Download Physics of Relativistic Jets

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
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, B2>>4c2 .
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
c
RL 
- 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
F  e E  1c j  B
E  v.  B  0
1
c
 e  41   E
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 the thermal and radiation energy via dissipation?
Poynting flux
s
plasma energy flux
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.
r
r
The flow is accelerated when expands g ~

c
RL
cylindrical equilibrium at any z
2. Non-equilibrium regime: Qg>1
Z=r2/RL
 Weak causal connection: 1 < gQ < s
 No causal connection: gQ > s
equilibrium
Weakly causally
connected flows are
slowly accelerated
until gQ ~ s and then
stop accelerating
Bp is negligible;
purely azimuthal field
 g max 
 Q2 


1/3
g terminal
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)

 RL 
pext  p0  
z


equilibrium
regime
1.  < 2
rz
r  z / 4
 /4
g  r / RL  z  /4
Qg < 1
Equipartition, g~gmax, is achieved at
4/ 
z0 / RL ~ g max
2
When   2, the acceleration rate is maximal; z0 ~ g max RL
g/gin
Beyond the equipartition:
1
s~
ln  z / z0 
s
MHD jet confined by the external
pressure
(cont)

pext
3.
 >2
- non-equilibrium
 RL 
 p0  
 z 
Jet asymptotically approaches
conical shape rQz
Q  0.01/  2.5 at   2.2
Q  0.2 / 
at   2.5
Q  0.56 /  at   3

r  Qz
8 p0
B02
r  z / 4
 g max 
Terminal Lorentz factor g t ~  2 
 Q 
1/3
MHD jet confined by the external pressure (cont)
pext
 c 
 p0 

 z 
2. A special case; 2
If <1/4, the flow is accelerated
till s~1 and then collapses.


8p0
BL2
Some implications
AGNs: g~10 implies the size of the confining zone
z0>100Rg~1016cm. 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 1000Rg?
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.
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, gQ<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
dg
In an accelerating flow, effective gravity force arises g  c
dr
2
D
j
1 / 2





g
D
Instability time-scale
D B2
Dissipation rate Q 
 8
Interplay between acceleration and dissipation;
a self-consistent picture
2
z
~
g
Complete dissipation: diss
max l
In accreting systems, l~Rg
 10

~
12
10

 
 
16
zdiss
g
2
10
g
1000
2
cm
cm
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 ( gQ  1 .
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.