Relativistic Magnetic Reconnection
Overview
Seiji ZENITANI
NAOJ
Ackn: Masahiro Hoshino (U. Tokyo),Michael Hesse, Alex Klimas (NASA/GSFC)

Outline• 0. Tutorial & Introduction• 1. MHD results– RRMHD simulations– Two-fluid simulations• 2. Kinetic results– 2D reconnection– Another 2D instability: Drift-Kink instability– 3D evolution– Weibel instability• 3. Summary

0. Tutorial & Introduction

Magnetic reconnectionSun• MHD-scale phenomena• Re-configuration of magnetic field lines• Release of magnetic energy to plasmaenergy

Earth’s MagnetosphereJetJet

Basics properties in RXBin ρin Vin

LEnergy conservation

ContinuityδBout
ρout pout
VoutReconnection rate: model-dependent~ Mach number of Vin
inA,in~ Energy transfer rate

R~ V / c

Outflow speed ~ Alfvén speed

Vout ~ cA,in© H. Oda

MHD reconnection models• Sweet-Parker (SP) model (1958,1957)• Petschek (PK) model (1964)• Slow：R ~ (η/L)**0.5• Fast : R ~ 0.1

L• Plasmoid-mediated model (2009~)• Moderately fast : R ~ 0.01

Kinetic reconnection• Collisionless reconnection is fast: R ~ 0.1• It looks different from MHD fast (Petschek) reconnection• What makes reconnection fast?
• Electron dynamics (Hesse+ 1999) vs Hall effects (Mandt+ 1994)

Zenitani 2011 PoP

Daughton+ 2011 Nature Phys.

Particle motion around the RX site
Be-e-Bz

EySpeiser motion

No fluid closure forelectron/ion/MHD fluids

Speiser 1965 JGRMagnetic reconnection
in relativistic
astrophysical settings• Electron-positron pairs (andfew baryons)• Strong magnetic fields• Relativity plays a role
– + radiation, pair creation …

Gamma-ray flares

Tavani2011

Magnetosphere model

Spitkovsky 2006

Striped windCoroniti 1990

Current status of relativisticreconnection research (2014Q1)
MHD theories
Blackman & Field 1994
Lyutikov & Uzdensky
2003
Lyubarsky 2005
Tenbarge+ 2010

Comisso & Asenjo 2014

• Basic properties
are under debate• Theories have been discussed over decades• Many works came out after 2011 (Crab flare)
Kinetic (PIC) simulations
MHD
simulations
Watanabe &Yokoyama 2006
Zenitani+ 2010
Takahashi+ 2011
Mizuno 2013
Takamoto 2013
Baty+ 2013
• Ideal for global
modeling

Two-ﬂuidsimulations

Zenitani & Hoshino
2001-2008
Jaroschek+ 2004
Jaroschek & Hoshino 2009

Zenitani+ 2009

Liu+ 2011
Sironi & Spitkovsky
2011, 2014
Cerutti+ 2012-2014
Kagan+ 2013

• Meso-scaleevolution• Fast evolution• Particle acceleration

1. Fluid simulations

Resistive Relativistic MHD (RRMHD) eqs.

Continuity

Maxwell eqs.

Ohm’s law

Energy & Momentum

Resistive Relativistic MHD (RRMHD) eqs.
Watanabe & Yokoyama 2006, Komissarov 2007

Continuity
Momentum

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

Charge conservation
Ohm’s lawfour velocity

momentumenergyenthalpy

Relativistic Petschek
reconnection• Magnetization parameter• Relativistic Alfvén speed

Outflow 4-velocityaUjet=γVjet
caoL

imax

lmekhtsc we
P tfloou1

Zenitani+ 2010

1

10

Watanabe & Yokoyama 2006

Relativistic Sweet-Parker reconnection
Reconnection rateSPtheoryTakahashi+ 2011

SPryeothTransition to theplasmoid regime
Takamoto 2013

Shock, shock, and shocks...
• Shock-capturing code is essential
in the relativistic high-sigma regime
color:

Ux=γVxPlasmoid boundary SS

Petschek slow shock

Postplasmoidslow shocks• See also Zenitani & Miyoshi (2011)

Intermediate shock

Fast shock

Oblique-shock reflection

• Shock diamonds / Mach disk (airplane)• Recollimation shock (jet)• Oblique-shock reflection (reconnection)

http://www.aerospaceweb.org/question/propulsion/q0224.shtml
http://en.wikipedia.org/wiki/Shock_diamondRelativistic two-fluid model of pair plasmas
Zenitani+ 2009a,b
Barkov+ 2014

Continuity (x 2)e+-e- interaction

Momentum (x 2)
Energy (x 2)
Faraday’s law
Ampére’s law
advectionviscous

Out-of-plane
Ohm’s lawfour velocity

specific enthalpy

Fluid inertia Frictional resistivity

Large-scale evolution• Developed stage (t=200)

-γvx

+γvx

• Long-term evolution (t=400)

Steady Petschek-type
structure

Features #1: narrower opening angle
Semi-relativistic (sigma=0.4)• Opening angle becomesnarrower in the ultrarelativistic
regime (Lyubarsky 2005)

V’A ∝ B’z = Bz/γout

Relativistic (sigma=4)

Jy

Features #2: faster reconnection speed• Normalized rate :Nonrelativistic  UltrarelativisticFeatures #3: enthalpy-flux dominated outflow

B2Upstream~ outflow p8π
Matter flow

γnmc 2 v(↔ nmc v)

Bulk kinetic

2€γ (γ −1) nmc v# 12 &%↔ nmv v($ 2'€ fluxEnthalpy€

Poynting fluxΓ €γpvΓ −122# 5 &%↔ pv($ 2 '€c(E × B)
4π€€
• Enthalpy flux (~ internal energy flux) carries outgoing energy€• Plasma pressure balances with the strong upstream magnetic pressureRelativistic features of PK reconnection• #1 Narrower opening angle• #2 Faster reconnection rate R ~ 0.1-1• #3 Enthalpy-flux dominated outflow• Relativistic enthalpy flux (~internal energy flux) allows
larger energy output per cross section

γ2~c€

Γpv
Γ −1

2. Kinetic simulations

Kinetic model: Particle-In-Cell simulation
particle quantities：q, x, v

• 101 ~103 virtual particles in a cell• 1. Solve particle motion• 2. Update J,ρ
• 3. Advance EM ﬁeld (E, B)
cell properties：J,ρ, E, B

• Huge computational cost
• Detail plasma physics• particle acceleration• anisotropic distribution function

2D Particle-In-Cell (PIC) simulation• Fast reconnection and particle acceleration occurs• Online version: http://th.nao.ac.jp/MEMBER/zenitani/files/reconnection.mov

Energy spectra

Zenitani & Hoshino 2001, 2007

DC particle acceleration
via relativistic Speiser motion
ZEy
X~ -1

E2-B2>0
Zenitani & Hoshino 2001

YEy

Bz
Zenitani & Hoshino 2007

X

Large-scale dynamic evolution~ -3

Jaroschek et al. 2004

Sironi & Spitkovsky 2014

• Power-law indexs ~ -1(near acc. region), -2.4~3 (global)• Hard emission spectra (Jaroschek+ 2004, Cerutti+ 2012)

Another 2D problem:
Drift-Kink Instability (DKI)
ZB
J

Relativistic drift kinkinstability (DKI)

XY

Magnetic reconnection (RX)Relativistic Drift-Kink Instability• A kink-type instability, driven by the electron-positron counter-stream(Zhu & Winglee 1996, Ozaki+ 1996, Pritchett+ 1996)• Online version: http://th.nao.ac.jp/MEMBER/zenitani/files/RDKI.mov+Bx
e--Bx

e+

Density

Electric field

Energy spectra

(1)

(2)

EJ
Joule dissipation(3)

Plasmaheating

Zenitani & Hoshino 2005a3D evolution

DKI dominates

Turbulent
Zenitani & Hoshino 2008

Growth rates of the competing modes
RX (tearing; acceleration) vs DKI (plasma heating).
In the relativistic regime, DKI grows faster.

• PIC simulation• Theoretical estimate
RXDKI
τcγ

DKI

τcγ

RX
nonrela.
regimerelativistic
regimenonrela.

relativistic

T/mc2

thin RCS

T/mc2
thick RCS

Zenitani & Hoshino 2007

Field topology effect -- a guide field• Antiparallel field + Uniform guide field By

BBy• Magnetic tension stabilizes DKIBy• RX is relatively insensitiveBy

3D evolution with guide field
B

Hybrid oblique modes
between RX and the driftsausage mode (an oddparity cousin of DKI)

Hybrid modes trigger
secondary RX

Zenitani & Hoshino 2005 PRL

Energy spectra in 3D simulations

3D DKI
plasma heating
3D + guide field RX
particle acceleration

Magnetic topology changes
the destination of released energy!
Plasma heat vs non-thermal energy.

Zenitani & Hoshino 2005 PRL

3D evolution: mode competition

Liu+ 2011

Anti-parallel
plasma heating

Kagan+ 2013

Cerutti+ 2014

Guid-ﬁeld RX
particle accelerationNew frontiers: radiation & GR
Kinetic withrad. cooling

RRRMHD

Takahashi & Ohsuga 2013

GRRMHD
Bucciantini & Del Zanna 2013
Palenzuela+ 2013
Dionysopoulou+ 2013
Koide+ 201X
Jaroschek & Hoshino 2009
Cerutti+ 2013, 2014
Tamburini+ 2010

Summary• RRMHD, Two-fluid picture– Straightforward extension of nonrelativistic MHD reconnection– Some differences• Narrower exhaust, faster reconnection rate, heat-dominated flow
– Various shocks!

• Kinetic picture– Reconnection (RX) - DC particle acceleration– Drift Kink instability (DKI) - plasma heating– 3D evolution - mode competition RX vs DKI• Guide field changes the winner– Weibel instability (WBI) - yet another player• Forefronts– Large-scale 3D kinetic evolution– Radiation effect– GRRMHD: application to BH

Reconnection gallery
MHD theory

Lyubarsky 2005

Kinetic simulations

Zenitani & Hoshino 2007

Successful launch in the 1st decade (2001-2010)
A lot more to come in the 2nd decade (2011~)

Watanabe & Yokoyama 2006

RRMHD simulations

Zenitani+ 2009a

Two-ﬂuid simulations