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)

=0.03

Dependence on field structure

b=10b=100

(Del Zanna et al 04)

B()

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