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Relativistic radiation mediated shocks: application to GRBs. 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. Motivation.

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## Amir Levinson Tel Aviv University

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**Relativistic radiation mediated shocks: application**to GRBs 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**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**Lazzati et al. 2009**Collapsar simulations Substantial fraction of bulk energy dissipates bellow the photosphere via collimation shocks**A model with magnetic dissipation**Magnetic jets may be converted to HD jets above the collimation zone Levinson & Begelman 13**Internal shocks**Bromberg et al. 2011 Sub-photospheric shocks Morsony et al. 2010 t collisionless shocks G**Scattered**photons Upstream Radiation dominated fluid Shock transition mediated by Compton scattering downstream What is a Radiation Mediated Shock? Shock mechanism involves generation and scattering of photons • downstream energy dominated by radiation • upstream plasma approaching the shock is decelerated by scattering of counter streaming photons**Under which conditions a RMS forms ?**Radiation dominance downstream: aTd4 > ndkTd From jump conditions: numpc2u2 aTd4 u > 4×10-5 (nu /1015 cm-3)1/6 In addition, photon trapping requires: Diffusion time tD ≈ shock crossing time tsh > 1/u**RMS versus RRMS**• Non-relativistic RMS • small energy gain: De/e<<1 • 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: De/e >1 • optical depth depends on angle: t a (1-b cosq) • copious pair production • Levinson & Bromberg 08; Katz et al. 10; Budnik et al. 10; Nakar & Sari 10,11; Levinson 12**Upstream**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) Photon advection Photon production - ff**Velocity profile for photon rich upstream**Levinson + Bromberg 2008**Solutions: cold upstream (eg., shock breakout in SN)**Numerical solutions – Budnink et al. 2010 Analytic solutions - Nakar+Sari 2012 Shock width (in shock frame) s=0.01(Tnu)-1u2 Optical depth inside shock is dominated by e pairs Velocity profile**Scattered photons**Upstream Upstream Radiation dominated fluid downstream downstream Shock transition mediated by collective plasma processes Shock transition mediated by Compton scattering Collisionless shocks versus RMS • Scale: c/p ~ 1(n15)-1/2 cm, c/B~ 3(B6)-1 cm • can accelerate particles to non-thermal energies. collisionless Plasma turbulence • scale: (T ns)-1 ~ 109 n15-1 cm • microphysics is fully understood • cannot accelerate particles RMS**Upstream**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 shock transition Immediate downstream Ts, ers Thermalization layer Td < Ts • Very hard spectrum inside shock • Thermal emission with local temp. downstream**Thermalization depth**Photon generation: Bremst. + double Compton Free-free: τ′ff = 105Λff−1(nu15)−1/8γu3/4 Double Compton: τ′DC= 106ΛDC−1(nu15)−1/2γu−1 Thermalization length >> shock width**Temperature profile behind a planar shock (no adiabatic**cooling) Thermalization by free-free + double Compton Levinson 2012 Ts Td < Ts = 0**Spectrum inside the shock (cold upstream)**shock frame Ts 200 keV h/mec2 Budnik et al. 2010 • Temperature in immediate downstream is regulated by pair production • Ts is much lower in shocks with photon rich upstream (as in GRBs)**Prompt phase in GRBs: shock in a relativistically expanding**outflow shock s/rph = (r/ rph )2-2 Γ Shocked plasma photosphere**Breakout and emission**• 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 photosphere**Upstream conditions**Example: adiabatic flow**Computation of single shock emission**Integrate the transfer eq. for each shocked shell to obtain its photospheric temperature rph rs r0 Ts Tph(rs) local spectrum of a single shell nIna (hn/kTph)4 e-(hn/kTph)**Time integrated SED: a single relativistic shock**Contribution from the shock transition layer is not shown Uniform dissipation u=2 u=5 u=10 u= const 0=10 R6=102 0.01 10 0.1 1 From Levinson 2012**Dependence on dissipation profile**u=10, 0=100 u=10(/0)1/2 1 10 0.1 0.01**Mildly relativistic shocks**Uniform dissipation (u=const) 0.01 0.1 0.001**Dependence on optical depth**Uniform dissipation 1 0.1 0.01**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**Keren & Levinson, in preparation nEn a n1.4 nEn Preliminaryresults 10-3 10-1 10-2 100 101 hn (MeV)**Sum of 4 shocks (uniform velocity, equal spacing)**Keren & Levinson in preparation nEn a n1.2 Preliminaryresults nEn 101 100 10-1 10-2 hn (MeV)**post breakout**photosphere • Shock becomes collisionless: • particle acceleration • nonthermal emission from accelerated particles • possible scattering of photospheric photons by nonthermal pairs To be addressed in future work**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

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