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

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 s Laser Energy = 1 Joule Gas 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

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)

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

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

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

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

Scaling Relations

Riding Wave Pictorial View

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

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

Consequences (I) GRB Luminosity depends on environment:

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

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

Consequences (III) New formula for evaluating jet opening angle

Consequences (IV) New relation among Epeak and Egamma

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.