Post on 22-Dec-2015
AronsFest 127 i 2012
Anisotropic Plasma Astrophysics
Roger BlandfordPaul SimeonYajie Yuan
KIPACStanford
AronsFest 227 i 2012
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
AronsFest 427 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 2012Cahill Dedication, Caltech
GeV TeV PeV EeV ZeV
Cosmic Rays
protons
protons??
heavies?
AronsFest 627 i 2012Cahill Dedication, Caltech
GeV TeV PeV EeV ZeV
Cosmic Rayssolar
system
active galacticnuclei ??
supernova remnants
pulsars?
AronsFest 727 i 2012
Supernova remnants
.
Chandra
Crab Nebula
Cassiopeia A
X-ray RadioCosmic rays
SN1006 X-ray
SN1006 Cas A Tycho
W44
AronsFest 827 i 2012
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
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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
Lxrgas
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 g-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…
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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
AronsFest 1527 i 2012
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
AronsFest 1627 i 2012
Particle Transport• Alfven waves scatter cosmic rays
– ~ (B/B)2rL • Bohm?
– D ~ c/3• Parallel vs perpendicular
– L ~ D/u > 100rL ~ 100 EPeVBG-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
AronsFest 1727 i 2012
Magnetic Bootstrap
• Assume:– Cosmic rays accelerated by DSA at shock front to ~PeV energy– PCR ~ 0.1u2 E9
-0.2
– Magnetic field amplified upstream l > 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
AronsFest 1827 i 2012
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 = jCRB
dB
dX= jP + jCR
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 2012
Electron synchrotron radiation: E~PeV, g~109; B~100nT
synchrotron spectrum
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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= 60g9B-7
-1mas 27 i 2012
W
SJ
T
P
=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
dB
dϖ+
Pφφ
Bϖ
AronsFest 26
MHD with Pressure Tensor
27 i 2012
Linear Perturbations
etc
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
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 emission
27 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