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Radiation from Poynting Jets and Collisionless Shocks
Edison Liang, Koichi NoguchiShinya Sugiyama, Rice University
Acknowledgements: Scott Wilks, Bruce Langdon
Bruce Remington
Talk given at AAS Seattle Meeting January 2007
Internal shocksHydrodynamic Outflow
Poynting fluxElectro-magnetic-dominated outflow
Two Paradigms for the Energetics of Relativistic Jets in Blazars & GRBs
e+e-ions
e+e-
What is primary energy source?How are the e+e- accelerated? How do they radiate?
shock-raysSSC, EC… -rays
B
Synchrotron Radiationis usually assumed in
All paradigms
We have developed a Particle-In-Cell code that simultaneously computes radiation output from each superparticle self-consistently.
We find that in-situ radiation output from electrons accelerated by Poynting flux and relativistic collisionless shocks are much below that predicted by the classical synchrotron formula.
This is because the highest energy electrons are preferentially accelerated by Lorentz forces that are parallel, not perpendicular, to the particle momentum.
From PIC runs, we compute the radiation power directly from the force terms
Prad = 2e2(F|| 2+ 2F+2) /3cm3
where F|| is force along vand F+ is force orthogonal to v
(algorithm is carefully calibrated against analyticformula using monoenergetic electrons radiating
in a uniform static B-field)
For Poynting flux acceleration, we find that Prad ~ e
22sin4<< Psyn ~e22
where is angle between v and Poynting vector k.Also critical frequencycr ~ e2sin2crsyn
This resultRadiation efficiency << classical synchrotron can be
understood as follows:
The most efficient accelerations to higher are produced by Lorentz forces parallel to the
particle momentum.But only forces perpendicular to particle momentum
can produce synchrotron radiation.
QuickTime™ and a decompressor
are needed to see this picture.
B
e+e-Poynting jet running into cool e-ion ambient plasma
(movie by Noguchi)
By
Ez
Jz
PlasmaJxB force snowplows all surface particles upstream:<> ~ max(B2/4nmec2, ao)“Leading PonderomotiveAccelerator” (LPA)Plasma
JxB force pulls out surface particles. Loaded EM pulse (speed < c) stays in-phase with the fastest particles, but gets “lighter” as slower particles fall behind. It accelerates indefinitely over time: <> >> B2 /4nmec2, ao “Trailing Ponderomotive Accelerator” (TPA).(Liang et al. PRL 90, 085001, 2003)
Entering
Exiting
Poynting Flux: Particle accelerationby induced j x
B(ponderomotive) force
x
x
EM pulse
By
x
y
z
Ez
Jz JxB
k
Prad
Panalytic =e22sin4x
px
pz
ByPrad
Electrons snowplowed by Poynting flux radiates at a level ~ 10-4
of synchrotron formula using local B and . This is due to
sin ~ pz/px < 0.1.
Momentum gets more and moreAnisotropic with time: pz/px<<1
Details of TPA expansion
The power-law index seems remarkably robust independent of initial plasma size or temperature
and only weakly dependent on B
f()
-3.5
Lo=105rce
Lo= 104rce
QuickTime™ and aGraphics decompressor
are needed to see this picture.
Prad
Panalytic =e22sin4
In TPA, we also see good correlation between Prad and Panalytic
Poynting Jet Prad asymptotes to ~ constant level at late times
as increase in is compensated by decrease in and B
Lo=120c/e Lo=105c/e
po=10
Prad
10*By
Prad
x x x
Asymptotic Prad scales as (e/pe)n with n ~ 2 - 3
e/pe=102 103 104
x x x
PradPrad
Inverse Compton scattering against ambient photons can slow or stop acceleration (Sugiyama et al 2005)
n=10-4ne n=10-2ne n=ne
1 eV BB ambient photon field epe=100 jet
Next we study radiation from Collisionless Shocks
3 Examples:
1.e+e-/e+e- Magnetized Shock (B2 ~ bulk KE)
2.e+e- /e-ion Magnetized Shock (B2 ~ bulk KE)
3.e+e- Nonmagnetized Shock (B2 << bulk KE)
px
By*100
f()
Magnetic Shock of e+e- sweeping up cold ambient e+e- shows broad (>> c/e, c/pe) transition region with 3-phases (nej=40no)
ejecta
ambient
deceleratedejectaspectralevolution
swept-upambientspectral evolution
xx
pz
px
Both ejecta and swept-up electrons are highly anisotropic: pz<<px
ejecta
swept-up
ejecta e- Swept-up ambient e-
Prad of swept-up electron is lower than Prad of decelerating ejecta electron.The radiative layer is very thin
Prad
xx
ejecta e+
ejecta e-ambient ion
ambient e-
f()-10pxe-
10pxej
100pxi
100Ex
100By
Prad
Magnetic shock in e+e-/e-ion plasma is very complex with 5 phases and broad transition region(>> c/i, c/pe). Swept-up electrons areaccelerated by ponderomotive force. Swept-up ions are accelerated
by charge separation electric fields.
x
ejecta e- swept-up e-
Prad of shocked swept-up electrons is comparable to the e+e-/e+e- case.But the radiation layer is much thicker
xx
Prad
Comparison of collisionless shocks: e+e- shocking B=0 e+e- cold plasma ejecta: hi-B, hi- weak-B, moderate B=0, low
swept-up
swept-up
swept-up
100By
ejecta px
swept-up px
100By
100Ex
100By100Ex
-px swept-up
-pxswrpt-up
ejecta ejecta
no power-law~ -3 power-law~ -3 power-law
f() f() f()
ejecta
Nonmagnetic
e+e-/e+e-shock:
Radiation not
DominatedBy Weibelturbulence
ejecta -px
swept-up px
nswept-up
Ex2
nejectaBy2
time
ejecta energyswept-up energy
Ex energy
By energy
energy evolution
Prad swept-up
Prad ejecta
x x
SUMMARY
1. Radiation power of Poynting jets are many orders of magnitude below classical synchrotron formula due to anisotropy of acceleration (Forces ~ parallel to velocity are most efficient in acceleration).
2. Structure and radiation power of collisionless shocks are highly sensitive to ejecta (upstream) B field strength and Lorentz factor.
3. Radiation power of collisionless shocks are also much lower than classical synchrotron formula for a given ejecta magnetic field and Lorentz factor. The highest energy particles are accelerated mainly by (electrostatic or ponderomotive) forces parallel to the velocity.
4. Swept-up electrons are accelerated by ponderomotive and/or electrostatic forces. Swept-up ions are accelerated by electrostatic force caused by charge separation.