A. MacFadyen & W. Zhang (NYU), Alexandria (Magneto-) Hydrodynamics of GRB Outflows 2D Afterglow Jet Relativistic MHD Turbulence arXiv: arXiv:

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)

Relativistic Blastwave 10^52 erg eta = E/m > 100 R = 1 = 3x10^10cm n = 1 cm^-3 Blandford & McKee (1976) Г >> 1 Self similarity

Fireball Acceleration pressureГ-1 Log R AM & Zhang, Kobayashi, Piran & Sari (1999)

Required Resolution ~ 1/Г 2

Transition to Non-relativistic -3 -3/2 E = 10^52 erg n = 1 cm^-3 Log ( Г -1) Log R

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) Please see talks by: Bucciantini, McKinney & Nagataki AMR Collapsar Jet + Ni-56 rich Wind Magnetic Tower

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

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) Collapsar vs. Magnetar Uzdensky & AM (2007,2008)

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) Uzdensky & AM (2006,2007), Kommisarov et al (2007), Bucciantini et al (2007), Dessart et al (2007) Magnetic Tower

Relativistic GRB Jet (AMR)

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) Adaptive Mesh Refinement (AMR) - Emery Step Test

Shear Flow Resolution

Smooth & Spherical

Clumpy & Spherical

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) Vorticity Generation A ≡ (ρ 1 -ρ 2 )/(ρ 1 +ρ 2 ) ρ1ρ1 ρ2ρ2 ∇P∇P ∇ρ∇ρ η t = k[u]Aη Ultra-relativistic Vorticity and Shock Dynamics Goodman & MacFadyen (2008)

Clumpy Medium

Jet & Shear

Jet & Clumps

Flying Pancakes

Misaligned

Oblique

Colliding Clumps

Shear Patches Kelvin-Helmholtz Instability

Kelvin Helmholtz Clouds Beverly Shannon

Big Whirls Have Little Whirls Joly et al (2008)

2D Relativistic HD KH

Twisting and Folding

KH:1024^3 Rel. MHD

Mag. & Kin. Energy

Power Spectra

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 = e10 zone equiv. R θ Г = 23.1 Text

2D GRB Blastwave

2D Blastwave (energy)

Energy Spreading

Light Curves Zhang & MacFadyen (2009)

Light Surface

Volume

A. MacFadyenJAS McGill 9/8/05 TM EOS e=0.5((9θ 2 +4) θ-2) θ≡P/ρUltrarelativistic Г=4/3 Newtonian Г=5/3 e= θ/(Г-1)

Conclusions (Mild) RMHD Turbulence has Kolmogorov-like spectrum GRB AG Jets take > 10 years to isotropize

Newton vs. Relativistic Hydro Conservation of mass momentum, energy j momentum coupled to i through Lorentz Factor Relativistic when W>1 AND/OR

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

Erice, J. Wheeler SchoolAndrew MacFadyen (NYU) 5 th order accuracy Method N L1 Error Convergence Rate

Alpha

CR acceleration (prelim) Zrake et al (2009)

CR acceleration (prelim) Zrake et al (2009)

A. MacFadyenNYU 1/27/06 Collapsar – Relativistic AMR (2005) rho ~ 10^9 g/cm^3 T ~ 10^10 K M_dot ~ 0.1 M_sun/s t_acc ~ 20 s R_in ~ 2 R_g AM, Zhang, Woosley (2005)

Alpha Zhang & MacFadyen (2009)

Blast Evolution Zhang & MacFadyen (2009)

Spectra Zhang & MacFadyen (2009)

2D Blastwave (density) Zhang & MacFadyen (2009)