Recent developments in the theory of Pulsar Wind Nebulae (Plerions) Yves Gallant LPTA, Université Montpellier II (relativistic) magneto-hydrodynamics of plerions –basic paradigm and issues –morphology: anisotropic winds –evolution: confinement by supernova remnant particle acceleration and plerion spectra –Fermi acceleration at relativistic shocks –radio emission and electron pre-acceleration summary

1D (sperically symmetric) relativistic MHD model (Kennel & Coroniti 1984a) relativistic, magnetised pulsar wind confinement by medium (SNR)  termination shock plerion  shocked pulsar wind flow wind magnetisation  B 2 /(4  N  mc 2 ), magnetic to particle energy flow ratio small  needed for flow deceleration post-shock B small, increases with radius until reaches ~equipartition, then slow B decrease outwards

…but plerions don’t look spherically symmetric!  2D (axially symmetric) relativistic MHD simulations Komissarov & Lyubarsky’s (2003) RMHD numerical solution + assumed injected spectrum and synchrotron losses (asymmetries due to relativistic beaming) Chandra image of the Crab Nebula: bright X-ray torus, jets, inner ring… many plerions show X-ray tori (Ng & Romani 2004), often with jets

Anisotropic wind: origin of “jet” and torus structures observed jets a puzzle: collimation inefficient in relativistic wind solution (Bogovalov & Khangoulian 2002, Lyubarsky 2002): “jet” confined in post-shock flow, by magnetic hoop stresses and backflow, as a result of latitude dependence of wind power f w  sin 2  “jet” then subsonic, as observed: v  c confirmed by fully RMHD numerical simulations: Komissarov & Lyubarsky 2003, Del Zanna, Amato & Bucciantini 2004, Bogovalov et al  v/c, from Komissarov & Lyubarsky 2003 “focusing” of the equatorial flow by post- rim-shock “funnel” to supersonic velocities, v  c, consistent with optical wisp observations (Hester et al. 2002) spherically symmetric model predicted post- shock v  0.3c, decreasing with radius

Plerion evolution inside a supernova remnant 2 - Pulsar bow shock nebulae initial ballistic velocity of pulsar eventually becomes supersonic  “bow shock nebula” phases inside SNRs: in Sedov remnants, past fixed fraction of R sh crossing SNR shell (van der Swaluw et al. 2002): strong confinement in interstellar medium: most “evolved” stage of plerion 1 - Classical “composite” supernova remnants van der Swaluw et al. (2001): 1D (hydrodynamical) simulations of plerion evolution inside supernova remnant; scenario confirmed through relativistic MHD simulations by Bucciantini et al. (2003) “free expansion” phase: 4 shocks (wind termination + outer plerion, SNR forward and reverse shock) unsteady “reverberation” phase after SNR reverse shock reaches and “crushes” plerion Blondin et al. (2001) suggest Rayleigh-Taylor instabilities in this phase can mix plerion and ejecta, and asymmetries in medium and reverse shock can shift plerion relative to the pulsar (e.g. Vela X) settles to steady “subsonic” expansion inside Sedov-phase remnant

Particle acceleration at the pulsar wind termination shock Kennel & Coroniti (1984b) found a best fit to the optical and X-ray spectrum of the Crab Nebula requiring injection of particles with p = 2.2–2.3, dN(  ) / d    -p a number of other plerions have X-ray spectra consistent with this value Ellison & Double (2002) showed that for highly relativistic shocks, this value is not significantly affected by non-linear effects these results assumed isotropic direction-angle scattering; Bednarz & Ostrowski 1998 found some dependence on the scattering regime Lemoine & Pelletier (2003), using realistic orbit integration in Kolmogorov turbulence, confirm p = 2.26  0.04 Kirk et al. (2000) and Achterberg et al. (2001), using independent methods, found that in the ultra-relativistic regime Fermi acceleration yields a ‘universal’ spectral index p = 2.23  0.01 Fermi acceleration at ultra-relativistic shocks

Plerion radio spectra and electron pre-acceleration X-ray spectrum of the Crab Nebula and other plerions compatible with (synchrotron- loss-steepened) relativistic Fermi acceleration spectrum (  X  1.1) plerion radio spectra (  R ~0) require a different mechanism Crab radio wisps (Bietenholz et al. 2004) and infrared spectral map (Gallant & Tuffs 2002) suggest radio-emitting electrons are accelerated at present time a possibility (Gallant et al. 2002) is the resonant ion wave acceleration mechanism of Hoshino et al. (2004), working from  w m e c 2 to  w m i c 2 would imply  w ~10 3 for the Crab (vs  10 6 in Kennel & Coroniti 1984b)! Oblique rotator wind has alternating magnetic polarities in equatorial wind (“striped” pattern): Coroniti (1990), Bogovalov (1999) reconnection too slow to annihilate stripes inside Crab termination shock (Lyubarsky & Kirk 2001)? Lyubarsky (2003) examined shock in striped wind, and concluded that stripes reconnect completely at shock, accelerating electrons to required p  1 spectrum Striped wind reconnection at termination shock? Resonant ion cyclotron wave acceleration?

Summary relativistic MHD — plerion morphology and evolution –K & C (1984a) model limited by 1D, steady confinement assumptions –wind anisotropy can explain “torus and jet” morphology of post-shock flow, and higher flow velocities than in 1D case –supernova remnant confinement:  several “classical composite” phases (relative to SNR reverse shock), followed by “bow shock” phases (relative to environment) particle acceleration — plerion spectra –Fermi acceleration can explain many plerion X-ray spectra –radio spectrum requires a distinct pre-acceleration mechanism