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

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.

Long GRBs and collapsars Stellar core

Hypernovae: shock breakout Baryon poor fireball (BPJ)  ~300 slow wind Bow shock: source of keV photons r < cm Radiation dominated internal shocks: Source of high-energy protons ? Emission of High energy Neutrinos? 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.

GRBs – post breakout BPJ slow wind external shock: r ~ cm collisionless internal shocks: Radiation dominated? Afterglow emission Γ-ray emission 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.

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: (  T n e ) -1 Upstream downstream Shock transition mediated by Compton scattering Radiation dominated fluid Scattered photons

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

Transmitted photon spectrum 1981

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

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

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.

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

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

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

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

Velocity profile (Γ - =2)

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

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 .

Preliminary results

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.