Analogy between laser plasma acceleration and GRB

G. Barbiellini(1)

F. Longo (1), N.Omodei(2), A.Celotti(3), M.Tavani (4)

(1) University and INFN Trieste (2) INFN Pisa (3) SISSA Trieste (4) INAF Roma & Roma2 University

(image credits to CXO/NASA)

Outline

Laboratory Wake Field acceleration Experimental results and relevant formulae Scaling with particle density n Compton Tails & GRB environment Stochastic Wake Field acceleration

Surface power and Stochastic Factor Applications

WakeField Acceleration

(Ta Phuoc et al. 2005)

WakeField Acceleration

(Ta Phuoc et al. 2005)

Laser Pulse tlaser = 3 10-14 sLaser Energy = 1 JouleGas Surface = 0.01 mm2

Gas Volume Density = 1019 cm3

Power Surface Density W= 3 1018 W cm-2

WakeField Acceleration

(Ta Phuoc et al. 2005)

Electron Spectrum

WakeField Acceleration

(Ta Phuoc et al. 2005)

Emitted Photon Spectrum

Collapsing compact object(Rapidly rotating BH + Disk)

Gamma-Ray Bursts in Space

An electromagnetic jet (I.e. photons) plays the role of the lab laser The Supernova Shell is the target plasma (at R~1015 cm, with n~109 cm-3) Stochasticity has to be taken into account (laser->not coherent radiation)

Supernova ShellWake Field Acceleration!

Explosion of a Massive

Star

Electromagnetic jets (photons, e+ e-)

SN explosion Accretion GRB

Accretion disk

Bright and Dim GRB(Connaughton 2002)

Q = cts/peak cts

BRIGHT GRB DIM GRB

The Compton Tail

Barbiellini et al. (2004) MNRAS 350, L5

r0 ~ n-1/3 1/2

b~ n-1/21/2

p~ n-1/2

Scaling relations

Scaling relations

V ~ r03 ~ n-1

Q+=enr03~n0

~n-1/3

Ep = 3/4 hc2 r0/p2

(1019) ~ 102

(109) ~ 2x105

(102) ~ 2x108

Scaling Relations

W

W Q

r04( / r0 )2

W(n) (1019 )n

10190.3n (W / cm2 )

Riding Wave

Pictorial View

Analogy Formulae (I)

Laser acceleration surface power and GRB surface power

22

33

22

2WCW

cmW

n10x5.1=tR

EcmW

n3.0==)SFA(

θ

ωσσ

γ

Stochastic factor = (plasma) x 1 s

Analogy Formulae (II)

Independent derivation: how to induce a collective phenomenon from many microscopic processes?

23

p2

22

p

T

222

n)eV(E10×3=tR

)Joule(E

E

E≈N

1=t

tR

N

θ

σλδ

θ

γ

γγ

γ

-

Consequences (I)

GRB Luminosity depends on environment:

nr-2x10=)x105(

n6cr

-=dtd

e2-

25e γ

γγ

Consequences (I)

GRB Luminosity depends on environment:

Effective Angle constrain by Jet opening angle generates a link between Epeak and Total Energy (~Amati, Ghirlanda, …)

nr-2x10=)x105(

n6cr

-=dtd

e2-

25e γ

γγ

25-2

jet2eff 22

R=≤ γ

λθθ

Consequences (II)

Large emission in the region with transition betwwenn low to high density value

Energy transmitted always in jet cone Assuming the afterglow produced by the prompt emission we

could calculate 2 from total energy

-0.5

isoE∝2θ

Consequences (III)

New formula for evaluating jet opening angle

5.0iso

4/3b

5.050

2/3

172

Entt

)z+1(10x2

=2

θ

Consequences (IV)

New relation among Epeak and Egamma

erg10x6E 49≈γ

Conclusions

Electron acceleration in a moderate density plasma (109 cm-3) similar to WFA acceleration produces many of the GRB properties

Luminosity is proportional to local density This efficient transformation of kinetic energy into

radiations ends when the surface power density crosses the threshold because of dilution over increasing surface.