1. 1 Physics of GRB Prompt emission Asaf Pe’er University of Amsterdam September 2005

2. 2 Outline  Dynamics  Basic facts  Why relativistic expansion ?  Constraints on the expansion Lorentz factor  Fireball hydrodynamics: Time evolution  The 4 different phases  Radiative Processes  Spectrum I: Simplified analysis  Complexities  Spectrum II: Modified analysis  Some open issues

3. 3 Basic Facts   - ray flux: f  ~ 10 -7 -10 -5 erg cm -2 s -1   ob.  MeV  Cosmological distance: z=1  d L = 10 28 cm  L iso,  = 4  f  d L 2  10 50 – 10 52 erg s -1  Duration: few sec.  Variability:  t~ ms Example of a lightcurve (Thanks to Klaas Wiersema)

4. 4 Why relativistic expansion ? ♦Variability:  t ~ 1ms  Source size: R 0 = c  t ~ 10 7 cm ♦Number density of photons at MeV: ♦Optical depth for pair production   e ± : Creation of e ±,  fireball !

5. 5 Why relativistic expansion ? ►Photons accelerate the fireball. ►In comoving frame:  co. =  ob. /  ►  Photons don’t have enough energy to produce pairs.

6. 6 Estimate of  Mean free path for pair production (   e ± ) by photon of comoving energy 100 MeV photons were observed  Idea: Optical depth to ~100 MeV photons ≤ 1 The (comoving) energy density in the BATSE range (20 keV – 2 MeV):

7. 7 Estimate of  (2) Constraint on source size in expanding plasma: R  -1 R  t relation: Q x  Q/10 x

8. 8 Some complexities ♦The observed spectrum is NOT quasi-thermal ♦Small baryon load (enough >10 -8 M  )  High optical depth to scattering Conclusion: Explosion energy is converted to baryons kinetic energy, which then dissipates to produce  -rays.

9. 9 Stages in dynamics of fireball evolution AccelerationCoastingSelf-similar: (Forward) shock Dissipation (Internal collisions, Shock waves) Transition (Rev. Shock) RR  R -3/2 (R -1/2 ) R0R0

10. 10 Stages in dynamics of fireball evolution AccelerationCoastingSelf-similar: (Forward) shock Dissipation (Internal collisions, Shock waves) Transition (Rev. Shock) RR  R -3/2 (R -1/2 ) R0R0

11. 11 Scaling law for an expanding plasma: I. Expansion phase Conservation of entropy in adiabatic expansion: Conservation of energy (obs. Frame): Combined together:

12. 12 Stages in dynamics of fireball evolution AccelerationCoastingSelf-similar: (Forward) shock Dissipation (Internal collisions, Shock waves) Transition (Rev. Shock) RR  R -3/2 (R -1/2 ) R0R0

13. 13 Scaling law for an expanding plasma: II. Coasting phase Fraction of energy carried by baryons: Baryons kinetic energy: Entropy conservation equation- holds

14. 14 Extended emission: Shells collisions The kinetic energy must dissipate. e.g.:  Magnetic reconnection  Internal collisions (among the propagating shells)  External collisions (with the surrounding matter)  Slow heating  Expansion as a collection of shells each of thickness R 0  R 0 =c  t v 1,  1 v 2,  2

15. 15 Stages in dynamics of fireball evolution AccelerationCoastingSelf-similar: (Forward) shock Dissipation (Internal collisions, Shock waves) Transition (Rev. Shock) RR  R -3/2 (R -1/2 ) R0R0

16. 16 Radiation ─Characteristic (synchrotron) observed energy - ─Characteristic inverse Compton (IC) energy- f~few Dissipation process: Unknown physics !!! Most commonly used model: Synchrotron + inverse Compton (IC) A fraction  e of the energy is transferred to electrons  B - to magnetic field Characteristic electrons Lorentz factor: magnetic field:

17. 17 Example of expected spectrum- optically thin case Synchrotron component Inverse-Compton Component

18. 18 Some complexities… Clustering of the peak energy Steep slopes at low energies Observational: Dissipation at mild optical depth ? Contribution from other radiative sources. Unknown shock microphysics (  e,  B …) Theoretical: From Preece et. al., 2000

19. 19 “The compactness problem” Optically thin Synchrotron – IC emission model is incomplete ! Synchrotron spectrum extends above  ob. syn ~0.1 MeV  Possibility of pair production Compactness parameter: High compactness  Large optical depth Put numbers: Or:  ob. syn ~0.1 MeV  High Compactness !!

20. 20 Example of optically thin spectrum Synchrotron component Inverse-Compton Component

21. 21 Physical processes – dissipation phase: Electrons cool fast by Synchrotron and IC scattering – ♦Synchrotron (cyclotron) ♦Synchrotron self absorption ♦Inverse (+ direct !) Compton ♦Pair creation:   e ± ♦Pair annihilation: e + + e -   ♦Contribution of protons –  production ( ’, high energy photons)

22. 22 Estimate of scattering optical depth by pairs Balance between pair production and annihilation Pair production rate – from energy considerations: At steady state: Pair annihilation rate: Conclusion: optical depth of (at least)  ± ≥ few is expected due to pairs!

23. 23 Spectrum at mild- high optical depth IC scattering by pairs: Steep slopes in keV – MeV : 0.5 <     peak ~ MeV High optical depth  Sharp cutoff at  m e c 2  100 MeV

24. 24 Electron distribution: high compactness  =0.08 Low energy distribution: quasi (but not) Maxwellian Steep power law above . l ’ = 250  = elec. temp. (in units of m e c 2 )

25. 25 Spectrum as a function of compactness Spectrum dependence on the Optical depth  Compactness  ± < few, l’≤few  Optically thin spectrum  ± >500, l’>10 5  Spectrum approach thermal Characteristic values – in between !! Estimate number of scattering required for thermalization:

26. 26 Summary  Dynamical evolution of GRB’s: different phases  Resulting spectrum : Complicated Low compactness High compactness AccelerationCoastingSelf-similar: Dissipation

27. 27 Estimate of  Full calculation) Given: Photons observed up to  1 ~100 MeV  Photons in the BATSE range (20 keV – 2 MeV): above MeV