Physics of Relativistic Jets

Yuri Lyubarsky

Ben-Gurion University Beer-Sheva, Israel

Universality of relativistic jets

M 87M 87

Crab in X-rays

GRBs

time, stime, s

PKS 2155-304

Pulsar magnetosphere Collapsing, magnetized supernova core

Magnetized accretion disks around neutron stars and black holes

Magnetospheres of Kerr black holes

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, B2>>4c2 .

Courtesy to David Meier

All these sources likely share a common basic mechanism, in which relativistic outflows are launched hydromagnetically

Rotational energy Poynting?

Beyond the light cylinder, each revolution of the source adds to the wind one more magnetic loop.

In expanding flows, Bf becomes dominating

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 Wr~c, the field gets wound up, Bp~Bf

L

cR

-light cylinder radius

Basic picture of relativistic magnetohydrodynamic

outflows

. 0c1 BvE E 4

1e

1e c F E j 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).

In relativistic flows, the electric force is important

In the far zone of the outflow, v c and E B.

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.

Externally confined jets

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 the thermal and radiation energy via dissipation?

Poynting dominated jets.What do we want to know?

How and where does s decrease from >>1 to <<1?

fluxenergy plasma

flux Poynting

cylindrical equilibrium at any z

Bp is negligible;

purely azimuthal field

2. Non-equilibrium regime: >1Qg

1. Equilibrium regime: signal crossing time is less than the expansion time (strong causal connection), <1.Qg

Collimation vs acceleration: two flow regimes

The flow is accelerated when expands

Weak causal connection: No causal connection:

1

~

equilibrium

non-equilibrium

Z=r2/RL

1/3

maxterminal 2

~L

r r

c R

Weakly causally connected flows are slowly accelerated until and then stop accelerating

MHD jet confined by the external pressure

Bp

Bf

E

v

pext

The spatial distribution of the confining pressure determines the shape of the flow and the acceleration rate

MHD jet confined by the external pressure (cont)

2 .1

Equipartition, ~g gmax, is achieved at 4/0 max/ ~Lz R

/4/ Lr R z

4/zr

When 2, the acceleration rate is maximal;

- equilibrium regime

4/zr

ext 0 LRp pz

20 max ~ Lz R

Beyond the equipartition:

0/ln

1~

zz

/g gin

s

1

2 .3

020

8 p

B

4/zr

zr

2.50.01/ at 2.2

0.2 / at 2.5

0.56 / at 3

MHD jet confined by the external pressure (cont)

1/3

maxt 2

Terminal Lorentz factor ~

- non-equilibrium

Jet asymptotically approaches conical shape r=Qz

ext 0 LRp pz

MHD jet confined by the external pressure (cont)

2 .A special case; =2k

If b<1/4, the flow is acceleratedtill ~s 1 and then collapses .

208 LB

p 0ext

z

cpp

GRBs: ~g 102 - 103; minimal z0~1011 cm – marginally OK. But achromatic breaks in the afterglow light curves and statistics imply gQ>>1, which is fulfilled only if the flow remains Poynting dominated. Magnetic dissipation is necessary.

Some implications

AGNs: ~10 g implies the size of the confining zone z0>100Rg~1016cm. The condition of efficient acceleration ( <1) Qgmay 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 1000Rg ?

Beyond the ideal MHD: magnetic dissipation in Poynting dominated outflows

current sheet

The magnetic energy could be extracted via anomalous dissipation in narrow current sheets.

How differently oriented magnetic fieldlines 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.

But: The necessary condition for the instability – strong causal connection, <1. gQ 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

MHD instabilities

The most dangerous is the kink instability

In an expanding flow, B becomes predominantly toroidal; current sheets are stretched. Local structure: plane current sheet separating oppositely directed fields.

Let alternating fields preexist in the jet

Striped jets?

Rayleigh-Taylor instability of currents sheets in accelerating flows

 jD

In an accelerating flow, effective gravity force arises

Dissipation rate

2 dg cdr

2/1 g

8

2BQ

Instability time-scale

Magnetic dissipation in striped jets

Interplay between acceleration and dissipation; a self-consistent picture

21610

2121000

10 cm~

10 cmdissz

AGNs

GRBs

Complete dissipation:

In accreting systems, l~Rg

2max~dissz l

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.

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 ( ).

2. External confinement is crucial for efficient collimation of Poynting dominated outflows.

Conclusions

14. 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 .