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 ?).
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 ?).
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 ?).
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 ?).
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.
(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.
(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.
(iii) Mass loading sets upper limit on the asymptotic speed.
To accelerate relativistic flows the energy supply must significantly
exceed the rest mass (energy) supply - low mass loading regime.
(Poynting flux)/( rest mass energy flux) =
Thus,
at the base.
in the magnetosphere.
Low particle inertia! FFE approximation!
Michel (1974): Steady-state axisymmetric flat spacetime FFE solution
for rotating monopole magnetosphere.
(iv) Mass loading argument favours BH over accretion disk
slow wind
heavy mass loading
relativistic jet
weak mass
loading
magnetic field suppresses
plasma transport from the
disk corona to the BH
magnetosphere
Kerr
black hole
accretion disk
inflow
outflow
outflow
Support from
numerical simulations
(v) Michel (1974) and Blandford-Znajek FFE solutions
Bt
Bp
• 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:
c
W
e+
Y - total magnetic flux,
W - angular velocity.
e¡
g
g
Wh
Blandford-Znajek (1977) generalised
this to slowly rotating black holes.
(v) Michel’s and Blandford-Znajek solutions
Bt
Bp
• 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:
c
W
e+
Y - total magnetic flux,
W - angular velocity.
e¡
g
g
Wh
Blandford-Znajek (1977) generalised
this to slowly rotating black holes.
(v) Michel’s and Blandford-Znajek solutions
Bt
Bp
• 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:
c
W
e+
Y - total magnetic flux,
W - angular velocity.
e¡
g
g
Wh
Blandford-Znajek (1977) generalised
this to slowly rotating black holes.
(v) Michel’s and Blandford-Znajek solutions
Bt
Bp
• 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:
c
W
e+
Y - total magnetic flux,
W - angular velocity.
e¡
g
g
Wh
Blandford-Znajek (1977) generalised
this to slowly rotating black holes.
(v) Michel’s and Blandford-Znajek solutions
Bt
Bp
• 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:
c
W
e+
Y - total magnetic flux,
W - angular velocity.
e¡
g
g
Wh
Blandford-Znajek (1977) generalised
this to slowly rotating black holes.
(vi) Initial collimation of relativistic jets requires a “nozzle”,
external confining medium.
Suspects:
jet
disk
disk
• Thick disk (torus)
• Disk corona
• Disk wind
• ISM
(vii) Collimation of high G jets is preserved.
Example: Flow in a tube with diverging
walls. 2D RMHD simulations.
Komissarov et al. (2009)
ballistic
separation
externally confined
Colour – log(magnetic pressure);
Lines – magnetic flux and flow surfaces.
• Even sub-fast-magnetosonic relativistic jets
do not de-collimate in the absence
of confining medium !
nozzle
Go
f
vo
v^
free expansion
Electromagnetic model of GRB jets
(Lyutikov & Blandford)
(viii) At the fast-magnetosonic point most of the energy of
relativistic magnetically-accelerated flows is still in the
magnetic form.
At the fast surface
(s - the ratio of Poynting flux and hydrodynamic energy flux.)
Magnetic acceleration in the super-fast magnetosonic
regime is rather delicate because of the possible
loss of causal connection across the jet.
(ix) Magnetic acceleration of conical flows with dominant
azimuthal magnetic field is inefficient.
v~c
v~c
Volume of the fluid element:
Its magnetic field:
Its magnetic energy:
The magnetic energy is conserved
No plasma acceleration !
(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.
v
v
dR
A
v
R
Komissarov et al. (2009)
Accelerates only when
decreases !
The poloidal magnetic flux distribution across the jet evolves towards
higher axial concentration.
• Collimation acceleration
(The “standard model”)
Prolonged slow acceleration of
externally confined jets.
Faster collimation of
inner stream lines due
to the magnetic hoop
stress
(slow self-collimation).
Vast literature.
Most recently, Beskin et al.
Lyubarsky (2009,2010),
Komissarov et al. (2007, 2009)
decreases
• Rarefaction acceleration
A short burst of acceleration
as the jet becomes unconfined.
rarefaction wave
decreases
v
jet
confinement
zone
conical expansion
weak acceleration
acceleration zone
Aloy & Rezzola (2006), Mizuno et al.(2008),
Tchekhovskoy et al.(2009), Komissarov et al.(2010)
(x) Causality limit on magnetic acceleration.
Coordinated restructuring of jets requires cross-jet connectivity
via fast magnetosonic signals.
qj
qMach
axis
v
Mach angle:
Connectivity condition:
AGN:
GRB:
- equipartition regime
- Poynting dominated
(x) Connectivity limit on magnetic acceleration.
Coordinated restructuring of jets requires cross-jet connectivity via
fast magnetosonic signals.
qj
qMach
axis
v
Mach angle:
Connectivity condition
AGN:
GRB:
- equipartition regime
- Poynting dominated
(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,
dissipates.
v
B
fast shock
(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,
dissipates.
v
B
fast shock
(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,
dissipates.
v
B
fast shock
(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,
;
v
B
fast shock
Thus, only a small fraction of the total energy,
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
tail
shell
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.
“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 dissipation
and 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 dissipation
and 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 dissipation
and 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.
pulse
gap
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.
From the magnetic flux conservation
and the radiation efficiency
For
(most of the energy is in the “pulse”)
This can be quite high !
• Numerical Simulations
1D RMHD with a cooling term:
- thermal energy density in the fluid frame
- temperature
- cooling time
Numerical models
- 50% emission time (in light crossing times)
- final magnetization of plasma
Rate of energy loss
Low gap magnetisation;
Strongly dumped oscillator.
High gap magnetisation;
Weakly dumped oscillator.
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-G 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.
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)
Animation
( mass density and magnetic field lines)
3D GR RMHD simulations
McKinney & Blandford
(2009)
Collimation by
torus or torus wind (?)
Domain size ~ 1000 rg
• Exact solutions of shock equations
Redistribution of kinetic
energy
Dissipation efficiency
• Searching for the way out
2. How to increase the efficiency of dissipation?
The flow remains highly magnetized.
Shock are inefficient at dissipation.
Instead, a direct dissipation of magnetic energy.
Magnetic reconnection.
( Lyutikov & Blandford 2003, Giannios et al. 2009,
McKinney & Uzdensky 2010, Zhang & Yan 2011, etc )