Relativistic photon mediated shocks

1. Relativistic photon mediated shocks Amir Levinson Tel Aviv University With Omer Bromberg (PRL 2008)

2. Motivation • Strong shocks that form in regions where the Thomson depth exceeds unity are expected to be radiation dominated. • Structure and spectrum of such shocks are different than those of collisionless shocks. • May be relevant to a variety of systems including: GRBs, microquasars, accretion flows, etc.

3. Long GRBs and collapsars Stellar core

4. Hypernovae: shock breakout Bow shock: source of keV photons r < 1011 cm Radiation dominated slow wind • shocks that form during shock breakout phase are expected to be radiation dominated. • Observational consequences (e.g., emission of VHE neutrinos, etc.) would depend on shock structure and population of nonthermal particles accelerated, if at all, at the shock front. Emission of High energy Neutrinos? Baryon poor fireball (BPJ) ~300 internal shocks: Source of high-energy protons ?

5. internal shocks: Radiation dominated? GRBs – post breakout external shock: r ~ 1015 cm collisionless slow wind • Shallow afterglow phase (SWIFT) → prolonged emission? • if true then implies extremely high radiative efficiency during prompt phase! • -naturally accounted for by pure e fireballs. Radiation dominated shocks formed on relevant scales can produce power law extension. Γ-ray emission Afterglow emission BPJ

6. Scattered photons Upstream Radiation dominated fluid Shock transition mediated by Compton scattering downstream Collisionless versus radiation dominated shocks Collisionless: mediated by collective plasma process characteristic scales: c/p , c/B Radiation dominated: mediated by Compton scattering characteristic scale: (Tne)-1

7. Upstream downstream Non-relativistic case ( β-<< 1) Weaver, Blandford/Payne, Lyubarski, Riffert Diffusion approximation is used. Equation of state prad=urad/3 provides a closure of shock equations.

8. Transmitted photon spectrum 1981

9. Upstream downstream Relativistic case ( Γ->1) • diffusion approximation invalid • equation of state prad=urad/3 invalid. closure of shock equations ?  pair production may be important

10. Basic equations (b)=baryons, ( ) = pairs, (r) = radiation In the Thomson regime

11. How to compute ? • Integrate kinetic equation over energy and angle and then compute the shock structure • Needs some scheme for the closure condition. • Use shock profile as input in the kinetic equations to calculate transmitted spectrum.

12. Shock profile Infinite, plane-parallel shock (Levinson/Bromberg, PRL 2008)

13. fluid rest frame downstream upstream Flux must be finite at singular point. Can be solved to yield at this “critical” point. Solve for net photon flux in fluid rest frame:

14. Perfect beaming particle dominated fluid far upstream radiation dominated fluid far upstream

15. (Radiation dominated unstream) Solution of moment equations. Closure: truncation at some order (blue=second order, red = third order) Shock structure

16. Velocity profile (Γ-=2)

17. Velocity profile (Γ-=10) Closure: Γ>>1 - two beam approximation (from upstream) Γ< 2 - truncation at some order (from downstream) iterate until two branches are matched

18. The photon spectrum – work in progress • Once the shock profile is known the spectrum can be computed by solving the transfer equation for the given profile, or performing MC simulations • The spectrum extends up to the KN limit in the shock frame, and is very hard above the thermal peak. • Preliminary results show that the equations have eigenfunctions of the sort A(τ) ν.

19. Preliminary results

20. Conclusions • Relativistic radiation mediated shocks are expected to form in regions where the Thomson optical depth exceeds unity. • The photon spectrum inside the shock has a hard, nonthermal tail extending up to the NK limit, as measured in the shock frame. For GRBs this may naturally account for a nonthermal spectral component extending up to tens of Mev. Doesn’t require particle acceleration! • The scale of the shock is a few Thomson m.f.p. This is typically much larger than skin depth and Larmor radii. Particle acceleration in such shocks would require diffusion length of macroscopic scale. • Implications for VHE emission? • e.g., site of prompt GeV photons? • production of TeV neutrinos during shock breakout is questionable. • May be relevant also to microquasars, accretion flows.