Transcript Recent developments in the Theory of Plerions Yves Gallant

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)
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relativistic, magnetised pulsar wind
confinement by medium (SNR) 
termination shock
plerion  shocked pulsar wind flow
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wind magnetisation B2/(4Nmc2),
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
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
Komissarov & Lyubarsky’s (2003)
RMHD numerical solution + assumed
injected spectrum and synchrotron losses
(asymmetries due to relativistic beaming)
Anisotropic wind: origin of “jet” and torus structures
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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
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confirmed by fully RMHD numerical
simulations: Komissarov & Lyubarsky 2003,
Del Zanna, Amato & Bucciantini 2004,
Bogovalov et al. 2005
 v/c, from Komissarov & Lyubarsky 2003
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“focusing” of the equatorial flow by postrim-shock “funnel” to supersonic velocities,
v  0.5 - 0.7c, consistent with optical wisp
observations (Hester et al. 2002)
spherically symmetric model predicted postshock v  0.3c, decreasing with radius
Plerion evolution inside a supernova remnant
1 - Classical “composite” supernova remnants
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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)
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“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
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2 - Pulsar bow shock nebulae
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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
Particle acceleration at the pulsar wind termination shock
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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
Fermi acceleration at ultra-relativistic shocks
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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
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
Plerion radio spectra and electron pre-acceleration
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X-ray spectrum of the Crab Nebula and other plerions compatible with (synchrotronloss-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
Resonant ion cyclotron wave acceleration?
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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)!
Striped wind reconnection at termination shock?
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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
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