Asymmetric Magnetic Reconnection in CoronalMass Ejection Current SheetsNicholas Murphy,1Mari Paz Miralles,1Crystal Pope,1,2JohnRaymond,1Kathy Reeves,1Dan Seaton,3& David Webb41Harvard-Smithsonian Center for Astrophysics2Elmhurst College3Royal Observatory of Belgium4Boston CollegeHinode 5: Exploring the Active SunCambridge, MassachusettsOctober 11–14, 2011Flux rope models of CMEs predict the formation of anelongated CS behind the rising plasmoidISunward outflow =⇒ post-flare loops, low solar atmosphereIAnti-sunward outflow =⇒ rising flux ropeISignificant gradients for upstream density, pressure, andmagnetic field strengthOpen questionsIAre post-eruption current sheets actively reconnecting?IAre these current sheets energetically important to theeruption as a whole?IWhere is the principal X-line? ⇐⇒ Where does the energy go?IAre CME CSs responsible for mass input and plasma heatingin CMEs? (e.g., Murphy et al. 2011)IAre large-scale blobs due to the plasmoid instability?IPerhaps, but some show C iii and other cool linesWe perform resistive MHD simulations of two initialX-lines which retreat from each other as reconnectiondevelops (Murphy, Phys. Plasmas, 17, 112310, 2010)IThe 2-D simulations start from a periodic Harris sheet whichis perturbed at two nearby locations (x = ±1)IUse the NIMROD extended MHD code (Sovinec et al. 2004)IDomain: −30 ≤ x ≤ 30, −12 ≤ z ≤ 12ISimulation parameters: η = 10−3, β∞= 1, S = 103–104,Pm = 1, γ = 5/3, δ0= 0.1IDefine:Ixnis the position of the X-lineIxsis the position of the flow stagnation pointIVx(xn) is the velocity at the X-lineIdxndtis the velocity of the X-lineIˆx is the outflow direction, ˆy is the out-of-plane direction, andˆz is the inflow directionIWe show only x ≥ 0 since the simulation is symmetricThe CSs have characteristic single wedge shapesThe flow stagnation point and X-line are not colocatedISurprisingly, the relative positions of the X-line and flowstagnation point switch!IThis occurs so that the stagnation point will be located nearwhere the tension and pressure forces cancelIReconnection develops slowly because the X-line is locatednear a pressure minimum early in timeLate in time, the X-line di ffuse s against strong plasma flowIThe stagnation point retreats more quickly than the X-lineIAny difference betweendxndtand Vx(xn) must be due todiffusion (e.g., Seaton 2008, Murphy 2010)IThe velocity at the X-line is not the velocity of the X-line!What se ts the rate of X-line retreat?IThe inflow (z ) component of Faraday’s law for the 2Dsymmetric inflow case is∂Bz∂t= −∂Ey∂x(1)IThe convective derivative of Bzat the X-line taken at thevelocity of X-line retreat, dxn/dt, is∂Bz∂txn+dxndt∂Bz∂xxn= 0 (2)The RHS of Eq. (2) is zero because Bz(xn, z = 0) = 0 bydefinition for this geometry.Deriving an e xact expression for the rate of X-line retreatIFrom Eqs. 1 and 2:dxndt=∂Ey/∂x∂Bz/∂xxn(3)IUsing E + V × B = ηJ, we arrive atdxndt= Vx(xn) − η"∂2Bz∂x2+∂2Bz∂z2∂Bz∂x#xn(4)I∂2Bz∂z2∂2Bz∂x2, so X-line retreat is caused by diffusion of thenormal component of the magnetic field along the inflowdirectionIThis result can be extended to 3D nulls and to includeadditional terms in the generalized Ohm’s lawThe X-line moves in the direction of inc reasing totalreconnection electric field strengthIX-line retreat occurs through a combination of:IAdvection by the bulk plasma flowIDiffusion of the normal component of the magnetic fieldIX-line motion depends intrinsically on local parametersevaluated at the X-lineIX-lines are not (directly) pushed by pressure gradientsCME CSs are often observed to drift with timeIAbove: Hinode/XRT observations after the ‘Cartwheel CME’show a CS drift of 4 deg hr−1(Savage et al. 2010)IThe CS observed by Ko et al. (2003) drifts at ∼1 deg hr−1ICSs observed by AIA or XRT that show drifts include the2010 Nov 3, 2011 Mar 8, and 2011 Mar 11 eventsThe are at l east four possible explanations for this driftIDifferent parts of CS become active at different times (above,from Savage et al. 2010)IThe reconnecting field lines are pulled along with the risingflux rope at an angleIReconnection is very strongly driven behind the CME, and theplasmas come in at different velocitiesIThe drift is associated with line-tied asymmetric reconnectionNIMROD simulations of line-tied asymmetric reconnectionIInitial equilibrium is a modified Harris sheetBz(x ) =B01 + btanhxδ0− b(5)I0 ≤ x ≤ 25, −7.5 ≤ z ≤ 7.5; conducting wall BCsIHigh resolution needed over a much larger areaIMagnetic field ratios: 1.0, 0.5, 0.25, and 0.125Iβ0= 0.25 in higher magnetic field upstream regionICaveats: 1-D initial equilibrium, outer conducting wall BCs,and we do not consider the rising flux rope in detailX-line drift is away from wall and toward stronger BThe line-tied lower boundary condition leads to skewing ofthe post-flare loopsIThis skewing occurs because flux contours are not evenlyspaced along the photospheric boundaryIPost-flare loops observed by Yohkoh/SXT and H inode/XRTmay show such a distortionDecreasing B for one upstream region le ads to a decreasein the rate of X-line motionIHinode/EIS observations of the Cartwheel CME CS providedensities of ∼2 × 108cm−3using a Fe xiii density diagnostic(Landi et al., submitted)IAssuming B ∼ 10–15 G, the 2:1 inflow drift rate iscomparable to obsevationsAgain, the plasm a velocity at the X-line differs greatlyfrom the rate of X-line motionIVx(xn, zn) and Vz(xn, zn) give the velocity at the X-lineIdxn/dt and dzn/dt give the rate of X-line motionINo flow stagnation point within the CSConclusionsIAsymmetric outflow reconnection occurs in planetarymagnetotails, laboratory plasmas, solar eruptions, andelsewhere in nature and the laboratoryIThe primary X-line in CME CSs is probably near the lowerbase of the CS (see also Seaton 2008; Shen et al. 2011)IMost of the energy is directed upwardILate in time there is significant flow across the X-line in theopposite direction of X-line retreatIX-line retreat is due to advection by the bulk plasma flow anddiffusion of the normal component of the magnetic fieldIThe observational signatures of line-tied asymmetricreconnection include:ISkewing/distortion of post-flare loopsISlow drifting to stronger magnetic field sideIPlasmoid preferentially propagates into low-field