Astrophysical jets
Yuri Lyubarsky
Ben-Gurion University
Universality of relativistic jet phenomenon
1. Radio galaxies and quasars
M 87
Universality of relativistic jet phenomenon
1. Radio galaxies and quasars (cont)
Apparent superluminal
motion (Rees 1967)
c
q
v
towards observer
 x  ct sin q
 t  t 1  ( v / c ) cos q 
v apparent 
x
t

sin q
1  ( v / c ) cos q
c
Universality of relativistic jet phenomenon
1. Radio galaxies and quasars (cont)
Blazars - AGNs with jet pointing towards the observer.
The observed emission is dominated by the jet.
synchrorton
IC
Rapid (few-minute) variability in
TeV flux of blazars implies g>50
(Levinson 06;Begelman etal 08)
PKS 2155-304
The flux above 200 GeV
(Aharonian et al 07)
Universality of relativistic jet phenomenon
2. Microquasars
Microquasar is a scaled
down (by a factor of 106)
version of active galactic
nuclei
Superluminal motion
in microquasar
GRS 1915+105;
Vapparent =1.5c
Scaling of X-ray binaries to AGNs
Merloni et al 03; Falcke et al 04
g min
Distribution of Lorentz factors
inferred from superluminal motion
Blue – AGNs; red – microquasars
(Fender 05)
Universality of relativistic jet phenomenon
3. Gamma-ray bursts
Optical afterglow
of GRB 990510
time, s
Universality of relativistic jet phenomenon
3. Gamma-ray bursts (cont)
GRBs apparently involve ultrarelativistic (g=100-1000), highly
collimated (q=1o-5o) outflows. They likely arise during the
collapse of star’s core.
All relativistic cosmic jet sources may be
connected by a common basic mechanism:
acceleration by rotating, twisted magnetic fields
Rotation twists up field into toroidal component, slowing rotation
Pulsar magnetosphere
Collapsing, magnetized
supernova core
Magnetized accretion
disks around neutron
stars and black holes
Magnetospheres of
rotating black holes
Courtesy to David Meier
Energy balance in magnetized outflows
In the proper plasma frame E '  0
In the lab frame E 
Poynting
flux
S
1
c
vB  0
c
4
EB 
B
2
4
v
By definition, ultrarelativistic
flow implies Ekinetic>> c2
Relativistic flow can be produced by
having a very strong rotating magnetic
field such that B2>>4c2  low “mass loading” of the field lines
The flow starts as Poynting dominated. How the EM
energy transformed into the plasma energy?
Rotational energy
Poynting
?
The characteristic size of the
magnetosphere, RL=c/W.
For rapidly rotating BH, RL~Rg.
At RL:
L EM ~
EB
4
B ~ B p ~ E
c   R L ~ B cR g
2
2
2
Equipartition: B ~
2
M c
2
Rg
L EM
2

 M c
Formation of jet during collapse of a
rotating massive star into a rotating
BH (Barkov&Komissarov 08)
Force balance in Poynting dominated flows
Magnetic hoop stress
Plasma pressure and inertia<< Lorentz force.
Does it mean that huge tension of
wound up magnetic field (hoop stress)
compresses the flow towards the axis?
NO!
In the current closure region,
the force is decollimating.
An external confinement
is necessary!
F
1
c
j B
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 the
(generally magnetized) wind from
the outer parts of the disk.
In GRBs, a relativistic jet from the
collapsing core pushes its way
through the stellar envelope.
Force balance in Poynting dominated flows (cont)
Total electromagnetic force F   e E  1c j  B
E
1
c
v.  B  0
In the far zone, v
c and E
e 
1
4
 E
B.
In highly relativistic flows, the electric
force nearly cancels the Lorentz force.
Acceleration is very slow!
As the jet moves out, acceleration converts the EM energy into
the matter kinetic energy. How efficient is this conversion?
Externally confined 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?
s 
Poynting
flux
plasma energy flux
How and where s decreases from >>1 to <<1?
When the flow becomes matter dominated?
The flow could be considered as
matter dominated if most of the
energy could be released at the
termination shock. This condition is
fulfilled only if s<0.1-0.2.
Jump conditions at relativistic shock.
f- fraction of energy transferred to the
plasma. Compression ratio = c/v2
Structure of relativistic MHD jet
Axisymmetric flows are nested magnetic
surfaces of constant magnetic flux.
These surfaces are equipotential.
Plasma flows along these surfaces.
At RL:
B ~ B p ~ E
In the far zone:
B 
2I
cr

1
r
;
Bp 
E, B.>>Bp
1
r
2
;
E   
1
r
Simple example: cylindrical configuration.
Bp
1. v=0; E=0
2
dB p
dr

1
r
2
d ( rB  )
dr
2
0
B ~ B p
2. v
B
Bp
c; B’p= Bp; B’gB; E’=(v/c)gB
E '  B ' >> B ' p
v
E
B
Relativistic MHD in the far zone, Wr>>c
Intimate connection between collimation and acceleration
Without external confinement, the flow is nearly radial;
the acceleration stops at an early stage (Tomimatsu94;
Beskin et al 98)
g  W r / c;
g  g max ln (W r / c g max
g  g max
1/ 3
1 / 3 ;
g > g max
1/ 3
gmax>>1 - the Lorentz factor achieved when and
if the Poynting flux is completely transformed
into the kinetic energy
Jet confined by the external pressure: the spatial distribution of
the confining pressure determines the shape of the flow boundary
and the acceleration rate (Tchekhovskoy et al 08,09; Komissarov
et al 09; Lyubarsky 09,10).
Collimation vs acceleration: two flow regimes
1. Wr2<<cz – equilibrium regime
g ~ Wr / c
Causality
:
 g  1;
ct '

z
r
gr
 
dr

zc
Wr
2
>1
- opening
cylindrical
equilibrium
at any z
Z=Wr2/c
angle
dz
2.
Wr2>>cz
– non-equilibrium regime
g  1
purely azimuthal field, Bp=0
equilibrium
non-equilibrium
MHD jet confined by the external pressure
v
p ext
 c 
 p0 

 Wz 

pext
B
E
Bp
MHD jet confined by the external pressure (cont)
p ext
1.
 2
r z
 /4
 c 
 p0 

 Wz 

r z
equilibrium regime,
g  Wr  z
g  1
 /4
The fastest accelerati on at   2 ; g ~ W r / c ~
Wz / c
4 /
Equipartition, g~gmax, at z 0 W / c ~ g max
At   2 ,
z 0 W / c ~ g max
2
Beyond the equipartition:
s ~
1
ln ( z / z 0 
g/gin
s
 /4
MHD jet confined by the external pressure (cont)
p ext
 >2
3.
Jet asymptotic
ally approaches
r  z
conical shape
 
1

(
 1
 2
  0 . 01 / 
  0 .2 / 
  0 . 56 /
(
2 .5
 c 
 p0 

 Wz 

(  2 )



r  z
1/[2(  - 2)]
 
;
8p0
2
B0
at   2.2
at   2.5
 at   3
 g max 
g grows until g t ~  2 
  
g t ~ g max ;
r z
 /4
1/ 3
;
g max  > 1
g max   1
non-equilibrium
equilibrium
Some implications
AGNs: g~10 implies the size of the
confining zone z0>100Rg~1016cm.
The condition of efficient acceleration
g~1 is fulfilled: <qg>0.26 (Pushkarev
etal 09)
GRBs: g~few 102; minimal z0~1011 cm –
marginally OK. But achromatic breaks in
the afterglow light curves and statistics
imply g>>1, which is fulfilled only
if the flow remains Poynting dominated.
Magnetic dissipation is necessary.
The observed opening angles
vs Lorentz factor (Pushkarev
etal 09)
To summarize the dissipationless MHD acceleration
The flow could be accelerated till s~1 provided it is confined
by an external pressure, which decreases with distance but
not too fast.
The acceleration zone spans a large range of scales so that
one has to ensure that the conditions for acceleration are
fulfilled all along the way. Transition to the matter dominated
stage, s~0.1, could occur only at an unreasonably large scale.
These conditions are rather restrictive. It seems that in real
systems, some sort of dissipation (reconnection) is necessary
in order to utilize the electromagnetic energy completely.
Some evidence for slow acceleration and
collimation of Poynting dominated jets.
1. M87: a
large opening
angle near
the base of
the jet and
tighter
collimation on
larger scales
Walker et al 2008
Gracia et al 2005
2. The absence of bulk-Comptonization spectral signatures in blazars
implies that Lorentz factors >10 must be attained at least on the scale
1000Rg ~ 1017 cm (Sikora et al. 05).
But according to spectral fitting, jets are already matter dominated at ~1000 Rg
(Ghisellini et al 10). Violent dissipation somewhere around1000Rg?
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.
Global MHD instabilities
The most dangerous is the kink instability
(Lyubarsky 92, 99; Eichler 93; Spruit et al. 97;
Begelman 98; Giannios&Spruit 06).
Mizuno et al 09
But: The necessary condition for the instability –
causal connection, g1. Not fulfilled in
GRBs; may be fulfilled in AGNs.
The growth rate is small in relativistic case
(Istomin&Pariev 94,96; Lyubarsky 99).
Some evidence for saturation of the
instability (McKinney&Blandford 09)
Moll et al 10
Dissipation of alternating magnetic fields in the jet
(Levinson & van Putten 97; Levinson 98; Heinz & Begelman 00;
Drenkhahn 02; Drenkhahn & Spruit 02; Giannios & Spruit 05;07;
Giannios 06;08)
g
j
B
l~Rg
If the reconnection rate is vrecc, the energy release scale is
 10

~ 
12
10


17 0 . 1
r ~
1
g Rg
2

0 .1

( 
( 
g
2
10
g
300
2
cm
cm
AGNs
GRBs
Advantage of the magnetic dissipation models
1. Dissipation easily provides large radiative efficiencies and
strong variability inferred in GRBs.
2. Reconnection at high s produces relativistic “jets in a jet”;
this could account for the fast TeV
variability of blazars (Giannios
et al 10; also talk by Giannios)
Caveat: why the fast reconnection occur in jets?
nT 
2
B
8
current sheet
rB 
T
eB

B
8  en
Anomalous resistivity implies vcurrent=j/en~c or rB=kT/eB~d
In AGNs and GRBs, rB<<l~Rg
Fast reconnection at rB<<l
inflow
outflow
resistivity
We still do not understand why such a
configuration is maintained within the jet
Conclusions
1. Magnetic fields are the most likely means of extracting the
rotational energy of the source and of producing relativistic,
outflows from compact objects (pulsars, GRBs, AGNs,
galactic X-ray binaries)
2. External confinement is crucial for efficient collimation and
acceleration of Poynting dominated outflows.
3. An extended acceleration region is a distinguishing
characteristic of the Poyntyng dominated outflows.
4. Efficient acceleration (up to g~gmax) is possible only in
causally connected flows, g   1 .
5. Dissipation (reconnection) is necessary in order to utilize
the EM energy of the outflow.