Particle acceleration in Pulsar Wind Nebulae

1
Particle acceleration 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 (?Rlt0.5)
• 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
(gtfew 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
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 103lt?lt107
(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 (? ??(Bn)) of the flow, which are
usually unknown.
7
The Pulsar Wind termination shock
RTSRN(VN/c)1/2109-1010 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/cltlt1, a paradox
At rRLC ?104 ?102 (pulsar and pulsar
wind theories)
More refined constraints on ? from 2D modeling
of the nebular emission
?-paradox!
At RTS ?VN/c1(!?!) ??(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
?gt0.01 required for Jet formation (a factor of
10 larger than within 1D MHD models)
?0.01
11
Dependence on field structure
?0.03
b100
b10
B(?)
(Del Zanna et al 04)
12
Synchrotron Emission maps
X-rays
optical
?0.025, b10
(Weisskopf et al 00)
Emax is evolved with the flow f(E)?E-?, EltEmax
(Del Zanna et al 06)
(Hester et al 95)
?0.1, b1
Between 3 and 15 of the wind Energy flows with
?lt0.001
(Pavlov et al 01)
13
Particle Acceleration mechanisms
Composition mostly pairs Magnetization
?gt0.001 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
Pros Cons

• 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 (?lt0.001) 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)
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 kTme?c2 over 10-100
?(1/?ce)
Ions take their time mi/me times longer
Plasma starts gyrating
16
Leading edge of a transverse relativistic shock
in 1D PIC
e.m. fields
Pairs can resonantly absorb the ion radiation at
nmi/me and then progressively lower n Effective
energy transfer if Ui/Utotgt0.5
(Amato Arons 06)
17
Subtleties of the RCA process I
?ci me/mi?ce
Pairs can resonantly absorb ion radiation at
nmi/me and then progressively lower n down to
n1 Emax mi/me?
In order to work the mechanism requires
effective wave growth up to nmi/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/Utotgt0.5
For low mass-ratios Ui/Utotgt0.5 requires large
fraction of p That makes waves crcularly
polarized and preferentially absorbed by e
For mi/me100 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
Spectrum is cut off at nu/?u
growth-rate independent of n if plasma cold
(Amato Arons 06)
19
Particle spectra and acceleration efficiency for
mi/me100
Acceleration efficiency few for Ui/Utot60
30 for Ui/Utot80 Spectral slope gt3 for
Ui/Utot60 lt2 for Ui/Utot80 Maximum
energy 20 mic2? for Ui/Utot60 80 mic2?
for Ui/Utot80
e-
?5 ?2.7
e
?27 ?1.6
Mechanism works at large mi/me for both e and
e-
ni/n-0.2 Ui/Utot0.8
Extrapolation to realistic mi/me predicts same
efficiency
20
Acceleration via RCA and related issues

• 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)

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!
22
(No Transcript)
23
Polarization of the waves
mi/me20, ni/n-0.4
mi/me40, ni/n-0.2
e-
e-
?lt2
?3 ?2.2
e
e
?20 ?1.7
?11 ?1.8
Upstream flow Lorentz factor ?40 Magnetization
??2
Simulation box ?xrLe/10 LxrLix10
First evidence of electron acceleration
Positron tail extends to ?maxmi/me?
Ui/Utot0.7 same in both simulations
24
Effects of thermal spread
?u/u0.1
?u/u0
?5 ?2.7
?3 ?4
?27 ?1.6
?4 ?3.3
ni/n-0.2 mi/me100 Ui/Utot0.8
Initial particle distribution function is a
gaussian of width ?u
Upstream flow Lorentz factor ?40 Magnetization
??2
Simulation box ?xrLe/10 LxrLix10
Acceleration effectively suppressed!!!
25
Particle In Cell Simulations

• The method
• Collect the current at the cell edges
• Solve Maxwells 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

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
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)?
RTSRN(VN/c)1/2109-1010 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)