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MHD Models of GRBs

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  1. MHD Models of GRBs Jonathan McKinney Stanford Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy (Princeton), RameshNarayan (Harvard)

  2. Outline Evidence for Magnetized GRB Jets MHD and Magnetic Reconnection Simulations of GRB Jets Prompt MHD Dissipation-Emission

  3. Evidence for Magnetized Jets 1 • Toroidal Field: Confines and Stabilizes Jet Spine • (Rosen et al. 99, Zhang et al. 05, Morsony et al., Wang et al. 08, Keppens et al. 09, Mignone et al. 10) 20483 vs. 40963 Toroidal MHD HD (Wang et al. 08) 640x1600x640 HD 640x1600x640 (Mignone et al. 10) Conclusion? Magnetized Jets Robust & Low Baryon-Loading

  4. Evidence for Magnetized Jets 2 • Swift Revolution: Sometimes Late-time Activity • (Di Matteo et al. 02, Gehrels, Beloborodov 08, Zalamea & Beloborodov 10) • Fermi Revolution: Sometimes Pair cut-off, SSC, Thermal • Conclusion?: Large Radii Emis., Few Electrons, Low Entropy O’Brien et al. 06 Abdo et al. (2009) GRB080916C Zhang & Pe’er 2009

  5. MagnetoHydroDynamics (MHD) • Fluid: Baryon-Energy-Momentum Conservation Laws • Maxwell’s Equations & Simplified Ohm’s Law (Mag. Flux Cons.) • MHD Applications • GRBs best, AGN/XRBs thin disks ok, RIAFs worst • Use Stationary Grad-Shafranov Equation? • Usually drop terms, Ad Hoc terms, 2D or 1D, No Stability Tests • Use Self-Consistent GR-MHD Model/Code V F

  6. Types of Magnetic Reconnection • Very Slow to Very Fast: • Magnetic Diffusion • Sweet-Parker (Slow) • Tearing -> Plasmoids • Spontaneous Turbulent • Driven Turbulent • Petschek (Very Fast) • Relativistic Petschek Spontaneous 3D Turb.: Lapenta & Bettarini 2011 Slow Sweet-Parker-like Slow Sweet-Parker-like Fast Petschek-like Plasmoids: Uzdensky, Loureiro, Huang, etc.

  7. Launching GRB Jets Z • General Issues: • BH Accretion vs. Magnetar • Growth of magnetic field • Power: - vs. EM Jets • Jet stability • Major specific Issues: • BH: Baryon loading (jet) • Magnetar: Magnetic stability (cavity) R Rezzolla et al. (2011) McKinney (2006) Sky & Telescope (Apr 2010) Wind Bucciantini et al. Wind

  8. Fully 3D GRMHD Sims • Issues: • Blandford-Znajek Works? • Unstable to Shear/Screw-Kink? • Unstable to Non-Dipolar Field? • Unstable to Disk Turbulence? • Setup: a=0.92 |h/r|» 0.2 • 512x256x64 & 256x128x32 etc. Dipolar Quadrupolar Quadrupolar Dipolar McKinney & Gammie (2004), McKinney (2006), McKinney & Blandford (2009)

  9. Fully 3D GRMHD Sims • Issues: • Blandford-Znajek Works? • Unstable to Shear/Screw-Kink? • Unstable to Non-Dipolar Field? • Unstable to Disk Turbulence? • Setup: a=0.92 |h/r|» 0.2 • 512x256x64 & 256x128x32 etc. Quadrupolar Dipolar McKinney & Gammie (2004), McKinney (2006), McKinney & Blandford (2009)

  10. Field Order & Current Sheets X Quadrupolar Dipolar Skip • Field Polarity Matters (MRI?) • New Jet Baryon-Loading Mechanism Play Pause McKinney & Blandford (2009)

  11. Applications to GRBs • Setup: • CollapsarModel • 2D GRMHD • Start with BH and collapsing star • Strong Ordered Magnetic Field • Realistic EOS • Neutrino Cooling (no heating) • Result: • Magnetic Switch Triggers Jet • BZ-effect drives MHD jet • Still no high Lorentz factors Komissarov & Barkov (2008-2009)

  12. Jet Diss-Prompt: Striped Wind • Chosen or Fast reconnection rate (Spruit 02, Giannios 06, Lyubarsky 10, etc.) • Too Fast: Significant dissipation inside photosphere • So inefficient non-thermal emission • Fine-tuned reconnection rate • Fast recon. rate only once collisionless (McKinney & Uzdensky 2010) • Little dissipation inside photosphere • No fine-tuning required for rate

  13. Magnetic Reconnection for GRBs Motivating Points: 1) Collisional simulations: Collapse to Slow “Sweet-Parker” or Fast Plasmoid/Turb. recon.: <~0.01c 2) Collisionless simulations: Very Fast Petschek: 0.1c–1c 3) GRB Jets: Naturally Transition from Collisional to Collisionless at Large Radii Slow Sweet-Parker-like (Collisional) Fast Petschek-like (Collisionless)

  14. Reconnection Switch Mechanism Very Fast Petschek-like (Collisionless) Thickness: Dpet Slow Sweet-Parker-like (Collisional) Thickness: Dsp Larger scale dominates smaller scale Fast EM dissipation starts when Dsp=Dpet (Validated by Princeton Plasma Physics Lab experiments. Need computer simulations.) E

  15. Reconnection Switch Mechanism • Radiation-dominated (tlayer¿ 1) • Compton Drag Resistivity Dominates • ttot < 1 leads to fast collisionless recon. E

  16. Review: • BH/Magnetar Launches Jet • BH Mass-Loading: Field Polarity • Jet Collimates inside star • Stellar Break-out: À 1 , » 20 • Current sheets (Stripes), but collisions -> Slow reconnection • Jet becomes collisionless once beyond Photosphere, triggering Fast reconnection • Prompt non-thermal emission + eventually Jet Breaks allowed