Particle acceleration in Pulsar Wind Nebulae

1. Particleacceleration 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 BISM) ordered(high degree of radio polarization) magnetic field Source of both magnetic field and particles: Neutron Star suggested before Pulsar discovery (Pacini 67)

4. RN electromagnetic braking of fast-spinning magnetized NS Magnetized relativistic wind pulsar wind RTS Synchrotron bubble Basic picture Star rotational energy visible as non-thermal emission of the magnetized relativistic plasma If wind is efficiently confined by surrounding SNR Kes 75 (Chandra) Wind is mainly made of pairs and a toroidal B 103<<107 (Gavriil et al., 2008)

5. Relativistic shocks in astrophysics AGNs~a few tens MQSs~a few Cyg A SS433 PWNe~103-107 GRBs~102 Crab Nebula

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 (=B2/4nmc2) and geometry( (B·n)) of the flow, which are usually unknown….

7. The Pulsar Wind termination shock RTS~RN(VN/c)1/2~109-1010 RLC from pressure balance (e.g. Rees & Gunn 74) assuming low magnetization In Crab RTS ~0.1 pc: ~boundary of underluminous (cold wind) region ~“wisps” location (variability over months) Composition:mainly pairs maybe a fraction of ions Geometry:perpendicular where magnetized even if field not perfectly toroidal Magnetization: ~VN/c<<1, a paradox At r~RLC: ~104~102 (pulsar and pulsar wind theories) More refined constraints on  from 2D modeling of the nebular emission -paradox! At RTS: ~VN/c«1(!?!)(104-107) (PWN theory and observations)

8. The anisotropic pulsar wind • 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) Streamlines asymptotically radial beyond RLC Most of energy flux at low latitudes: Fsin2() Magnetic field components: Br1/r2 Bsin()/r Within ideal MHD  stays large Current sheet around the equatorial plane: The best place to lower wind magnetization (Kirk & Lyubarsky 01)

9. Termination Shock structure Axisymmetric RMHD simulations of PWNe Komissarov & Lyubarsky 03, 04 Del Zanna et al 04, 06 Bogovalov et al 05 Fsin2() sin2() Bsin()G() A: ultrarelativistic PSR wind B: subsonic equatorial outflow C: supersonic equatorial funnel a: termination shock front b: rim shock c: FMS surface

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

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

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

13. ParticleAcceleration mechanisms Composition: mostly pairs Magnetization:>0.001 for most of the flow Geometry: transverse • Requirements: • Outcome: power-law with ~2.2 for optical/X-rays ~1.5 for radio • Maximum energy: for Crab ~few x 1015 eV (close to the available potential drop at the PSR) • Efficiency: for Crab ~10-20% of total Lsd • 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)

14. DSA and SDA • Not 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) • Small fraction of the flow satisfies the low magnetization (<0.001) condition (see MHD simulations) Pros & Cons • 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. Resonant cyclotron absorption in ion doped plasma Configuration at the leading edge ~ cold ring in momentum space Magnetic reflection mediates the transition Coherent gyration leads to collective emission of cyclotron waves Drifting e+-e--p plasma B increases Pairs thermalize to kT~mec2 over 10-100 (1/ce) Ions take their time: mi/me times longer Plasma starts gyrating

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

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

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

19. Particle spectra and acceleration efficiency for mi/me=100 Acceleration efficiency: ~few% for Ui/Utot~60% ~30% for Ui/Utot~80% Spectral slope: >3 for Ui/Utot~60% <2 for Ui/Utot~80% Maximum energy: ~20% mic2 for Ui/Utot~60% ~80% mic2 for Ui/Utot~80% e- =5% =2.7 e+ =27% =1.6 Mechanism works at large mi/me for both e+ and e- ni/n-=0.2 Ui/Utot=0.8 Extrapolationto realistic mi/me predicts same efficiency

20. Nicely fits with correlation (Kargaltsev & Pavlov 08; Li et al 08) between X-ray emission of PSRs and PWNe : everything depends on Ui/Utot and ultimately on electrodynamics of underlying compact object • If ~ few x 106 • Maximum energy ~ what required by observations • Required (dNi/dt)~1034 s-1~(dNi/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) Acceleration via RCA and related issues Puzzle with  Radio electrons dominant by number require (dN/dt)~1040 s-1 and ~104 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 ~106 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 mi/me=20, ni/n-=0.4 mi/me=40, ni/n-=0.2 e- e- <2% =3% =2.2 e+ e+ =20% =1.7 =11% =1.8 Upstream flow: Lorentz factor: =40 Magnetization: =2 Simulation box: x=rLe/10 Lx=rLix10 First evidence of electron acceleration Positron tail extends to max=mi/me Ui/Utot=0.7same in both simulations

24. Effects of thermal spread u/u=0 u/u=0.1 =5% =2.7 =3% =4 =27% =1.6 =4% =3.3 ni/n-=0.2 mi/me=100 Ui/Utot=0.8 Initial particle distribution function is a gaussian of width u Upstream flow: Lorentz factor: =40 Magnetization: =2 Simulation box: x=rLe/10 Lx=rLix10 Acceleration effectively suppressed!!!

25. 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 Particle In Cell Simulations Powerful investigation tool for collisionless plasma physics: allowing to resolve the kinetic structure of the flow on all scales But Computational limitations force: reduced dimensionality of the problem Reduced spatial and time extent Far-from-realistic values of the parameters e--e+ plasma flow: • in 1D: • No shock if =0 • No accel. for any  • in 3D • Shock for any  • Fermi accel. for =0 Mistaken transients An example of the effects of reduced mi/mein the following For some aspects of problems involving species with different masses 1D WAS still the only way to go

26. RN pulsar wind RTS Synchrotron bubble The Pulsar Wind termination shock Wind mainly made of pairs (e.g.Hibschman & Arons 01: ~103-104 for Crab) and a toroidal magnetic field: ions? =?=B2/(4nmc22)=? RTS~RN(VN/c)1/2~109-1010 RLC from pressure balance (e.g. Rees & Gunn 74) assuming low magnetization Most likely particle acceleration site In Crab RTS ~0.1 pc: ~boundary of underluminous (cold wind) region ~“wisps” location (variability over months)