The Theory of Supernova Remnants

1

• The Theory of Supernova Remnants
• Some comments on Supernova Remnants and the
  production of Cosmic Rays
• Don Ellison, North Carolina State University

104
Galactic Cosmic Rays
Tychos Supernova Remnant
Flux
Solar modulation blocks low energy CRs
1020 eV
1015 eV
10-28
http//chandra.harvard.edu/photo/2005/tycho/
Energy eV
109 eV
1021 eV
Hillas_Rev_CRs_JPhysG2005.pdf
2
Consider efficient production of Cosmic Rays by
Diffusive Shock Acceleration (DSA) in SNRs DSA
is also called the first-order Fermi mechanism
? Particle acceleration in Collisionless Shocks ?
Many 100s of references. Some review
papers Axford 1981 Drury 1983 Blandford
Eichler 1987 Jones Ellison 1991 Berezhko
Ellison 1999 Malkov Drury 2001 Bykov
2004 Bykov et al 2011, 2012, 2013
Discovery papers for first-order Fermi mechanism
in shocks Krymskii (1976), Axford, Leer
Skadron (1977), Bell (1978), Blandford
Ostriker (1978)
So called Universal test-particle power law for
particles (in a strong shock)
If particles are fully relativistic
3
1-D Model Type Ia or core-collapse SN with
Pre-SN wind
Forward Shock
Reverse Shock
Contact Discontinuity
Spherically symmetric No clumpy structure for
now (Note Yamazakis talk)
4
1-D Model Type Ia or core-collapse SN with
Pre-SN wind
Shocked ISM material Weak X-ray lines Strong
DSA and CR prod.
Forward Shock
Reverse Shock
Contact Discontinuity
Spherically symmetric No clumpy structure for
now (Note Yamazakis talk)
5
1-D Model Type Ia or core-collapse SN with
Pre-SN wind
Shocked ISM material Weak X-ray lines Strong
DSA and CR prod.
Forward Shock
Reverse Shock
Shocked Ejecta material Strong X-ray emission
lines ! DSA not obvious for RS
unless B-field strongly amplified
Contact Discontinuity
Spherically symmetric No clumpy structure for
now (Note Yamazakis talk)
6
1-D Model Type Ia or core-collapse SN with
Pre-SN wind
Shocked ISM material Weak X-ray lines Strong
DSA and CR prod.
Forward Shock

• Cosmic Ray electrons and ions accelerated at FS
• Protons ? pion-decay ?-rays
• Electrons ? synchrotron, IC, non-thermal
  brems.
• High-energy CRs escape from shock precursor
  interact with external mass
• Evolution of shock-heated plasma between FS and
  contact discontinuity (CD)
• Electron temperature, density, charge states of
  heavy elements, and X-ray line emission varies
  with ionization age

Reverse Shock
Escaping CRs
Shocked Ejecta material Strong X-ray emission
lines ! DSA not obvious for RS
unless B-field strongly amplified
Contact Discontinuity
Spherically symmetric No clumpy structure for
now (Note Yamazakis talk)
7

• Main effects from DSA that influence SNR
  hydrodynamics
• Nonthermal particles (i.e., swept-up ISM or
  ejecta) are turned into relativistic CRs by DSA.
  This lowers specific heat ratio (5/3 ? 4/3)
• Some of the highest energy CRs will escape
  upstream from the forward shock. This also lowers
  specific heat ratio (4/3 ? 1)
• ? Effects (1) and (2) cause the shock compression
  ratio to increase above r 4 (find typical
  values with efficient DSA r 5 - 10 )
• 3) If DSA is efficient, to conserve energy,
  temperature of shocked gas MUST decrease below
  value expected without CR production

SNR shocks that efficiently produce CRs will have
large compression ratios and low shocked
temperatures ? Production of CRs influences SNR
hydrodynamics thermal X-ray emission
8
Test-particle power law hardens with increasing
comp. ratio, r

• For strong shocks, universal power law diverges
  unless acceleration stopped by finite size or
  finite age.

Universal power law diverges for r 4
Diverges for strong shocks with compression ratio
r ? 4
? In strong shocks, CRs must modify the shock,
and some of the highest energy CRs must escape if
acceleration is efficient ? strong nonlinear
effects
9
What happens to the test-particle prediction when
nonlinear effects are taken into account?
First Collisionless plasmas
10
Collisionless plasmas
? We see thin structures in solar wind and ISM
e.g., planetary bow shocks and SNR shocks ? The
length scale of these structures must be many
orders of magnitude smaller than the collisional
mean-free-path
NGC 2736 The Pencil Nebula
Thin structures are possible because
wave-particle interactions produce short mfp for
particle isotropization
Hydrogen emission SN 1006
11
Charged particle, helix, no ?B/B
scattering Particle-particle collisions are rare
Uniform B
12
Charged particle, helix, no ?B/B
scattering Particle-particle collisions are rare
Uniform B
If particle flux large enough, particles will
distort the field
Turbulent B
13
Charged particle, helix, no ?B/B
scattering Particle-particle collisions are rare
Uniform B
If particle flux large enough, particles will
distort the field
Turbulent B
Particles pitch-angle scatter and turn around ?
can define a collisionless mean free path. This
collision is nearly elastic in frame of B-field
14
In collision-dominated plasmas, particle-particle
collisions drive the plasma to thermal
equilibrium. If an individual particle gets
more energy than average, it will immediately
transfer energy via collisions to slower
particles ? scatterings are
Inelastic In a collisionless plasma, particles
interact with the background B-field ? one
proton scatters off of Avogadros number of
particles tied together by nearly frozen-in
turbulent B-field ? scatterings are nearly
elastic An individual particle can gain, and
keep for long times, much more energy than an
average thermal particle
B-fields are frozen-in because of high
conductivity of diffuse plasmas. If the plasma
moves, currents are generated to produce B-fields
so magnetic flux remains unchanged. B-field
moves with bulk plasma
15
Hillas_Rev_CRs_JPhysG2005.pdf
Extremely non-equilibrium plasma maintained for
many millions of years in ISM. Do not see this
in laboratory plasmas !!
Galactic Cosmic Rays ?
LHC
Need vast machines to produce high energy beam
for a brief instant
? Do not have diffusive shock acceleration in
collision dominated (i.e., lab) shocks ?
16
Diffusive Shock Acceleration Shocks set up
converging flows of ionized plasma
Shock wave
Interstellar medium (ISM), cool with speed VISM
0
SN explosion
Vsk u0
VDS
Post-shock gas ? Hot, compressed, dragged along
with speed VDS lt Vsk
17
Diffusive Shock Acceleration Shocks set up
converging flows of ionized plasma
Shock wave
Interstellar medium (ISM), cool with speed VISM
0
SN explosion
Vsk u0
VDS
shock frame
shock
flow speed, u0
charged particle moving through turbulent B-field
u2
X
Upstream
DS
Post-shock gas ? Hot, compressed, dragged along
with speed VDS lt Vsk
u2 Vsk - VDS
Particles make nearly elastic collisions with
background plasma ?
gain energy when cross shock ? bulk kinetic
energy of converging flows put into individual
particle energy ? some small fraction of thermal
particles turned into (approximate) power law
18
Test Particle Power Law
Plot p4 f(p)
Krymsky 77, Axford at al 77, Bell 78, Blandford
Ostriker 78
f(p) p-3r/(r-1) where r is compression ratio,
f(p) d3p is phase space density
Quasi-Universal power law
p4 f(p)
If r 4, ? 5/3, f(p) p-4
shock
flow speed
X
Normalization of power law not defined in
test-particle approximation
19
Test Particle Power Law
Plot p4 f(p)
Krymsky 77, Axford at al 77, Bell 78, Blandford
Ostriker 78
f(p) p-3r/(r-1) where r is compression ratio,
f(p) d3p is phase space density
Quasi-Universal power law
p4 f(p)
If r 4, ? 5/3, f(p) p-4
shock
flow speed
X
Test particle results ONLY for superthermal
particles, no information on thermal particles
Normalization of power law not defined in
test-particle approximation
20
Temperature
If acceleration is efficient, shock becomes
smooth from backpressure of CRs
p4 f(p)
test particle shock
Flow speed
subshock
p4 f(p) f(p) is phase space distr.
X
NL
? Concave spectrum ? Compression ratio, rtot gt
4 ? Low shocked temp. rsub lt 4
TP f(p) ? p-4
B-field effects may reduce curvature
In efficient acceleration, entire particle
spectrum must be described consistently,
including escaping particles ? much harder
mathematically

BUT, connects thermal emission to radio GeV-TeV
emission
21
Efficient acceleration ? shock becomes smooth
from CR backpressure
test particle shock
Flow speed
Weak subshock, r lt 4 ? lower
shocked temperature Overall compression ratio gt 4
? higher shocked density
subshock
Temperature and density determine non-equilibrium
ionization state of shocked plasma ? SNR
evolution X-ray emission modified by
efficient shock acceleration
X

• Caution while basic predictions are extremely
  robust They only depend on particle diffusion
  length being increasing function of energy,
• Size of nonlinear effects depend on acceleration
  efficiency.

22
Modifications brought on by efficient CR
production depend on Mach number (here show
extreme example)
Increase in compression ratio and Decrease in
shocked temperature with efficient CR
acceleration These are large effects when BISM
is low. Not so large if B-field amplifed
Comp. ratio
20
? Efficient DSA
NL
10
TP
? Test-particle accel.
4
Shocked proton temp.
TP
? Test-particle accel.
Compression ratios gtgt 4 should show in SNR
morphology
NL
? Efficient DSA
SNR Age yr
23
Chandra observations of Tychos SNR (Warren et
al. 2005)
Green line is contact discontinuity (CD) CD lies
close to outer blast wave determined from 4-6 keV
(non-thermal) X-rays
No acceleration
FS
Morphology can be explained by large compression
ratio from efficient DSA
Efficient DSA acceleration
2-D Hydro simulation Blondin Ellison 2001
24
Efficient acceleration ? shock becomes smooth
from CR backpressure
test particle shock
Flow speed
subshock
High momentum CRs feel larger effective
compression than low p CRs ? Smooth shock
produces concave spectrum
X
Note plot p4 f(p)
Particle spectrum that determines highest energy
emission is fundamentally connected to lowest
energy thermal plasma
High efficiency example
25
Particle distributions
continuum emission
ps
es
synch
Kep
pion
IC
Several parameters needed for modeling !!
e.g., Electron/proton ratio, Kep
brems
In addition, emission lines in thermal
X-rays. Depends on Te/Tp and electron
equilibration model
In nonlinear DSA, Thermal Non-thermal emission
coupled ? big help in constraining
parameters
26

• Have developed a Composite SNR Model
  (CR-hydro-NEI code)
• SNR hydrodynamics, Nonlinear Shock Acceleration,
  Broadband
  continuum radiation, and X-ray emission line
• Collaborators Andrei Bykov, Daniel Castro,
  Herman Lee, Hiro Nagataki, Dan Patnaude,
  Pat Slane (early work with Anne
  Decourchelle Jean Ballet 2000,2004)
• VH-1 code for 1-D hydrodynamics of evolving SNR
  (e.g., J. Blondin)
• Semi-analytic, nonlinear DSA model (from P.
  Blasi and co-workers)
• Non-equilibrium ionization for X-ray line
  emission (D. Patnaude, J. Raymond)
• NL shock acceleration coupled to SNR
  hydrodynamics (Herman Lee)
• Magnetic field amplification (Blasis group
  Andrei Bykov)
• Electron and Ion distributions from thermal to
  relativistic energies (T. Kamae)
• Continuum photon emission from radio to TeV

Apply model to individual SNRs RX J1713, CTB
109, Vela Jr., Tycho
27
One example Thermal Non-thermal Emission in
SNR RX J1713 (Ellison, Lee, Slane, Patnaude,
Nagataki et al 2007--2012)
Core-collapse SN model SN explodes in a 1/r2
pre-SN wind ? Shell of swept-up wind material ?
Inverse-Compton dominates GeV-TeV emission Note
good fit to highest energy HESS observations
synch
Note Large majority of CR energy is still in
ions even with IC dominating the radiation
? SNRs produce CR ions!
Inverse-Compton fit to HESS obs Pre-SN wind
B-field lower than ISM ? Can have MFA and still
have B-field low enough to have high electron
energy. For J1713, we predict average shocked
B 10 µG !
28
Multi-component model for SNR RX J1713 (Inoue,
Yamazaki et al 2012 Fukui et al 2012)
Average density of ISM protons 130 cm-3 Total
mass 2 104 Msun over SNR radius 0.1 of
supernova explosion energy in CR protons
!! This may be a problem for CR origin
Inoue et al (2012)
High densities needed for pion-decay may be in
cold clumps that dont radiate thermal X-ray
emission
29
Warning many parameters and uncertainties in
CR-hydro-NEI model, but

• For spherically symmetric model of SNR RX J1713
  Vela Jr.
• Inverse-Compton is best explanation for GeV-TeV
• Other remnants can certainly be Hadronic or
  mixed, e.g. Tychos SNR
• and CTB 109.
• Important For DSA most CR energy (17 of ESN
  for J1713) is in ions even with inverse-Compton
  dominating the radiation
• ? All nonlinear models show that SNRs produce CR
  ions !!! ? There is no fundamental difference
  between IC and pp dominated SNRs
• Besides question of CR origin
  
  Careful modeling of SNRs can provide constraints
  on critical parameters for shock acceleration
• Shape and normalization of CR ions from
  particular SNRs
• electron/proton injection ratio
• Acceleration efficiency
• Magnetic Field Amplification
• Properties of escaping CRs
• Geometry effects in SNRs such as SN1006

What about CRs observed at Earth?
CREAM Balloon flights
30
CREAM Balloon flights in Antarctica 40 million
cubic foot balloon
Float between 38 and 40 km Average
atmospheric overburden of 3.9 g/cm2 Total
exposure for 5 flights 156 days
31
Cosmic rays measured at Earth
Spectral shape of cosmic ray electron spectrum is
similar to ions when radiation losses are
considered.
Figure from P. Boyle D. Muller via Nakamura et
a. 2010
Side note Stochastic (second-order) acceleration
cannot reproduce such similar spectral shapes.
Stochastic acceleration is NOT acceleration
mechanism for these galactic CRs
32
Recent balloon and spacecraft observations of
cosmic rays show unexpected spectral shapes,
e.g.
ATIC-2 (Wefel et al. 2008) CREAM (Ahn et al
2010) PAMELA (Adriani et al. 2011)

• Hint of curvature in CR spectra ? this
  might be concave curvature predicted by nonlinear
  DSA !?
• CR helium spectrum is slightly harder that the
  proton spectrum at energies where both are fully
  relativistic
• ? This is impossible to explain with
  simple NL DSA. Must be more complicated.

p/He
Rigidity (GV), R pc/(eZ)
PAMELA (Adriani et al. 2011)
33
Different shape for H and He spectra
Hint of curvature in CR spectra seen at Earth !?
He
C
Protons (open)
O
Helium (solid)
Ne
Mg
CREAM data from Ahn et al 2010
Si
Concave curvature?
iron
34
What does basic model of Nonlinear DSA predict ?
Consider spectral curvature when have different
ion species. ? In test-particle acceleration, DSA
predicts spectra ordered by velocity
Velocity Scale, v ltlt c
Electrons
Test-particle
Protons
High A/Q ions
Log f(v) (p.s.d.)
Test-particle All have identical spectral
shapes in velocity (if scale to number of
particles accelerated)

• This results from assumption that scatterings are
  elastic in local frame
• nature of collisionless plasma
• Once all particles are fully relativistic they
  are treated the same

Test-particle power laws
Log Velocity
35
Test Particle Shock Acceleration
Momentum scale
Velocity Scale, v ltlt c
electrons
electrons, proton high A/Q identical
protons
High A/Q
Log f(v) (p.s.d)
Log f(p) (phase space)
Test-particle power laws
Test-particle power laws
Log Momentum
Log Velocity
Heavy particles get more energy purely from the
kinematics of energy gain in the converging
plasmas on either side of the shock
Test-particle power-law same for all ion species
36
If shock is efficient, nonlinear effects are
important and shock is smoothed Small A/Q
particles feel a smaller effective compression
ratio, reff, high A/Q ions feel a larger reff
than protons at same velocity High A/Q particles
gain more energy in each crossing ? have a
flatter spectrum than protons until both are
relativistic This effect depends on acceleration
efficiency and on shock Mach number
Test Particle
Flow speed
Modified shock
Modified shock ? concave spectrum
Note plot p4 f(p)
X
37
Test Particle
When nonlinear effects become important, momentum
dependence of mfp gives CONCAVE spectra (Eichler
79, 84)
Flow speed
Modified shock
Momentum scale
electrons
protons
high A/Q ions
X
es
p
A/Q
Log f(p) (phase space)
Diffusion length proportional to A/Q means high
A/Q species suffer LESS from modified shock
Non-linear effects
A/Q
p
Log Momentum
es
enhancement
depletion
If shock is modified mainly by protons, high
A/Q ions will be enhanced, in acceleration
process
38

• Bottom line
• Nonlinear DSA predicts
• Enhancement of high A/Q (mass/charge)
  particles. Heavy
  elements accelerated more efficiently than
  protons
• Observed at quasi-parallel Earth bow shock
• May explain difference in H/He slopes, but
  detailed modeling necessary
• Essential for modeling the composition of
  Galactic Cosmic Rays

High A/Q (mass / charge) ions gain more energy in
each crossing and have a flatter spectrum than
protons as long as they are non-relativistic.
Enhancement then persists to relativistic energies
Test Particle
Flow speed
Modified shock
X
39
Quasi-parallel Earth Bow Shock
AMPTE / IRM observations of diffuse ions at
Q-parallel Earth bow shock H, He2,
CNO6 Observed during time when solar wind
magnetic field was nearly radial.
Ellison, Mobius Paschmann 90
H
He2
CNO6
DS
UpS
DS
Critical range for injection
Modeling suggests nonlinear effects important
Data shows high A/Q solar wind ions injected and
accelerated preferentially. These observations
are consistent with A/Q enhancement in nonlinear
DSA (Eichler 1979)
40
A/Q enhancement applied to Galactic Cosmic Ray
Composition Observed CR composition NOT so
similar to solar system !!!
Scale to Silicon
Here, scale to Silicon Note composition
measurements restricted to low energy CRs lt 100
GeV
Li, Be, B produced by heavier CRs breaking up as
collide in ISM
Lodders 2003
41
Galactic Cosmic Ray Composition
Simpson 83
Scale to Hydrogen
Consistent explanation of CR source
material Nonlinear SNR shocks accelerate ISM gas
and dust with A/Q enhancement
Li
B
Be
Galactic abundances
? Main effect is enhancement of all heavy
elements relative to Hydrogen Helium (factor
of 10) ? Secondary effect is enhancement of
refractory elements (Dust) relative to volatile
ones (Gas) (factor of 10)
Meyer, Drury Ellison 1997
42
ISM gas-phase abundances
100 in gas phase
Si
Silicon
Iron
Fe
gt99 in dust
Ni
Al
Aluminum
Ti
Calcium
Ca
Dust
Meyer, Drury, Ellison 97
You must accelerate ISM dust to reproduce
observed (low energy) CR composition
43
Ellison, Drury Meyer 1997
A/Q enhancement of ISM gas and dust accelerated
by SNR shock. Dust sputters off refractory ions
which are then re-accelerated by
shock
100
Elements that are locked in dust in ISM
10
CR source/solar
Gaseous elements
H
Large error bars here, but more recent
observations by TIGER and ACE are much better ?
1
He
1
10
100
Mass, A (A/Q)
Scale to Hydrogen
44
Figure (preliminary) from M. Israel (Denver CR
meeting, June 2012)
New data from TIGER and ACE. M. Israel et al.
compare with 80 mixed ISM and 20 massive star
outflow ejecta. Support for Gas-Dust model.
Clear evidence for A/Q enhancement of both
Volatiles Refractories
Refractories (Dust)
Volatiles (Gas)
Note Mass, A (A/Q)
H and He are not on this plot. Until Meyer et al
1997, H and He were treated as exceptions and
not included with heavy elements. H and He
did not fit FIP scenario.
45
Magnetic Field Amplification (MFA)
Particle acceleration requires magnetic
turbulence to work. This turbulence must be far
stronger than typical ISM ?B/B to produce CRs to
high energy Shocks can, and do, produce their
own turbulence. No independent, external source
of turbulence is necessary for DSA to take place.

• When a supersonic plasma, even one with zero
  B-field, encounters a barrier
• currents will be generated by particles
  reflecting off barrier,
• small-scale B-fields result (call this the
  Weibel instability if you like),
• fresh, unshocked particles now gyrate in these
  fields and become randomized,
• a shock quickly forms,
• particles start to be accelerated by the shock
  and the streaming instability generates more
  magnetic field, etc.

46
Self-generated turbulence at weak Interplanetary
shock
Baring et al ApJ 1997
?B/B
Indirect evidence for strong turbulence produced
by CRs at strong SNR shocks
?B/B
Tychos SNR
?B/B
Sharp X-ray synch edges
47
How do you start with BISM ? 3 ?G and end up with
B ? 300 ?G at the shock? Efficient diffusive
shock acceleration (DSA) not only places a large
fraction of shock energy into relativistic
particles, but also amplifies magnetic field by
large factors
MFA is connected to efficient CR production, so
nonlinear effects essential
Bell Lucek 2001 ? apply Q-linear theory when
?B/B gtgt 1 Bell 2004 ? non-resonant streaming
instabilities Amato Blasi 2006 Blasi, Amato
Caprioli 2006 Vladimirov, Ellison Bykov 2006,
2008

calculations coupled to nonlinear particle accel.
48

• A lot of work by many people on nonlinear
  Diffusive Shock Acceleration (DSA) and Magnetic
  Field Amplification (MFA)
• Some current work (in no particular order)
• Amato, Blasi, Caprioli, Morlino, Vietri
  Semi-analytic
• Bell Semi-analytic and PIC simulations
• Berezhko, Volk, Ksenofontov Semi-analytic
• Malkov Semi-analytic
• Niemiec Pohl PIC
• Pelletier and co-workers MHD, relativistic
  shocks
• Reville, Kirk co-workers MHD, PIC
• Spitkovsky and co-workers Hoshino and
  co-workers other PIC simulators
  Particle-In-Cell simulations, so far, mainly rel.
  shocks
• Caprioli Spitkovsky Giacalone et al. hybrid
  simulations
• Vladimirov, Ellison, Bykov Monte Carlo
• Zirakashvili Ptuskin Semi-analytic, MHD
• Bykov et al
• Apologies to people I missed

49
Magnetic Field Amplification in DSA is a hard
problem

• Magnetic field generation intrinsic part of
  particle acceleration ?
  cannot treat DSA and MFA separately
• Strong turbulence means Quasi-Linear Theory (QLT)
  not good approximation ? But QLT is our main
  analytic tool (QLT
  assumes ?B/B ltlt 1)
• Length and momentum scales are currently well
  beyond reach of 3D particle-in-cell (PIC)
  simulations if wish to see full nonlinear effects
  ? Particularly true for non-relativistic
  shocks
• Problem difficult because TeV protons influence
  injection of keV protons and electrons
• To cover full dynamic range, must use approximate
  methods e.g., Monte Carlo,
  Semi-analytic, MHD simulations

50
Work with Bykov, Osipov Vladimirov
Using approximate plasma physics (quasi-linear
theory, Bohm diffusion, etc.) Can iteratively
solve nonlinear DSA problem with MFA (Monte Carlo
work with Andrei Bykov, Andrey Vladimirov
Sergei Osipov)
Thermal leakage Injection
Acceleration Efficiency
magnetic turbulence, ?B/B ? diffusion coefficient
dissipation, cascading
iterate
Shock structure
If acceleration is efficient, all elements
feedback on all others
Iterative, Monte Carlo model of Nonlinear
Diffusive Shock Acceleration
(i.e., Vladimirov, Ellison Bykov
2006,2008 Ellison Vladimirov 2008) Similar
semi-analytic results Amato Blasi (2006)
Blasi, Amato Caprioli (2006)
51

• Essential features of MFA in diffusive shock
  acceleration
• Production of turbulence, W(x,k) (assuming
  quasi-linear theory)
• Resonant (CR streaming instability) (e.g.,
  Skilling 75 McKenzie Volk 82
  Amato Blasi 2006)
• Non-resonant current instabilities (e.g., Bell
  2004 Bykov et al. 2009
  Reville et al 2007 Malkov Diamond)
• CR current produces waves with scales short
  compared to CR gyro-radius
• CR current produces waves with scales long
  compared to CR gyro-radius
• Calculation of D(x,p) once turbulence is known
• Resonant (QLT) Particles with gyro-radius
  ?waves gives ?part ? p
• Non-resonant Particles with gyro-radius gtgt
  ?waves gives ?part ? ps
• Production of turbulence and diffusion must be
  coupled to NL shock structure including injection
  of lowest energy particles and escape of highest
  energy

All coupled ? (1) Thermal injection (2) shock
structure modified by back reaction of
accelerated particles (3) turbulence generation
(4) diffusion in self-generated turbulence
(5) escape of maximum energy particles ?
All coupled
52
Conclusions

• The production of CRs in young SNRs is expected
  to be efficient and nonlinear theory and
  observations support this in individual remnants
• DSA is intrinsically efficient and difficult !
• Shock structure, CR production, B-field
  turbulence, Injection of thermal particles, all
  non-trivially connected
• DSA is multi-scale (Intrinsic concave CR
  spectrum)
• ? Large fraction of total energy is in highest
  energy CRs with longest diffusion lengths
• ? To conserve energy, highest energy CRs must
  feedback on injection of lowest energy particles
  with shortest diffusion lengths
• Injection of thermal particles, escape of high
  energy CRs, and self-generation of turbulence,
  all involve highly anisotropic distributions
• ? Quasi-linear theory not good approximation
• Detailed plasma physics important for nonlinear
  effects, but
• Multi-scale nature currently beyond reach of PIC
  simulations
• Need to know how NL DSA works to explain origin
  of CRs and to properly interpret broadband SNR
  observations (also radio jets, GRBs . )
• ? NL DSA influences the evolution and morphology
  of SNRs and the thermal X-ray emission

53
Extra Slides
54
PAMELA (Adriani et al. 2011)
ATIC-2 (Wefel et al. 2008)
protons
Helium
Confirm different slopes Helium harder than
protons at fully relativistic energies ! ? This
is impossible to explain with simple NL DSA.
Must be more complicated.
55
Chandra observations of Tychos SNR (Warren et
al. 2005)
After Warren et al. adjust for distortions at the
CD
Radius (arcsec)
FS
FS
CD
CD
Observed
Radius / FS
Reverse shock
Azimuthal angle (deg)
56
If you want clumpy
Don Warren John Blondin 2013
RS-CD-FS positions

• 3D hydro simulations showing positions of forward
  shock, reverse shock and contact discontinuity.
• Includes a
• phenomenological model of NL DSA
• Efficient DSA causes CD-FS separation to decrease
• Rayleigh-Taylor instabilities alone can allow
  ejecta knots to move ahead of FS

No DSA
Efficient DSA
RS-CD-FS positions
57
Don Warren John Blondin 2013
ejecta knot
Knots of ejecta material have overtaken forward
shock
No DSA
Tycho
Line-of-sight simulation of thermal X-ray and
non-thermal synchrotron emission (crude model for
synch.) Compared to Chandra X-ray obs. of
Tychos SNR (J.Warren et al. 2005)
efficient DSA
medium eff.
For now, stay with 1-D spherically symmetric
model with good NL DSA calculation
58
3D hydro simulation with X-ray lines and
efficient DSA (Ferrand et al. 2012)
Thermal emission (0.3 10 keV) from shocked ISM
and ejecta material Includes effects from back
reaction of CRs on thermal plasma Hydro
simulations are important steps forward but not
so easy to include NL-DSA in 3D models
No CR back-reaction
With CR back-reaction