Particle Acceleration and Radiation from Poynting Jets and Collisionless Shocks Edison Liang, Koichi Noguchi Rice University Acknowledgements: Scott Wilks, Bruce Langdon Talk given at Xian AGN Meeting 2006

Internal shocks Hydrodynamic Outflow Poynting flux Electro-magnetic -dominated outflow Two Distinct Paradigms for the Energetics of Relativistic Jets e+e- ions e+e- What is primary energy source? How are the e+e- accelerated? How do they radiate? shock  -rays SSC, IC …  -rays B

What astrophysical scenarios may give rise to Poynting-flux driven acceleration? magnetic tower head w/ mostly toroidal field lines internal  via toroidal EM expansion rising flux rope from BH accretion disk small section modeled as cylinder Reconnection leads to free expansion of EM-dominated torus Bulk  from hoop stress

t.  e =800 t.  e =10000  e /  pe =10 L o =120c/  e Poynting flux Is an efficient accelerator (Liang & Nishimura PRL 91, )

By Ez Jz Plasma JxB force snowplows all surface particles upstream: ~ max(B 2 /4  nm e c 2, a o ) “ Leading Ponderomotive 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 Ponderomotive 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

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

Radiation detected at infinity is strongly linearly polarized  e /  pe =10  e /  pe =10 2

3D magnetic e+e- donut with pure toroidal fields (movies by Noguchi)

PIC simulation can compute the radiation power 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 Poynting jet does NOT radiate synchrotron radiation. Instead P rad ~  e 2  2 sin 4  << P syn ~  e 2  2 where  is angle between v and Poynting vector k. Also  cr ~  e  2 sin 2  crsyn

(movie by Noguchi 2004)

Poynting Jet P rad asymptotes to ~ constant level at late times as increase in  is compensated by decrease in  and B L o =120c/  e L o =10 5 c/  e p o =10 P rad 10*B y P rad

Inverse Compton scattering against ambient photons can slow or stop acceleration (Sugiyama et al 2005) n  =10 -4 n e n  =10 -2 n e n  =n e 1 eV photon field  e  pe =100

B

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 directed outflow) is a highly efficient, robust accelerator, leading to ultra-high energy particles. 2. In mixed e+e- and e-ion plasmas, Poynting flux preferentially captures and accelerates e+e- component and leave e-ion behind. 3. In 3D, expanding toroidal fields mainly accelerates particles along axis. 4.Intrinsic radiation power of both Poynting jet and collisionless shocks are much lower than classical synchrotron radiation. This may favor IC over SSC in some cases. 4. Structure and radiation power of collisionless shocks are highly dependent on ejecta B field strength and Lorentz factor.

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

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

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

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

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

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

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

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

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 relativistic plasmas are “ collisionless ” They need to be modeled correctly via Particle-in-Cell (PIC) simulations

Side Note MHD, and in particular, magnetic flux freezing, often fails in the relativistic regime, despite small gyroradii. Moreover, nonlinear collective processes behave very differently in the ultra- relativistic regime, due to the v=c limit.

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

Poynting jet P rad increases with initial temperature roughly as (kT o ) 2 p o =0.5

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