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MHD Dissipation in GRB Jets
Jonathan McKinneyStanford
Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy (Princeton), Ramesh Narayan
(Harvard)
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Outline
Evidence for Magnetized GRB Jets
MHD and Magnetic Reconnection
Simulations of GRB Jets
Prompt MHD Dissipation-Emission
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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)
Conclusion? Magnetized Jets Robust & Low Baryon-Loading
Toroidal MHD
640x1600x640 (Mignone et al. 10)
HD
20483 vs. 40963
HD (Wang et al. 08)
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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
Zhang & Pe’er 2009Abdo et al. (2009)
GRB080916C
O’Brien et al. 06
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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/CodeVF
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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-likePlasmoids: Uzdensky, Loureiro, Huang, etc.
Fast Petschek-like
Spontaneous 3D Turb.: Lapenta & Bettarini 2011
Slow Sweet-Parker-like
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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)
WindBucciantini et al.
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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 Quadrupola
r
Quadrupolar
Dipolar
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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.
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Field Order & Current Sheets
McKinney & Blandford (2009)
Field Polarity Matters (MRI?)
Jet Power drops by ~10x New Jet Baryon-Loading
Mechanism
Dipolar Quadrupolar
X
Pause
Play
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BZ vs. BP
BP82 MT82BZ77
• 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 / a2
• 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/ H
2n
H/R» 0.3: Pbh>Pdisk for a>0.5 & H/R» 1: Pbh>Pdisk for a>0.9
19
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Applications to GRBs 1Setup:• 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)
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Applications to GRBs 2Problem:
• 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
givesµ =2
{ 100
”Achromatic break” in the light curve when
(µ)t ≃ 1
1 day 10 days 100 days
Tchekhovskoy, +, McKinney (2010)
GRB 090323 27090328 18090902B 70090926A 90
Cenko+
2010
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Simulation setup
MHD & Temperature=0 Spinning compact object: Collimating wall of shape z/ R
Magnetization: ¾0
Central black hole
Wal
l
star
(image credit: Zhang)
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3210
Jet Break-Out
¡0:2r¤ 0:2r¤BH BH
star
= 100 µ =
0.02
µ = 2
= 500 µ =
0.04
µ = 20
Tchekhovskoy, Narayan, McKinney (2010)
log()
Komissarov et al. (2010)
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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.
= 500 µ =
0.04µ = 20¾ = 1
{
Analytic fully unconfined jet(AT+ 2010)
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Magnetized Shocks in GRB Jets
Internal Shock w/ e e=1
Reverse Shock Shock w/ e e=1
Narayan et al. (2011)
K
E
E E
2
final
sin
15j j
=10
=199
=0.01
=300
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Generating Current Sheets
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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) Usually 1D, assuming
inefficient acc. 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
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Magnetic Reconnection for GRBsMotivating 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)
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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
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Reconnection Switch Mechanism
• Radiation-dominated (tlayer¿ 1)
• Compton Drag Resistivity Dominates
• ttot < 1 leads to fast collisionless recon.
E
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GRB Jet Solution 1• Jet Sim (Bfp , r* , )
• Striped wind (l, m)
• One-zone Recon Layer
n, p, e+-, g , nArbitrary ¿Base thermal distrib.
• SolveIterate for T, npairs
Compute other quants.
(McKinney & Uzdensky 2010)
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GRB Jet Solution 2• Fast
Reconnection:Dpet=DspAt r» 1014cmCoincides with ¿» 1
• Pairs reemerge as ¿»1
• Leads to T» 108 K
• T drops once ¾¿ 1
• Explored:Field Strength: Bfp
Magnetization: ¾0
Dynamo timescale: mField multipole order: l
(McKinney & Uzdensky 2010)
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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