Two-Fluid Simulations ofRelativistic Magnetic Reconnection
in Electron-Positron Plasmas
Seiji Zenitani

Michael Hesse, Alex Klimas
NASA Goddard Space Flight Center(c) nps.gov

Outline• Introduction• Problem setup– Two-fluid model– Initial conditions• Simulation results– System evolution– 3 new features– Implications for the theories– Other issues• SummaryMagnetic reconnection
in relativistic
astrophysical settings• Electron-positron pairs (andfew baryons)• Strong magnetic fields• Relativity plays a role
– + radiation, quantum …

1015G

Magnetar flares

Lyutikov 2006Pulsar magnetosphere

1012G

Spitkovsky 2006

Striped pulsar windCoroniti 1990

Current status of relativisticreconnection works
MHD models

Blackman & Field 1994

Huge gap

Kinetic Simulations
Zenitani & Hoshino 2001

Lyutikov & Uzdensky
2003

Jaroschek+ 2004

MHD Simulation
Lyubarsky 2005

Watanabe &Yokoyama 2006

Tenbarge+ 2010
• Reconnection rate
(later in this talk)• Energy composition• Numericallyunstable

Two-Fluid
Simulations

Bessho & Bhattacharjee 2007
Zenitani & Hoshino 2007, 2008
Zenitani & Hesse 2008

Zenitani+2009a,b

Jaroschek & Hoshino 2009This work• Particle acceleration• Fast reconnection (R~0.x)• Drift-kink and Weibel
instabilities

Relativistic two-fluid modelContinuity (x 2)e+-e- interaction

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

viscousEquivalent
Ohm’s lawfour velocity

specific enthalpy

Fluid inertia Frictional resistivity

Recovery of primitive variables• Conserved variables• Primitive variables

Density

Proper density

Momentum
EnergyLorentz factor

Proper pressure
Flow 4-vector• Quartic equation of u = γv

G=Γ/(Γ-1)• We analytically solve the equation in all cells at every time step
• CPU-expensive fluid simulation

Simulation setup

Z

Localized friction= resistive spot

Upstream parameter

T = mc2

Alfvén Lorentz factor

=4X

-γvx

+γvx

• Consistent with previous PIC and MHD results• Four velocity u=γv : outflow ~2.x, max ~3.5
• Online version: http://homepage.mac.com/zenitani/files/2RMHD_ux.mov

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

-γvx

+γvx

• Long-term evolution (t=400)

Steady Petschek-typestructure

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

V’A ∝ B’z = Bz/γoutRelativistic (sigma=4)

Jy

Features #2: faster reconnection rate
• Normalized rate :Nonrelativistic ←→ Ultrarelativistic

Features #3: enthalpy-flux dominated outflow

B2Upstream~ outflow p8π
Matter flow

γnmc 2 v(↔ nmc v)

Bulk kinetic

γ (γ −1) nmc 2 v€ 12 ↔ nmv v
 2

€ fluxEnthalpyΓ €γpv
Γ −1

 5 ↔ pv
 2 €

Poynting flux

22€c(E × B)
4π€€
• Enthalpy flux (~ internal energy flux) carries outgoing energy€• Plasma pressure balances with the strong upstream magnetic pressureImplication for relativistic theory• Blackman & Field 1994 etc.

• Lyubarsky 2005

– Superfast reconnection R ~ 1– Slow reconnection R ~ 0.1– Lorentz contraction allows larger
energy output per cross section– The narrower exhaust etc.
slow down the energy output

γ2nmc2v~c• Our result~0.1c– Faster reconnection R ~ 0.x or 1– Relativistic enthalpy flux allows
larger energy output per crosssection~cγ2

Γ
pv
Γ −1

Implication for nonrelativistic theory• “Sweet-Parker”-type analysis

Outgoing energy flux

Bin nin, !in, pinvinvout"LBout!outpout

Bulk kinetic : Enthalpy flux

• Enthalpy-flux can not be neglected in the energy budget• Relativistic reconnection is an extreme sample

Role of the resistivity profile

No resistive spot

• Turbulent outflow with secondary islands– Biskamp 1986, Shibata & Tanuma 2001, Daughton & Karimabadi 2007,
Loureiro et al. 2007

• Inertial tearing mode?
– Zelenyi & Krasnosel’skikh 1979 (Coppi 1966)

Summary• Two-fluid simulations of relativistic magnetic reconnection• Key results– System evolution• Transition to steady Petschek-type structure• Narrower opening angle– Reconnection rate
• Faster in ultrarelativistic regime• Enthalpy flux is the missing piece of the standard theory– Other• The resistivity profile (resistive spot) plays a role

• References– Zenitani, Hesse, & Klimas 2009a ApJ, 696, 1385 (Main work)– Zenitani, Hesse, & Klimas 2009b ApJ, 705, 907 (Updates & guide field)