anisotropic plasma astrophysics

AronsFest 127 i 2012

Anisotropic Plasma Astrophysics

Roger BlandfordPaul SimeonYajie Yuan

KIPACStanford


Describing Cosmic Plasma• Fluid description

– P, , v, B…– Magneto Fluid Dynamics

• Flux-freezing, conservation of mass, momentum, energy• P ~ isotropic!

– Relativistic flows– Electromagnetic Flows

• Kinetic description– f(p,x,t), E, B…– Collisionless plasmas

• Vlasov equation for f– Nonthermal distributions– Transport effects– Ultrarelativistic plasmas

Need a hybrid approach to tackle contemporary problem

AronsFest 3

Anisotropic MHD• MHD commonly developed and computed

assuming isotropic pressure• Collisionless plasmas are observed and expected

to be anisotropic• How and when can we discuss this at the fluid

level using a pressure tensor? • Interesting and possibly different when dominant

pressure (and current) is due to ultrarelativistic particles while the flow is locally non-relativistic

• Dissipation due to radiation not collisions or plasma instabilities

• Diffusive Shock Acceleration – SNR, clusters…– Pinches - PWN, jets…

27 i 2012


Particle Acceleration

V ~ I ~ V / Z0

Z0~100P ~ V I ~ V2/Z0

Unipolar Induction

Stochastic Acceleration

U

c

DE/E ~ +/-u/cln(E) ~ u/c (Rt)1/2

AronsFest 527 i 2012 Cahill Dedication, Caltech

GeV TeV PeV EeV ZeV

Cosmic Rays

protons

protons??

heavies?

AronsFest 627 i 2012 Cahill Dedication, Caltech

GeV TeV PeV EeV ZeV

Cosmic Rayssolar

system

active galacticnuclei ??

supernova remnants

pulsars?


Supernova remnants

.

Chandra

Crab Nebula

Cassiopeia A

X-ray RadioCosmic rays

SN1006 X-ray

SN1006 Cas A Tycho

W44


Particle acceleration in SNR • ~ 100TeV gamma rays

– ~0.3 PeV cosmic rays– Hadronic and leptonic (Fermi)

• Variable X-rays– 100 TeV electrons– ~ 1 mG magnetic field

• Shocks also amplify magnetic field– Details controversial

SN1006

Cas ATycho

Perseus Cluster

AronsFest 9

Ultra High Energy Cosmic Rays

• Zevatrons?– Top down exotica

• GZK cutoff• EM channel not seen and hard to avoid

– Massive BH in AGN (~30-50 Mpc)• AGN may be too weak• Acceleration must be remote from BH

– Gamma-Ray Bursts• Stellar BH or millisecond magnetar?• Too distant? Too much radiation?

– Cluster Shocks (Norman,Ryu,Bohringer…)• High Mach accretion shocks• Hard to accelerate p to ZeV energy • Heavy elements may be predicted• e.g. Fe; range ~ 10 Mpc?• Composition controversial• Analysis should be aided by LHC

27 i 2012

AronsFest 10

Entropy Matters• Sgas=1.5 ln[(T/Trec)(n/nrec)-2/3]k (relative to

recombination)– Much more in CMB

• Shocks create gas entropy – DS[M]=1.5ln[(5M2/4-1/4)(1/4+3/4M2)5/3]k

• Before reionization– Weak shocks M ~ 1-3– DS < k

• During reionization (z~10)– Ionization entropy– Moderate shocks M ~1-20– DS <3k

• After reionization– May need DS as large as 10k– Would imply M~100

• e.g. V~1000, s~10 km s-1 27 i 2012

r

Simionescu et alPerseus

M

Recent strong evidence for presence of high M accretion shocks around clusters

16

15

14

13

17

18

Sgas/k

AronsFest 11

(100 Mpc/h)2 2D slice

pancake filamen

t

Shocks in Structure Formation Simulations

Lxgas

T Ms

27 i 2012LCDM simulation with 10243 cells, computational box: (100h-1 Mpc)3 , TVD: grid-based Eulerian hydro code

(Ryu et al 2003)

cluster

Simulations exhibit high M shocks

AronsFest 12

GeV -rays from Clusters of Galaxies

• Active Galactic Nuclei • Primordial cosmic rays• Dark Matter Annihilation

Upper limits are interesting!

Keith Bechtol

27 i 2012

Han et al 2012

AronsFest 13

UHECR at accretion shocks??• Accretion shocks

• Invisible • v~500-1000 km/s?• R ~ 3-10Mpc• B ~ 3 x 1020V/v R ~10mG!• However, SNR generate phenomenal

fields• OK if UHECR is Fe• Counter-evolutionary tendency

27 i 2012

NormanRyuBohringer…

AronsFest 14

Collisionless Shocks

27 i 2012€

f+(p) = qp−q dp' p'q−1 f−(p')0

p∫ ;q = 3r /(r −1)

Explain intensity and spectrum of Galactic cosmic rays

Scatter off magnetic waves


Too good to be true!• Diffusion: CR create their own magnetic irregularities

ahead of shock through instability if <v>>a– Instability likely to become nonlinear - Bohm limit– What happens in practice?– Parallel vs perpendicular diffusion?

• Cosmic rays are not test particles – Include in Rankine-Hugoniot conditions– u=u(x)– Include magnetic stress too?

• Acceleration controlled by injection– Cosmic rays are part of the shock

• What happens when v ~ u?– Relativistic shocks

• Energy cutoff?– E < euBR ~ PeV for mG magnetic field


Particle Transport• Alfven waves scatter cosmic rays

– ~ (B/B)2rL • Bohm?

– D ~ c/3• Parallel vs perpendicular

– L ~ D/u > 100rL ~ 100 EPeVBmG-1Z-1pc

• RSNR < 10pc– Highest energy cosmic rays stream furthest ahead of shock

• L ~ E ?– “Magnetic Bootstrap”

• Firehose and other instabilities

P(E) / u2

GeVTeVPeV

0.1

Shock

X

P(E) / u2

EGeV TeV PeV

Cosmic Ray Pressure dominates Magnetic and Gas Pressure far ahead of Shock


Magnetic Bootstrap

• Assume:– Cosmic rays accelerated by DSA at shock front to ~PeV energy– PCR ~ 0.1u2 E9

-0.2

– Magnetic field amplified upstream > rL– Dynamical effects on background small

• Wave turbulence maintained at Bohm level mainly by Firehose modes– Also mirror, gyroresonant, Bell-Lucek– Transport by field line modeling– “Uniform” field is turbulent field created by higher energy upstream

• Cosmic rays with energy ~ Emax stream away from the shock – Firehose dominates if u > (aISM c)1/2 (PCR/u2)-1/4 ~1000 km s-1

• Fermi observations are instructive!

RB Funk 2007


Magnetic Bootlaces• How can a small

magnetic pressure mediate the interaction between two particle “fluids”?

th CR

mag

X

P

X

j

€

∇PP = jP B∇PCR = jCRBdBdX

= jP + jCR


Cygnus A

3C31

3C75

Extragalactic Jets

Pictor A

M87

NGC 326

3C273

PictorA


McKinneyTschekhoskoyRB2012

AronsFest 21

Crab Nebula

27 i 2012

AronsFest 22

Flaring behavior

27 i 2012

April 2011

Buehler et al

Singular events or power spectrum? No variation seen in other bands

Power~1029W

AronsFest 23

Spectrum of “Flare”

27 i 2012Electron synchrotron radiation: E~PeV, ~109; B~100nT

synchrotron spectrum

AronsFest 24

Where does the variation originate ?• Long term variation of nebula

likely due to changes in magnetic field

• Peak power is ~ 3 percent of nebular power

• Flare energy equals that stared in a region of size

L~ 20B-71/2 lt d ~ 2B-7

1/2 arcsec• We want to learn where and how

nature accelerates particles to high energy

• Not the Pulsar– No correlation with rotation frequency

• Wind shocks when momentum flux equals nebular pressure

• Wind, Shock, Jet, Torus are all possibilities

1 lt hr = 3 masLarmor radius= 609B-7

-1mas 27 i 2012

W

SJ

TP

=10,000mas

AronsFest 25

Pinch?• Resistance in line current

– Current carried by high energy particles

– Resistance due to radiation reaction– Pairs undergo poloidal gyrations

which radiate in all directions– Relativistic drift along direction of

current Jet!!– Compose current from orbits self-

consistently– Illustration of Poynting’s theorem!– Variation intrinsic due to instability

27 i 2012

jBf

r

X

E

€

E⋅ j = −∇⋅N

jz =1

cμ0

∇⋅ E

< j >=Prr

B2

dBdϖ

+Pφφ

Bϖ

AronsFest 26

MHD with Pressure Tensor

27 i 2012

Linear Perturbationsetc

Double Adiabatic Ansatz (CGL)

First invariant has validity but second is questionable in real plasmas(Kulsrud…). However something like this may be a reasonable approximation for some problems including those of current interest

etc


Friedrich Diagrams Vf(q)


Firehose (and mirror) instabilities

AronsFest 29

Conjectures• Relativistic CR ahead of nonrelativistic

shock wave behave like a highly anisotropic fluid with an equation of state and this dictates the growth of magnetic field

• Firehose dominates, resonant, Bell, Weibel…

• Cosmic ray acceleration kinetics can be solved self-consistently in this background

27 i 2012

AronsFest 30

Particle drifts and current

27 i 2012

Normal approach is to analyze particle orbits and deduce currentsCan also start from static equilibrium and understand what is happening

Curvature perpendicular magnetization gradient ExB

Parallel current contains a part that is magnetization driftAlso a part that is resistive – collisional/radiative

AronsFest 31

Conjectures• Unipolar inductor potential

differences maintained into jets and nebulae

• Pinches (relatively) stabilized by flow, expansion…

• Highest energy particles with largest gyro radii carry current and dissipate resistively through radiation

• Steady and explosive instability generic leading to in situ acceleration and emission27 i 2012

AronsFest 32

Summary• Major challenges to particle acceleration

from Crab, blazar flares UHECR…• Hybrid – fluid/kinetic problems• Currents may be carried by highest energy

particles and dissipation can be primarily radiative

• May be possible to gain insight at fluid level using anisotropic RMHD

• Drift currents etc can emerge from MHD rather than vice versa

• Particle trajectories must still be solved in this background

27 i 2012

anisotropic plasma astrophysics

Documents