1. Analogy between laser plasma acceleration and GRB
(image credits to CXO/NASA)
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

2. 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

3. WakeField Acceleration
(Ta Phuoc et al. 2005)

4. WakeField Acceleration
(Ta Phuoc et al. 2005)
Laser Pulse tlaser = s
Laser Energy = 1 Joule
Gas Surface = 0.01 mm2
Gas Volume Density = 1019 cm3
Power Surface Density W= W cm-2

5. WakeField Acceleration
(Ta Phuoc et al. 2005)
Electron Spectrum

6. WakeField Acceleration
(Ta Phuoc et al. 2005)
Emitted Photon Spectrum

7. Gamma-Ray Bursts in Space
SN explosion
Accretion
GRB
Electromagnetic jets
(photons, e+ e-)
Accretion disk
Explosion of a Massive Star
Collapsing compact object
(Rapidly rotating BH + Disk)
Supernova Shell
Wake Field Acceleration!
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)

8. Bright and Dim GRB Q = cts/peak cts (Connaughton 2002) BRIGHT GRB

9. The Compton Tail
Barbiellini et al. (2004) MNRAS 350, L5

10. Scaling relations
p~ n-1/2
b~ n-1/21/2
r0 ~ n-1/3 1/2

11. Scaling relations (1019) ~ 102 (109) ~ 2x105 (102) ~ 2x108 ~n-1/3
V ~ r03 ~ n-1
Q+=enr03~n0
(1019) ~ 102
(109) ~ 2x105
(102) ~ 2x108
~n-1/3
Ep = 3/4 hcg2 r0/p2

12. Scaling Relations

13. Riding Wave
Pictorial View

14. Analogy Formulae (I)
Laser acceleration surface power and GRB surface power
Stochastic factor = (plasma) x 1 s

15. Analogy Formulae (II)
Independent derivation: how to induce a collective phenomenon from many microscopic processes? -

16. Consequences (I)
GRB Luminosity depends on environment:

17. Consequences (I) GRB Luminosity depends on environment:
Effective Angle constrain by Jet opening angle generates a link between Epeak and Total Energy (~Amati, Ghirlanda, …)

18. 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

19. Consequences (III)
New formula for evaluating jet opening angle

20. Consequences (IV)
New relation among Epeak and Egamma

21. 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.