Amir Levinson Tel Aviv University Levinson+Bromberg PRL 08 Bromberg et al. ApJ 11 Levinson ApJ 12 Katz et al. ApJ 10 Budnik et al. ApJ 10 Nakar+Sari ApJ 10,11 Relativistic radiation mediated shocks: application to GRBs

Motivation In GRBs a considerable fraction of the outflow bulk energy may dissipate beneath the photosphere. - dissipation mechanism: shocks? magnetic reconnection ? other ? In this talk I consider sub-photospheric shocks 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 vastly different than those of collisionless shocks. Other examples: shock breakout in SNs, LLGRB, etc accretion flows

Photospheric emission GRB090902B

Collapsar simulations Lazzati et al Substantial fraction of bulk energy dissipates bellow the photosphere via collimation shocks

A model with magnetic dissipation Levinson & Begelman 13 Magnetic jets may be converted to HD jets above the collimation zone

Internal shocks Bromberg et al Morsony et al Sub-photospheric shocks collisionless shocks  

What is a Radiation Mediated Shock?  downstream energy dominated by radiation  upstream plasma approaching the shock is decelerated by scattering of counter streaming photons Upstream downstream Shock transition mediated by Compton scattering Radiation dominated fluid Scattered photons Shock mechanism involves generation and scattering of photons

Under which conditions a RMS forms ?  u > 4×10 -5 (n u /10 15 cm -3 ) 1/6 Radiation dominance downstream: aT d 4 > n d kT d From jump conditions: n u m p c 2  u 2  aT d 4 In addition, photon trapping requires: Diffusion time t D ≈ shock crossing time t sh   > 1/  u 

RMS versus RRMS Non-relativistic RMS small energy gain:  diffusion approximation holds. Used in most early treatments Zeldovich & Raiser 1967; Weaver 1976; Blandford & Pyne 1981; Lyubarsky & Sunyaev 1982; Riffert 1988 Relativistic RMS photon distribution is anisotropic energy gain large:   optical depth depends on angle:  cos  copious pair production Levinson & Bromberg 08; Katz et al. 10; Budnik et al. 10; Nakar & Sari 10,11; Levinson 12

Photon source: two regimes Photon production inside the shock (dominant in shock breakouts from stellar envelopes, e.g., SN, LLGRBs..) Photon advection by upstream fluid (dominant in GRBs; Bromberg et al ‘11) Upstream Photon production - ff Photon advection

Velocity profile for photon rich upstream Levinson + Bromberg 2008

Solutions: cold upstream (eg., shock breakout in SN) Numerical solutions – Budnink et al Analytic solutions - Nakar+Sari 2012 Shock width (in shock frame)  s =0.01(  T n u ) -1  u 2 Optical depth inside shock is dominated by e  pairs Velocity profile

Upstream downstream Shock transition mediated by collective plasma processes Upstream downstream Shock transition mediated by Compton scattering Radiation dominated fluid Scattered photons Collisionless shocks versus RMS Scale: c/  p ~ 1(n 15 ) -1/2 cm , c/  B ~ 3  (B 6 ) -1 cm can accelerate particles to non-thermal energies. scale: (  T n  s ) -1 ~ 10 9 n cm microphysics is fully understood cannot accelerate particles Plasma turbulence collisionless RMS

Detailed structure Shock transition – fluid decelerates to terminal DS velocity Immediate DS – radiation roughly isotropic but not in full equilibrium Far DS – thermodynamic equilibrium is established Upstream Immediate downstream T s, e rs Thermalization layer T d < T s shock transition Very hard spectrum inside shock Thermal emission with local temp. downstream

Thermalization depth Double Compton: τ′ DC = 10 6 Λ DC −1 (n u15 ) −1/2 γ u −1 Free-free: τ′ ff = 10 5 Λ ff −1 (n u15 ) −1/8 γ u 3/4 Photon generation: Bremst. + double Compton Thermalization length >> shock width

Temperature profile behind a planar shock (no adiabatic cooling) Thermalization by free-free + double Compton Levinson 2012 TsTs T d < T s  = 0

Spectrum inside the shock (cold upstream) Temperature in immediate downstream is regulated by pair production T s is much lower in shocks with photon rich upstream (as in GRBs) Budnik et al T s  200 keV h /m e c 2 shock frame

Prompt phase in GRBs: shock in a relativistically expanding outflow  s /r ph = (r/ r ph ) 2  -2 shock Shocked plasma Γ photosphere

Breakout and emission photosphere shock emerges from the photosphere and eventually becomes collisionless shells of shocked plasma that reach the photosphere start emitting time integrated spectrum depends on temperature profile behind the shock at the highest energies contribution from shock transition layer might be significant

Example: adiabatic flow Upstream conditions

Computation of single shock emission Integrate the transfer eq. for each shocked shell to obtain its photospheric temperature T ph (r s ) r ph rsrs TsTs r0r0 local spectrum of a single shell  I  (h /kT ph ) 4 e -(h /kT ph )

Time integrated SED: a single relativistic shock  u = const Uniform dissipation  0 =10 R 6 =10 2  u =2  u =10  u =5 Contribution from the shock transition layer is not shown From Levinson

Dependence on dissipation profile  u =10,  0 =100  u =10(  /  0 ) 1/

Mildly relativistic shocks Uniform dissipation (  u =const)

Dependence on optical depth Uniform dissipation

Multipole shock emission Single shock emission produces thermal spectrum below the peak. Multiple shock emission can mimic a Band spectrum

Several shocks with different velocities h (MeV) E E   Keren & Levinson, in preparation

Sum of 4 shocks (uniform velocity, equal spacing) h (MeV) E E   Keren & Levinson in preparation

Non-equal spacing

post breakout Shock becomes collisionless: particle acceleration nonthermal emission from accelerated particles possible scattering of photospheric photons by nonthermal pairs To be addressed in future work photosphere

Conclusions Relativistic radiation mediated shocks are expected to form in regions where the Thomson optical depth exceeds unity. Time integrated SED emitted behind a single shock has a prominent thermal peak. The location of the peak depends mainly on upstream conditions and the velocity profile of the shock. The photon spectrum inside the shock has a hard, nonthermal tail extending up to the NK limit, as measured in the shock frame. Doesn’t require particle acceleration! Multiple shock emission can mimic a Band spectrum