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:
Supernova Remnants with a center filled
morphology
Flat radio spectrum (R<0.5)
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)
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
SS433
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 (=B2/4nmc2)
and geometry ( (B·n))
of the flow, which are usually unknown….
The Pulsar Wind termination
shock R ~R (V /c) ~10 -10 R
TS
N
N
1/2
9
10
LC
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/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 2D modeling
of the nebular emission
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)
(Kirk & Lyubarsky 01)
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
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
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 1D MHD
models)
=0.01
Dependence on field structure
=0.03
b=100
b=10
B()
(Del Zanna et al 04)
Synchrotron Emission maps
X-rays
optical
=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:
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)
Pros & Cons
DSA and SDA
oNot 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)
oSmall 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
kT~mec2 over
10-100 (1/ce)
Plasma starts
gyrating
Ions take their time:
mi/me times longer
Leading edge of a transverse
relativistic shock in 1D 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
1D 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% mic2 for Ui/Utot~60%
~80% mic2 for Ui/Utot~80%
Mechanism works at
large mi/me
for both e+ and eExtrapolation to realistic mi/me predicts same efficiency
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!
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!
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
e
+
=20% =1.7
Upstream flow:
Lorentz factor: =40
Magnetization: =2
Simulation box:
x=rLe/10
Lx=rLix10
Ui/Utot=0.7 same in both simulations
+
=11% =1.8
Positron tail
extends to
max=mi/me
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=rLe/10
Lx=rLix10
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:
Collect the current at the cell edges
Solve Maxwell’s 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
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 1D 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 1D:
•No shock if =0
•No accel. for any 
in 3D
•Shock for any 
•Fermi accel. for =0
The Pulsar Wind termination
R
shock
N
Wind mainly made of pairs
(e.g. Hibschman & Arons 01: ~103-104 for Crab)
and a toroidal magnetic field:
ions? =? =B2/(4nmc2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