1. Les sursauts gamma : la phase des chocs internes.
Frédéric Daigne
Atelier POLAR – Annecy – 18 janvier 2008

2. Prompt emission — Internal shocks
R in meters

3. Variability of the lightcurve  Activity of the central engine
Prompt emission — Internal shocks
Internal shocks (Rees & Meszaros 94)
Variability of the lightcurve  Activity of the central engine
Matter ejection by the central engine : energy injection rate and/or mass injection rate can vary on a dynamical timescale (ms)  the final distribution of the Lorentz factor at the end of the acceleration phase can be highly variable  shock waves propagate within the relativistic ejecta = internal shocks GRB = emission of the shocked material
R in meters

4. Prompt emission — Internal shocks
Ejection : G2>G1
Ejection : G3>G2
Ejection : G1
Ris : internal shocks
Ris  G22 tvar,s cm
Gamma-rays
Gamma-rays
Obs.
Racc
GRB time profile
Rph
Relativistic ejecta : -Width  tw,s cm - Variable Lorentz factor (G≥100)
- Kinetic energy Lkin,4p  erg/s
Ris
Ris : internal shocks
Ris  G22 tvar,s cm

5. Prompt emission — Internal shocks : dynamics
Simple model : Validation using hydrodynamical simulations (relativistic, Lagragian, 1D in spherical symmetry) Daigne & Mochkovitch 2000
Daigne & Mochkovitch 1998

6. Prompt emission — Internal shocks : dynamics
The central source is ejecting relativistic matter from t=0 to t=tw : * Shell ejected at tejec : Lorentz factor Gmin » 1 * Shell ejected at tejec+tvar : Lorentz factor Gmax » 1
If contrast k = Gmax / Gmin > 1  shock at Rshock = f Gmin2 c tvar
tshock = tejec + 2 f Gmin2 tvar
with f ≈ k2/(k2-1) ≈ 1 for k > 2-3
(for simplicity, assume the two shells have same mass M) two shells merge :
* new mass 2M
* new Lorentz factor Gr ≈ (Gmin Gmax)1/2 = Gmin k1/2 * dissipated energy : e ≈ (Gmin + Gmax -2 Gr ) Mc * efficiency : fd ≈ (k0.5-1)2 / (1+k) ≈ 10% - 40% for k = 3-10

7. Lightcurve  source activity
Prompt emission — Internal shocks : dynamics
Shock : Rshock = f Gmin2 c tvar and tshock = tejec + 2 f Gmin2 tvar
with f ≈ k2/(k2-1) ≈ 1 for k > 2-3
shocked material : Lorentz factor Gr ≈ Gmin k1/2
Lightcurve  source activity
Observer time * arrival time of photons ta = t – R / c ≈ tejec * angular spreading Dta = R / (2 G2 c) ≈ tvar
Observer
Central source R
1 / G
DR = R ( 1- cos(1/G)) = R / (2 G2)

8. Prompt emission — Internal shocks : microphysics
Internal shocks : mildly relativistic
Shocked material : density r* ≈ 7 r energy density e* / c2 ≈ a few 100 MeV/p
Equipartition parameters :
Magnetic field eB B2/8p ≈ eB r* e* Electrons ee, z, p Density : z r* / mp
Energy density : ee r* e*
Distribution : n(Ge)  Ge-p for Ge>Gm Lorentz factor : Gm ≈ (ee/z) (mP/me) (e*/c2)
Another possibility : Large-scale magnetic field (central engine)

9. Prompt emission — Internal shocks : magnetic field
Large scale magnetic field : (Spruit, Daigne & Drenkhahn 01)
Trapped field : (if no reconnection)  magnetic energy = cst.
 “Passive” field (no dynamical effect)

10. Prompt emission — Internal shocks : magnetic field
Large scale magnetic field : (Spruit, Daigne & Drenkhahn 01)
Trapped field : (if no reconnection)  magnetic energy = cst.
 “Passive” field (no dynamical effect)
 “Active” field (dynamical effect)

11. Prompt emission — Internal shocks : magnetic field
Large scale magnetic field : (Spruit, Daigne & Drenkhahn 01)
Trapped field : (if no reconnection)  magnetic energy = cst.
 “Passive” field (no dynamical effect)
 “Active” field (dynamical effect)
BUT :  Reconnection can modifiy this picture Early reconnection : acceleration and then “passive” field Late reconnection : an alternative to internal shocks for the prompt emission ?  In shocks, a turbulent B seems necessary to accelerate particles…

12. Prompt emission — Internal shocks : radiative processes
Synchrotron / IC : ■ if z ≈ 1 : Gm ≈ : GRB = IC pb = low efficiency (low B is needed)
■ if z small : Gm is larger : GRB = synchrotron ; HE=KN efficiency is better
Global efficiency = f(dissipation) (10-40 %...) x ee (10%-50% ???) x f(rad) (close to 100% fast cooling) x f(BATSE) (close to 100% if syn)

13. Prompt emission — Internal shocks : pulses
Spectral evolution in GRB pulses :
■ Favors a continuous outflow (vs single shells with initial large separations, e.g. Kobayashi et al. 1997) This avoids to be dominated by the “curvature effect” (see Fenimore 1994) ■ Evolution of microphysics parameters ? (e.g. more electrons accelerated in violent shocks) Daigne & Mochkovitch 2003
Ryde & Svensson 2002 G m g
G1>G2 m

14. Prompt emission — Internal shocks: high energy emission
ANR project : high-energy gamma-ray emission from relativistic jets With Z. Bosnjak (IAP), G. Dubus (LAOG), B. Giebels (LLR) and F. Piron (LPTA)
An example :
Front
Evolution of the physical conditions in the shocked medium
Initial distribution of the Lorentz factor

15. Prompt emission — Internal shocks: high energy emission
ANR project : high-energy gamma-ray emission from relativistic jets With Z. Bosnjak (IAP), G. Dubus (LAOG), B. Giebels (LLR) and F. Piron (LPTA)
An example :
Lightcurves
Time dependant spectrum
Time integrated spectrum

16. Prompt emission — Internal shocks: high energy emission
ANR project : high-energy gamma-ray emission from relativistic jets With Z. Bosnjak (IAP), G. Dubus (LAOG), B. Giebels (LLR) and F. Piron (LPTA)
An other example : a more optimistic case for GLAST…
Lightcurves
Time integrated spectrum
Time dependant spectrum

17. Prompt emission — Internal shocks : polarization
Granot & Königl 2003 ; Granot 2003 ; Nakar, Piran & Waxman 2003
■ Synchrotron radiation : local polarization (with p ~ 2.5) : P ~ 75 %
■ Observation : averaging over a region ~ 1/G
■ Necessary conditions to reach a high observed polarization :
 peculiar field geometry (ordered field) or  peculiar geometry (off axis observation …) : not favored by statistics
If we exclude off-axis observations :
■ No large-scale magnetic field or dominant random field : a small polarization is expected (0 to a few %)
■ Dominant large-scale magnetic field : a larger polarization (~ %) can be expected. Warning : if the large-scale magnetic field is very large (s ~ 1 or more), internal shocks disappear (as well as the reverse shock : see Robert’s talk). Then, the emission has to be explained by magnetic reconnection in the outflow...

18. Prompt emission — Internal shocks : conclusion
Status of the model:
■Dynamics is well understood ■Microphysics is poorly understood (GLAST, SVOM, …)
■Many GRB properties are reproduced (variability, spectral evolution, …)
■The model can reproduce the diversity of the GRB population
■Some difficulties/problems: a low efficiency, the low-energy slope (see Ghisellini, Celotti & Lazzati 2000).
In the future :
■origin of « Amati » relation
■ Optical prompt emission
■Diagnostics from the HE emission
■Polarization ? ■…
R in meters