Physics of GRB Prompt emission

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

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. Basic Facts • g- ray flux: fg ~ 10-7 -10-5 erg cm-2 s-1 • eob. MeV • Cosmological distance: z=1  dL = 1028 cm  Liso,g = 4 p fg dL21050 – 1052 erg s-1 • Duration: few sec. • Variability: dt~ ms Example of a lightcurve (Thanks to Klaas Wiersema)

4. Why relativistic expansion ? • Variability: dt ~ 1ms  Source size: R0 = cdt ~ 107 cm • Number density of photons at MeV: • Optical depth for pair production gg e±: Creation of e±, gg fireball !

5. Why relativistic expansion ? • Photons accelerate the fireball. • In comoving frame: eco. = eob./G • Photons don’t have enough energy to produce pairs.

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

7. qG-1 R Estimate of G (2) Constraint on source size in expanding plasma: Rdt relation: QxQ/10x

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 g-rays.

9. Acceleration Coasting Self-similar: (Forward) shock GR GR0 GR-3/2 (R-1/2) Transition(Rev. Shock) Dissipation (Internal collisions,Shock waves) Stagesin dynamics of fireball evolution

10. Acceleration Coasting Self-similar: (Forward) shock GR GR0 GR-3/2 (R-1/2) Transition(Rev. Shock) Dissipation (Internal collisions,Shock waves) Stagesin dynamics of fireball evolution

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

12. Acceleration Coasting Self-similar: (Forward) shock GR GR0 GR-3/2 (R-1/2) Transition(Rev. Shock) Dissipation (Internal collisions,Shock waves) Stagesin dynamics of fireball evolution

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

14. v1, G1 v2,G2 dR0=cdt 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 R0

15. Acceleration Coasting Self-similar: (Forward) shock GR GR0 GR-3/2 (R-1/2) Transition(Rev. Shock) Dissipation (Internal collisions,Shock waves) Stagesin dynamics of fireball evolution

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

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

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

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

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

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

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

23. Spectrum at mild- high optical depth IC scattering by pairs: • Steep slopes in keV – MeV : 0.5 < a< 1 • epeak ~ MeV • High optical depth  Sharp cutoff at Gmec2 100 MeV

24. Low energy distribution: quasi (but not) Maxwellian • Steep power law above q • . Electron distribution: high compactness l’ = 250 q=0.08 q = elec. temp. (in units of mec2)

25. Spectrum as a function of compactness Estimate number of scattering required for thermalization: Spectrum dependence on the Optical depth  Compactness t± < few, l’≤few Optically thin spectrum t±>500, l’>105 Spectrum approach thermal Characteristic values – in between !!

26. Summary • Dynamical evolution of GRB’s: different phases • Resulting spectrum : Complicated Low compactness High compactness Acceleration Coasting Self-similar: Dissipation

27. q Estimate of G (Full calculation) • Given: Photons observed up to e1~100 MeV • Photons in the BATSE range (20 keV – 2 MeV): above MeV