Rela%vis%c Reconnec%on in Pairs: Mass Transport (Accelera%on?)

Transcription

1 Rela%vis%c Reconnec%on in Pais: Mass Tanspot (Accelea%on?) J. Aons UC Bekeley Ques%on: How Does Retun Cuent in PSR Magnetosphee Fom? What is density of cuent caies? Consequences (many): How do beamed gamma ays get emined? How do beamed lowe enegy photons fom oute magnetosphee get emined? What is the oigin of toque fluctua%ons? Basic Model: MHD Magnetosphee, fed by e ± pais fom low al%tude pola flux tube (pai cea%on in high al%tude may contibute)

2 Magne%c Y- line feeds J Pola OuTlow v = c 2δ J Reconnec%on inflow Pola Cap Acute otato R L Ω i µ > 0 2l D B Field Aligned cuent φ pecipita%ng electons supplied by diffusion box + upwad ions fom stella atmosphee) Reconnec%on E (adial in geomety shown) sustained by off diagonal pessue tenso p i / x j ( collisionless viscosity seen in all ela%vis%c econnec%on in pais 2D & 3D PIC simula%ons: Hoshino & Zenitani; Bessho & BhaNachajee; Kagan, Milosavljeic & Spitkovsky,.) E + v c B = X e mw i P + 4πe mwc J B ω p ( ) + i cγ ( 2 βj + J β ) t γ J w=ela%vis%c enthalpy; anomalous esis%vity, ad eac%on neglected Obtuse geomety ( Ωiµ < 0) has pecipita%ng positons, electon outlow Non- MHD ine%al E n - 1 (T/mc 2 ): favos low density; hot = high enegy 2 (Ohm)

3 Reconnec%on/Retun j Buccian%ni et al Spoadic X- Point, Plasmoid foma%on occus con(nuously Pais all come fom pole, on open field lines Spoadic econnec%on moves plasma acoss B ExB dio in non- coota%on E, %me vaiable E at all %mes Contopoulos Buccian%ni et al 2006 ela%vis%c MHD with numeical dissipa%on (Contopoulos & Spitkovsky) Plasma, j flow to sta in thin sepaatix laye dynamics in E (standing Kine%c Alfven wave bounday laye) AURORAL ACCELERATION E 3 Kine%c Alfven wave extacts etun cuent (Toque fluctua%ons, limit cycles built in (dioing subpulses)?)

4 J Unmagne%zed Diffusion egion Pola OuTlow v = c J 2δ J Reconnec%on inflow E,J Field Aligned Retun Cuent 2l D B φ Magne%c Y- line Diffusion Region X PIC econnec%on simula%on in pais Zenitani & Hesse (2½ D) 05/21/13 Electic etun cuent channel Ω i µ > 0 Downwad electon beam, upwad ion beam Ω i µ < 0 Downwad positon beam, upwad electon beam 4 R L

5 n diff = Accelea%on in the Retun Cuent Channel (including cuent sheet beyond the light cylinde) Total value of cuent fixed by the foce fee magnetosphee; Reconnec%on modeled by steady flow, 2 fluid theoy of diffusion egion E ec suppoted by off diagonal pessue tenso - viscosity Channel cuent modeled as steady countesteaming beams Density of pecipita%ng beam in the etun cuent channel at = R L set by density in diffusion egion n diff : econnec%on inflow=exhaust: β ec β exhaust β wind D δ n pai eφ / m ± c 2 (Lyubasky 96) = GJ density at LC 10 n GJ 2πR L2 6.2 cm - 3 (Cab), β ec ~0.1, e β wind =1, l D /δ = (PIC sims, theoy) Mul%plicity κ ± = n pai /n GJ 10 4 (pehaps 10 7 in the Cab), B LC = Φ/R LC Diffusion egion unmagnetized, paticles bounce feely inside: Lamo (δ ) = δ = mc 2 γ bounce = T d eb LC eφ R L Viscosity in diffusion egion (bounce mo%on exchanges momentum acoss flow) heats diffusion egion plasma; synchoton cooling (cuvatue adia%on with adius of cuvatue = δ) balances hea%ng: T d m ± c = R L eφ 2 12 e m ± c 2 1/5 v wind v ec κ ± D δ 3 2/5 D = ,500,10 7 κ ± 10 4 (170 MeV < T d < 10 GeV) 5

6 Reconnec%on flow supplies pa%cles to Y- line/cuent Sheet: Retun Cuent Foma%on space chage limited flow out of hot unmagne%zed diffusion egion Diect Acceleato? Geophysics says no, acceleato = field aligned E, econnec%on E is pep; could acceleate in B = 0 cuent channel (Alfven, 1968) guide field usually exists, suppesses fee accelea%on PIC Simula%ons of Rela%vis%c Reconnec%on (in Pai Plasma) Simple Cuent Sheet Geomety no Y- line/magnetospheic obstacle Zenitani and Hoshino Bessho and BhaNachajee 2005, 2012 Hesse & Zenitani (NR pais, 2007) Sioni & Spitkovsky (2012); Kagan et al (2013) Ceu% et al (2013 not analyzed fo econnec%on physics)

7 Zenitani & Hoshino snapshots pais cuent sheets tea (fast) Density & B t/τ c =40 t/τ c =60 t/τ c =100 t/τ c =300 Acceleated Pa%cles spa%ally, ε > 50 mc 2 2D Plasmoid

8 Sheet Kinks (Dio Kink Instability) 3D Teaing & Kinks togethe Femi II like accelea%on, cuent sheet boadening 3D plasmoid = flux tube Maximum enegies set by esidence %me kinks cause dios out of accelea%ng E, speise obits focus pa%cles back into E NO UNIQUE ANSWER set by cuent sheet length macoscopic? tubulence coheence lengths? gadient dios in bent sheets? Accelea%on efficiency how many pa%cles flow though accelea%on (B 0) egion elated to what sets econnec%on etun cuent density volume?

9 Reconnec%on Flow Model 2 fluid theoy of E ec, l D /δ, etc J Pola OuTlow v = c Takes pais fom pola outlow/ wind into diffusion egion/closed zone/cuent sheet at speed v z =ce ec /B ext = v ec Inflow ate diff =2 n wind v z 2πR LC (2l D ) OuTlow ate = v A (out): locally steady flow, δ set inflow = outlow n diff : 2 n diff v A (out)2πr LC (2δ) = 2 n pola wind v z 2πR LC (2l D ) J Reconnec%on inflow 2l D B φ Plasmoid 2δ Ε, Β out, l D, δ = T diff /eb in Simula%ons show l D /δ fom a few to ~ 100, v A (out) = c??? ALL simulatos epot fast econnec%on v ec =( )v A (upsteam) All epot E ec based on pessue anisotopy: E y P xy / x, P zy / z X E + v c B = X e mw i P + 4πe mwc J B ω p ( ) + i cγ ( 2 βj + J β ) t γ J (Ohm)

10 Diffusion egion unmagne8zed, shea flow: Useful model: Pessue anisotopy viscous P ij = p diff ij + c j i 3 l u i = 4velocity/c = i, p diff = 2n diff T diff, = c = ct diff /eb in Useful model woks in non- ela%vis%c cuent sheet econnec%on, gets E, Β out, l D, δ = T diff /eb in of simula%ons ~ OK: viscous hea%ng = adiaba%c cooling Rela%vis%c (young PSR): viscous hea%ng = adia%on ( synchoton cooling Rela%vis%c (simula%ons): viscous hea%ng = adiaba%c cooling (Ceu% adia%ve) Solve as in Sweet- Pake model (2D cuent sheet geomety): deiva%ves: / z 1/δ, / x 1/ l D - solu%on s%ll in pogess Use l D, E fom simula%ons (Kagan et al):, l D /δ = 15, v ec = 0.05 v A (in)

11 β ec n diff = β exhaust β wind n D pai eφ / m ± c 2 δ n GJ 2πR L2 e = GJ density at LC cm - 3 (Cab), β ec ~0.1, β wind =1, l D /δ = (PIC sims, model) n diff n pai (wind) = β ec β exhaust β wind D δ Mul%plicity κ ± = n pai /n GJ 10 4 (pehaps > 10 7 in the Cab) Diffusion egion unmagnetized, paticles bounce feely inside: Lamo (δ ) = δ = mc 2 γ bounce eb LC = T d eφ R L Viscous hea%ng in diffusion = synchoton cooling: T d m ± c = R L eφ 2 12 e m ± c 2 1/5 v wind v ec κ ± D δ 3 2/5 = ,500,10 7 κ ± 10 4 (170 MeV < T d < 10 GeV) Density of pa%cles at stat of wind cuent sheet and pecipita%ng onto sta = n diff at stat of cuent channels ~ /cc in Cab Y- line model same as 2d cuent sheet?

12 Cuent Sheet as Acceleato: Cab flaes (Blazas) a) Whee b) How long? Islands between X- lines mege? c) E/B in? d) B in? Is the B field outside the sheet unifom? Fo Cab flaes, with no Dopple Boost, L = light days, E/B in < few: B ~ milligauss Had o easy? Had to have lage magne%c oveshoots in high σ pola egions, if flux doesn t accumulate, even 1 mg had to each Time inteval between flaes flux accumula%on %me? A%fact of beaming (Dopple o kine%c)?

13 J 0 Kagan+ - 3D pais, flux tubes quasi 2D (plasmoids), fac%on of volume with E along X- lines small Teaing dominated (σ not lage) B 0 Whee is E?