1. Relativistic Explosions: AMR Hydrodynamics 1.RAM Code 2. Collapsars/GRB Central Engine 3. GRB Afterglow Blastwave A. MacFadyen (IAS, Princeton) W. Zhang (KIPAC, Stanford) astro-ph/0505481

2. A. MacFadyenBanff URJA 7/14/05 GRB/SN dynamics Relativity (SR & GR) Range of length scales ↔ resolution Rotation 2D/3D Magnetic Fields Nuclear Physics Neutrinos EOS

3. A. MacFadyenBanff URJA 7/14/05 RAM Special Relativistic Adaptive Mesh Refinement (AMR) Self Gravity w/ Pseudo GR potential Nuclear Reactions w/ photodisint. Neutrino Cooling (optically thin) EOS Based on ASCI/FLASH code Zhang & MacFadyen (2005)

4. A. MacFadyenBanff URJA 7/14/05 Method WENO 5 th order (Jiang & Shu,1996) SRHD characteristic stucture (Donat et al 1998) Runge-Kutta 3 rd order (Shu & Osher 1988) Also PPM and PLM reconstruction w/ minmod (Kurganov & Tadmor, 2000) F-WENO, F-PLM, U-PPM, U-PLM AMR from PARAMESH/FLASH2.3

5. A. MacFadyenBanff URJA 7/14/05 Riemann Problem “Shock Tube” Breakup of two constant states when barrier is removed

6. A. MacFadyenBanff URJA 7/14/05 Shock Tube Test

7. A. MacFadyenBanff URJA 7/14/05 1D Tests 100 zones W=70,711 V=0.999999999c Density error: a)3.9% b)2.4% c)8.9% d) 4.3% 400 zones t=0.4 F-WENOF-PLM U-PPMU-PLM Compression = (Г+1)/(Г-1) + Г/(Г-1)e, e≈W-1

8. A. MacFadyenBanff URJA 7/14/05 Riemann w/ Transverse Velocity 1 Left State: Vy=0 Right State: Vy = 0.99c 400 zones

9. A. MacFadyenBanff URJA 7/14/05 Riemann w/ Transverse Velocity 2 400 zones 3200 zones 51200 zones 1 level 4 levels 8 levels Left State: Vy=0.99c Right State: Vy = 0.99c

10. A. MacFadyenBanff URJA 7/14/05 TM EOS e=0.5((9θ 2 +4) 0.5 +3θ-2) θ≡P/ρ Ultrarelativistic Г=4/3 Newtonian Г=5/3 e= θ/(Г-1)

11. A. MacFadyenBanff URJA 7/14/05 Relativistic Blastwave 10^52 erg eta = E/m = 100 R = 1 = 3x10^10cm n = 1 cm^-3 Blandford & McKee (1976) Г >> 1

12. A. MacFadyenBanff URJA 7/14/05 Fireball Acceleration pressureГ-1 Log R MacFadyen & Zhang (2005), Kobayashi, Piran & Sari (1999)

13. A. MacFadyenBanff URJA 7/14/05 Required Resolution ~ 1/Г 2

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15. A. MacFadyenBanff URJA 7/14/05 Deceleration Relativistic E ~ Г 2 ρ R 3 Г ~ R -3/2 Jet spreading Г ~ 1/θ jet Newtonian E ~ v 2 ρ R 3 v 2 ~ Г-1 ~ R -3

16. A. MacFadyenBanff URJA 7/14/05 Transition to Non-relativistic -3 -3/2 E = 10^52 erg n = 1 cm^-3 Log (Г-1) Log R

17. A. MacFadyenBanff URJA 7/14/05 Relativistic Thin Shells Resolution required ΔR/R ~ 1/Г 2 R 0 ~ 5e16 cm, R max ~ 5e18 cm Г=20, ΔR ≈ R/25Г 2 ~ 1e13 cm ΔR/ R max ~ 1e-6 → (1e6) n zones Need AMR ~15 levels or more For Г=50 18 levels Parallel supercomputing (days-weeks on 128 processors)

18. A. MacFadyenBanff URJA 7/14/05 Spherical Implosion (Noh)

19. A. MacFadyenBanff URJA 7/14/05 2D Riemann Problem

20. A. MacFadyenBanff URJA 7/14/05 Emery Step

21. A. MacFadyenBanff URJA 7/14/05 2D Jet EOS in weak shocks

22. A. MacFadyenBanff URJA 7/14/05 GRB photons are made far away from engine. Can’t observe engine directly with light. (neutrinos, gravitational waves?) Electromagnetic process or neutrino annihilation to tap power of central compact object. Hyper-accreting black hole or high field neutron star (rotating)

23. A. MacFadyenBanff URJA 7/14/05 Pre-Supernova Density Structure Woosley & Weaver (1995) Bigger stars: Higher entropy Shallower density gradients Fukuda (1982)

24. A. MacFadyenBanff URJA 7/14/05 IF Two conditions occur (sometimes): 1. Failure of neutrino powered SN explosion a. complete b. partial (fallback) 2. Rotating stellar cores j > 3 x 10 16 cm 2 /s THEN Rapidly accreting black hole, (M~0.1 M  /s) fed by collapsing star (t dyn ~ 446 s/  ½ ~ 10 s) Disk formation  COLLAPSAR

25. A. MacFadyenBanff URJA 7/14/05  = 0.1 = 0.07 M sun /s = 1.3 x 10 53 erg/s Nucleon fraction Accretion Rate Msun/s

26. A. MacFadyenBanff URJA 7/14/05 Thermal vs. URCA neutrinos URCA 10 times more important

27. A. MacFadyenBanff URJA 7/14/05 Stanek et al., Chornock et al. Eracleous et al., Hjorth et al., Kawabata et al. GRB030329/ SN2003dh Smoking gun number 2 z = 0.1685 One of the brightest GRBs ever – HETE2

28. A. MacFadyenBanff URJA 7/14/05 Exceptionally --- bright fast high velocity radio bright Supernova simultaneous with the GRB (+- 2 days). L peak implies (again) ~0.5 solar masses of 56 Ni

29. A. MacFadyenBanff URJA 7/14/05 Exploding star   Supernovae Radioactive decay of Ni56 tail of Type II, ALL of Type I Type I compact star WD or W-R E exp -> adiabatic expansion not light no Ni56 -> no Supernova SN 1998bw & 2003dh need 0.5 M sun

30. A. MacFadyenBanff URJA 7/14/05 Disk Outflow Diagram MacFadyen (2003) Kohri, Narayan & Piran (2005)

31. A. MacFadyenBanff URJA 7/14/05 R star ~ 10 11 cm (3 lt-s) R hole ~ 10 6 cm (3e-5 lt-s)

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35. A. MacFadyenBanff URJA 7/14/05.. E jet = f M acc c 2 MHD T = 5.7 ms E = 5 x 10 50 erg/s E dep = 2.8 x 10 48 erg Jet Birth Thermal energy deposition focused by toroidal funnel structure f max ~.06 -.4

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41. A. MacFadyenBanff URJA 7/14/05 Relativistic Jet Simulations with RAM (2004)

42. A. MacFadyenBanff URJA 7/14/05 Relativistic Mixing When hot and slow after shocks e.g. recollimation

43. A. MacFadyenBanff URJA 7/14/05 B 2 /8π > ρc 2 for B ~ 10 12 G

44. A. MacFadyenBanff URJA 7/14/05 AG Jet Initial Conditions Blandford-McKee E iso = 1e52 erg n o = 1cm -3 Г = 23.1 Θ jet = 0.2, 0.4 Spherical R o = 1.59e17 cm R/ΔR = 196608 4e10 zone equiv. R θ Г = 23.1 Granot et al (2001)

45. A. MacFadyenBanff URJA 7/14/05 Blastwave Questions Lateral spreading: How fast? When? Afterglow Light curves Calorimetry Non-relativistic Transition: When? Spherical? Misaligned jets: When should we see them? Observations ↔ relativistic hydro lab

46. A. MacFadyenBanff URJA 7/14/05 Jet Spreading

47. A. MacFadyenBanff URJA 7/14/05 Decelerating Blastwave R θθ R

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86. A. MacFadyenBanff URJA 7/14/05 Ramirez-Ruiz & AM (2005) Ayal & Piran (2001)

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89. A. MacFadyenBanff URJA 7/14/05 Conclusions New SR AMR code RAM Microphysics:photodis., neutrinos, EOS 1D fireball acceleration Transition to Non-Relativistic BM Collapsar: BH + jet inside star Thin shells require high resolution 2D jet spreading

90. A. MacFadyenBanff URJA 7/14/05 Lateral Expansion

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92. A. MacFadyenBanff URJA 7/14/05 GRB 980425

93. A. MacFadyenBanff URJA 7/14/05 long GRBs from rotating WR stars. t engine > t escape Need SN failure & angular momentum –Low metallicity, binary can help SN IF nickel is made. GRB/SN association. Type Ibc. SN/GRB ratio may depend on angular momentum. “Nickel wind” can explode star -> hypernova –H env. Type II (no GRB), no H Type I + GRB Relativity important for death of stars like Eta Car. – needs high resolution. Magnetic processes may power jet/explosion. Fallback -> asymmetric SN, very long GRBs.

94. A. MacFadyenBanff URJA 7/14/05 Observations of GRB/SN Need to consider ultra-relativistic stellar explosions Range of length scales 1e6 to 1e18 cm Need relativistic hydro coupled to stellar microphysics Need to resolve ΔR/R ~ 1/Г 2

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96. A. MacFadyenBanff URJA 7/14/05 Recent calculations by MacFadyen and Zhang Model T16A

97. A. MacFadyenBanff URJA 7/14/05 Model He15B3 – different j-distribution

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105. A. MacFadyenBanff URJA 7/14/05 Accretion rate - rapid decline after 4.5 sec