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Amir Levinson Tel Aviv University

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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  1. 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

  2. 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

  3. Photospheric emission GRB090902B

  4. Lazzati et al. 2009 Collapsar simulations Substantial fraction of bulk energy dissipates bellow the photosphere via collimation shocks

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

  6. Internal shocks Bromberg et al. 2011 Sub-photospheric shocks Morsony et al. 2010 t collisionless shocks G

  7. 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

  8. Under which conditions a RMS forms ? Radiation dominance downstream: aTd4 > ndkTd From jump conditions: numpc2u2  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

  9. 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

  10. 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

  11. Velocity profile for photon rich upstream Levinson + Bromberg 2008

  12. 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)-1u2 Optical depth inside shock is dominated by e pairs Velocity profile

  13. 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 ns)-1 ~ 109 n15-1 cm • microphysics is fully understood • cannot accelerate particles RMS

  14. 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

  15. 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

  16. Temperature profile behind a planar shock (no adiabatic cooling) Thermalization by free-free + double Compton Levinson 2012 Ts Td < Ts  = 0

  17. 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)

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

  19. 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

  20. Upstream conditions Example: adiabatic flow

  21. 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)

  22. 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

  23. Dependence on dissipation profile u=10, 0=100 u=10(/0)1/2 1 10 0.1 0.01

  24. Mildly relativistic shocks Uniform dissipation (u=const) 0.01 0.1 0.001

  25. Dependence on optical depth Uniform dissipation 1 0.1 0.01

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

  27. 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)

  28. 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)

  29. Non-equal spacing

  30. 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

  31. 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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