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

The Theory of Supernova Remnants Some comments on Supernova Remnants and the production of

Cosmic RaysDon Ellison, North Carolina State University

Tycho’s Supernova Remnant

http://chandra.harvard.edu/photo/2005/tycho/

1020 eV

Energy [eV]

Flux

1015 eV

Solar modulation blocks low energy CRs

1021 eV109 eV

Hillas_Rev_CRs_JPhysG2005.pdf

Galactic Cosmic Rays

10-28

104

Don Ellison, NCSU

Consider efficient production of Cosmic Rays by Diffusive Shock Acceleration (DSA) in SNRs

DSA is also called the first-order Fermi mechanism

Many 100’s 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)

Particle acceleration in Collisionless Shocks

4)( ppfSo called “Universal” test-particle power law for particles (in a strong shock)

24 )( EdE

dNppfIf particles are fully relativistic:

Contact Discontinuity

Forward Shock

Reverse Shock

1-D: Model Type Ia or core-collapse SN with Pre-SN wind

Spherically symmetric: No clumpy structure for now (Note Yamazaki’s talk)


Forward Shock

Reverse Shock

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






Forward Shock

Reverse Shock




Escaping CRs

1) Cosmic Ray electrons and ions accelerated at FS

a) Protons pion-decay -raysb) Electrons synchrotron,

IC, & non-thermal brems. c) High-energy CRs escape

from shock precursor & interact with external mass

2) Evolution of shock-heated plasma between FS and contact discontinuity (CD)

a) Electron temperature, density, charge states of heavy elements, and X-ray line emission varies with ionization age

Shocked Ejecta material : Strong X-ray emission lines ! DSA not obvious for RS unless B-field strongly amplified


Don Ellison, NCSU

Main effects from DSA that influence SNR hydrodynamics :

1)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)

2)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

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

injinj

2 4 /p

p

Ep p dp dp p

injln |pp

Diverges for strong shocks with

compression ratio r 4

“Universal” power law diverges for 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

)1/(3)( rrppf Test-particle power law hardens with increasing comp. ratio, r

What happens to the test-particle prediction when nonlinear effects are taken into account?

First: Collisionless plasmas :

NGC 2736: The Pencil Nebula

Hydrogen emission SN 1006

Thin structures are possible because wave-particle interactions produce short mfp for particle isotropization

Collisionless plasmas : We see “thin” structures in solarwind 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

Uniform B

Charged particle, helix, no “B/B scattering”Particle-particle collisions are rare

Uniform B


Turbulent B

If particle flux large enough, particles will distort the field :

Uniform B


Turbulent B

mfp ,

Particles pitch-angle scatter and turn around can define a collisionless mean free path. This “collision” is nearly elastic in frame of B-field

If particle flux large enough, particles will distort the field :

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 ~ Avogadro’s 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

1020 eV

Energy [eV]

Flu

x

1015 eV

Solar modulation blocks low energy CRs

1021 eV109 eV

Hillas_Rev_CRs_JPhysG2005.pdf

Galactic Cosmic Rays Extremely non-equilibrium plasma maintained for many millions of years in ISM.

Do not see this in laboratory plasmas !!

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

Diffusive Shock Acceleration: Shocks set up converging flows of ionized plasmaShock wave

Vsk = u0VDS

Interstellar medium (ISM), cool

with speed VISM ~ 0

Post-shock gas Hot, compressed, dragged along with speed VDS < Vsk

SN explosion

Diffusive Shock Acceleration: Shocks set up converging flows of ionized plasmaShock wave

Vsk = u0VDS

Interstellar medium (ISM), cool

with speed VISM ~ 0

Post-shock gas Hot, compressed, dragged along with speed VDS < Vsk

X

flow speed, u0shock

u2

Upstream DS

charged particle moving through turbulent B-field

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

shock frame

u2 = Vsk - VDS

SN explosion

Plot p4 f(p)

4)( ppf

Normalization of power law not defined in test-particle approximation

Test Particle Power Law

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

If r = 4, & = 5/3,

f(p) ~ p-4

X

flow speed shock

Quasi-Universal power law

p4 f

(p)

Plot p4 f(p)

4)( ppf

Normalization of power law not defined in test-particle approximation

Test Particle Power Law

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

If r = 4, & = 5/3,

f(p) ~ p-4

X

flow speed shock

Test particle results: ONLY for superthermal particles, no information on thermal particles

Quasi-Universal power law

p4 f

(p)

X

subshock

Flow speed

► Concave spectrum

► Compression ratio, rtot > 4

► Low shocked temp. rsub < 4

Temperature

TP: f(p) p-4

test particle shock

NL

If acceleration is efficient, shock becomes smooth from backpressure of CRs

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

p4 f

(p)

[f(

p)

is p

has

e sp

ace

dis

tr.] p4 f(p)

B-field effects may reduce curvature

X

subshock

Flow speed test particle shock

Efficient acceleration shock becomes smooth from CR backpressure

Weak subshock, r < 4 lower shocked temperature

Overall compression ratio > 4 higher shocked density

Temperature and density determine non-equilibrium ionization state of shocked plasma SNR evolution & X-ray emission modified by efficient shock acceleration

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.

Efficient DSA

Efficient DSA

Test-particle accel.

Test-particle accel.

Comp. ratio

Shocked proton temp.

Modifications brought on by efficient CR production depend on Mach number (here show extreme example)

TP

NL

NL

TP

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

4

Compression ratios >> 4 should show in SNR morphology

20

10

SNR Age [yr]

Green line is contact discontinuity (CD)

CD lies close to outer blast wave determined from 4-6 keV (non-thermal) X-rays

Chandra observations of Tycho’s SNR (Warren et al. 2005)

2-D Hydro simulation Blondin & Ellison 2001

No acceleration

Efficient DSA acceleration

FS

Morphology can be explained by large compression ratio from efficient DSA

X

subshock

Flow speed test particle shock

Efficient acceleration shock becomes smooth from CR backpressure

High momentum CRs feel larger effective compression than low p CRs Smooth shock produces concave spectrum

effr

eB

pcgyroradius

Note: plot p4 f(p)

High efficiency example

Particle spectrum that determines highest energy emission is fundamentally connected to lowest energy thermal plasma

synch

IC

brems

pion

Particle distributionscontinuum emission

p’se’s

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

Several parameters needed for modeling !!

e.g., Electron/proton ratio, Kep

Kep

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)

1)VH-1 code for 1-D hydrodynamics of evolving SNR (e.g., J. Blondin)

2)Semi-analytic, nonlinear DSA model (from P. Blasi and co-workers)

3)Non-equilibrium ionization for X-ray line emission (D. Patnaude, J. Raymond)

4)NL shock acceleration coupled to SNR hydrodynamics (Herman Lee)

5)Magnetic field amplification (Blasi’s group & Andrei Bykov)

6)Electron and Ion distributions from thermal to relativistic energies (T. Kamae)

7)Continuum photon emission from radio to TeV

8)Simple model of escaping CRs propagating beyond SNRApply model to individual SNRs: RX J1713, CTB 109, Vela Jr., Tycho

p-p

IC

brems

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

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 !

Note: Large majority of CR energy is still in ions even with IC dominating the radiation SNRs produce CR ions!

synch

One example: Thermal & Non-thermal Emission in SNR RX J1713(Ellison, Lee, Slane, Patnaude, Nagataki et al 2007--2012)

High densities needed for pion-decay may be in cold clumps that don’t radiate thermal X-ray emission

Inoue et al (2012)

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

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. Tycho’s SNRand 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:

a) Shape and normalization of CR ions from particular SNRsb) electron/proton injection ratioc) Acceleration efficiencyd) Magnetic Field Amplificatione) Properties of escaping CRsf) Geometry effects in SNRs such as SN1006

What about CRs observed at Earth? CREAM Balloon flights

Float between ~38 and ~40 km

Average atmospheric overburden of ~3.9 g/cm2

Total exposure for 5 flights ~156 days

CREAM Balloon flights in Antarctica 40 million cubic foot balloon

Figure from P. Boyle & D. Muller via Nakamura et a. 2010

Spectral shape of cosmic ray electron spectrum is similar to ions when radiation losses are considered.

Cosmic rays measured at Earth

Side note: Stochastic (second-order) acceleration cannot reproduce such similar spectral shapes. Stochastic acceleration is NOT acceleration mechanism for these galactic CRs

Don Ellison, NCSU

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)

1) Hint of curvature in CR spectra this might be concave curvature predicted by nonlinear DSA !?

2) 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.

1.0 Hep qqq

PAMELA (Adriani et al. 2011)

p/H

e

Rigidity (GV), R = pc/(eZ)

CREAM data from Ahn et al 2010

Protons (open)

Helium (solid)

iron

O

Si

C

He

Different shape for H and He spectra & Hint of curvature in CR spectra seen at Earth !?

Concave curvature?

Ne

Mg

Log Velocity

Lo

g f

(v)

(p.s

.d.)

Velocity Scale, v << c

Test-particle power laws

Electrons

Protons

High A/Q ions

Test-particle: All have identical spectral shapes in velocity (if scale to number of particles accelerated)

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

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

Log Velocity Log Momentum

protons

electrons

Lo

g f

(v)

(p.s

.d)

electrons, proton high A/Q identical

Velocity Scale, v << c Momentum scale

Lo

g f

(p)

(ph

as

e s

pac

e)

Test-particle power laws Test-particle power laws

Heavy particles get more energy purely from the kinematics of energy gain in the converging plasmas on either side of the shock

Test Particle Shock Acceleration

High A/Q

)1/(3)( rrppfTest-particle power-law: same for all ion species

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

X

Flow speed

effr

Test Particle

Modified shock

gyroradius pm vcA

Q eB

Modified shock concave spectrum

Note: plot p4 f(p)

Log Momentum

Momentum scale

Non-linear effects

X

Flow speed

effr

Test Particle

Modified shock

electrons

protonshigh A/Q ions

e’s p A/Q

Diffusion length proportional to A/Q means high A/Q species suffer LESS from modified shock

If shock is modified mainly by protons, high A/Q ions will be enhanced, in acceleration process

When nonlinear effects become important, momentum dependence of mfp gives CONCAVE spectra (Eichler 79, 84)

e’s p A/Qenhancement

depletion

Lo

g f

(p)

(ph

ase

sp

ace

)

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

X

Flow speed

effr

Test Particle

Modified shock

gyroradius pm vcA

Q eB

Ellison, Mobius & Paschmann 90

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.

Critical range for injection

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)

DS UpS DS

Modeling suggests nonlinear effects important

H+

He2+

CNO6+

A/Q enhancement applied to Galactic Cosmic Ray Composition

Observed CR composition NOT so similar to solar system !!!

Lodders 2003

Scale to Silicon

Li, Be, B produced by heavier CRs breaking up as collide in ISM

Here, scale to Silicon

Note composition measurements restricted to low energy CRs < 100 GeV

Scale to Hydrogen

Galactic Cosmic Ray Composition

Galactic abundances

Li

Be

B

Simpson 83

► 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)

Consistent explanation of CR source material:

Nonlinear SNR shocks accelerate ISM gas and dust with A/Q enhancement

Meyer, Drury & Ellison 1997

Ni

Fe

Ca

Al

Si

Ti

Silicon

Iron

Calcium

100% in gas phase

>99% in dust

Meyer, Drury, & Ellison 97

Aluminum

ISM gas-phase abundances

Dust

Those elements that are most abundant in CRs are locked in dust in ISM !

You must accelerate ISM dust to reproduce observed (low energy) CR composition

Ellison, Drury & Meyer 1997

Elements that are locked in dust in ISM

Gaseous elements

H

He

C

R s

ou

rce

/so

lar

Mass, A ~ (A/Q)Scale to Hydrogen

10

100

1

1 10010

A/Q enhancement of ISM gas and dust accelerated by SNR shock. Dust sputters off refractory ions which are then re-accelerated by shock

Large error bars here, but more recent observations by TIGER and ACE are much better

Figure (preliminary) from M. Israel (Denver CR meeting, June 2012)

Refractories (Dust)

Volatiles (Gas)

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

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.

Note: Mass, A ~ (A/Q)

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….

Magnetic Field Amplification (MFA):

Baring et al ApJ 1997

Self-generated turbulence at weak Interplanetary shock

B/B

B/B

B/B

Indirect evidence for strong turbulence produced by CRs at strong SNR shocks

Tycho’s SNR

Sharp X-ray synch edges

Bell & Lucek 2001 apply Q-linear theory when B/B >> 1; Bell 2004 non-resonant streaming instabilities

Amato & Blasi 2006; Blasi, Amato & Caprioli 2006; Vladimirov, Ellison & Bykov 2006, 2008

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

} calculations coupled to nonlinear particle accel.

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):

1)Amato, Blasi, Caprioli, Morlino, Vietri: Semi-analytic2)Bell: Semi-analytic and PIC simulations3)Berezhko, Volk, Ksenofontov: Semi-analytic 4)Malkov: Semi-analytic5)Niemiec & Pohl: PIC6)Pelletier and co-workers: MHD, relativistic shocks7)Reville, Kirk & co-workers: MHD, PIC8)Spitkovsky and co-workers; Hoshino and co-workers; other PIC simulators: Particle-In-Cell simulations, so far, mainly rel. shocks9)Caprioli & Spitkovsky; Giacalone et al.: hybrid simulations10)Vladimirov, Ellison, Bykov: Monte Carlo11)Zirakashvili & Ptuskin: Semi-analytic, MHD12)Bykov et al

13)Apologies to people I missed …

1) Magnetic field generation intrinsic part of particle acceleration cannot treat DSA and MFA separately

2) Strong turbulence means Quasi-Linear Theory (QLT) not good approximation But QLT is our main analytic tool (QLT assumes B/B << 1)

3) 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

a) Problem difficult because TeV protons influence injection of keV protons and electrons

4) To cover full dynamic range, must use approximate methods: e.g., Monte Carlo, Semi-analytic, MHD simulations

Magnetic Field Amplification in DSA is a hard problem

Thermal leakage Injection

Acceleration Efficiency magnetic turbulence,

B/B diffusion coefficient dissipation, & cascading

Shock structure

If acceleration is efficient, all elements feedback on all others

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)

iterate

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)

Work with Bykov, Osipov & Vladimirov

Essential features of MFA in diffusive shock acceleration: 1) Production of turbulence, W(x,k) (assuming quasi-linear theory)

a) Resonant (CR streaming instability) (e.g., Skilling 75; McKenzie & Volk 82; Amato & Blasi 2006)

b) Non-resonant current instabilities (e.g., Bell 2004; Bykov et al. 2009; Reville et al 2007; Malkov & Diamond)

i. CR current produces waves with scales short compared to CR gyro-radius

ii. CR current produces waves with scales long compared to CR gyro-radius

2) Calculation of D(x,p) once turbulence is knowna) Resonant (QLT): Particles with gyro-radius ~ waves gives part ∝ p

b) Non-resonant: Particles with gyro-radius >> waves gives part ∝ pσ

3) 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

Conclusions:

1) The production of CRs in young SNRs is expected to be efficient and nonlinear: theory and observations support this in individual remnants

2) DSA is intrinsically efficient and difficult ! Shock structure, CR production, B-field turbulence, Injection of thermal particles,

all non-trivially connected

3) 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

4) 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

5) Detailed plasma physics important for nonlinear effects, but : Multi-scale nature currently beyond reach of PIC simulations

6) 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

Extra Slides

PAMELA (Adriani et al. 2011)

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.

ATIC-2 (Wefel et al. 2008)

Don Ellison (NCSU) Talk at UNC March 2006

FS FS

CD

Reverse shock

Rad

ius

(arc

sec)

Rad

ius

/ FS

Azimuthal angle (deg)

CD

0.95CD

FS

R

R

Chandra observations of Tycho’s SNR (Warren et al. 2005)

After Warren et al. adjust for distortions at the CD:

Observed

02.093.0 FS

CD

R

R

Don Warren & John Blondin 2013

3D hydro simulations showing positions of forward shock, reverse shock and contact discontinuity.

Includes aphenomenological 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

RS-CD-FS positions

If you want clumpy:

Don Warren & John Blondin 2013

Knots of ejecta material have overtaken forward shock

ejecta knot

No DSA

medium eff.

efficient DSA

TychoLine-of-sight simulation of thermal X-ray and non-thermal synchrotron emission (crude model for synch.) Compared to Chandra X-ray obs. of Tycho’s SNR (J.Warren et al. 2005)

For now, stay with 1-D spherically symmetric model with good NL DSA calculation

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

Documents

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