Magnetic accelerations of relativistic jets.

Serguei Komissarov University of Leeds

UK

N.Vlahakis (Athens) Y.Granot (Hertfordshire) A.Konigl (Chicago) A.Spitkovsky (Princeton)M.Barkov (Moscow)

1. Introduction.2. Standard model: Steady-state axisymmetric jets.

3. Alternatives to the standard model;4. Impulsive acceleration;5. Conclusions.

Plan

• Relativistic regime versus non-relativistic one;• Thermal mechanism versus magnetic one; • Problems of the standard magnetic model;

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 cold MHD

Kinetic energy ~ magnetic energy at the magneto-sonic point !

•Non-relativistic gasdynamics

Kinetic energy ~ thermal energy at the sonic point !

Kinetic energy << thermal energy at the sonic point !

•Relativistic gasdynamics

only !

•Relativistic cold MHD

High Lorentz factor at the magnetosonic point ! However,

(kinetic energy) << (magnetic energy) at the sonic point !

- magnetic field in the fluid frame

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.

So what ?

•Thermal acceleration mechanism (conical flow)

v~c

Mass conservation:

Energy conservation:

Bernoulli equation:

A

Rj

from Bernoulli eq. Very fast acceleration !

z

• Ideal MHD acceleration mechanism (conical flow)

v~cA

Rj

Mass conservation:

Energy conservation:

Bernoulli equation:

from Bernoulli eq. No acceleration !

Another explanation:

v~c v~c

Volume of the fluid element:

Its magnetic field:

Its magnetic energy:

Thus, the magnetic energy is preserved !

• Ideal MHD acceleration mechanism Non-conical flows

( toroidal magnetic field):

R

v

v

vR A

Consider the flow between two close flux surfaces,

Mass conservation:

Energy conservation:

Bernoulli equation:

from Bernoulli eq.

In a conical flow is constant (no acceleration).

Curved stream lines? Try

R

vR

z

R0

R0

z0

is still constant (no acceleration) !

should decrease for acceleration !

where .

Further from the axis a stream-lines is faster it moves away from it with z - the geometric condition of acceleration.

and decreases if .

equidistant here

concentratedtowards theaxis here

Try

Now

In any case there has to be a communication across the jet - the causal connectivity condition !

Can this condition be satisfied?

The Lorentz factor grows as until ~one half of the magnetic energy is converted into the kinetic one. (Not particularly efficient still !?)

Komissarov et al. (2009), Lyubarsky (2009)

Summary of recent numerical and theoretical results

• Freely expanding (unconfined) flows quickly loose causal connectivity, become conical and stop accelerating;

• Externally confined jets with remain causally connected and accelerate if < 2;

• If > 2 jets still loose causal connectivity and stop accelerating.

Terminal Lorentz factor and opening angle

Causal connectivity condition:

Jet half openingangle

Mach angle

Upper limit on Lorentz factor(full conversion of magnetic energy )

Efficient conversion implies

For GRBs with ~1000 this gives the opening angle !

OK for AGN jets.

The model predict almost purely toroidal magnetic field.

3C120

Another problem:

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 are constant then the magnetic field behaves as an ultra-relativistic gas

Magnetic (pressure) acceleration is as efficient as the thermal one !?

• Dissipation of tangled magnetic field (e.g. Drenkhahn 2002; Drenkhahn & Spruit 2002)

(magnetic energy) (heat) (kinetic energy)

(radiation)

• 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

total

magnetic

kinetic

magneticpressure

magnetic field

Lorentz factor

the initial width =1; the wall is at x=-1; 0 = 30.

Solution at t=1 when the rarefaction just reaches the wall (c=1).

At the boundary with vacuum

The mean value

Simple rarefaction wave – self-similal solution.

magnetic field

magneticpressure

Lorentz factortotal

magnetic

kinetic

The shell has separatedfrom the wall.

The total energy, mass, and momentum and the width of the shell hardlychange as it moves.

The Lorentz factor growsbecause the energy and momentum of magnetic field are transferred to plasma.

Solution at t=20.

The mean Lorentz factor grows asuntil 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.