Anatoly Spitkovsky (Princeton)home.physics.ucla.edu/calendar/Workshops/cmpd/cmpd_2009/..." sh! relativistic PWN GRB AGN jets Solar SNRs Virial Astrophysical collisonless shocks can:

Astrophysical Collisionless ShocksAnatoly Spitkovsky (Princeton)

Astrophysical Collisionless ShocksAnatoly Spitkovsky (Princeton)

Outline:•Diversity of shocks in astrophysics

•Similarity of shocks in astrophysics

•Basics of particle acceleration in shocks

•Simulations of shocks: PIC method

•Internal structure of shocks: magnetized vs unmagnetized & instabilities

•Particle acceleration: dependence on shock structure & geometry

•Electron-ion and non-relativistic shocks

•Effect of accelerated particles on the shocks

•Applications to astrophysical models

The physics of collisionless shocks

Shock: sudden change in density, temperature, pressure that decelerates supersonic flow

Thickness ~mean free pathin air: mean free path ~micron

On Earth, most shocks are mediated by collisions

Astro: Mean free path to Coulomb collisions in enormous: 1000pc in supernova remnants,

~Mpc in galaxy clustersMean free path > scales of interest

shocks must be mediated without direct collision, but through interaction with

collective fields

collisionless shocks








collective fields

collisionless shocks








collective fields

lCoul =m2

ev4

8!nZ2e4ln!! 1.4" 104(

T

K)2(

n

cm!3)!1cm

Shocking astrophysics

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Shocks span a range of parameters:nonrelativistic to relativistic flows magnetization (magnetic/kinetic energy ratio)

composition (pairs/e-ions/pairs + ions)

Age 300 yr (1670 AD)

Casiopea A

Supernova Remnants

Age 954 yr (1054 AD)

Crab Nebula

Age 436 yr (1572 AD)

Tycho

SN 1006; age 1002 yrs G347.3 TeV γ-rays

Chandra X-ray observatory

Explosions release 1051 ergs of energy

X-ray luminosity:3.8x1036 erg/s

Sun: 1033 erg/s in optical

Supernova Remnants

Stages of evolution of supernova remnants

Tycho

ESN ! 1051ergs ESN ! 12Mejv

2ej vej ! 104km/s

Free expansion ~ 200 yrsBlast wave -- Sedov-Taylor E=const solution 10^6 KRadiative shock -- momentum conservingMerge with ISM

3% of the SNR energy is enough to explain energy density of galactic cosmic rays.

SN remnant: Cas A (3-70 kev; Chandra)

Age 300 yr (1670 AD)

SNe II remnant

Mass of x-ray gas10-15 solar mass.


SN remnant: Cas A (3-70 kev; Chandra)

Age 300 yr (1670 AD)

SNe II remnant


Background: synchrotron radiation

Pulsar Wind Nebulae

PSR B1509-58 (X-rays; Slane et al 2006) Vela (Pavlov et al 2001)Crab (Weisskopf et al 2000)

G21.9 (Safi-Harb et al 2004)

Center-filled morphology, nonthermal spectrum, linear polarization

3C58 (Slane et al. 2004) AS, 2006

Shocking astrophysics: Pulsar Wind Nebulae

PSR B1509-58 (X-rays; Slane et al 2006) Vela (Pavlov et al 2001)Crab (Weisskopf et al 2000)


Properties of pulsar winds:

v<<c

shock

Highly relativistic (γ~106) upstream, ~c/2 downstream

Kinetic energy dominated at the nebula (“σ-problem”). ~Toroidal field

σ = B2/(4πγnmc2) ~10-3-10-1

Pole-equator asymmetry and collimation

Produce nonthermal particles (at the termination shock?); γ>109 Kennel & Coroniti 84

Rees & Gunn 74

Crab nebula

Blue: x-rayRed: opticalGreen:radio

Luminosity ~ 1038 erg/s(mostly x-ray & gamma)

Synchrotron radiation:(linear polarization of 9%

averaged over nebula).

Electrons with energy > 1014 ev are needed for emission at 10 kev;

lifetime for these e’s < 1 year. So electrons must be injected

continuously & not come from SNe.

(Plerion)

Crab shows pulsed emission from radio to optical to >50 Mev! And moreoverThe pulse shape is nearly the same over this entire EM spectrum, suggesting

A common origin for the radition which is believed to be synchrotron(curvature radiation). The radio is produced not too far away from theNeutron star (within 5-10 radaii) and high energy pulsed radiation is

Likely produced near the light cylinder.

The bolometric luminosity is pulsed radiation is about a factor 100 smallerThan nebular radiation; pulsed radio is smaller than total pulsed radiation

By a factor of 10^4.

v<<c

shock

Shocking astrophysics: Pulsar Wind Nebulae


Properties of pulsar winds:

v<<c

shock

Highly relativistic (γ~106) upstream, ~c/2 downstream

Kinetic energy dominated at the nebula (“σ-problem”). ~Toroidal field

σ = B2/(4πγnmc2) ~10-3-10-1

Pole-equator asymmetry and collimation

Produce nonthermal particles (at the termination shock?); γ>109

Composition: pairs (+ions?)

Kennel & Coroniti 84Rees & Gunn 74

Radio Infrared Optical X-ray γ-ray

1996A&AS..120C.453A

Atoyan & Aharonian 1996

Cen A

HST & 6 cm VLA

VLA: 6 cm

(distance ~ 2.5 Mpc)

Radio lobe size ~ 200 kpc!

The radio lobes are fed by relativistic jets; we see only

one sided jet due to relativistic beaming.

AGN jet from the quasar GB 1508+5714 (distance 4Gpc)

Chandra x-ray obs.

(x-ray produced by IC of CMB-photons with jet e-s)

Obs. jet size~30 kpc

Faster than light: one-sided jets in M87

Apparent velocity ~ 10-20 c

Can set a limit on the bulk flow velocity

Gamma-ray Bursts

Short bursts of gamma-rays and X-rays, with afterglowLikely model -- explosion of rare type of supernovae, or merger of two compact objects (neutron stars). Releases 1051ergs in jetted relativistic outflow, as central black hole forms.

Emission comes from shocks as shells with different velocities collide.

Composition: e-ions for shocked interstellar medium (afterglow). Could be pairs for internal shocks.

Shocks in binary pulsar

J0737 double pulsar: pulsar wind modifies the magnetosphere of a slow pulsar (Arons, Backer, A.S. 04)

Shock in relativistic wind (presumably pairs + moderate magnetization)


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Astrophysical collisonless shocks can:

1. accelerate particles

2. amplify magnetic fields (or generate them from scratch)

3. exchange energy between electrons and ions






Power law spectra of synchrotron emission are observed in PWNs, SNRs, AGNs, GRBs

Thin synchrotron rims in young SNRs and their TeV emission imply > 10TeV electrons

SNRs show direct evidence of CR acceleration (shock modification); ~10% energy in CRs; CRs up to 1015eV thought to come from SNRs.






Synchrotron afterglow emission from GRBs implies at least 1% of kinetic energy in the magnetic field after the external shock. Upstream magnetization is essentially zero.

Thinness and variability of synchrotron rims. SNRs imply fast cooling time -- constrains magnetic fields ~100 microG >> than expected from shock compression alone.






Shock jump conditions suggest that kTi,e~mi,e vsh2

(equlibrate due to collisions or plasma physics)

GRB observations suggest large fraction of energy in electrons after relativistic shocks (~10%)

Spectral fits of SNRs (Ballmer lines) allow measurement of Te and Ti, suggesting velocity-independent electron heating (Ghavamian et al 2007, Heng et al 2008).






(Ghavamian et al 2007)

, Heng et al 2008).

Supernova remnants:

G347.3 HESS TeV (Aharonian et al 2006) Tycho X-rays (CXC)SN 1006 X-rays (CXC/J. Hughes)

SNR 3C 391 radio (Moffet & Reynolds 1994)

Properties of SNRs: Nonrelativistic shocks (few-10e3 km/s)

Class of young SNRs emitting synchrotron X-rays

Direct evidence of electron acceleration to 50-100TeV (Slane et al 1999, 2001; Vink et al 2006)

100 GeV-TeV emission (HESS sources) hadronic or IC leptonic?

Cosmic ray protons modify shock dynamics -- SNRs probably accelerate CRs; B field amplification

Shock diagnostics:

Ghavamian, Laming & Rakowski (2007)

In SNRs magnetic field of up to 100 µG is inferred from fitting IC and synchrotron together, and from year-scale variability. Much more than expected from compression of ISM field (e.g. Vink & Laming 2003, Uchiyama et al 2007).

In SNRs partition of energy between electrons and ions can be studied with Balmer lines (narrow and broad components from charge-exchange) [Ghavamian et al 07]. Surprizing result -- constant electron energy independent of velocity!

Field amplification is required for relativistic shocks in GRBs to give any synchrotron emission (εB~1%) in GRB afterglows.

Significant energy transfer to electrons in relativistic e-ion shocks (εe~10%) in GRBs

also work by Heng and van Adelsberg (2008)

Colliionless shocks

In these systems colliionless shocks span a range of conditions: SNRs PWNs AGNs/GRBs

relativistic shocks: ✓ ✓ gamma-factor: 1 104-106 2-500nonrelativ. shocks: ✓ ✓electron-ion: ✓ ✓ pairs: ✓ ✓?(internal shock?) pairs+ions: ✓? ✓?magnetization: ~10-4-1 ~10-4-.1 ~10-9-104





Colliionless shocks

In these systems colliionless shocks span a range of conditions: SNRs PWNs AGNs/GRBs

relativistic shocks: ✓ ✓ gamma-factor: 1 104-106 2-500nonrelativ. shocks: ✓ ✓electron-ion: ✓ ✓ pairs: ✓ ✓?(internal shock?) pairs+ions: ✓? ✓?magnetization: ~10-4-1 ~10-4-.1 ~10-9-104

How?Investigate this using ab-initio particle-in-cell method


Open issues:What is the structure of collisionless shocks? Do they exist? How do you collide without collisions?

Particle acceleration -- Fermi mechanism? Other? Efficiency?

Generation of magnetic fields? GRB/SNR shocks, primordial fields?

Equilibration between ions and electrons?

Turns out that all questions are related, and particle acceleration is the crucial link

Understanding conditions when particles are accelerated can constrain astrophysical models

Particle acceleration:

Original idea -- Fermi (1949) -- scattering off moving clouds. Too slow (second order in v/c) to explain CR spectrum, because clouds both approach and recede.

In shocks, acceleration is first order in v/c, because flows are always converging (Blandford & Ostriker 78,Bell 78, Krymsky 77)

Efficient scattering of particles is required. Particles diffuse around the shock. Monte Carlo simulations show that this implies very high level of turbulence. Is this realistic? Are there specific conditions?

u u / r

B

ΔE/E ~ vshock/c

N(E) ~ N0 E-K(r)


From downstream, the upstream is approaching

From upstream, the downstream is approaching

Either crossing results in energy gainfirst order in velocity of the shock

E! = E + px!v

px = E/c

!E

E=

!v

c

How does this lead to power law?

for head-onkick

E = E0!j N = N0P

j log(N/N0)log(E/E0)

=log P

log !

N(> E)N0

=!

E

E0

"log P/ log !

n(E) = E(log P/ log !)!1 = Ek

Enew = Eold!

Particle acceleration:Flux of high energy particles crossing the shock:

Power law index:

n(E) = E(log P/ log !)!1 = Ek

Flux of high energy particles escaping through the downstream:

Fin =14n0c

Fesc = n0V2 = n0Vshock

r

Probability of escape: Pesc =Fesc

Fin=

4r

Vshock

c

Probability to remain: log P = log(1! Pesc) = log!

1! 4r

Vshock

c

"" !4

r

Vshock

c

Average energy gain: ! =E

E0= 1 +

43

r ! 1r

Vshock

clog ! ! 4

3r " 1

r

Vshock

c

r = 4for strong shock withk = !r + 2r ! 1

= !2

In the same range as CR spectrum (2.1-3). Very plausible source of nonthermal power-laws in the Universe

for relativistic shocks k=-2.2


Need to understand the microphysics of collisionless shocks

For this need plasma simulations

Is particle acceleration robust? When does it occur? What are the conditions?

Typically, it is assumed that CR streaming can generate waves that scatter particles. Chicken and the egg problem! Injection problem depends on shock structure.

Particle-in-Cell (PIC) method

PIC method (aka PM method):

•Collect currents at cell edges•Solve fields on the mesh (Maxwell’s eqs)•Interpolate fields to particle positions•Move particles under Lorentz force

The code: relativistic 3D EM PIC code TRISTAN-MP Optimized for large-scale simulations with more than 20e9 particles. Noise reduction, improved treatment of ultra-relativistic flows.Works in both 3D and 2D configurations. Most of the physics is captured in 2DMost of our results are now starting to be confirmed by independent groups

Commonly used in accelerator/plasma physics, and now starting to be accepted in astrophysics

Advances in computer hardware and better algorithms have enabled running large enough simulations to resolve shock formation, particle acceleration, and back-reaction of particles on the shock.

Most fundamental way to treat plasma physics without (m)any approximationsprice: have to resolve tiny and fast scales (plasma skin depth and plasma freq.)to be interesting, simulations have to be large

Problem setup

Simulation is in the downstream frame. If we understand how shocks work in this simple frame, we can boost the result to any frame to construct astrophysically interesting models.

(in these simulations we do not model the formation of contact discontinuity)

We verified that the wall plays no adverse effect by comparing with a two-shell collision.

γ =15 γ =15

c/3 (3D) or c/2(2D)

Use reflecting wall to initialize a shock

c/3(3D) or c/2(2D)

upstream downstreamshock

“Shock” is a jump in density & velocity

c c

c

Problem setup

Problem setup

γ =15

How collisionless shocks workWe need to decelerate the flow to have it “feel” the obstacle. We have two agents: electric and magnetic fieldsElectric fields: electrostatic “Sagdeev” solitonsworks for sonic M < 2.7anomalous dissipation needed

at higher Mach numbers, reflected particles generate “turbulence upstream”...

Magnetic fields: magnetic reflection slows down the plasmaat very high M reflected particles slow down the upstream to bring it to effective critical Mach number.

Turbulence generation by reflected particles is essential component of collisionless shocks. Turbulence can be electrostatic, or electromagnetic.

Turns out shocks can appear even without initial B field in relativistic flows. Field can be created from scratch.

B

E E

B

Properties of shocks can be grossly characterized by several dimensionless parameters: Alfven Mach

number Composition

Parameter space of collisionless shocks

MA =v

vA

! ! B2/4"

(# " 1)nmc2=

1M2

A

=!$c

$p

"2! c

v

"2=

#c/$p

RL

$2

r =mi

meMagnetization

Ms =v

cs

Sonic Mach number

!c =qB

"mc

!p =!4"q2n

#m

" 12


number Composition


MA =v

vA

! ! B2/4"

(# " 1)nmc2=

1M2

A

=!$c

$p

"2! c

v

"2=

#c/$p

RL

$2

r =mi

meMagnetization

Ms =v

cs

Sonic Mach number

We explored the parameter space for pair and e-ion plasmas in 2D and 3D.

Low magnetization: shock mediated by Weibel instability, which generates field > background

High magnetization: shock mediated by magnetic reflection, compressing background

True for both pairs and e-ions, relativistic and nonrelativistic shocks


number Composition


MA =v

vA

! ! B2/4"

(# " 1)nmc2=

1M2

A

=!$c

$p

"2! c

v

"2=

#c/$p

RL

$2

r =mi

meMagnetization

Ms =v

cs

Sonic Mach number

We explored the parameter space for pair and e-ion plasmas in 2D and 3D.

Low magnetization: shock mediated by Weibel instability, which generates field > background

High magnetization: shock mediated by magnetic reflection, compressing background

True for both pairs and e-ions, relativistic and nonrelativistic shocks

γ =15

B

E E

B

Efficiency of shock acceleration depends on shock mediation mechanism and the geometry of the field

We performed a survey of collisionless shocks in different parameter regimes to constrain the

conditions necessary for particle acceleration.

Relativistic pair shocksShock structure for σ=0.1

3D density 3D density

Shock structure for σ=0

Magnetized shock is mediated by magnetic reflection, while the unmagnetized shock -- by field generation from filamentation instability. Transition is near σ=1e-3 (A.S. 2005)

Magnetic field generation: Weibel instability Field cascades from c/ωp scale to larger scale due to current filament merging

Unmagnetized pair shock

Weibel instability generates subequipartition B fields that decay. Is asymptotic value nonzero? Competition between decay and inverse cascade (Chang, AS, Arons 08).

Density jump: MHD jump conditions

15%B field

Weibel instability

Weibel (1959)Moiseev & Sagdeev (1963)Medvedev & Loeb (1999)

Electromagnetic streaming instability. Works by filamentation of plasmaSpatial growth scale -- skin depth,

time scale -- plasma frequency

Relativistic pair shocksEstablishment of a self-propagating shock structure for σ=0

Magnetized shock is mediated by magnetic reflection, while the unmagnetized shock -- by field generation from filamentation instability. Transition is near σ=1e-3 (A.S. 2005)

3D density

Magnetic Energy

Density

<Magnetic Energy>

<Density>

min max

Relativistic pair shocksEstablishment of a self-propagating shock structure for σ=0

3D density

Magnetic Energy

Density

<Magnetic Energy>

<Density>

Upstream Waves

Shock compression

Generated fieldField decay

Upstream tangled filaments (turbulence)Downstream field

min max

3D shock structure: long term

50x50x1500 skindepths. Current merging (like currents attract). Secondary Weibel instability stops the bulk of the plasma. Pinching leads to randomization.

3D unmagnetized pair shock: magnetic energy






✓

Unmagnetized pair shock: particle trajectories

Magnetized shock is mediated by magnetic reflection, while the unmagnetized shock -- by field generation from filamentation instability. Transition is near σ=1e-4.

color: magnetic energy density

Unmagnetized pair shock: shock is driven by returning particle precursor (CR!)Steady counterstreaming leads to self-replicating shock structure

Shock structure for σ=0 (AS ’08)


x- px momentum space

x- py momentum space

Long term 2D simulation

Unmagnetized pair shock:

downstream spectrum: development of nonthermal tail!


Nonthermal tail deveolps, N(E)~E-2.4. Nonthermal contribution is 1% by number, ~10% by energy.

Early signature of this process is seen in the 3D data as well.

A.S. 2008, ApJ, 682, L5



Nonthermal tail develops, N(E)~E-2.4. Nonthermal contribution is 1% by number, ~10% by energy. Well fit by low energy Maxwellian + power law with cutoff.

Same process is seen in the 3D data as well. Easy to have ΔB/B>>1 when B=0!

Injection works self-consistently from the thermal distribution.

Particles that are accelerated the most, graze the shock surface

Magnetic filaments

Particle energy



Nonthermal tail develops, N(E)~E-2.4. Nonthermal contribution is 1% by number, ~10% by energy. Well fit by low energy Maxwellian + power law with cutoff.

Same process is seen in the 3D data as well. Easy to have ΔB/B>>1 when B=0!

Injection works self-consistently from the thermal distribution.



Density Magnetic Energy

Transition between magnetized and unmagnetized shocks:

σ=0.1

σ=10-3

σ=10-5

σ=0

Pair shocks: magnetization σ<10-3 is mediated by Weibel, larger magnetization -- magnetic reflection.



σ=0

Magnetic energy


Density



σ=10-3


B field



σ=10-1


Acceleration: σ<10-3 produce power laws, σ>10-3 just thermalize

B field

Magnetized perpendicular relativistic pair shock:

Shock structure σ=0.1 -- particle phase space

Shock structure is dominated by magnetic reflections as in 1D (Hoshino & Arons,92).

px

py

pz

flow

γ =15

B

E E

B

Magnetized perpendicular relativistic pair shock:

Shock structure σ=0.1 -- particle phase space

Shock structure is dominated by magnetic reflections as in 1D (Hoshino & Arons,92).

No nonthermal acceleration even in 3D.

px

py

pz

flow

γ =15

B

E E

B

Can magnetized pair shocks accelerate particles?

Investigate the dependence of acceleration on the angle between the background field and the shock normal (Sironi & AS 08): σ=0.1, γ=15; Find p-law index near -2.3

Observe transition between subluminal and superluminal shocks. Shock drift acceleration is important near transition.

Perpendicular shocks are poor accelerators.

45 0 15 30βsh/cosθ < 1 -- subluminalSelf-turbulence is not enough to exceed superluminal constraint

θ

!upstream < 32!/"In upstream frame need:

for acceleration

Acceleration mechanisms: “Fermi” vs shock-drift


Drift acceleration becomes increasingly important for higher obliquities.

0˚ 32˚

Acceleration mechanisms: “Fermi” vs shock-drift


Drift acceleration becomes increasingly important for higher obliquities.

0˚ 32˚

Returning particles and upstream waves0 degrees, subluminal 45 degrees, superluminal

Upstream oblique waves are caused by returning particles which are scattered by these waves

Behavior close to superluminality threshold

Fast and slow shocks

Upstream waves clearly related to returning particles

Accelerated particles head upstream along oblique field

High-energy particles drift along the shock front via drift!B






✓✓

Relativistic Electron-ion shocksWe explored electron-ion shocks up to mass ratio of 1000.

We observe electron-ion energy exchange in the shock. Electrons come close to equipartition with the ions. Behaves like pair shock! This helps to explain the high electron energy fraction inferred in GRB afterglows.

Fermi acceleration proceeds very similarly in unmagnetized e-ion shocks

Perpendicular e-ion shocks do heating, but not significant acceleration.

A.S. 2008, ApJ, 673, L39

Magnetic field growth and evolution

Returning particles cause filamentation far in the upstream region and cause growth of the scale and amplitude of the upstream field. This affects the rate of decay of the field in the downsream (longer wavelengths decay slower). 1% magnetization is not unreasobable (Keshet, Katz, A.S, Waxman 2008).

Hededal et al 04Medvedev 06

Relativistic Electron-ion shocks

We observe electron-ion energy exchange in the shock. Electrons come close to equipartition with the ions. Behaves like pair shock! This helps to explain the high electron energy fraction inferred in GRB afterglows.

Fermi acceleration proceeds very similarly in unmagnetized e-ion shocks

Perpendicular e-ion shocks do heating, but not significant acceleration.

A.S. 2008, ApJ, 673, L39

Energy in ions

Energy in electrons

Magnetic field growth and evolution

Returning particles cause filamentation far in the upstream region and cause growth of the scale and amplitude of the upstream field. This affects the rate of decay of the field in the downsream (longer wavelengths decay slower). 1% magnetization is not unreasobable (Keshet, Katz, A.S, Waxman 2008).

Hededal et al 04Medvedev 06

Electron heating is related to electron oscillation in ion filaments, and the longitudinal instability of the filaments.






✓✓✓

Pair shocks: magnetic field evolution


Can Weibel shocks generate enough field for downstream synchrotron emission?

Chang, AS, Arons (08) see decay below εB<10-4



we see growth of field energy and scale with time near shock, and slower decay downstream at 104 skindepths

Can Weibel shocks generate enough field for downstream synchrotron emission?

Returning particles cause filamentation far in the upstream region and cause growth of the scale and amplitude of the upstream field.

This affects the rate of decay of the field in the downsream (longer wavelengths decay slower).

1% magnetization is not unreasonable (Keshet, Katz, A.S., Waxman 2008).



Field evolution:

Without high energy particles:

With high energy particles:Keshet, Katz, AS, Waxman 08 see growth of field energy and scale with time near shock, and slower decay downstream at 104

Scale growth is caused by accelerated particles. Larger field

accelerates more particles -- bootstrapping!

CR accelerating shocks can cause a current of protons to propagate through the upstream. Bell (04, 05) found an MHD instability of CRs flying through magnetized plasma.

The interaction is nonresonant at wavelength << Larmor radius of CRs.

We simulated this instability with PIC in 2D and 3D (Riquelme and A.S. 08)

Saturation is due to plasma motion (VA ~ Vd,CR), or CR deflection; for SNR conditions expect ~10 field increase.

B field amplification Bell’s nonresonant CR instability

Cosmic rays

Cosmic ray current Jcr=encrvsh

CR accelerating shocks can cause a current of protons to propagate through the upstream. Bell (04, 05) found an MHD instability of CRs flying through magnetized plasma.

The interaction is nonresonant at wavelength << Larmor radius of CRs.

We simulated this instability with PIC in 2D and 3D (Riquelme and A.S. 08)

Saturation is due to plasma motion (VA ~ Vd,CR), or CR deflection; for SNR conditions expect ~10 field increase.


electrons

CRs

Bo

kmax c=2πJcr/B0γmax=kmaxVAlfven,0

Need magnetized plasma: ωci>>γmax

Magnetic energy growth

B field amplification: 3D runs Bell’s nonresonant CR instability

Field amplification of ~10 in SNRs can be due to Bell’s instability

(Riquelme and A.S. arXiv:0810.4565)


PIC simulations of shocks






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Virial

Magnetic reflection

Filamentation (Weibel) instability






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PWN

GRB

AGNjets

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SNRs

Virial

Acceleration for subluminal shocks; efficient e- heating

Fermi acceleration in unmagnetized

shocks

To be explored

Turbulence

T upstream

Inhomogeneities

Present relatively small 2D simulations show shock formation for a range of magnetizations (Mach numbers 3<M<500), mass ratios 20,100,1000

For high Mach numbers (>50), Weibel filamentation is still important (surprizingly).

Degree of heating is consistent with approaching equipartition with the ions at high Machs.

At fixed Mach, see smaller Te/Ti with v/c.

Two possibilities:

1) non-relativistic shocks depend on both Mach and v/c (or, on ωp/ωc)

2) we can be overestimating the Mach numbers if there is B field amplification upstream.

So what about supernova remnants (SNRs)? Mach 3 vs Mach 30, v=30000 km/s, mass ratio 100

x-px ions

x-px electrons

x-px electrons

x-px ions

Mach 30, mi/me=1000

Mach 3, mi/me=1000

Astrophysical implications: Pulsar Wind Nebulae (PWNe)


Shock acceleration in PWN implies low magnetization shock. σ=0.001-0.01 is inferred from modeling of the nebulae. This is a “transition” regime between magnetized and unmagnetized shocks -- expect Weibel instability to dominate the shock.

Equatorial shock occurs where the current sheet lies -- hence expect a weakly magnetized “equatorial wedge” -- consistent with shock physics.

At the moment pair composition could be ok, although other arguments suggest the presence of pair-ion plasma (A.S. & Arons 04).

Alternative -- reconnecting flow at the termination shock (Lyubarsky & Petri 07)

Gamma Ray Bursts

Very low magnetization σ=10-8 shocks can operate even in electron-ion plasma.

Electron heating to near equipartition with the ions implies that high electron energy fraction (εe=0.1) is not unreasonable. Magnetic fields near (εB=0.01) could also be generated. Can we see thermal component?

AGN and other jets

High magnetization perpendicular pair flows are unlikely to generate nonthermal particles through Fermi acceleration. Other physics needed? Not pure pair flows? Sheath flow?

Astrophysical Implications

Supernova Remnants

We see field amplification due to streaming CRs: Bell’s instability is part of the amplification puzzle.

Parallel shocks are more likely to accelerate particles than perpendicular shocks (e.g. SN1006?).

?

Conclusions

• Collisionless shocks exist from first principles!

• Shocks are mediated by Weibel instability or magnetic reflection

• Shock structure is controlled mainly by magnetization parameter: σ~0.001 is the transition region for pairs (for nonrelativistic shocks, shock speed also important)

• First evidence of self-consistent Fermi-type process operating in the unmagnetized shocks and nearly-parallel shocks. Efficiency ~ 1%, Energetics ~ 10% (for relativistic shocks).

• Magnetized perpendicular pair shocks do not efficiently produce nonthermal particles, weakly magnetized shocks and oblique shocks show more promise. Implications for geometry of PWN current layers and AGN jet fields.

• Do all accelerating relativistic shocks have to be weakly magnetized or parallel? Pulsar wind nebulae may have interestingly small σ to work as unmagnetized shocks.

• First signatures of back-reaction of self-consistently accelerated particles on the shock: generation of upstream turbulence and growth of field scale with time. Magnetic field amplification due to CR current (Bell’s instability).

Need to understand:

Effect of pre-existing and self-generated upstream turbulence on particle accleration, and field generation

Radiation properties of shocks: spectra, variability

Nonrelativistic shocks: injection fraction

Is 3D really the same as 2D?

More astrophysical applications: GRBs, AGNs, SNRs

Documents

Anatoly Spitkovsky (Princeton)home.physics.ucla.edu/calendar/Workshops/cmpd/cmpd_2009/..." sh! relativistic PWN GRB AGN jets Solar SNRs Virial Astrophysical collisonless shocks can: