1. Particle acceleration in Pulsar Wind Nebulae Elena Amato INAF-Osservatorio Astrofisico di Arcetri Collaborators: Jonathan Arons, Niccolo’ Bucciantini,Luca Del Zanna, Delia Volpi

2. Pulsar Wind Nebulae Plerions: Supernova Remnants with a center filled morphology Flat radio spectrum (  R <0.5) Very broad non-thermal emission spectrum (from radio to X-ray and even  -rays) (~15 objects at TeV energies) Kes 75 ( Chandra ) (Gavriil et al., 2008)

3. THE Pulsar Wind Nebula Primary emission mechanism is synchrotron radiation by relativistic particles in an intense (>few x 100 B ISM ) ordered (high degree of radio polarization) magnetic field Source of both magnetic field and particles: Neutron Star suggested before Pulsar discovery ( Pacini 67 )

4. Basic picture pulsar wind Synchrotron bubble R TS RNRN electromagnetic braking of fast-spinning magnetized NS Magnetized relativistic wind If wind is efficiently confined by surrounding SNR Star rotational energy visible as non-thermal emission of the magnetized relativistic plasma Kes 75 ( Chandra ) (Gavriil et al., 2008) Wind is mainly made of pairs and a toroidal B 10 3 <  <10 7

5. Relativistic shocks in astrophysics Cyg A SS433 Crab Nebula AGNs  ~a few tens MQSs  ~a few PWNe  ~10 3 -10 7 GRBs  ~10 2

6. 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….

7. The Pulsar Wind termination shock In Crab R TS ~0.1 pc: ~boundary of underluminous (cold wind) region ~“wisps” location (variability over months) R TS ~R N (V N /c) 1/2 ~10 9 -10 10 R LC from pressure balance ( e.g. Rees & Gunn 74 ) assuming low magnetization Composition: mainly pairs maybe a fraction of ions Geometry: perpendicular where magnetized even if field not perfectly toroidal Magnetization:  ~V N /c<<1, a paradox At r~R LC :  ~10 4  ~10 2 ( pulsar and pulsar wind theories ) At R TS :  ~V N /c«1(!?!)  (10 4 -10 7 ) ( PWN theory and observations )  -paradox! More refined constraints on  from 2D modeling of the nebular emission

8. The anisotropic pulsar wind Streamlines asymptotically radial beyond R LC Most of energy flux at low latitudes: F  sin 2 (  ) Magnetic field components: B r  1/r 2 B   sin(  )/r Within ideal MHD  stays large Current sheet around the equatorial plane: The best place to lower wind magnetization  2D RMHD simulations of PWNe prompted by Chandra observations of jet in Crab  Jet closer to the pulsar than TS position cannot be explained by magnetic collimation  Easily explained if TS is oblate due to gradient in energy flow ( Lyubarsky 02; Bogovalov & Khangoulian 02 )  This is also what predicted by analytical split monopole solutions for PSR magnetosphere ( Michel 73; Bogovalov 99 ) and numerical studies in Force Free ( Contopoulos et al 99, Gruzinov 04, Spitkovsky 06 ) and RMHD regime ( Bogovalov 01, Komissarov 06, Bucciantini et al 06 ) (Kirk & Lyubarsky 01)

9. Axisymmetric RMHD simulations of PWNe Komissarov & Lyubarsky 03, 04 Del Zanna et al 04, 06 Bogovalov et al 05 A: ultrarelativistic PSR wind B: subsonic equatorial outflow C: supersonic equatorial funnel a: termination shock front b: rim shock c: FMS surface Termination Shock structure F  sin 2 (  )  sin 2 (  ) B   sin(  )G(  )

10.  =0.003  =0.01  =0.03 Constraining  in PWNe (Del Zanna et al 04)  >0.01 required for Jet formation (a factor of 10 larger than within 1D MHD models)

11.  =0.03 Dependence on field structure b=10 b=100 (Del Zanna et al 04) B(  )

12. Synchrotron Emission maps  =0.025, b=10  =0.1, b=1 optical X-rays (Hester et al 95) E max is evolved with the flow f(E)  E - , E<E max ( Del Zanna et al 06 ) Between 3 and 15 % of the wind Energy flows with  <0.001 (Pavlov et al 01) (Weisskopf et al 00)

13. Particle Acceleration mechanisms Requirements: Outcome: power-law with  ~2.2 for optical/X-rays  ~1.5 for radio Maximum energy: for Crab ~few x 10 15 eV (close to the available potential drop at the PSR) Efficiency: for Crab ~10-20% of total L sd Proposed mechanisms:  Fermi mechanism if/where magnetization is low enough  Shock drift acceleration  Acceleration associated with magnetic reconnection taking place at the shock ( Lyubarsky & Liverts 08 )  Resonant cyclotron absorption in ion doped plasma ( Hoshino et al 92, Amato & Arons 06 ) Composition: mostly pairs Magnetization:  >0.001 for most of the flow Geometry : transverse

14. Pros & Cons DSA and SDA oNot effective at superluminal shocks such as the pulsar wind TS unless unrealistically high turbulence level ( Sironi & Spitkovsky 09 ) Power law index adequate for the optical/X-ray spectrum of Crab ( Kirk et al 00 ) but e.g. Vela shows flatter spectrum ( Kargaltsev & Pavlov 09 ) In Weibel mediated e+-e - (unmagnetized) shocks Fermi acceleration operates effectively ( Spitkovsky 08 ) oSmall fraction of the flow satisfies the low magnetization (  <0.001) condition (see MHD simulations) Magnetic reconnection Spectrum: -3 or -1? ( e.g. Zenitani & Hoshino 07 ) Efficiency? Associated with X-points involving small part of the flow… Investigations in this context are in progress (e.g. Lyubarsky & Liverts 08 ) Resonant absorption of ion cyclotron waves Established to effectively accelerate both e + and e - if the pulsar wind is sufficiently cold and ions carry most of its energy (Hoshino & Arons 91, Hoshino et al. 92, Amato & Arons 06)

15. Drifting e + -e - -p plasma Plasma starts gyrating B increases Configuration at the leading edge ~ cold ring in momentum space Coherent gyration leads to collective emission of cyclotron waves Pairs thermalize to kT~m e  c 2 over 10-100  (1/  ce ) Ions take their time: m i /m e times longer Resonant cyclotron absorption in ion doped plasma Magnetic reflection mediates the transition

16. Leading edge of a transverse relativistic shock in 1D PIC Drifting species Thermal pairs Cold gyrating ions Pairs can resonantly absorb the ion radiation at n=m i /m e and then progressively lower n Effective energy transfer if U i /U tot >0.5 e.m. fields (Amato & Arons 06)

17. Subtleties of the RCA process I Pairs can resonantly absorb ion radiation at n=m i /m e and then progressively lower n down to n=1: E max = m i /m e  In order to work the mechanism requires effective wave growth up to n=m i /m e 1D PIC sim. with m i /m e up to 20 (Hoshino & Arons 91, Hoshino et al. 92) Showed e + effectively accelerated if U i /U tot >0.5 Growth-rate independent of n (Hoshino & Arons 91) For low mass-ratios U i /U tot >0.5 requires large fraction of p That makes waves crcularly polarized and preferentially absorbed by e + For m i /m e =100: polarization of waves closer to linear Comparable acceleration of both e + and e -  ci = m e /m i  ce

18. frequency Growth-rate Spectrum is cut off at n~u/  u growth-rate ~ independent of n if plasma cold (Amato & Arons 06) Subtleties of the RCA process II If thermal spread of the ion distribution is included Acceleration can be suppressed

19. Acceleration efficiency: ~few% for U i /U tot ~60% ~30% for U i /U tot ~80% Spectral slope: >3 for U i /U tot ~60% <2 for U i /U tot ~80% Maximum energy: ~20% m i c 2  for U i /U tot ~60% ~80% m i c 2  for U i /U tot ~80% Particle spectra and acceleration efficiency for m i /m e =100  =5%  =2.7  =27%  =1.6 e-e- e+e+ Mechanism works at large m i /m e for both e + and e - n i /n - =0.2 U i /U tot =0.8 Extrapolation to realistic m i /m e predicts same efficiency

20. Acceleration via RCA and related issues Nicely fits with correlation ( Kargaltsev & Pavlov 08; Li et al 08 ) between X-ray emission of PSRs and PWNe : everything depends on U i /U tot and ultimately on electrodynamics of underlying compact object If  ~ few x 10 6 Maximum energy ~ what required by observations Required (dN i /dt)~10 34 s -1 ~(dN i /dt) GJ for Crab: return current for the pulsar circuit Natural explanation for Crab wisps ( Gallant & Arons 94 ) and their variability ( Spitkovsky & Arons 04 ) (although maybe also different explanations within ideal MHD) ( e.g. Begelman 99; Komissarov et al 09 ) Puzzle with  Radio electrons dominant by number require (dN/dt)~10 40 s -1 and  ~10 4 Preliminary studies based on 1-zone models (Bucciantini et al. in prep.) contrast with idea that they are primordial!

21. Summary and Conclusions  What particle acceleration mechanisms might operate at relativistic shocks depend on the properties of the flow  In the case of PWNe we can learn about these by modeling the nebular radiation  When this is done there are not many possibilities left: Fermi mechanism in the unmagnetized equatorial region, but very little energy flows within it Magnetic reconnection at the termination shock, poorly known RCA in e + -e - -p plasma, rather well understood  RCA of ion cyclotron waves works effectively as an acceleration mechanism for pairs provided the upstream plasma is cold enough  In order to account for particle acceleration in Crab a wind Lorentz factor  ~10 6 is required: then a number of features are explained in addition but radio particles must have different origin  A possibility to be considered is that different acceleration mechanisms operate at different latitudes along the shock surface Thank you!

23. Polarization of the waves m i /m e =20, n i /n - =0.4m i /m e =40, n i /n - =0.2 U i /U tot =0.7 same in both simulations e-e-  =20%  =1.7  <2% e+e+ e-e- e+e+  =3%  =2.2  =11%  =1.8 Positron tail extends to  max =m i /m e  First evidence of electron acceleration Upstream flow: Lorentz factor:  =40 Magnetization:   =2 Simulation box:  x=r Le /10 Lx=r Li x10

24. Effects of thermal spread  u/u=0.1  =5%  =2.7  =4%  =3.3  =27%  =1.6  =3%  =4  u/u=0 Initial particle distribution function is a gaussian of width  u Acceleration effectively suppressed!!! Upstream flow: Lorentz factor:  =40 Magnetization:   =2 Simulation box:  x=r Le /10 Lx=r Li x10 n i /n - =0.2 m i /m e =100 U i /U tot =0.8

25. Particle In Cell Simulations The method: Collect the current at the cell edges Solve Maxwell’s eqs. for fields on the mesh Compute fields at particle positions Advance particles under e.m. force Approximations In principle only cloud in cell algorithm Mistaken transients e - -e + plasma flow:  in 1D: No shock if  =0 No accel. for any   in 3D Shock for any  Fermi accel. for  =0 An example of the effects of reduced m i /m e in the following Reduced spatial and time extent reduced dimensionality of the problem But Computational limitations force: Powerful investigation tool for collisionless plasma physics: allowing to resolve the kinetic structure of the flow on all scales Far-from-realistic values of the parameters For some aspects of problems involving species with different masses 1D WAS still the only way to go

26. The Pulsar Wind termination shock Wind mainly made of pairs ( e.g. Hibschman & Arons 01 :  ~10 3 -10 4 for Crab) and a toroidal magnetic field: ions?  =?  =B 2 /(4  nmc 2  2 )=? In Crab R TS ~0.1 pc: ~boundary of underluminous (cold wind) region ~“wisps” location (variability over months) R TS ~R N (V N /c) 1/2 ~10 9 -10 10 R LC from pressure balance ( e.g. Rees & Gunn 74 ) assuming low magnetization pulsar wind Synchrotron bubble R TS RNRN Most likely particle acceleration site