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A. MacFadyen & W. Zhang (NYU), Alexandria
(Magneto-) Hydrodynamics of GRB
Outflows
2D Afterglow JetRelativistic MHD Turbulence
arXiv:0902.2396
arXiv:0811.3638
A. MacFadyen Banff 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 ergeta = E/m > 100R = 1 = 3x10^10cm
n = 1 cm^-3
Blandford & McKee (1976)
Г >> 1
Self similarity
Fireball Acceleration
pressure Г-1
Log RLog R
AM & Zhang, Kobayashi, Piran & Sari (1999)
Required Resolution ~ 1/Г2
Transition to Non-relativistic
-3
-3/2
E = 10^52 erg
n = 1 cm^-3
Log (Г-1)
Log R
Erice, J. Wheeler School Andrew MacFadyen (NYU)
Please see talks by: Bucciantini, McKinney & Nagataki
AMR Collapsar Jet + Ni-56 rich Wind Magnetic Tower
Deceleration
• Relativistic E ~ Г2ρ R3 Г ~ R-3/2
• Jet “spreading” Г ~ 1/θjet
• Newtonian E ~ v2ρ R3 v2 ~ Г-1 ~ R-3
Erice, J. Wheeler School Andrew MacFadyen (NYU)
Collapsar vs. Magnetar
Uzdensky & AM (2007,2008)
Erice, J. Wheeler School Andrew MacFadyen (NYU)Uzdensky & AM (2006,2007), Kommisarov et al (2007), Bucciantini et al (2007), Dessart et al (2007)
Magnetic Tower
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Relativistic GRB Jet (AMR)
Erice, J. Wheeler School Andrew MacFadyen (NYU)
Adaptive Mesh Refinement (AMR) - Emery Step Test
Shear Flow Resolution
400
3200
51200
Smooth & Spherical
Clumpy & Spherical
Erice, J. Wheeler School Andrew MacFadyen (NYU)
Vorticity Generation
A ≡ (ρ1-ρ2)/(ρ1+ρ2)
ρ1
ρ2
∇P
∇ρ
ηt = k[u]Aη
Ultra-relativistic Vorticity and Shock DynamicsGoodman & MacFadyen (2008)
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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
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KH:1024^3 Rel. MHD
Mag. & Kin. Energy
Power Spectra
AG Jet Initial Conditions
• Blandford-McKee• Eiso = 1e52 erg
• no = 1cm-3
• Г = 23.1• Θjet = 0.2, 0.4
• Spherical
• Ro = 1.59e17 cm
• R/ΔR = 196608
• 4e10 zone equiv.R
θ
Г = 23.1
Text
2D GRB Blastwave
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2D Blastwave (energy)
Energy Spreading
Light Curves
Zhang & MacFadyen (2009)
Light Surface
Volume
A. MacFadyen JAS McGill 9/8/05
TM EOS
e=0.5((9θ2+4)0.5+3θ-2) θ≡P/ρ Ultrarelativistic 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 HydroConservation of mass momentum, energy
j momentum coupled to i through Lorentz Factor
Relativistic when W>1 AND/OR
A. MacFadyen IPAM UCLA 5/3/05
Method
• WENO 5th order (Jiang & Shu ,1996)
• SRHD characteristic stucture (Donat et al 1998)
• Runge-Kutta 3rd 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 School Andrew MacFadyen (NYU)
5th order accuracyMethod N L1 Error Convergence Rate
Alpha
CR acceleration (prelim)
Zrake et al (2009)
CR acceleration (prelim)
Zrake et al (2009)
A. MacFadyen NYU 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)
Zhang & MacFadyen (2009)
Zhang & MacFadyen (2009)
Blast Evolution
Zhang & MacFadyen (2009)
Spectra
Zhang & MacFadyen (2009)
2D Blastwave (density)
Zhang & MacFadyen (2009)