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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. - PowerPoint PPT Presentation
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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.