Radiation from Poynting Jets and Collisionless Shocks

Edison Liang, Koichi NoguchiShinya Sugiyama, Rice University

Acknowledgements: Scott Wilks, Bruce LangdonBruce Remington

Talk given at Glast Symposium 2007(see http://spacibm.rice.edu/~liang/picsim

and spacibm.rice.edu/~knoguchi)

Internal shocksHydrodynamic Outflow

Poynting fluxElectro-magnetic-dominated outflow

Popular Paradigms for the radiation of relativistic outflows in GRBs & Blazars

e+e-ions

e+e-

What is energy source? How are the e+e/ion accelerated?How do they radiate?

shock-raysSSC, EC… -rays

B

>>1PIC sims can address

difficultmicrophysics

Highlight We have developed a Particle-In-Cell code that

simultaneously computes total radiation output from each superparticle.

We find that in-situ radiation output of highest energy electrons accelerated by Poynting Flux (and some Collisionless Shocks) are much below that predicted by the classical synchrotron formula.

This may solve the problem of too rapid synchrotron cooling in many internal shock models of GRBs.

Question: How do particles radiate while they are

being accelerated to high energies?

We compute the power radiated simultaneously from the force terms

used in the particle movers of the PIC code:

Prad = 2e2(F|| 2+ 2F+2) /3m3c

where F|| is force along vand F+ is force orthogonal to v

(we have carefully calibrated our procedureagainst analytic results)

p

By

Ez

k

In Poynting flux acceleration, most energeticparticles ~ comoving with local EM field

Prad ~ e22sin4< Psyn ~e

22

where is angle between v and Poynting vector k.

critical frequencycr ~ e2sin2crsyn~ e2

<< 1 in the limit Ez ~ By

and ~ wave

By

Ez

Jz

Plasma

JxB force pushes 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

Relativistic Poynting Flux Accelerationvia 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 accelerated by LPA radiate at a level ~ 10- 4

of classical synchrotron formula, due to sin ~ pz/px ≤ 0.1

2e2~105

50

px

Prad

By

Evolution of e+e- plasma accelerated by Poynting flux (LPA) shows decline of radiative power output Prad

despite increase of

By

Ez

Jz

Plasma

JxB force pushes 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

Relativistic Poynting Flux Accelerationvia induced j x B(ponderomotive) force

x

x

EM pulse

By

x

y

z

Ez

Jz JxB

k

t.e=800 t.e=10000

magnify

e/pe =10

TPAOccurs

whenever EM-

dominated plasma is rapidly

unconfined(Liang &

NishimuraPRL 91,175005 2004)

te=1000

5000

10000

18000

Fourier peak wavelength scales as ~ c.m/ pe

logdN/dE

logE

Epk~200 keV

~0--1.5

β~-2--2.5

time

Epk

dN/dthard-to-soft GRB spectralevolution

diverseandcomplexBATSElightcurves

TPA produces Power-Law spectra with low-energy cut-off.Peak Lorentz factor m corresponds roughly to the

profile/group velocity of the EM pulse

logdN/dE

logE

Epk~200 keV

~0--1.5

β~-2--2.5

time

Epk

dN/dt

m

the maximum max ~ e E(t)βzdt /mc where E(t) is the comoving electric field

Typical GRB spectrum

β=(n+1)/2

m(t) = (2fe(t)t + Co)1/2 t ≥ Lo/cBulk Lorentz factor grows as ~square-root of time

f=1.33 Co=27.9

e/ep=10e/ep=100

The power-law index (p ~ 3 - 4) is remarkably robust independent of initial plasma size or temperature

and only weakly dependent on B

f()

-3.5

Lo=105rce

Lo= 104rce

PhotonIndex

n=(p+1)/2~ 2 -2.5

x

300px

By*100

Prad

2e2~3x106

Prad from TPA << Psyn

QuickTime™ and aGraphics decompressor

are needed to see this picture.

Prad

Panalytic ~e22sin4

In TPA, we also find Prad ~ Panalytic

for the highest energy particles

In TPA jets, Prad asymptotes to ~ constant level at late timesas increase in is compensated by decrease in and B

Lo=120c/eLo=105c/e

po=10

PradPrad

x x

Inverse Compton scattering against ambient photons can slow or stop PF acceleration (Sugiyama et al 2005)

n=10-4ne n=10-2ne n=ne

1 eV photon field epe=100

We have studied radiation from Collisionless Shocks

3 Examples:

1. e+e-/e+e- Magnetic Shock (B2 ~ bulk KE)

2. e+e- /e-ion Magnetic Shock (B2 ~ bulk KE)

3. e+e- Nonmagnetic Shocks (B2 << bulk KE)

QuickTime™ and a decompressor

are needed to see this picture.

B

Poynting jet running into cool e-ion ambient plasma

(movie by Noguchi)

ejecta e+

ejecta e-ambient ion

ambient e-

f()-10pxe-10pxej

100pxi

100Ex

100By

Magnetized collisionless shock produced by collision of e+e- Poynting Jet with cold e-ion plasma .

radiative shock layer

x

swept-up e-

The radiative shock layer bifurcates and gets thicker with time due to ion drag, but max Prad stays ~ constant

x

Prad

SUMMARY

1. Radiation power of Poynting Flux acceleration are orders of magnitude below classical synchrotron formula due to Force ~ parallel to velocity. This feature may be generic and also apply to

some Collisionless Shocks.

2. Structure and radiation power of collisionless shocks are highly sensitive to magnetization and ion loading. Shocked radiative layeris much thicker and bifurcates in e-ion shocks..

3. Inverse Compton of external photons may dominate synchrotron and SSC.

4. Critical frequency of PF acceleration radiation is much lower than the classical synchrotron critical frequency.

Momentum gets more and moreAnisotropic with time: pz/px<<1

Details of TPA expansion

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

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

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

Nonmagnetice+e-/e+e-

shock:Radiation notDominatedBy 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