Resistive Magnetohydrodynamic
Simulations ofRelativistic Magnetic Reconnection
Seiji Zenitani
NASA/GSFC

Collaborators: Michael Hesse, Alex Klimas,
Masha Kuznetsova

Outline• Introduction• Resistive Relativistic MHD (RRMHD) Equations• Problem setup• Results– General features of relativistic Petschek reconnection– Shock structures– New shock structures– Dependence to resistivity models• SummaryMagnetic reconnection
in relativistic
astrophysical settings• Electron-positron pairs (andfew baryons)• Strong magnetic fields• Relativity plays a role
– + radiation, quantum …

1015GMagnetar flares

Lyutikov 2006

Pulsar magnetosphere

1012G

Spitkovsky 2006

Striped pulsar windCoroniti 1990

Current status of relativisticreconnection research (2010)
MHD models
Blackman & Field 1994

• Reconnection physics = a basic piece todiscuss high-energy plasma environments
around astrophysical objects

Huge gap

PIC simulations
Zenitani & Hoshino 2001

Lyutikov & Uzdensky
2003
Lyubarsky 2005

Tenbarge+ 2010

MHD simulations Two-Fluid
simulations
Watanabe &Yokoyama 2006
Zenitani+ 2010

This talk• Lyubarsky model isfavorable• Scale-free• Ideal for globalmodeling

Jaroschek+ 2004

Zenitani & Hoshino 2007
Bessho & Bhattacharjee 2007
Zenitani+ 2009
Hesse & Zenitani 20072009 Alaska
Zenitani & Hesse 2008
• Meso-scaleevolution• Particle acceleration• A lot of kinetic instabilities

Current status of
RRMHD simulation works• RMHD (Relativistic MHD) simulations: 1990s ~• RRMHD (Resistive Relativistic MHD) simulation is a frontier field
Reconnection work
• Watanabe &Yokoyama 2006––

Lax-Wendroff scheme
Early evolution• Zenitani+ 2010
–Shock structures

This talk
Watanabe & Yokoyama 2006Numerical work
• Komissarov 2007
–Time-split HLL scheme• Palenzuela+ 2009
–Semi-implicit scheme• Dumbser & Zanotti 2009–

Galerkin scheme

RRMHD equations
Continuity
Momentum

EnergyMaxwell eqs.
Virtual potentials to fix div B, E
(Munz ’00, Dedner ‘02)

Charge conservation
Ohm’s law(1) Isotropic MHD fluid
four velocity
momentum(2) Simplest Ohm’s law
energyenthalpy

Numerical scheme• Shock-capturing RRMHD scheme (e.g., Komissarov 2007)– Operator splitting for the stiff source term
– Two-step marching in the hyperbolic part
– HLL-type Riemann solver with v = ±c
• ~ Local Lax-Friedrichs (Rusanov) method with c– 2nd order slope limiter (MC)• With a primitive variable solver (Zenitani+ 2009a)– Every timestep, in all cells, we solve quartic equations

U: fluid conserved variables

V: primitive variables

Simulation setup• “Harris”-type configuration with anti-parallel magnetic fields+B0

Point-symmetric(180 -rotation)

Localized resistivity-B0

Upstream parameter

T = mc2

Alfvén Lorentz factor=4-γVx+γVx• Typical outflow Lorentz factor ~2• Online version: http://homepage.mac.com/zenitani/files/RRMHD_ux.movFeatures #1: Alfvénic outflow
Ux=γVxLocalmaxima

1Petschekoutflow

1
Nonrelativistic ←10→ Ultrarelativistic

Features #2: narrower exhaust
Opening angle

0.1

θPK
θ
V’A ∝ B’z = Bz/γout

0.01

Two-fluid

Nonrelativistic ←• Predicted by Lyubarsky 2005
• Narrower energy output channel

110Sigma (σ) → Ultrarelativistic

Features #3: faster rec. rate
0.2
0.15
0.1
0.05
00.1
Nonrelativistic ←110→ Ultrarelativistic

Features #4: enthalpy-flux dominated outflow

Matter flow

γnmc 2 v(↔ nmc v)

Bulk kinetic

γ (γ −1) nmc 2 v⎛ 12 ⎞⎜↔ nmv v⎟⎝ 2⎠

€ fluxEnthalpy

Γ €γpv
Γ −1⎛ 5 ⎞⎜↔ pv⎟⎝ 2 ⎠€

Poynting flux

22€c(E × B)
4π€€

• Faster reconnection rate, but€narrower energy output channel• Enthalpy flux improves the energy throughput (Zenitani+ 2009b)

Shock structures (1/2)
Out-of-plane current (Jy)
Plasmoid boundary SS (Ugai 1995)

Slow shock (Petschek 1964)
Intermediate shock(Abe & Hoshino 2001)
Fast shocks(Forbes & Priest 1983,Ugai 1987)

Shock structures (2/2)
log n

Low density
channelShock-heated
Joule-heatedWeak contact discon.
(Abe & Hoshino 2001)

New shock structures #1, #2
color:

Ux=γVxvector: ( Vx, Vz )(2) forward
Pressureslow shocks

Z(1) post-plasmoid
slow shocks
PressureX

New shock structures #3
color:Z

Ux=γVxvector: ( Vx, Vz )Diamond-shapedstructure

hocksetiademr
InteXTime-evolution of the plasmoid edge
color: Ux=γVx• Online version: http://homepage.mac.com/zenitani/files/RRMHD_diamond.mov

“Diamond-chain” structure• Condition : vedge (~0.9cA,in) > cs
• Mechanism should be universal• It will be found in nonrelativistic MHD simulations, too

color: Ux=γVx
shock
Intermediate~0.9cA,in
cfms ~ csGuide field effect
By• Consistent with previous
two-fluid results

Upstream ~0.5

Outflow ~1.5

ρc+-• Guide-field compression
and charge separation• Poynting-dominatedenergy flowDependence to the resistivity model• Spatially localized ==> Petschek reconnection• Uniform resistivity

Slow Sweet-Parkerreconnection• Current-dependent resistivity

Repeated plasmoidformation

Summary• RRMHD simulation of magnetic reconnection• Key results– General features• Faster rec. rate
• Petschek reconnection with narrower exhaust• Enthalpy-flux-dominated, Alfvénic outflow– A lot of shocks• Petschek slow shocks• Intermediate shocks• Post-plasmoid vertical shocks (new)• Reflected diamond-chain (new)– Resistivity model• Uniform : Slow Sweet-Parker reconnection• Current-driven : Plasmoid-mediated reconnection• Reference–Zenitani, Hesse, & Klimas 2010b ApJ, 716, L214

Coming

GEM challenge for relativistic astrophysics
RRMHD

Two-ﬂuid

Zenitani+ 2010b

Zenitani+ 2009aPIC

Zenitani & Hoshino 2007

+ some mathsoon

Thank you!