Particle Acceleration and Radiation of Poynting Jets and Collisionless Shocks Edison Liang, Koichi Noguchi Rice University Acknowledgements: Scott Wilks, Bruce Langdon (talk given at Xian AGN 2006) Work supported by LLNL, LANL, NASA, NSF

This talk will focus on particle acceleration and radiation of: 1. Poynting jets = EM-dominated directed outflows 2. Relativistic collisionless shocks

High Energy Astrophysics Ultra-Intense Lasers Relativistic Plasma Physics Particle Acceleration New Technologies

 e /  pe log GRB Galactic Black Holes INTENSE LASERS Phase space of laser plasmas overlaps most of relevant high energy astrophysics regimes High-  Low-  PulsarWind Blazar

(Lyubarsky 2005) Pulsar equatorial striped wind from oblique rotator collisionless shock

Internal shocks: Hydrodynamic Outflow Poynting flux: Electro-magnetic -dominated Outflow Gamma-Ray Bursts: Two Competing Paradigms: “to B(magnetic) or not to B?” e+e- Woosley & MacFadyen, A&A. Suppl. 138, 499 (1999) What is primary energy source? How are the e+e- accelerated? How do they radiate?

Relativistic Plasmas Cover Many Regimes: 1. kT or internal > mc 2 2. Flow speed v bulk ~ c (  >>1) 3. Strong B field: v A /c =    e  p > 1 4. Vector potential a o =eE/mc  o > 1 Most of these regimes are “collisionless” They can be studied mainly via Particle-in-Cell (PIC) simulations

Side Note MHD, and in particular, magnetic flux freezing, often fails in the relativistic regime, despite small gyroradii. This leads to many novel, counter-intuitive kinetic phenomena unique to the relativistic regime. Moreover, nonlinear collective processes behave very differently in the ultra- relativistic regime, due to v=c limit.

x y (into plane) in NN code. x is open in Zohar code. Example of In dynamic problems, we often use zones << initial Debye length to anticipate density compression

What astrophysical scenarios may give rise to Poynting jet driven acceleration? magnetic tower head w/ mostly toroidal field lines collapsar envelope global torus rapid deconfinement rising flux rope from BH accretion disk Popular GRB Scenario local cylinder

By Ez Jz Plasma JxB force snowplows all surface particles upstream: ~ max(B 2 /4  nm e c 2, a o ) “Leading Poynting Accelerator” (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: >> B 2 /4  nm e c 2, a o “Trailing Poynting Accelerator”(TPA). (Liang et al. PRL 90, , 2003) Entering Exiting Particle acceleration by relativistic j x B force x x EM pulse By x y z Ez Jz JxB k

t.  e =800 t.  e =10000 magnify  e /  pe =10 L o =120c/  e TPA reproduces many GRB signatures: profiles, spectra and spectral Evolution (Liang & Nishimura PRL 91, )

Momentum gets more and more anisotropic with time Details of early e+e- expansion

t  e = Fourier peak wavelength scales as ~ c.  m /  pe hard-to-soft GRB spectral evolution diverse and complex BATSE light curves

(movie by Noguchi 2004)

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 mm the maximum  max ~ e  E(t)  z dt /mc where E(t) is the comoving electric field Typical GRB spectrum  =(n+1)/2

 m (t) = (2f  e (t)t + C o ) 1/2 t ≥ L o /c This formula can be derived analytically from first principles f=1.33 C o =27.9  e /  ep =10  e /  ep =10 0

Lorentz equation for particles in an EM pulse with E(t,  ), B(t,  ) and profile velocity  w d(  x )/dt = -  z  e (t)h(  ) d(  z )/dt = -(  w -  x  e (t)h(  ) d(  y )/dt = 0 d  /dt = -  w  z  e (t)h(  ) For comoving particles with  w ~  x we obtain:  z = -   o /  ;  y =   yo /  ;  x = (   o 2 -  yo 2 ) 1/2 /  p o ~ transverse jitter momentum due to E z Hence: d  2 /dt = 2 p o  e (t)h(  )  x As   x ~ 1:d /dt ~ 2 p o  e (t) Integrating we obtain: (t) = 2f  e (t).t +  o 2

The power-law index seems remarkably robust independent of initial plasma size or temperature and only weakly dependent on B f(  )  -3.5 L o =10 5 r ce L o = 10 4 r ce

3D cylindrical geometry with toroidal fields (movies by Noguchi)

3D donut geometry with pure toroidal fields (movies by Noguchi)

PIC simulation allows us to compute the radiation directly from the force terms P rad = 2e 2 (F || 2 +  2 F + 2 ) /3c where F || is force along v and F + is force orthogonal to v TPA does NOT radiate synchrotron radiation. Instead P rad ~  e 2 p z 2 sin 2  << P syn ~  e 2  2 where p z is momentum orthogonal to both B and Poynting vector k, and  is angle between v and k.

Poynting Jet P rad asymptotes to ~ constant level at late times L o =120c/  e L o =10 5 c/  e p o =10 P rad 10*B y P rad

Initially cold ejecta plasma results in much lower radiation p o =0.5

Asymptotic P rad scales as (  e /  pe ) n with n ~  e /  pe =

We have added radiation damping to PIC code using the Dirac-Lorentz Equation (see Noguchi 2004) to calculate radiation output and particle motion self-consistently r e  e /c=10 -3 Averaged Radiated Power by the highest energy electrons

Using ray-tracing Noguchi has computed intensity and polarization histories seen by detector at infinity  e /  pe =10  e /  pe =10 2

TPA e-ion run e ion

In pure e-ion plasmas, TPA transfers EM energy mainly to ion component due to charge separation e+e- e-ion

e-ion Poynting jet gives weaker electron radiation

100% e-ion: ions get most of energy via charge separation 10%e-ion, 90%e+e- : ions do not get accelerated, e+e- gets most energy e ion e+e- ion In mixture of e-ion and e+e- plasmas, Poynting jet selectively accelerates only the e+e- component

PIC simulations of Relativistic Magnetized e+e- Collisionless Shocks

pxpx B y *100 f(  )  Interaction of e+e- Poynting jet with cold ambient e+e- shows broad (>> c/  e, c/  pe ) transition region with 3-phase “Poynting shock” ejecta ambient ejecta spectral evolution ambient spectral evolution 

ejecta e- shocked ambient e- P rad of “shocked” ambient electron is lower than ejecta electron

Propagation of e+e- Poynting jet into cold e-ion plasma: acceleration stalls after “swept-up” mass > few times ejecta mass. Poynting flux decays via mode conversion and particle acceleration ejecta e+ ambient e- ambient ion p x /mc ByBy x B y *100 p i *10 pipi

ejecta e+ ejecta e- ambient ion ambient e-  f(  ) -10p xe -10p xej 100p xi 100E x 100B y P rad Poynting shock in e-ion plasma is very complex with 5 phases and broad transition region(>> c/  i, c/  pe ). Swept-up electrons are accelerated by ponderomotive force. Swept-up ions are accelerated by charge separation electric fields.

ejecta e- shocked ambient e- P rad of shocked ambient electron is comparable to the e+e- case

Examples of collisionless shocks: e+e- running into B=0 e+e- cold plasma ejecta hi-B, hi-  weak-B, moderate  B=0, low  swept-up 100B y ejecta swept-up 100B y 100E x 100B y 100E x -p x swept-up -p xswrpt-up ejecta

SUMMARY 1.Poynting jet (EM-dominated outflow) can be a highly efficient, robust comoving accelerator, leading to ultra-high Lorentz factors. 2.TPA reproduces many of the telltale signatures of GRBs. 3.In 3D, expanding toroidal fields mainly accelerates particles along axis, while expanding poloidal fields mainly accelerates particles radially. 4.Radiation power of TPA is higher than collisionless shocks. But in either case it is much lower than classical synchrotron radiation. This solves the “cooling problem” of synchrotron shocks. 5. Structure and radiation power of collisionless shocks is highly sensitive to EM field strength. 6. In hybrid e+e- and e-ion plasmas, TPA preferentially accelerates The e+e- component and leave the e-ion plasma behind.