PIC Simulations of relativistic transverse magnetosonic shocks Elena Amato INAF-Osservatorio Astrofisico di Arcetri In collaboration with Jonathan Arons (Berkeley)
Outline Astrophysical relevance of the subject � PIC simulations of relativistic transverse � magnetosonic shocks in e - -e + -p plasmas Resonant cyclotron absorption • Questions left open by previous work on the subject • What can still be learned from 1D PIC • Simulations with increased mass-ratio � between ions and pairs (up to 100): now outdated Acceleration mechanism still effective • Electron acceleration seen for the first time • Effects of finite temperature of the plasma • Summary and Conclusions �
Relativistic shocks in astrophysics AGNs � ~a few tens MQSs � ~a few Cyg A SS433 PWNe � ~10 4 -10 6 GRBs � ~10 2 Crab Nebula
Properties of the flow and particle acceleration � These shocks are collisionless : transition between non-radiative (upstream) and radiative (downstream) takes place on scales too small for collisions to play a role � They are generally associated with non-thermal particle acceleration but with a variety of spectra and acceleration efficiencies Self-generated electromagnetic turbulence mediates the shock transition: it must provide both the dissipation and particle acceleration mechanism The detailed physics and the outcome of the process strongly depend on composition (e - -e + -p?) magnetization ( � =B 2 /4 � n � mc 2 ) and geometry ( � �� ( B·n )) of the flow, which are usually unknown….
Relativistic transverse magnetosonic shocks � ( B·n )>>1/ � Geometry Common for Magnetized Relativistic shocks Magnetized relativistic shocks in PWNe accelerate particles very efficiently!!! 3D PIC of magnetized pair Look at the Crab Nebula: shocks hint at low efficiency � Efficiency >20% of total L sd (Spitkovsky 08) � Maximum energy: for Crab ~few x 10 15 eV (close to total available � V at the PSR) Or maybe Magnetic � unmagnetized shock: efficient Fermi I reconnection ? ions? (Spitkovsky 08) � acceleration associated to reconnection (Lyubarsky & Petri 07) Resonant cyclotron absorption
Synchrotron Emission maps from 2D MHD simulations of PWNe optical X-rays � =0.025, b=10 (Del Zanna et al. 06) (Hester et al 95)
Particle In Cell Simulations The method: Powerful investigation � Collect the current at the cell edges tool for collisionless � Solve Maxwell’s eqs. for fields on the mesh plasma physics: � Compute fields at particle positions allowing to resolve the � Advance particles under e.m. force kinetic structure Approximations of the flow on all In principle only cloud in cell algorithm scales But Computational reduced dimensionality limitations force: of the problem Reduced spatial and time extent Far-from-realistic values of the parameters e - -e + plasma flow: � in 1D: Mistaken •No shock if � =0 transients An example of the effects of •No accel. for any � reduced m i /m e in the following � in 3D •Shock for any � For some aspects of problems involving species with •Fermi accel. for � =0 different masses 1D WAS still the only way to go
Leading edge of the shock Configuration at the leading edge ~ cold ring in momentum space B z1 B z2 u x 1 Magnetic reflection mediates Coherent gyration leads to the transition collective emission of cyclotron waves Drifting e + -e - -p B increases plasma Pairs thermalize to kT~m e � c 2 over 10-100 � (1/ � ce ) Ions take their time: m i /m e times longer Pairs can absorb ion Plasma starts gyrating radiation resonantly
1D PIC Simulations of shocks in e - -e + -p plasmas Drifting species Thermal pairs From 1D PIC with m i /m e =100 (Amato & Arons 06) Using XOOPIC (Verboncouer et al. 95) e.m. fields Cold gyrating ions 1D PIC sim. with m i /m e up to 20 (Hoshino & Arons 91, Hoshino et al. 92) • Particles enter simulation box from left e + effectively accelerated • Impact on a wall on the right if U i /U tot >0.5 • Wait until shock far from right boundary
Resonant cyclotron absorption in ion-doped plasma � ci = m e /m i � ce Pairs initially need frequency n~m i /m e for resonant absorption!!! Then lower n Growth-rate Growth-rate~independent of n ( Hoshino & Arons 91 ) m i /m e much lower than reality implies ni/n - correspondingly larger to guarantee sufficiently large U i /U tot Elliptical polarization of ion waves Spectrum is cut growth-rate ~ independent of n Preferential off at n~u/ � u if plasma cold (Amato & Arons 06) absorption by e +
Polarization of the waves m i /m e =20, n i /n - =0.4 m i /m e =40, n i /n - =0.2 e - e - � <2% � =3% � =2.2 e + e + � =20% � =1.7 � =11% � =1.8 Upstream flow: Simulation box: First evidence Positron tail Lorentz factor: � =40 � x=r Le /10 of electron extends to Magnetization: � ± =2 Lx=r Li x10 acceleration � max =m i /m e � U i /U tot =0.7 same in both simulations
Particle spectra and acceleration efficiency for m i /m e =100 e - Acceleration efficiency: ~few% for U i /U tot ~60% � =5% � =2.7 ~30% for U i /U tot ~80% Spectral slope: >3 for U i /U tot ~60% e + <2 for U i /U tot ~80% � =27% � =1.6 Maximum energy: ~20% m i c 2 � for U i /U tot ~60% ~80% m i c 2 � for U i /U tot ~80% Mechanism still works at large m i /m e for both e + and e - Upstream flow: Simulation box: Lorentz factor: � =40 � x=r Le /10 n i /n - =0.2 Magnetization: � ± =2 Lx=r Li x10 U i /U tot =0.8
Effects of thermal spread � u/u=0 � u/u=0.1 � =5% � =2.7 � =3% � =4 � =27% � =1.6 � =4% � =3.3 n i /n - =0.2 m i /m e =100 Initial particle distribution U i /U tot =0.8 function is a gaussian of width � u Upstream flow: Simulation box: Lorentz factor: � =40 � x=r Le /10 Acceleration effectively suppressed!!! Magnetization: � ± =2 Lx=r Li x10
Summary and Conclusions We have explored the physics of relativistic transverse magnetosonic shocks in ion-doped plasmas through 1D PIC simulations: still about the only possibility to explore the behaviour of the system for large m i /m e Aims : � Checking whether RCA would still provide any particle acceleration � Checking whether any electron acceleration for larger mass-ratios (upstream plasma closer to quasi-neutrality) Results: � Pairs are efficiently accelerated even for m i /m e =100 if U i /U tot >0.5 � Electron acceleration finally seen!!! � Less efficient than for positrons due to elliptical polarization of the waves (forced by low m i /m e which implies large n i /n e to ensure U i /U tot >0.5) � Extrapolation to realistic m i /m e predicts same efficiency for accelerating e + and e - � Efficiencies and spectra as observed in PWNe can be obtained depending on ion fraction � The acceleration is effectively suppressed if initial thermal spread larger than m e /m i
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