MHD Dissipation in GRB Jets

Jonathan McKinneyStanford

Roger Blandford (Stanford), Dmitri Uzdensky (Boulder), Alexander Tchekhovskoy (Princeton), Ramesh Narayan

(Harvard)

Outline

Evidence for Magnetized GRB Jets

MHD and Magnetic Reconnection

Simulations of GRB Jets

Prompt MHD Dissipation-Emission

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)

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

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

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

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.

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

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.

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

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

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)

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

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)

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)

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)

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

Generating Current Sheets

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

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)

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

Reconnection Switch Mechanism

• Radiation-dominated (tlayer¿ 1)

• Compton Drag Resistivity Dominates

• ttot < 1 leads to fast collisionless recon.

E

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)

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)

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