Recent developments in the theory of

Pulsar Wind Nebulae (Plerions)

Yves GallantLPTA, 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 B2/(4Nmc2), 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 fw sin2

• “jet” then subsonic, as observed: v 0.3 - 0.7c

• confirmed by fully RMHD numerical simulations: Komissarov & Lyubarsky 2003, Del Zanna, Amato & Bucciantini 2004, Bogovalov et al. 2005

v/c, from Komissarov & Lyubarsky 2003

• “focusing” of the equatorial flow by post-rim-shock “funnel” to supersonic velocities, v 0.5 - 0.7c, 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 Rsh

• 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 (X1.1)

• 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 wmec2 to wmic2

• would imply w~103 for the Crab (vs 106 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