Formation, acceleration and structure of relativistic jets. Serguei Komissarov University of Leeds...

Formation, acceleration and structure of relativistic jets.

Serguei Komissarov University of Leeds

UK

Few comments on formation, acceleration and structure of

relativistic jets.

Serguei Komissarov University of Leeds

UK

N.Vlahakis, Y.Granot, A.Konigl, A.Spitkovsky, M.Barkov,J.McKinney, Y.Lyubarsky, M.Lyutikov, N.Bucciantini

Magnetic paradigm of relativistic jets (R.Blandford)

• Jets are produced by rapidly rotating BH (NS ?) with accretion disks. Power source - the rotational energy. (Role of accretion disk ?);

• The energy is extracted via magnetic torque as Poynting flux;

• Jet collimation is due to the magnetic hoop stress. (Efficiency ?);

• Jet acceleration is via conversion of the electromagnetic energy into the bulk kinetic energy. (Efficiency ?); • Jet emission is via energy dissipation at shocks (kinetic energy) and/or reconnection cites (magnetic energy). (Efficiency of dissipation and particle acceleration ?).

(i) Magnetic paradigm of relativistic jets (R.Blandford)

• Jets are produced by rapidly rotating BH (NS ?) with accretion disks. Power source - the rotational energy. (Role of accretion disk ?);

• The energy is extracted via magnetic torque as Poynting flux;

• Jet collimation is due to the magnetic hoop stress. (Efficiency ?);

• Jet acceleration is via conversion of the electromagnetic energy into the bulk kinetic energy. (Efficiency ?); • Jet emission is via energy dissipation at shocks (kinetic energy) and/or reconnection cites (magnetic energy). (Efficiency of dissipation and particle acceleration ?).

(ii) Two frameworks:

Relativistic MHD Force-Free Electrodynamics

FFE is RMHD in the limit of negligible plasma inertia. Magnetic energy flows under the action of Maxwell’s stresses (Another name – Magnetodynamics, MD).

FFE is good for the problems of power supply and structure of magnetospheres at the jet base.

RMHD is needed for the jet acceleration, collimation, and dissipation.

(ii) Two frameworks:

Relativistic MHD Force-Free Electrodynamics

FFE is RMHD in the limit of negligible plasma inertia. Magnetic energy flows under the action of Maxwell’s stresses (Another name – Magnetodynamics, MD).

FFE is good for the problems of power extraction and structure of magnetospheres at the jet base.

RMHD is needed for the jet acceleration, collimation, and dissipation.

(Poynting flux)/( rest mass energy flux) = at the base.

(iii) Mass loading sets upper limit on the asymptotic speed.

Thus, in the magnetosphere.

To accelerate relativistic flows the energy supply must significantly exceed the rest mass (energy) supply - low mass loading regime.

Low particle inertia! FFE approximation!

Michel (1974): Steady-state axisymmetric flat spacetime FFE solution for rotating monopole magnetosphere.

inflow

outflow

outflow

accretion diskKerr black hole

(iv) Mass loading argument favours BH over accretion disk

heavy mass loading

weak massloading

slow wind relativistic jetmagnetic field suppressesplasma transport from the disk corona to the BH magnetosphere

Support from numerical simulations

B

B

p

t

e+e¡

h

c

• Magnetic spirals advance with the speed of light. • The twist has nothing to do with the particle inertia!• The structure of poloidal field is unaffected by the rotation - the hoop stress collimation does not work!• The total Poynting flux:

- total magnetic flux, - angular velocity.

Blandford-Znajek (1977) generalised this to slowly rotating black holes.

(v) Michel (1974) and Blandford-Znajek FFE solutions

B

B

p

t

e+e¡

h

c

• Magnetic spirals advance with the speed of light. • The twist has nothing to do with the particle inertia!• The structure of poloidal field is unaffected by the rotation - the hoop stress collimation does not work!• The total Poynting flux:



(v) Michel’s and Blandford-Znajek solutions

B

B

p

t

e+e¡

h

c

• Magnetic spirals advance with the speed of light. • The twist has nothing to do with the particle inertia!• The structure of poloidal field is unaffected by the rotation -the hoop stress collimation does not work!• The total Poynting flux:



(v) Michel’s and Blandford-Znajek solutions

(vi) Initial collimation of relativistic jets requires a “nozzle”, external confining medium.

disk disk

jet • Thick disk (torus)• Disk corona• Disk wind• ISM

Suspects:

Example: Flow in a tube with divergingwalls. 2D RMHD simulations. Komissarov et al. (2009)

Colour – log(magnetic pressure);Lines – magnetic flux and flow surfaces.

separation

ballistic

(vii) Collimation of high jets is preserved.

externally confined

o

v < c

v

v

• Even sub-fast-magnetosonic relativistic jets do not de-collimate in the absence of confining medium !

nozzle

free expansion

Electromagnetic model of GRB jets (Lyutikov & Blandford)

At the fast surface

Magnetic acceleration in the super-fast magnetosonic regime is rather delicate because of the possible loss of causal connection across the jet.

(viii) At the fast-magnetosonic point most of the energy of relativistic magnetically-accelerated flows is still in the magnetic form.

( - the ratio of Poynting flux and hydrodynamic energy flux.)

v~c v~c

Volume of the fluid element:

Its magnetic field:

Its magnetic energy:

The magnetic energy is conserved No plasma acceleration !

(ix) Magnetic acceleration of conical flows with dominant azimuthal magnetic field is inefficient.

(x) Magnetic acceleration requires flow restructuring.

- azimuthal magnetic field

- azimuthal magnetic flux of fluid element

- corresponding magnetic energy

The magnetic energy decreases as a increases towards unity.

Bunching of the streamlines (poloidal flux surfaces) towards the jet axis.

(x) Magnetic acceleration requires flow restructuring.

R

v

v

vR A

Accelerates only when decreases !

Komissarov et al. (2009)

The poloidal magnetic flux distribution across the jet evolves towards higher axial concentration.

• Collimation acceleration

Prolonged slow acceleration of externally confined jets.

Faster collimation of inner stream lines dueto the magnetic hoopstress (slow self-collimation).

Most recently, Beskin et al.Lyubarsky (2009,2010),Komissarov et al. (2007, 2009)

(The “standard model”)

Vast literature.decreases

• Rarefaction acceleration

v

confinementzone acceleration zone

jet

rarefaction wave

Aloy & Rezzola (2006), Mizuno et al.(2008),Tchekhovskoy et al.(2009), Komissarov et al.(2010)

A short burst of acceleration as the jet becomes unconfined.

conical expansionweak acceleration

decreases

j Mach

characteristic

v

(x) Causality limit on magnetic acceleration.

Coordinated restructuring of jets requires cross-jet connectivity via fast magnetosonic signals.

boundary

axis

Mach angle:

Connectivity condition:

AGN:

- Poynting dominated

- equipartition regime

GRB:

j Mach

characteristic

v

(x) Connectivity limit on magnetic acceleration.

Coordinated restructuring of jets requires cross-jet connectivity via fast magnetosonic signals.

boundary

axis

Mach angle:

Connectivity condition

AGN:

- Poynting dominated

- equipartition regime

GRB:

Only the kinetic energy dissipates;

At strong shocks ( Mach >>1 ) in high sigma flow, only one half of the kinetic energy dissipates and the other half is converted into magnetic energy.

Kinetic energy is only a small fraction of the total energy, ;

Thus, only a small fraction of the total energy,

dissipates.

B

fast shock

v

(xi) Shock dissipation is problematic in highly magnetised plasma.

Only the kinetic energy dissipates;

At strong shocks ( Mach >>1 ) in high sigma flow, only one half of the kinetic energy dissipates and the other half is converted into magnetic energy.

Kinetic energy is only a small fraction of the total energy, ;

Thus, only a small fraction of the total energy,

B

fast shock

v

(xi) Shock dissipation is problematic in highly magnetised plasma.

dissipates.

In contrast, the prompt emission of GRBs is ~10% (up to 90%) of the total jet energy (Zhang et al. 2007).

(xii) Impulsive magnetic acceleration (Granot et al. 2010)

Expansion of a highly magnetized plasma shell into vacuum

vacuum

v

Once detached from the wall the shell keeps spreading longitudinally with the front section reaching very high Lorentz factor. The shell leaves behind a rarefied low-magnetised tail.

shelltail

“Plasma gun” (Contopoulos, 1995)

The averaged over energy shell’s Lorentz factor grows as

until total conversion is reached.

Real cosmic shells do not expand into vacuum. The shock interaction with the external gas limits this effect (Levinson 2010). The gaps between shells are also filled with plasma, either from the shell tails or/and the external gas.

Highly variable jets may have highly variable magnetization. The low magnetization regions may be the cites of efficient dissipationand emission ?

The averaged over energy shell Lorentz factor grows as

until total conversion is reached.

Real cosmic shells do not expand into vacuum. The shock interaction with the external gas limits this effect (Levinson 2010). The gaps between shells are also filled with plasma, either from the shell tails or/and the external gas.

Highly variable jets may have highly variable magnetization. The low magnetization regions may be the cites of efficient dissipationand emission ?

Instead of Conclusions. Things to explore.

• Instability (Kink-mode)? (e.g. Istomin & Pariev 1996, Lyubarsky 1999) More 3D simulations needed to see how destructive it can be (like McKinney & Blandford, 2009). The role of velocity gradient across the jet, non-cylindrical geometry, time-dilation effect etc ?

• Magnetic dissipation in high sigma plasma (relativistic reconnection) (e.g. Lyutikov & Blandford 2003, Giannios et al. 2009, McKinney & Uzdensky 2010, Zhang & Yan 2011)

• Instability may promote more efficient magnetic acceleration of jets. (e.g. Heinz & Begelman 2000, Drenkhahn & Spruit 2002).

• If initial magnetization determines the terminal Lorentz factor then what processes determine the magnetisation ? Why the Lorentz factors of XRB, AGN, and GRB are so different?

• Origin of regular magnetic field in accretion disks? Its role in the accretion dynamics? Vertical transport of angular momentum? ( e.g. Blandford & Payne 1982, Spruit & Uzdensky, 2005, Lubow et al. 1994, Livio et al. , 1999)

• Nature of the variability and its effects on the jet acceleration? (Granot et al. 2010, Lyutikov 2010). Dynamic of inhomogeneous jets with variable magnetization and shock dissipation in such jets?

• Particle acceleration mechanisms? Inefficient shock acceleration at high sigma superluminal shocks (e.g. Spitkovsky & Lorenzo 2009).

• Other missing ingredients. e.g. Compton drag and photon breading (Stern & Poutanen)?

• Alternative models ? Thermal acceleration of GRB jets (fireball ?).

Too many more questions, too few answers.

• Another way out? The “magnetic pump” model.

Variability of the central engine -> highly magnetised pulses are separated by low magnetised gaps (most of the jet energy is magnetic) -> expansion of pulses drives strong shocks -> their energy dissipates when these shocks cross the gaps -> multiple crossings result in high dissipation and radiation efficiencies.

gap

pulse

shocks in the gaps shock in the pulse

The 1D toy model

Chamber

Key parameters:

Oscillations continue until the all of the dissipated energy is radiated and the magnetic pressure is uniform.

For (most of the energy is in the “pulse”)

From the magnetic flux conservation

and the radiation efficiency

This can be quite high !

• Numerical Simulations

- thermal energy density in the fluid frame

- temperature

- cooling time

1D RMHD with a cooling term:

Numerical models

- 50% emission time (in light crossing times)

- final magnetization of plasma

Low gap magnetisation;Strongly dumped oscillator.

High gap magnetisation;Weakly dumped oscillator.

Rate of energy loss

V. Conclusions

1) The magnetic field provides a robust mechanism of powering outflows from rotating central engines. When the magnetosphere is highly magnetically-dominated (relativistic Alfven speed) the outflow is relativistic.

2) An external collimation is required close to the central engine in order to produce jets. But it is not required further out in order to preserve their collimation.

3) The magnetic acceleration has to continue well beyond the fast magnetosonic surface in order to ensure efficient conversion of the Poynting flux into the kinetic energy. In this regime it becomes rather problematic. The high- GRB jets are likely to remain magnetically-dominated to the very end.

4) Shock dissipation in homogeneous magnetically-dominated flows is very inefficient, and cannot explain the prompt emission of GRBs. Alternative models involving magnetic reconnection are becoming increasingly popular.

5. In inhomogeneous magnetically dominated flows, with weakly magnetised patches, the shock dissipation can still be very efficient, and can explained the observed high radiation efficiency of GRBs.

Generation of relativistic MHD flows in numerical simulations. Winds: Komissarov (2001,2004), Koide (2004), Bucciantini et al.(2006,2007), and others.

Jets: McKinney (2006), Komissarov & Barkov (2007,2008), Bucciantini et al.(2009), McKinney & Blandford (2009), and others.

Animation

Example: Collapsar jets. 2D GRMHD. Collapse of a rapidly rotating magnetic star. Evolution after BH formation. Fixed Kerr metric. Dipolar magnetic field of the collapsing star.

(Komissarov & Barkov, 2007)

( mass density and magnetic field lines)

C:\Program Files\K-Lite Codec Pack\Media Player Classic\mplayerc.exe E:\Presentations\Animations\collapsar1\c3b95bzrm_mpegp.avi

3D GR RMHD simulations

McKinney & Blandford (2009)

Collimation by torus or torus wind (?)

Domain size ~ 1000 rg

• Exact solutions of shock equations

Dissipation efficiencyRedistribution of kineticenergy

• Searching for the way out

2. How to increase the efficiency of dissipation?

( Lyutikov & Blandford 2003, Giannios et al. 2009,McKinney & Uzdensky 2010, Zhang & Yan 2011, etc )

The flow remains highly magnetized. Shock are inefficient at dissipation.

Instead, a direct dissipation of magnetic energy. Magnetic reconnection.

Formation, acceleration and structure of relativistic jets. Serguei Komissarov University of Leeds...

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