1. MHD Dissipation in GRB Jets
Jonathan McKinney
Stanford
Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy (Princeton), Ramesh Narayan (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
640x1600x640
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)
Toroidal MHD vs
HD (Wang et al. 08)
2048^3 vs. 4096^3 vs. 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
2048^3 vs. 4096^3 vs.
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
Say verbally:
1) Same as before, but do not drop any terms
2) Replaces ad hoc Viscosity (magneto-rotational instability – MRI)
Flux Ratios + Flow Lines + Wave Constraints F V

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

7. Launching GRB Jets Wind Wind General Issues: Major specific Issues: Z
McKinney (2006) Z R
Rezzolla et al. (2011)
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)
Wind
Bucciantini et al.
BH-BH: Clean GW signal – informs about gravity
astrogravs.nasa.gov/docs/catalog.html
Sky & Telescope (Apr 2010)
Wind

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

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

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

11. BZ vs. BP
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/ H2n
H/R» 0.3: Pbh>Pdisk for a>0.5 & H/R» 1: Pbh>Pdisk for a>0.9
Further, the reference to Ghosh & Abramowicz (1997) and Livio et al. (1999) should be balanced by discussions in McKinney & Narayan (2007).  The arguments made in McKinney & Narayan (2007) appear to include issues such as: a) GA97 + LOP99 assumed ordered field threads the disk, while simulations show no ordered field threads the disk in a steady-state.  This is because they treat the disk as a boundary condition, which is not a good approximation for a turbulent disk. b) GA97 + LOP99 assumed disk as boundary condition, while turbulent disk moves foot points around and mass-loads the disk to be heavily baryon-loaded.  So only the BH can have a clean electromagnetic jet that would allow a very relativistic jet.  The turbulence in the disk also leads to much of the field to be dissipated in reconnection so that the wind is more (or as much) gas pressure driven than magnetically driven. c) LOP99: Assumed constant \\alpha(r) from local shearing box calculations, which were (at the time) unresolved.  We now know that such simulations (with no net flux and no gravitational stratification) lead to smaller and smaller \\alpha as resolution increases. So they are irrelevant astrophysically. However, when vertical gravity (or sufficient vertical resolution across many scale heights) is included or one uses a global simulation/model (Krolik 2005 and Hawley & Krolik 2001 and Beckwith 2008 and McKinney & Narayan 2007), the \\alpha at large radii stays at around 0.1 and near the BH becomes 1.0.  So their assumptions of using local models was based upon poor models and inapplicable non-GR results.  Put another way, the field and gas pressure DO become equipartition near the BH (i.e. gas and magnetic pressures become comparable) unlike outside the ISCO. d) GA97 + LOP99: Ignored behavior of plunging region and hoop stresses at high spin (Komissarov & McKinney 2007, McKinney 2005, Tchekhovskoy, Narayan, McKinney 2010) that lead to significant enhancements of the flux near the BH. e) Overall, self-consistent simulations by Hawley's group and Narayan's group show that their assumptions were not good and that indeed the BZ effect can account for the most powerful radio loud objects and indeed the BZ effect is probably required to get a clean enough jet to explain the high Lorentz factor of such jets.  Any disk wind appears to only drive mildly relativistic (\\Gamma\\lesssim 3) jets due to the turbulent mass-loading of the field lines near the disk.
BZ77
BP82 19
MT82

12. Applications to GRBs 1 Setup: Result: 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 ( )

13. Applications to GRBs 2 Problem: Resolution: 090323 27 090328 18
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
”Achromatic break” in the light curve when (µ)t ≃ 1
Light curve modeling gives µ =2 { 100
1 day
10 days
100 days
GRB 
090902B 70
090926A 90
Cenko+ 2010
Tchekhovskoy, +, McKinney (2010)

14. Simulation setup MHD & Temperature=0 Spinning compact object: 
(image credit: Zhang)
MHD & Temperature=0
Spinning compact object: 
Collimating wall of shape z/ R
Magnetization: ¾0
Wall
star
Central black hole

15. Jet Break-Out log() µ = 2 = 500 µ = 20 1 2 3 µ = 0.02 µ = 0.041 2 3
log()
= 100
µ = 0.02
µ = 2
= 500
µ = 0.04
µ = 20
star BH BH
Tchekhovskoy, Narayan, McKinney (2010)
Komissarov et al. (2010)

16. Deconfined jet: along field lines
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  {
Numerical deconfined jet
Analytic fully unconfined jet (AT+ 2010)
Stellar surface
Analytic fully confined jet

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

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)
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

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

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

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

24. GRB Jet Solution 2 Fast Reconnection: Dpet=Dsp At r» 1014cm
Coincides with ¿» 1
Pairs reemerge as ¿»1
Leads to T» 108 K
T drops once ¾¿ 1
Explored:
Field Strength: Bfp
Magnetization: ¾0
Dynamo timescale: m
Field multipole order: l
(McKinney & Uzdensky 2010)

25. 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