Particle acceleration in Pulsar Wind Nebulae Elena Amato

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

Pulsar Wind Nebulae Plerions: üSupernova Remnants with a center filled morphology üFlat radio spectrum ( R<0. 5) üVery broad non-thermal emission spectrum (from radio to X-ray and even -rays) (~15 objects at Te. V energies) Kes 75 (Chandra) (Gavriil et al. , 2008)

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)

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

Relativistic shocks in astrophysics AGNs ~a few tens MQSs ~a few Cyg A SS 433 PWNe ~103 -107 GRBs ~102 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….

The Pulsar Wind termination shock R ~R (V /c) ~10 -10 RLC from pressure balance (e. g. Rees & Gunn 74) assuming low magnetization TS N N 1/2 9 10 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) -paradox! At RTS: ~VN/c « 1(!? !) (104 -107) (PWN theory and observations) More refined constraints on from 2 D modeling of the nebular emission

The anisotropic pulsar wind § 2 D 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) Streamlines asymptotically radial beyond RLC Most of energy flux at low latitudes: F sin 2( ) Magnetic field components: Br 1/r 2 B sin( )/r Within ideal MHD stays large Current sheet around the equatorial plane: The best place to lower wind magnetization

Termination Shock structure Axisymmetric RMHD simulations of PWNe Komissarov & Lyubarsky 03, 04 Del Zanna et al 04, 06 Bogovalov et al 05 F sin 2( ) 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

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 1 D MHD models) =0. 01

Dependence on field structure =0. 03 b=100 b=10 B( ) (Del Zanna et al 04)

Synchrotron Emission maps optical X-rays =0. 025, b=10 (Weisskopf et al 00) (Hester et al 95) Emax is evolved with the flow f(E) E- , E<Emax (Del Zanna et al 06) =0. 1, b=1 Between 3 and 15 % of the wind Energy flows with <0. 001 (Pavlov et al 01)

Particle Acceleration mechanisms Composition: mostly pairs Magnetization: >0. 001 for most of the flow Geometry: transverse Requirements: üOutcome: power-law with ~2. 2 for optical/X-rays ~1. 5 for radio üMaximum energy: for Crab ~few x 1015 e. V (close to the available potential drop at the PSR) üEfficiency: 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)

Pros & Cons DSA and SDA o. Not effective at superluminal shocks such as the pulsar wind TS unless unrealistically high turbulence level (Sironi & Spitkovsky 09) üPower 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) üIn Weibel mediated e+-e- (unmagnetized) shocks Fermi acceleration operates effectively (Spitkovsky 08) o. Small 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)

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

Leading edge of a transverse relativistic shock in 1 D PIC Drifting species Thermal pairs e. m. fields Cold gyrating ions (Amato & Arons 06) Pairs can resonantly absorb the ion radiation at n=mi/me and then progressively lower n Effective energy transfer if Ui/Utot>0. 5

Subtleties of the RCA process I ci= me/mi ce Pairs can resonantly absorb ion radiation at n=mi/me and then progressively lower n down to n=1: Emax= mi/me Growth-rate independent of n (Hoshino & Arons 91) In order to work the mechanism requires effective wave growth up to n=mi/me 1 D 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-ratios Ui/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-

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

Particle spectra and acceleration efficiency for mi/me=100 e =5% =2. 7 e+ =27% =1. 6 ni/n-=0. 2 Ui/Utot=0. 8 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% mic 2 for Ui/Utot~60% ~80% mic 2 for Ui/Utot~80% Mechanism works at large mi/me for both e+ and e. Extrapolation to realistic mi/me predicts same efficiency

Acceleration via RCA and related issues üNicely 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 üMaximum energy ~ what required by observations üRequired (d. Ni/dt)~1034 s-1~(d. Ni/dt)GJ for Crab: return current for the pulsar circuit üNatural 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 (d. N/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!

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: üFermi mechanism in the unmagnetized equatorial region, but very little energy flows within it üMagnetic reconnection at the termination shock, poorly known üRCA 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!

Polarization of the waves mi/me=20, ni/n-=0. 4 mi/me=40, ni/n-=0. 2 e- <2% e =3% =2. 2 e+ =20% =1. 7 Upstream flow: Lorentz factor: =40 Magnetization: =2 e+ =11% =1. 8 Simulation box: x=r. Le/10 Lx=r. Lix 10 Positron tail extends to max=mi/me Ui/Utot=0. 7 same in both simulations First evidence of electron acceleration

Effects of thermal spread u/u=0 =5% =2. 7 =27% =1. 6 ni/n-=0. 2 mi/me=100 Ui/Utot=0. 8 Upstream flow: Lorentz factor: =40 Magnetization: =2 Simulation box: x=r. Le/10 Lx=r. Lix 10 u/u=0. 1 =3% =4 =4% =3. 3 Initial particle distribution function is a gaussian of width u Acceleration effectively suppressed!!!

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

RN 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? =B 2/(4 nmc 2 2)=? pulsar wind R TS Synchrotron bubble 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) Most likely particle acceleration site