Collisionless shocks in Gamma Ray BurstsCurrent results and future perspectives.

Århus, September 2005

Troels Haugbølletroels_h@astro.ku.dk

Dark Cosmology Centre, Niels Bohr Institute

Collaborators: Jacob Trier Frederiksen, Christian Hededal, Åke Nordlund

Contents

● Gamma Ray Bursts as extreme physics laboratories

●Simulation tool: A Particle-In-Cell code●Collisionless Shocks

● Current results:●Magnetic field generation●Particle Acceleration

● A Next Generation Particle-In-Cell code:●Design and preliminary results

The GRB Fireball Model

(Aloy et 99)

The GRB Fireball Model

Mean Free Path >> Shock extent => A collisionless shock

(Aloy et 99)

Low Density

High Density

>> 1

Low Density

>> 1

High Density

A collisionless =15 shock

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Collisionless shocks

● Collisionless shocks are abundant in the universe.They are found in:

● Gamma Ray Burst afterglows

● Internal shocks in AGNs

● Supernova remnants

● Shocks in the large scale structure

Collisionless shocks● The fluid picture, used

as the basis for large scale models, must be abandoned

● Collisions are mediated through the macroscopic electro magnetic field

● Charge separation occurs

● There is no local equilibrium

● We need to understand the physics on a more fundamental level!

Simulation tool:Relativistic Particle-in-cell code

Fields on mesh

Sampledparticles

● The code solves Maxwell's equations together with the Lorentz force on the particles

Magnetic Field Generation in Gamma Ray Burst Afterglows● Strong synchrotron like radiation is observed from Gamma Ray

Burst Afterglows● Two main components are needed to explain the radiation

● A strong magnetic field

● A powerlaw distributed population of electrons

● Obvious candidates for explaining the magnetic field fails:● The magnetic field of the interstellar medium

compressed in front of the shock is too weak by afactor of at least 1000

● The magnetic field generated by the central engine carried along with the plasma is too weak

Magnetic field generationThe Weibel instability

● An alternative explanation:

The magnetic field is generated in situ

● Two counter streaming collisionless plasma are susceptible to the Weibel instability

● In our simulations we are at rest in the outflow from the Gamma ray burst

(Here inflow =3, density jump=3)

The Weibel instability

The linear phase

The non linear phase

The Weibel instability

The linear phase

The non linear phase

The Weibel instability

The linear phase

The non linear phase

The Weibel instability for a two component plasma

The Weibel instability for a two component plasma

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First result: Magnetic field generation

● The magnetic field generated by the Weibel instability is● Containing up to 5% of equipartition● At least 1000 times stronger than

the shock compressed ISM field● Selfsimilar: The Fourier trans-form

of the field is a powerlaw● Is highly turbulent: B/B ~ 1● Transverse to the flow B∥/B⊥~ 0.1● Not possible to parameterize simply

with B (Frederiksen et al., 2002, 2004)

Second ingredient: Particle Acceleration● Strong synchrotron like radiation is observed from

Gamma Ray Burst Afterglows● Two main components are needed to explain the

radiation

●A strong magnetic field

●A powerlaw distributed population of high energy electrons

● The acceleration of the electrons is normally explained by invoking Fermi acceleration

● From test particle simulations it has been shown that the power law index for the electrons should universally be p=2.2

● Observations of GRB afterglows points to no universal p

Second ingredient: Particle Acceleration● Strong synchrotron like radiation is observed from

Gamma Ray Burst Afterglows● Two main components are needed to explain the

radiation

●A strong magnetic field

●A powerlaw distributed population of high energy electrons

● Fermi acceleration works by scattering particles across the shock in a recursive process

● If the “Weibel picture” is correct, themagnetic field is much weaker outsidethe shock front. How can the electronsbe backscattered then?

Potential acceleration of the electrons:

Electrons inside the Debye sphere are accelerated because of the ion Weibel instability.

(Hededal et al., 2004)

`

A Non-Fermi Power law acceleration scenario

Pow

er

Wavenumber JIon

v

v

d

N/d

log

(v)

Conclusions

● We have demonstrated the importance of the Weibel instability in understanding collisionless shocks● It creates a highly tangled, transverse magnetic field

containing up to 5% of equipartition energy● In electron-ion dominated plasmas electrons can be

accelerated/heated and a non-thermal tail is formed

● It is not possible to consider B,

e and p as separate

parameters, but rather a product of the same process physical process

The project has been successful so far...but the code is limited

● No radiative transfer

● No collisions

● No photon-plasma or other general particle interactions

● Only radiative (synchrotron) cooling

Challenges ahead – what we would like to model ● Collisionless shocks are prevalent; but still there are

interesting scenarios with collisions/ interactions playing an important role: ● Black hole coronas and inner jets ● The solar corona/space weathering

● Internal shocks in GRBs

● Pre-acceleration in Supernovae remnants for CR

Our answer: A next generation PIC code● Characteristics to keep in mind:

● Radiative cooling ● General scattering processes using discrete

methods

● Annihilation/pair creation; neutron decay

● A kinetic particle description with the EM-

fields on a mesh – but with general particles

First test of Compton interactionsA laser beam shining on a thin pair plasma

● To compare directly with theory we

● Fixed a pair plasma with T~0K● Injected a laser beam with E=10m

ec2

First test of Compton interactionsA laser beam shining on a thin pair plasma

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Differential cross section

Future outlook:

● Internal shocks in GRBs is a prime target● But many other interesting things to do – photon

transport makes it easier to compare with observations● The code in itself is the perfect infrastructure for

general particle/field simulations with general _microphysical_ interactions

For the dessert: Eye candy!

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