Physics of Relativistic Jets Yuri Lyubarsky BenGurion University

Physics of Relativistic Jets Yuri Lyubarsky Ben-Gurion University Beer-Sheva, Israel

Universality of relativistic jets M 87 Crab in X-rays M 87 time, s PKS 2155 -304 GRBs

All these sources likely share a common basic mechanism, in which relativistic outflows are launched hydromagnetically Pulsar magnetosphere Collapsing, magnetized supernova core Magnetized accretion disks around neutron stars and black holes Magnetospheres of Kerr black holes Courtesy to David Meier A rapidly spinning central body twists up the magnetic field into a toroidal component and the plasma is ejected by the magnetic tension. Relativistic flow can be produced by having a very strong rotating magnetic field, B 2>>4 c 2. Rotational energy Poynting ?

Basic picture of relativistic magnetohydrodynamic outflows Magnetic field lines rotate rigidly at the rate . Plasma moves along the rotating field lines. Rotation twists up the field into toroidal component, slowing rotation. At r~c, the field gets wound up, Bp~Bf - light cylinder radius Beyond the light cylinder, each revolution of the source adds to the wind one more magnetic loop. In expanding flows, Bf becomes dominating

In relativistic flows, the electric force is important . In the far zone of the outflow, v c and E B. In highly relativistic flows, the Lorentz and electric forces nearly cancel each other. Acceleration and collimation are only due to a small residual force. Without external confinement, the flow remains nearly radial and Poynting dominated (no collimation, no acceleration).

Externally confined jets In accreting systems, the relativistic outflows from the black hole and the internal part of the accretion disc could be confined by a slow wind from the outer parts of the disk. In long GRBs, a relativistic jet from the collapsing core bores its way through the envelope of the progenitor stare.

Poynting dominated jets. What do we want to know? § What are the conditions for acceleration and collimation? § What is the final collimation angle? § Where and how the EM energy is released? Conversion to the kinetic energy via gradual acceleration? Or to thermal and radiation energy via dissipation? How and where does s decrease from >>1 to <<1?

Collimation vs acceleration: two flow regimes 1. Equilibrium regime: signal crossing time is less than the expansion time (strong causal connection), Qg<1. The flow is accelerated when expands cylindrical equilibrium at any z 2. Non-equilibrium regime: Qg>1 Z=r 2/RL § Weak causal connection: § No causal connection: Weakly causally connected flows are slowly accelerated until and then stop accelerating Bp is negligible; purely azimuthal field equilibrium non-equilibrium

MHD jet confined by the external pressure v The spatial distribution of the confining pressure determines the shape of the flow and the acceleration rate pext Bf E Bp

MHD jet confined by the external pressure (cont) - equilibrium regime Equipartition, g~gmax, is achieved at g/gin Beyond the equipartition: s

MHD jet confined by the external pressure (cont) - non-equilibrium Jet asymptotically approaches conical shape r=Qz

MHD jet confined by the external pressure (cont) 2. A special case; k=2 If b<1/4, the flow is accelerated till s~1 and then collapses.

Some implications AGNs: g~10 implies the size of the confining zone z 0>100 Rg~1016 cm. The condition of efficient acceleration (Qg<1) may be fulfilled: <Qg>=0. 26 (Pushkarev et al ‘ 09). But according to spectral fitting of blazars, jets are already matter dominated at ~1000 Rg (Ghisellini et al ‘ 10). Violent dissipation somewhere around 1000 Rg? GRBs: g~102 - 103; minimal z 0~1011 cm – marginally OK. But achromatic breaks in the afterglow light curves and statistics imply g. Q>>1, which is fulfilled only if the flow remains Poynting dominated. Magnetic dissipation is necessary.

Beyond the ideal MHD: magnetic dissipation in Poynting dominated outflows The magnetic energy could be extracted via anomalous dissipation in narrow current sheets. current sheet How differently oriented magnetic field lines could come close to each other? 1. Global MHD instabilities could disrupt the regular structure of the magnetic field thus liberating the magnetic energy. 2. Alternating magnetic field could be present in the flow from the very beginning.

MHD instabilities The most dangerous is the kink instability But: The necessary condition for the instability – strong causal connection, g. Q<1. Not fulfilled in GRBs; may be fulfilled in AGNs. The growth rate is small in relativistic case. Evidences for saturation of the instability. Mizuno et al ‘ 12

Striped jets? Let alternating fields preexist in the jet In an expanding flow, B becomes predominantly toroidal; current sheets are stretched. Local structure: plane current sheet separating oppositely directed fields.

Magnetic dissipation in striped jets Rayleigh-Taylor instability of currents sheets in accelerating flows In an accelerating flow, effective gravity force arises D j Instability time-scale Dissipation rate

Interplay between acceleration and dissipation; a self-consistent picture Complete dissipation: In accreting systems, l~Rg AGNs GRBs

Conclusions 1. Magnetic fields are the most likely means of extracting the rotational energy of the source and of producing relativistic outflows from compact astronomical objects. 2. External confinement is crucial for efficient collimation of Poynting dominated outflows. 3. An extended acceleration region is a distinguishing characteristic of the Poyntyng dominated outflows. Within the scope of ideal MHD, acceleration up to g~gmax is possible only in highly collimated flows ( ). 4. Even though an externally confined jets are accelerated by magnetic tensions, conditions for efficient transformation of the Poynting into the kinetic energy are rather restrictive. Dissipation (reconnection) is necessary in order to utilize the EM energy of the outflow. 5. If alternating field preexisted in the flow, they are efficiently dissipated via the Rayleigh-Taylor instability.