Magnetic (pressure) acceleration is as efficient as thermal one !? • Dissipation of tangled magnetic field (e. g. Drenkhahn 2002; Drenkhahn & Spruit 2002) (magnetic energy) (heat) (radiation) (kinetic energy)

• Impulsive magnetic acceleration (Contopoulos 1995, “plasma gun”) (unsteady central engine) Lyutikov (2010); Granot, Komissarov, Spitkovsky (2010); Expansion of highly magnetized plasma shell into vacuum (slab geometry) vacuum - initial magnetization parameter

magnetic field magnetic pressure Solution at t=1 when the rarefaction just reaches the wall (c=1). Simple rarefaction wave – self-similal solution. magnetic Lorentz factor At the boundary with vacuum total kinetic the initial width =1; the wall is at x=-1; s 0 = 30. The mean value

magnetic field magnetic pressure Solution at t=20. The shell has separated from the wall. total Lorentz factor The total energy, mass, and momentum and the width of the shell hardly change as it moves. magnetic kinetic The Lorentz factor grows because the energy and momentum of magnetic field are transferred to plasma.

The mean Lorentz factor grows as until it approaches the value Complete conversion of magnetic energy!

This appears to be a very robust mechanism. • works in spherical geometry; • stream lines can radial; • places no constrains on the jet opening angle; • should not be sensitive to the field geometry Can explain the acceleration of GRB shells and blobs of AGN and micro-quasar jets.

Conclusions • Magnetic acceleration of relativistic jets in the standard steady-state axisymmetric model is not robust, slow and not particularly efficient; • It may even be in conflict with observations – opening angles of GRB jets and polarization of AGN jets; • Intermitted central engine and current driven instabilities could be crucial factors in the acceleration of astrophysical relativistic jets.