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MHD Dissipation in GRB Jets Jonathan McKinney Stanford Roger Blandford (Stanford), Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy.

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Presentation on theme: "MHD Dissipation in GRB Jets Jonathan McKinney Stanford Roger Blandford (Stanford), Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy."— Presentation transcript:

1 MHD Dissipation in GRB Jets Jonathan McKinney Stanford Roger Blandford (Stanford), Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy (Princeton), Ramesh Narayan (Harvard)

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

3 Evidence for Magnetized Jets 1 Toroidal Field: Confines and Stabilizes Jet Spine 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) 640x1600x640 Conclusion? Magnetized Jets Robust & Low Baryon-Loading Toroidal MHD 640x1600x640 (Mignone et al. 10) HD 2048 3 vs. 4096 3 HD (Wang et al. 08)

4 Evidence for Magnetized Jets 2 Swift Revolution: Sometimes Late-time Activity 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 Fermi Revolution: Sometimes Pair cut-off, SSC, Thermal Conclusion?: Large Radii Emis., Few Electrons, Low Entropy Zhang & Peer 2009 Abdo et al. (2009) GRB080916C OBrien et al. 06

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

6 Types of Magnetic Reconnection Very Slow to Very Fast: 1)Magnetic Diffusion 2)Sweet-Parker (Slow) 3)Tearing -> Plasmoids 4)Spontaneous Turbulent 5)Driven Turbulent 6)Petschek (Very Fast) 7)Relativistic Petschek Slow Sweet-Parker-like Plasmoids: Uzdensky, Loureiro, Huang, etc. Fast Petschek-like Spontaneous 3D Turb.: Lapenta & Bettarini 2011 Slow Sweet-Parker-like

7 Wind Launching GRB Jets 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) McKinney (2006) Z R Rezzolla et al. (2011) Sky & Telescope (Apr 2010) Wind Bucciantini et al.

8 Fully 3D GRMHD Sims McKinney & Gammie (2004), McKinney (2006), McKinney & Blandford (2009) 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 Dipolar

9 Fully 3D GRMHD Sims McKinney & Gammie (2004), McKinney (2006), McKinney & Blandford (2009) Dipolar Quadrupolar 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.

10 Field Order & Current Sheets McKinney & Blandford (2009) Field Polarity Matters (MRI?) Field Polarity Matters (MRI?) Jet Power drops by ~10x Jet Power drops by ~10x New Jet Baryon-Loading Mechanism New Jet Baryon-Loading Mechanism Dipolar Quadrupolar X Pause Play Skip

11 BZ vs. BP BP82 MT82 BZ77 Ghosh & Abramowicz (97) ; Livio, Ogilvie, Pringle (99) Ordered field threads disk (as boundary condition) ® -viscosity is assumed constant & small as from old local shearing box sims. Ignored trapping of flux by plunging region & assumed Pbh / a 2 McK (05) ; McK & Narayan (07) ; Komissarov & McK (07) ; Tchek+ (10) Turbulence leads to mass-loaded disk wind: ¡ bh jet À ¡ disk wind ® not constant reaching ® » 1 near BH Plunging region traps magnetic flux & BH spin generates hoop stress: P / 2n H/R » 0.3: Pbh>Pdisk for a>0.5 & H/R » 1: Pbh>Pdisk for a>0.9 19

12 Applications to GRBs 1 Setup: Collapsar Model 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)

13 Applications to GRBs 2 Problem: (Lithwick & Sari 2001, Piran 2005) Ultrarelativistic motion: ~ 400 (Lithwick & Sari 2001, Piran 2005) Afterglow Breaks: » 2-100 Standard MHD Jet Models give » 1 (Komissarov et al. 2009) Resolution: Stellar Break-Out Rarefaction Light curve modeling gives µ =2 { 100 Achromatic break in the light curve when ( µ) t 1 1 day10 days 100 days Tchekhovskoy, +, McKinney (2010) GRB 09032327 090328 18 090902B70 090926A90 Cenko+ 2010

14 Simulation setup Simulation setup MHD & Temperature=0 MHD & Temperature=0 Spinning compact object: Spinning compact object: Collimating wall of shape z / R Collimating wall of shape z / R Magnetization: ¾ 0 Magnetization: ¾ 0 Central black hole Wall star (image credit: Zhang)

15 32 1 0 Jet Break-Out BH star = 100 µ = 0.02 µ = 2 = 500 µ = 0.04 µ = 20 Tchekhovskoy, Narayan, McKinney (2010) log( ) Komissarov et al. (2010)

16 Deconfined jet: along field lines Stellar surface Numerical deconfined jet Analytic fully confined jet Just outside the star, the jet experiences an abrupt burst of acceleration: increases by ~5x and µ increase by ~2x. So, µ increases from ~2 to ~20. Just outside the star, the jet experiences an abrupt burst of acceleration: increases by ~5x and µ increase by ~2x. So, µ increases from ~2 to ~20. = 500 µ = 0.04 µ = 20 ¾ = 1 { Analytic fully unconfined jet (AT+ 2010)

17 Magnetized Shocks in GRB Jets Internal Shock w/ e =1 Reverse Shock Shock w/ e =1 Narayan et al. (2011) =10 =199 =0.01 =300

18 Generating Current Sheets

19 Jet Diss-Prompt: Striped Wind Chosen or Fast reconnection rate (Thompson 94, Lyubarsky+ 01, Spruit+ 02, Drenkhahn+ 02, Kirk+ 03, Giannios+ 06, Lyubarsky 10 ; Medvedev, Lyutikov) Chosen or Fast reconnection rate (Thompson 94, Lyubarsky+ 01, Spruit+ 02, Drenkhahn+ 02, Kirk+ 03, Giannios+ 06, Lyubarsky 10 ; Medvedev, Lyutikov) Usually 1D, assuming inefficient acc. Usually 1D, assuming inefficient acc. Too Fast: Significant dissipation inside photosphere Too Fast: Significant dissipation inside photosphere So inefficient non-thermal emission So inefficient non-thermal emission Fine-tuned reconnection rate Fine-tuned reconnection rate Fast recon. rate only once collisionless (McKinney & Uzdensky 2010) Fast recon. rate only once collisionless (McKinney & Uzdensky 2010) Little dissipation inside photosphere Little dissipation inside photosphere No fine-tuning required for rate No fine-tuning required for rate

20 Magnetic Reconnection for GRBs Motivating Points: 1) Collisional simulations: Collapse to Slow Sweet- Parker or Fast Plasmoid/Turb. recon.: <~0.01c (Uzdensky & Kulsrud 98,00) 2) Collisionless simulations: Very Fast Petschek: 0.1c–1c (Zenitani+, Hoshino+, etc.) 3) GRB Jets: Naturally Transition from Collisional to Collisionless at Large Radii Slow Sweet-Parker-like (Collisional) Fast Petschek-like (Collisionless)

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

22 Reconnection Switch Mechanism Radiation-dominated ( layer ¿ 1) Radiation-dominated ( layer ¿ 1) Compton Drag Resistivity Dominates Compton Drag Resistivity Dominates tot < 1 leads to fast collisionless recon. tot < 1 leads to fast collisionless recon. E

23 GRB Jet Solution 1 Jet Sim (B fp, r *, ) Striped wind (l, m) One-zone Recon Layer n, p, e +-,, Arbitrary ¿ Base thermal distrib. Solve Iterate for T, n pairs Compute other quants. (McKinney & Uzdensky 2010)

24 GRB Jet Solution 2 Fast Reconnection: Dpet=Dsp At r » 10 14 cm Coincides with ¿ » 1 Pairs reemerge as ¿ » 1 Leads to T » 10 8 K T drops once ¾ ¿ 1 Explored: Field Strength: B fp Magnetization: ¾ 0 Dynamo timescale: m Field multipole order: l (McKinney & Uzdensky 2010)

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


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