RelativisticReconnection:radiativeand3Deffects

GregWernerDmitriUzdenskyVladimirZhdankinMitchBegelman(CUBoulder)SashaPhilippov(UCBerkeley)

UsingPICcodes:ZeltronTristan-MP

Relativisticreconnectioninpairplasma

Howare-reconnectiondynamics/energetics-andNTPAaffectedby:-lengthinthe3rddimension(z);i.e.,3D-ness-guidemagneticfield-externalinverseComptoncooling?

Bonus:CodeComparison

Reconnection’smainjob:magneticfieldenergy->particle/plasmaenergy

B0¤¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤Jz

-Jz

Reconnection->particleenergization/NTPA->radiation

Maxwellian with same average energy as final (green) distribution.

power-law

Evolution of background particle energy spectrum during reconnection

(The Lorentz factor ϒ is used interchangeably with particle energy ϒmc2.)

(observable)externalinverseCompton(IC)radiation

abovefrom2Dsimulations(e.g.,Sironi&Spitkovsky2014,Guoetal2015,Werneretal2016)

NTPA=NonthermalParticleAccelerationobservationaldiagnostic

softphoton

upscatteredphotonelectron/positron

σ h =B02

4πh≈

B02

4π (4nbTb )= 25,100

ReconnectionparametersUpstreamParameters:pairplasmanb,Tb,B0,Bgz(guidefield)Dimensionlessparameters:Tb/mec2>>1(ultrarelativistically-hot)

Howdotheseparametersaffectreconnection?Specifically:-energetics-NTPA

nominallengthscale:Systemsize:Lx,Ly,LzLx/σρ0=40(3D)–320(2D)Ly/Lx=2Lz/Lx=varying(2D->3D)

σ =B02

4πnbmec2>>

Tbmec

2

Upstream:nb,Tb,B0,Bgz

n

(relativisticreconnection)

Bgz/B0=0,0.25,0.5,1,2(guidefield)

relativisticreconnection:relativisticoutflows,significantenergization

ρ0 =mec

2

eB0,ρc =σρ0

Later:varyinverseCompton(IC)radiativecooling

Focusontwo“outputs”ofreconnection:basicdynamics/energetics,andNTPA

reconnectionrate,magneticenergydissipation,plasmoidformation,etc.

strongICcoolingtotalmagneticenergy

transverse/in-planemagneticenergy

radiatedenergy

plasma(kinetic)energy

guidemagneticenergy

Focusontwooutputsofreconnection:basicdynamics/energetics,andNTPA

NTPA:(shownhere,forweakICcooling)

particleenergyspectra photonenergyspectra

Inthefollowing,variousinputparameterswillbevaried(Bgz,Lz/Lx,ICcooling)withoutputs(dissipatedmagneticenergyandNTPA)shown.

-2->-(2-1)/2=-0.5

VaryLz/Lx(3D-ness)andBgz/B0andseewhathappens...

3Deffects:doesLz/Lxaffectreconnection?

Inparticular,doestherelativisticdrift-kinkinstability(RDKI)inhibitparticleacceleration?Here,guidemagneticfieldmaybeimportant:itinhibitsRDKI.

fromZenitani&Hoshino,2008:

However,morerecentsimulations(e.g.,Sironi&Spitkovsky2014,Guoetal2015,Werner&Uzdensky2017)havesuggestedthatparticleaccelerationisrobustto3Deffects.

Bgz/B0

DespitesignificantRDKI,2Dand3DreconnectionhavesimilarreconnectionratesandNTPA.

x!

y!

z!

|Je|/enbc!

2 !

1 !

0 !

Bxinthex-zreconnectionmidplane

RDKI

3D,Lz=Lx,Bz=0

3Dcurrentsheetevolution

Energeticsof2Dand3Dreconnectionaresimilarregardlessofguidefield(forlater:guidefieldhasasignificanteffect)

Energyinin-planeB

σh=25

And2Dand3Dparticlespectraaresimilar!

Lx=40σρ0Ly=80σρ0

Nonthermalaccelerationremainsrobustfrom2Dto3D!Also,alittleguidefieldBgzhardlydisturbsacceleration.

Electron/Positronenergyspectra

σh=25

Compressingplasmoids

n/nb

Duringreconnection,thein-planemagneticfieldcompressesplasmoids.Whenthere’saguidefield,thatguidefieldrestscompression.Thisslowsreconnectionandinhibitsparticleacceleration.

Guidefieldnotonlyslowsreconnectionrate,butsteepenstheNTPApowerlaw.

Guidefieldslowsreconnection,dissipateslessmagneticenergy(guidefieldresistscompression).

σ h,eff =B

0

2 / 4πhparticle +Bz

2 / 4π

σh=25

Reconnectioninabathofsoft(low-energy)photons

externalinverseCompton(IC)radiation

softphoton

upscatteredphotonelectron/positron

Highenergyelectrons(orpositrons)scatterofphotons,emittinghighenergyphotons,andexperiencesradiationreaction(radiaction)force.IfUphisthephotonenergydensity,thenthepowerloss,foranelectronwithγmec2is:

γ rad =3(0.1)eB04σ TU ph

Prad =43σ TcU phγ

2

Pacc = (0.1)eB0cPowergain(accel.)inthereconnectionelectricfieldE=0.1B0:

These2forces(powers)balanceforγ=γrad:

Particlescan’tgainmuchmoreenergythanthis.

ReconnectionsetupwithphotonbathUpstreamParameters:pairplasmanb,Tb,B0,Bgz(guidefield),Uph(softradiationbathenergydensity)Dimensionlessparameters:Tb/mec2>>1(ultrarelativistically-hot)

Howdotheseparametersaffectreconnection?

γ radσ

=1σ

3(0.1)eB04σ TU ph

nominallengthscale:Systemsize:Lx,Ly,LzLx/σρ0=40(3D)–320(2D)Ly/Lx=2Lz/Lx=varying(2D->3D)

σ =B02

4πnbmec2>>

Tbmec

2

σ h =B02

4πh≈

B02

4π (4nbTb )= 25,100

Upstream:nb,Tb,B0,Bgz,Uph

n

(relativisticreconnection)

Bgz/B0=0,0.25,0.5,1,2

relativisticreconnection:relativisticoutflows,significantenergization

ρ0 =mec

2

eB0,ρc =σρ0

γradmec2istheenergyatwhichaccelerationbyreconnectionEequalsdecelerationbyICradiationreaction.

nominalreconnectionrate

ICscatteringdoesn’taffectbasicreconnectiondynamicsverymuchγrad=∞(nocooling) γrad=2σ(strongcooling)

color=plasmadensity(normalizedtonb)

ICcoolinghaslittleeffectonmagneticenergydissipation,reconnectionrate

σh=100,Bgz=B0/4

Strongcoolingdoesn’taltertheamountofmagneticenergytransferredtoparticles...butstrongcoolingmeansparticlespromptlyradiatethatenergy.

ICcoolingchangesparticlespectrasignificantly:noisy,steeper

σh=100,Bgz=B0/4

ICcoolingchangesparticlespectrasignificantly

Weakcooling:usualhardpowerlawStrongcooling:variablesteeppowerlawIntermediate:bothpowerlaws

σh=100,Bgz=B0/4

Time-dependenceofpowerlawsshowsbothpowerslawspresent(mostly);steeppowerlawishighlyvariable

RegardlessofICcooling,(plasmoid-dominated)reconnectionisburstyprocesswithdiscreteaccelerationepisodesthatyieldNTPAspectrawithahardslope(ph=1.9inthiscase).Coolingoccursbetweenepisodes,steepeningtheslope.Dependingonepisodesofaccelerationandcooling,thesteepslopepsfallsbetween3and5.Continuousacceleration/coolingwouldyieldps,min=ph+1=3...butadditionalcoolingresultsinhigherps.

σh=100,Bgz=B0/4

Time-integratedICphotonspectra

Photonpowerlawindexalpha=(p-1)/2.Hardslopeph=1.9->alpha=0.45(measured0.5)Steepslopeps=3-5->alpha=1-3however:aharderslopemeansmoreICemission,soalphashouldbedominatedbythehardestps,min=3->alpha=1(measured1.1)Inthisparticularcase(ultrarelativisticpairplasma,sigma_h=100,B_gz=B_0/4),addingasoftphotonbathchangesindexfromalpha=0.5toalpha=1.1.

Simulationcomparison:TRISTAN-MPandZeltronBothcodesimplementsamefundamentalalgorithms:explicitEM-PICwithminorvariants.Both(asofthisyear)usecharge-conservingcurrentdeposition(divE=rhoisautomaticallymaintainedtohighprecision),thoughdifferentvariants.BothcodesimplementICradiationreactionforce(insomewhatdifferentways).Theimplementationsareentirelyindependent.Dotheyagree?Yes;verywell.

Particlespectra(noICcooling) Spectrapowerlawindices

Conclusions•  3Dness(Lz/Lx)haslittleeffect–despitesignificantRDKI– onreconnectionrateandNTPA•  GuidefieldslowsreconnectionandinhibitsNTPA

•  magnitudeofeffectdependsonguidefieldenthalpyvs.particleenthalpy•  ifguidefieldenthalpyislarge,theguidefieldresistscompressionandslows

reconnection•  ifguidefieldenthalpyissmall(comparedtoparticleenthalpy),notmucheffect

•  ICcooling(dragduetoradiationreaction)haslittleeffectonreconnectionrate•  ICcoolingsignificantlyaffectsNTPA

•  Particlespectrumformsabrokenpowerlaw,with•  ahardslopeph(independentofICcoolingstrength)•  ahighly-variablesteepslopeps,withps>ph+1(alsoindependentofcooling)

•  ps=ph+1wouldmeancontinousaccelerationandcooling•  ps>ph+1forepisodesofaccelerationfollowedbyfurthercooling

•  abreakthatdecreasesinenergyascoolingstrengthincreases•  Forveryweakcooling,thebreakisabovethereconnection-high-energy-cutoffand

onlythehardpowerlawappears;•  forintermediatecooling,bothpowerlawsarevisible;•  forstrongcooling,thehardpowerlawappearsonlyattheverybeginningbeforebeing

overwhelmedbythesteeppowerlaw•  TheICradiationspectrumvarieswiththeparticlespectrum.

•  Forweakcooling,ph=1.9->alpha=0.5•  Forstrongcooling,psvaries,ps>=3=ph+1,butthehardestcomponentdominatesso

thephotonspectrumcorrespondsroughlytops=3,oralpha=1(measured1.1).