particle acceleration in pulsar wind nebulae elena amato inaf-osservatorio astrofisico di arcetri...
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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 NebulaePlerions:
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
pulsar wind
Synchrotron bubble
RTS
RN
electromagnetic braking of
fast-spinning magnetized NS
Magnetized relativistic
wind
If wind is efficiently confined by surrounding
SNR
Star rotational energy visible as
non-thermal emission of the magnetized relativistic
plasma
Kes 75 (Chandra)
(Gavriil et al., 2008)Wind is mainly made of pairs and a toroidal B
103<<107
Relativistic shocks in astrophysics
Cyg ASS433
Crab Nebula
AGNs ~a few tensMQSs ~a few
PWNe ~103-107 GRBs ~102
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 (=B2/4nmc2)and geometry ( (B·n))
of the flow, which are usually unknown….
The Pulsar Wind termination shock
In Crab RTS ~0.1 pc:~boundary of underluminous (cold
wind) region~“wisps” location (variability over
months)
RTS~RN(VN/c)1/2~109-1010 RLC
from pressure balance (e.g. Rees & Gunn 74)
assuming low magnetization
Composition: mainly pairs maybe a fraction of ionsGeometry: perpendicular where magnetized even if field not perfectly toroidalMagnetization: ~VN/c<<1, a paradox
At r~RLC: ~104 ~102
(pulsar and pulsar wind theories)
At RTS: ~VN/c«1(!?!) (104-107)
(PWN theory and observations)
-paradox!
More refined constraints on from 2D modeling of the nebular emission
The anisotropic pulsar wind
Streamlines asymptotically radial beyond RLC
Most of energy flux at low latitudes: Fsin2()
Magnetic field components: Br1/r2 Bsin()/r
Within ideal MHD stays largeCurrent sheet around the equatorial
plane: The best place to lower wind
magnetization
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)
Axisymmetric RMHD simulations of PWNeKomissarov & Lyubarsky 03, 04
Del Zanna et al 04, 06Bogovalov et al 05
A: ultrarelativistic PSR windB: subsonic equatorial outflowC: supersonic equatorial funnel
a: termination shock frontb: rim shockc: FMS surface
Termination Shock structure
Fsin2()
sin2()
Bsin()G()
=0.003
=0.01
=0.03
Constraining in PWNe
(Del Zanna et al 04)
>0.01 required forJet formation
(a factor of 10 largerthan within 1D MHD
models)
Synchrotron Emission maps
=0.025, b=10
=0.1, b=1
opticalX-rays
(Hester et al 95)
Emax is evolved with the flow f(E)E-,
E<Emax (Del Zanna et al 06)
Between 3 and 15 % of the wind
Energy flows with <0.001
(Pavlov et al 01)
(Weisskopf et al 00)
Particle Acceleration mechanisms
Requirements:Outcome: power-law with ~2.2 for optical/X-rays ~1.5 for radioMaximum 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 enoughShock 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)
Composition: mostly pairs Magnetization: >0.001 for most of the flow
Geometry: transverse
Pros & ConsDSA 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)
Drifting e+-e--p
plasma
Plasma starts
gyrating
B increases
Configuration at the leading edge~ cold ring in momentum space
Coherent gyration leads tocollective emission of cyclotron waves
Pairs thermalize tokT~mec2 over
10-100 (1/ce)
Ions take their time:mi/me times longer
Resonant cyclotron absorption in ion doped
plasma
Magnetic reflection mediates the transition
Leading edge of a transverse relativistic
shock in 1D PICDrifting species Thermal pairs
Cold gyrating ions
Pairs can resonantly absorb the ion radiation at n=mi/me and then progressively lower n Effective energy transfer if
Ui/Utot>0.5
e.m. fields
(Amato & Arons 06)
Subtleties of the RCA process I
Pairs can resonantly absorb ion
radiation at n=mi/me and then
progressively lower n down to n=1:Emax= mi/me
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
Growth-rate independent of n(Hoshino & Arons 91)
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-
ci= me/mice
frequency
Growth-rate
Spectrum is cut off at n~u/u
growth-rate ~ independent of n
if plasma cold (Amato & Arons 06)
Subtleties of the RCA process II
If thermal spread of the ion distribution
is included
Acceleration can be suppressed
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%
Particle spectra and acceleration efficiency for
mi/me=100
=5% =2.7
=27% =1.6
e-
e+
Mechanism works at large mi/me
for both e+ and e-ni/n-=0.2Ui/Utot=0.8
Extrapolation to realistic mi/me predicts same efficiency
Acceleration via RCA and related issuesNicely 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 ConclusionsWhat 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 radiationWhen this is done there are not many possibilities left:
Fermi mechanism in the unmagnetized equatorial region, but very little energy flows within itMagnetic reconnection at the termination shock, poorly knownRCA 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 wavesmi/me=20, ni/n-=0.4 mi/me=40, ni/n-=0.2
Ui/Utot=0.7 same in both simulations
e-
=20% =1.7
<2%
e+
e-
e+
=3% =2.2
=11% =1.8
Positron tail extends to max=mi/me
First evidence of electron acceleration
Upstream flow:Lorentz factor: =40Magnetization: =2
Simulation box:x=rLe/10Lx=rLix10
Effects of thermal spreadu/u=0.1
=5% =2.7
=4% =3.3=27% =1.6
=3% =4
u/u=0
Initial particle distribution
function is a gaussian of width u
Acceleration effectively suppressed!!!
Upstream flow:Lorentz factor: =40Magnetization: =2
Simulation box:x=rLe/10Lx=rLix10
ni/n-=0.2 mi/me=100Ui/Utot=0.8
Particle In Cell SimulationsThe method:
Collect the current at the cell edgesSolve Maxwell’s eqs. for fields on the meshCompute fields at particle positionsAdvance particles under e.m. force ApproximationsIn principle only cloud in cell algorithm
Mistaken transients
e--e+ plasma flow:
in 1D:•No shock if =0•No accel. for
any in 3D
•Shock for any •Fermi accel.
for =0
An example of the effects of reduced
mi/mein the following
Reduced spatial and time extent
reduced dimensionality of the problem
But Computational limitations force:
Powerful investigation
tool for collisionless plasma physics:allowing to resolve the
kinetic structure of the flow on all scales
Far-from-realistic values
of the parameters
For some aspects of problems involving species with different masses 1D WAS still the only way to go
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/(4nmc22)=?
In Crab RTS ~0.1 pc:~boundary of underluminous (cold
wind) region~“wisps” location (variability over
months)
RTS~RN(VN/c)1/2~109-1010 RLC
from pressure balance (e.g. Rees & Gunn 74)
assuming low magnetization
pulsar wind
Synchrotron bubble
RTS
RN
Most likely particle acceleration site