A Model for the Coupled Eruption of a Pseudostreamer and Helmet Streamer
P. F. Wyper, S. K. Antiochos, C. R. DeVore, B. J. Lynch, J. T. Karpen, P. Kumar
DDraft version January 7, 2021
Typeset using L A TEX twocolumn style in AASTeX63
A Model for the Coupled Eruption of a Pseudostreamer and Helmet Streamer
P. F. Wyper, S. K. Antiochos, C. R. DeVore, B. J. Lynch, J. T. Karpen, and P. Kumar
2, 4 Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK Heliophysics Science Division, NASA Goddard Space Flight Center, 8800 Greenbelt Rd, Greenbelt, MD 20771, USA Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA Department of Physics, American University, Washington, DC 20016, USA
ABSTRACTA highly important aspect of solar activity is the coupling between eruptions and the surroundingcoronal magnetic-field topology, which determines the trajectory and morphology of the event and caneven lead to sympathetic eruptions from multiple sources. In this paper, we report on a numericalsimulation of a new type of coupled eruption, in which a coronal jet initiated by a large pseudostreamerfilament eruption triggers a streamer-blowout coronal mass ejection (CME) from the neighboring hel-met streamer. Our configuration has a large opposite-polarity region positioned between the polarcoronal hole and a small equatorial coronal hole, forming a pseudostreamer flanked by the coronalholes and the helmet streamer. Further out, the pseudostreamer stalk takes the shape of an extendedarc in the heliosphere. We energize the system by applying photospheric shear along a section ofthe polarity inversion line within the pseudostreamer. The resulting sheared-arcade filament channeldevelops a flux rope that eventually erupts as a classic coronal-hole-type jet. However, the enhancedbreakout reconnection above the channel as the jet is launched progresses into the neighboring hel-met streamer, partially launching the jet along closed helmet streamer field lines and blowing out thestreamer top to produce a classic bubble-like CME. This CME is strongly deflected from the jet’s initialtrajectory and contains a mixture of open and closed magnetic field lines. We present the detaileddynamics of this new type of coupled eruption, its underlying mechanisms and the implications of thiswork for the interpretation of in-situ and remote-sensing observations.
Keywords:
Sun: corona; Sun: magnetic fields; Sun; coronal mass ejections (CMEs); Sun: flares INTRODUCTIONThe solar corona hosts a tremendous amount of erup-tive activity and flare energy release that plays out [email protected]@[email protected]@[email protected]@nasa.gov across a vast range of sizes and time scales. At thelargest scales, eruptive active-region flares produce sub-stantial bubble-like coronal mass ejections (CMEs) thatcan strongly influence near-Earth space weather (e.g.Webb & Howard 2012). At the smallest end of the spec-trum, tiny filament-channel eruptions form coronal jets(e.g. Sterling et al. 2015). The ultimate unifying featureof all these eruptions are filament channels, consisting ofstrongly sheared magnetic field lines that follow polar-ity inversion lines (PILs) of the normal magnetic fieldcomponent on the solar surface (Martin 1998). Fila-ment channels provide the free magnetic energy for theeruption, but it is the interaction between the filamentchannel and the surrounding magnetic field that dictates a r X i v : . [ a s t r o - ph . S R ] J a n Filament
PROBA2/SWAP 2014-07-24 03:39 NP Figure 1.
PROBA2/SWAP 174 ˚A processed image of apseudostreamer. NP = apparent null point lying betweentwo open field regions. how the eruption is triggered and its eventual morphol-ogy.A prime example of this variety is the array of erup-tion morphologies that result from filament channelsformed within multipolar magnetic topologies. At thelargest scales, these eruptions can be triggered by thesystematic removal of strapping flux by reconnection ata coronal null point, magnetic breakout (Antiochos et al.1999). Such events ultimately lead to fast, large-scale,bubble-like CMEs (e.g., Lynch et al. 2008, 2009, 2016;Karpen et al. 2012; Masson et al. 2013, 2019; Chen et al.2016; Dahlin et al. 2019). At much smaller scales, bothobservations (e.g. Sterling et al. 2015; Moore et al. 2018;Kumar et al. 2018, 2019) and simulations (e.g. Wyperet al. 2017, 2018, 2019) have shown that the same erup-tion mechanism is at work in the mini-filament eruptionsthat form many coronal jets. The key difference deter-mining the eruption morphology is how the erupting fluxrope that forms from the filament channel interacts withthe surrounding magnetic field. In jets, the flux rope re-connects at the null point low in the corona, transferringmagnetic twist and filament plasma to the surroundingopen field and creating a narrow plasma ejection thatadds no new open flux to the heliosphere. In eruptionsat active-region scales, on the other hand, the erupt-ing flux rope remains connected to the surface at bothends, opening new flux into the heliosphere as part ofthe bubble-shaped CME. The local magnetic environ-ment around the filament channel clearly plays a crucialrole in its eventual eruptive morphology. Perhaps the most definitive, and certainly the moststriking, example of the interaction between the filamentchannel and its surrounding is the phenomenon of sym-pathetic eruptions. That flares can be sympathetic hasbeen known for many decades (e.g. Richardson 1951),but sympathetic eruptions have attracted much atten-tion recently due to the high-cadence, full-Sun coronalobservations of
STEREO and
SDO (e.g., Schrijver &Title 2011; Titov et al. 2012; Jin et al. 2016). By exam-ining a series of eruptions that included filament ejec-tions, flares, and CMEs, and whose locations covereda large fraction of the solar surface, Schrijver & Title(2011) presented compelling observational evidence thatthe sympathetic nature was due to the reconnection inthe corona of neighboring magnetic flux systems, as oc-curs in the breakout model. Subsequent numerical mod-eling by T¨or¨ok et al. (2011) and Lynch & Edmondson(2013) demonstrated that null-point reconnection in thecorona, as in breakout, naturally couples different fluxsystems and leads to the sympathetic eruptions. A keyfeature of these and other studies, both observationaland theoretical, is that each eruption has its own fila-ment channel. Consequently, each flux system is primedto erupt and one simply destabilizes the next. Our newwork presented here, in contrast, shows that a couplederuption of multiple flux systems can be driven by a sin-gle filament channel. Furthermore, it shows that break-out reconnection can energize, as well as destabilize, cou-pled eruptions.The vast difference in scales and energies betweeneruptions that produce large-scale, bubble-like CMEsversus small-scale, collimated coronal jets implies thatthere is a continuum of eruption scenarios in between,unified by the role of breakout reconnection in dictatingthe eruption morphology. One scenario in this middleground is a filament eruption from a pseudostreamer. Atfirst glance, pseudostreamers have the same topology ascoronal jets, simply on a much larger scale. Figure 1shows a SWAP image of a pseudostreamer harbouringa small filament observed on the limb. In profile, thepseudostreamer topology resembles that of a single nullpoint above two coronal arcades, which sit between coro-nal holes of like polarity. The presence of this multipo-lar topology assures that, like mini-filament coronal-holejets, pseudostreamers can host filament eruptions thatoccur via magnetic breakout.In general, however, the large-scale nature of pseu-dostreamers leads to a much richer variety of mag-netic structure than those that underlie jets. The clos-est to jets are small pseudostreamers associated withnewly emerged active regions within low-latitude coro-nal holes. These pseudostreamers have a quasi-circular
NP1 NP2 NP3NP4 NP5OS1
OS2(a) (b)(c) (d)
F2F2 F2F4F4 F2
Figure 2.
Overview of the topology and connectivity of the magnetic configuration hosting the eruption. (a) Field lines showingthe five null points (NP1, ..., NP5) that define the pseudostreamer. Two open separators (OS1 and OS2) are shown in magenta.(b) A zoomed-out view showing that the fan plane of the central null (NP2) maps to an arc in the heliosphere. Isosurfaces showregions of high plasma β within the centre of the heliospheric current sheet. (c) log( Q ) on the solar surface. PILs are shownwith dashed lines. Open field regions are shaded yellow, showing the disconnected coronal hole. Circles show the spine-linefootpoints of the nulls (coloured as in (a)). F2 and F4 are high- Q strips associated with NP2 and NP4, respectively. (d) log( Q )at 30 R s showing the S-Web arc around the open field of the disconnected coronal hole. Yellow regions show disconnected flux.The dashed red line shows the PIL of B r within the heliospheric current sheet. base, anemone-like when view from above, with a sin-gle magnetic null (Shibata et al. 1994; Asai et al. 2008;Kumar et al. 2021) in the “embedded bipole” topology(Antiochos 1990). More complex are the pseudostream-ers that form above the long tails of minority polar-ity, stretched out by differential rotation and meridionalflow, that are associated with decaying active regions.These often involve multiple nulls and/or bald patchesalong the length of the pseudostreamer, and they are solarge that their proximity to the nearby helmet-streamerboundary also must be taken into account (Titov et al.2011, 2012; Scott et al. 2018, 2019; Masson et al. 2019).Large pseudostreamers are key contributors to thecomplexity of the S-Web (Antiochos et al. 2011), inwhich the outer spines and/or fan planes of the nulls sep-arating the magnetic flux of neighbouring coronal holesform broad arcs that extend far out into the heliosphere.Pseudostreamers bordering equatorial coronal holes andtheir associated S-Web arcs are common features of thecorona throughout the sunspot cycle (Scott et al. 2019).Yet to date, no simulation studies that we have seenmodel a large-scale pseudostreamer eruption and exam- ine its effects on the global helmet streamer and theS-Web.In this work, we present a simulation that addressesboth of these interactions, along with the specifics of thepseudostreamer eruption itself. We constructed a largepseudostreamer that has multiple null points and sepa-rator lines (Fig. 2(a)), is bounded north and south bythe polar and an equatorial coronal hole, and that par-tially underlies the global helmet streamer that formsthe polar coronal-hole boundary to the east and west ofthe pseudostreamer (Fig. 2(c)). The pseudostreamer isrooted in a large, elliptical region of minority polaritythat represents a decayed active region. There are sev-eral important differences between this simulation andour previous studies of jets and CMEs. First, the “over-lying” coronal field consists of both open (coronal-hole)and closed (helmet-streamer) flux. In earlier work, theoverlying field was either entirely open (jets) or entirelyclosed (CMEs). The separatrix dome of the minoritypolarity forms a section of the open/closed flux bound-ary and connects the polar and equatorial coronal holes.In addition, the dome connects the pseudostreamer tothe neighboring helmet streamer, so that reconnectionbetween the pseudostreamer and helmet-streamer fluxesis possible. As we shall see, the breakout reconnectionindeed involves both the usual open/closed interchangereconnection of jets (Wyper et al. 2018) and the usualclosed/closed reconnection of CMEs (e.g., Masson et al.2019; Dahlin et al. 2019). Second, the reconnection inthe corona can occur at multiple null points and alongthe separator line. Consequently, it could be expectedto be much more efficient than single-null-point recon-nection, but the effect this should have on the eruptionis not clear. Highly efficient breakout reconnection maylimit the amount of free energy that can be built up inthe filament channel; but it also may allow more of thestored free energy to be released. Third, as will be shownbelow, the filament channel that we formed extends overa rather small fraction ( < § §§
3, 4, and 5 describe, respectively,the pre-eruptive changes to the magnetic field, the low-coronal evolution of the eruption, and the energy re-lease. §§ §§ § MODEL DESCRIPTION2.1.
Equations and Initial Condition
The simulation was performed using the AdaptivelyRefined Magnetohydrodynamics Solver (ARMS), whichuses a Flux-Corrected Transport algorithm to captureshocks and minimize numerical diffusion (DeVore 1991).The following ideal MHD equations were solved in spher- ical coordinates: ∂ρ∂t + ∇ · ( ρ u ) = 0 , (1) ∂ρ u ∂t + ∇ · ( ρ uu ) = 14 π ( ∇ × B ) × B − ∇ P + ρ g , (2) ∂ B ∂t − ∇ × ( u × B ) = 0 , (3)where ρ is the plasma mass density, u the plasma ve-locity, B the magnetic field, P the plasma pressure, and g = − GM (cid:12) r /r the gravitational acceleration. Mag-netic reconnection in the model occurs due to numer-ical diffusion associated with the algorithm. We as-sume a fully ionised hydrogen plasma, so that P =2( ρ/m p ) k B T . The temperature is further assumed tobe constant and uniform throughout the volume with T = 1 MK.The simulation volume is given by φ ∈ [ − ◦ , ◦ ]in longitude, θ ∈ [ − ◦ , +81 ◦ ] in latitude, and r ∈ [1 R s , R s ] in radius. The domain is periodic in φ .At the inner radial boundary, mass is allowed to flowinto, but not out of, the volume. The three radial guardcells below the inner boundary are fixed at their initialdensities, with their velocity components set to zero.These cells act as a reservoir of mass sustaining thewind solution described below. The magnetic field atthe radial inner boundary is line-tied, with the tangen-tial velocity components set to zero except where pre-scribed otherwise by the driving flow given below. Atthe outer radial boundary, flow-through (zero-gradientextrapolated) conditions are applied to the radial ve-locity component and half-slip (zero-value outside) con-ditions are applied to the tangential components. Onthe θ boundaries, the normal velocity is reflecting andthe tangential components are free-slip (zero-gradient).Altogether, these boundary conditions maintain a quasi-steady, isothermal solar wind throughout the open fieldin the domain.The initial magnetic field is given by a potential-fieldsource-surface (PFSS) solution, with the source surfaceat 3 R s . The magnetic field at the radial inner boundaryis defined analytically by combining sub-surface mag-netic dipoles with a Sun-centered dipole that definesthe global dipolar magnetic field. The global dipoleis chosen so that | B r | = 10 G at the poles. The sub-surface dipoles are placed so as to create a strip of neg-ative polarity in the northern hemisphere, bordering astrong equatorial bipolar active region, Fig. 3(a). Theequatorial active region acts to pull the helmet streamersouthward whilst the strip of negative polarity cuts offa section of northern polar coronal hole, forming a dis-connected coronal hole separated from the north-polehole by a pseudostreamer (Titov et al. 2011; Scott et al. -40 -20 0 20 40 0 400100 200 300B r (G) v (km/s) Figure 3.
Simulation grid (a) on the surface, with field lines from near the fan planes of null points NP1 and NP3 (see Fig.2) drawn for context, and (b) in a plane of constant longitude, showing how the adaptive refinement localises the grid to theheliospheric current sheet. v c s exp (cid:18) − v c s (cid:19) = r s r exp (cid:16) − r s r (cid:17) . (4)Here v ( r ) is the radial velocity, c s = (2 k B T /m p ) isthe isothermal sound speed, and r s = GM (cid:12) m p / k B T is the radius of the sonic point. With T = 1 × K, v = c s = 128 km/s at r = r s = 5 . R (cid:12) . The plasmanumber density at the base of the atmosphere is a freeparameter that we set to 7 . × cm − . This value givesa minimum plasma β (ratio of thermal to magnetic pres-sure) in the vicinity of the pseudostreamer of about 10%,so the dynamics is properly field-dominated. The den-sity and the resultant Alfv´en speed are intended to bemore typical of closed-field regions below pseudostream-ers and helmet streamers, where our eruption occurs,than of open-field regions in the neighboring coronalholes.The magnetic field defined by the PFSS solution andthe plasma wind solution are not initially in equilibrium,so before the surface driving was applied the simula-tion was first run out through a long relaxation phase( > × s) until the plasma and magnetic field evolved to near pressure balance. Figure 3(b) shows the plasmavelocity in a plane of constant longitude after the relax-ation. Away from the heliospheric current sheet, the so-lar wind reaches ≈
350 km/s at 30 R s . This wind speed,more typical of slow rather than fast wind, is due to thelow temperature T and our simplifying isothermal ap-proximation. However, our main goals of tracking withhigh fidelity the low-coronal evolution of the eruptionand its interaction with the helmet streamer are not af-fected significantly by the asymptotic wind speed.The base grid is uniformly spaced in φ and θ and isstretched exponentially in radius. Four levels of grid re-finement were allowed in the simulation. A fixed regionof maximal resolution was included that encompassedthe pseudostreamer. Figure 3(a) shows the grid blockson the surface in this region. Each grid block consists of8 × × ≈ . ◦ in both φ and θ , corresponding to a maximumgrid resolution (at the finest grid level) on the inner ra-dial boundary of ≈ . φ ∈ [ − , − ∪ [+90 , +180]) was limited to three,rather than four, levels of refinement.2.2. Topology of the Relaxed State
The magnetic topology of the pseudostreamer afterthe relaxation is shown in Figure 2(a). The surface B r distribution was chosen such that there were two localminima of B r within the negative-polarity strip, Fig-ure 3(a). This naturally creates a system of at leastthree nulls, one associated with each minimum (NP1and NP3) and another that resides between them (NP2).Two separators connect the three nulls along the top ofthe separatrix surface dome. In the PFSS solution onlythese three nulls were present. However, during the re-laxation currents naturally developed around the nullsand along the separators. Combined with changes in thefield around the pseudostreamer as the helmet streamerrelaxed, this led to a bifurcation of NP3 and the for-mation of two further nulls, labeled NP4 and NP5, con-nected by an additional two separators. Due to where westore the magnetic free energy in our simulation, theseadditional nulls are not involved in the eruption.The key elements of the pseudostreamer topology canbe understood by considering NP1, NP2, and NP3 (withNP4 and NP5 understood by extension). The fan planesof NP1 and NP3 form the main sections of the sepa-ratrix surface that divide the closed field beneath thepseudostreamer from the surrounding open (or distantlyclosing) field in the rest of the corona (blue and red fieldlines, Fig. 2(a)). The inner spines of each null connectto the strip of negative B r beneath the pseudostreamer;the outer spines connect to negative B r in the southernhemisphere. Both nulls therefore reside in the closedfield beneath the helmet streamer.NP2 sits at the intersection of the fan planes of NP1and NP3. The spines and fan of NP2 are oppositely ori-ented to those of NP1 and NP3, so that the spines ofNP2 sit on the separatrix surface of the pseudostreamerand its fan plane is aligned radially (yellow field lines,Fig. 2(a)). The spines of adjacent nulls actually boundthe fan plane of the other, so the radial partially openfan plane of NP2 is bounded on either side by the closedspines of NP1 and NP3. As a consequence, the fan ofNP2 must straddle the open-closed separatrix of thehelmet streamer (note the closed yellow field lines ad-jacent to NP1 and NP3, Fig. 2(a)). Therefore, theremust be two separators connecting the base of the helio-spheric current sheet with NP2 (shown in magenta, Fig.2(a)). A similar alternation of null orientation occursfor NP3, NP4, and NP5, although the fan plane of NP4lies entirely within the closed field beneath the helmetstreamer. The surface connectivity of the relaxed state is shownin Figure 2(c). Yellow regions show open field, high-lighting the triangular low-latitude corona hole cut offby the pseudostreamer. The logarithm of the squashingfactor ( Q ; Titov 2007) is shown in gray scale. Stripsof high Q show regions where the field-line connectiv-ity varies rapidly between adjacent footpoints, and Q is formally infinite at separatrix surfaces. The foot-print of the global helmet streamer is evident, alongwith a closed curve of high Q showing the footprint ofthe pseudostreamer separatrix dome. The footpoints ofthe spines of each null and the strips of high Q asso-ciated with fan planes of NP2 and NP4 are also high-lighted (F2 and F4, respectively). The fan plane of NP2is truly global, in that it connects to the surface be-neath the pseudostreamer, to distant positions in thesouthern hemisphere, and also out into the solar wind,where it forms an S-web arc (Antiochos et al. 2011) di-viding the open fluxes of the equatorial and northernpolar coronal holes. Field lines within the arc and theassociated high- Q arc at 30 R s are shown in Figure 2(b)and (d). Given such global connectivity, one should ex-pect a global influence of the eruption, which indeedis what we find. Figure 2(d) also shows several smallregions of disconnected magnetic flux that are associ-ated with concave-up field lines (“U-loops”) that enterand leave the domain through the outer radial boundaryand localised bundles of spiral field lines and compressedplasma (“plasmoids”) within the heliospheric currentsheet. These features are formed and expelled period-ically as part of the dynamic quasi-steady state of themagnetic structure (Higginson et al. 2017; Titov et al.2017). 2.3. Filament Channel Formation
In the classic 2D picture of a pseudostreamer, fil-ament channels can form at the PILs beneath eitheror both of the two closed field regions associated withthe null point. In 3D, these two separate PILs jointo form a closed loop. Theoretically, filament channelscan form along any section of this PIL, but the mostenergetic would be expected to form between strongconcentrations of B r associated with stronger strappingfield. That is, these sections of PIL are able to sup-port higher energy density (higher magnetic pressure)because of their increased strapping field. Due to thedistribution of B r on the solar surface, chosen so as togenerate the pseudostreamer topology described above,there are four sections of PIL bordered by local peaks in | B r | as shown in green in Figure 4(a). These various lo-cations for energetic filament-channel formation wouldbe expected to stress different nulls and separators in -60-303060 B r ( G ) | J | s t a t a m p / c m (e)(c)(d)(b)(a) Figure 4. (a) Log Q and coronal holes overlaid with contours of B r (between −
40 G and 40 G); the four sections of PIL borderedby strong concentrations of B r are shown in green. (b) Arrows show the direction and strength of the shear driving; red/blueshading shows the magnitude of the v φ component. (c) Log Q at t = 15 hrs 50 min showing two J -shaped hooks characteristicof a sigmoidal field. (d) Field lines in the filament channel showing its sigmoidal shape. (e) Side view showing the inflation ofthe pseudostreamer and the opening of the outer spine of NP1. the pseudostreamer topology, with associated differencesin the connectivity changes occurring during eruption.Furthermore, combinations of filament channels in dif-ferent locations can produce sympathetic eruptions (e.g.T¨or¨ok et al. 2011; Lynch & Edmondson 2013).We performed several simulations in which filamentchannels formed along each of the highlighted sections.In this paper, we focus on the case where a filamentchannel is formed at PIL1, leaving the exploration oferuption morphologies and coupling behaviour of fila-ment channels formed along the other sections to futurestudies. To create the filament channel, a tangential ve-locity field was imposed on the lower boundary. Thevelocity profile, a generalisation of one used by Higgin-son et al. (2017), is an elliptical flow pattern, tilted withrespect to the θ, φ coordinates, that preserves B r on thesurface throughout the evolution. It is shown in Figure4(b). In order to satisfy ∂B r ∂t = − ∇ ⊥ · ( v ⊥ B r ) = 0 , (5) v ⊥ is constructed from the curl of a radial vector, v ⊥ = 1 B r ∇ ⊥ × ( ψ, , , (6)where ψ is a function of θ , φ , t , and B r in the form ψ ( θ, φ, t ) = V f ( t ) g ( ξ ) h ( η ) . (7)By construction, streamlines of the driving flow followthe contours of ψ over a compact surface region where ψ (cid:54) = 0. The function g ( ξ ) defines a simple tilted ellipsethat depends upon the spatial coordinates ( θ, φ ); h ( η ) depends solely upon B r and serves to keep the boundaryof the flow region slightly removed from the PIL, so thelatter is not distorted by the flow. We choose g ( ξ ) = m + (cid:96) + 1 (cid:96) + 1 (cid:104) − ξ (cid:96) +1) (cid:105) − (cid:104) − ξ m + (cid:96) +1) (cid:105) , (8) h ( η ) = η, (9)where we set m = (cid:96) = 1 and ξ = min (cid:18) α a + β b , (cid:19) , (10) η = max (min ( B r , B ) , B ) − B . (11)We define the tilted orthogonal angle coordinates α ≡ δ ( θ − θ ) + (cid:15) ( φ − φ ) , (12) β ≡ δ ( φ − φ ) − (cid:15) ( θ − θ ) , (13)whose direction cosines are δ and (cid:15) , whose origin is posi-tioned at ( θ , φ ), and whose maximum extents are ± a and ± b , respectively. The direction cosines define thetilt angle arctan( δ/(cid:15) ) of the ellipse with respect to linesof longitude; the ellipse’s semi-major and -minor axesare a and b , respectively. Within the ellipse, the flow isfurther restricted to the region where B r < B , whence h ( η ) (cid:54) = 0. We chose constants B = − , B = − θ = +0 . π , φ = − . π , δ = +0 . , (cid:15) = +0 . a = 0 . π, b = 0 . π . These choices centered theellipse at 55 ◦ latitude and − ◦ longitude, and tilted it11 ◦ with respect to lines of longitude, as can be seenin the figure. We set the magnitude and sign of V (= − . × ) to quasi-statically create a filament BCS FCSOpenLobeClosedLobeExternalField StrappingFieldPIL 0.021.517.212.98.64.3 | J | (a)(b) Dimming
Figure 5. (a) Pre-eruption magnetic field at t = 24 hrs10 min. BCS = breakout current sheet, FCS = flare currentsheet. Field lines indicate the four flux regions separated bythe BCS. The semi-transparent grey shading shows currentdensity (statamp cm − ). (b) Synthetic EUV base-differenceimage (from t = 22 hrs 30 min) showing the density depletionabove the BCS. channel of dextral chirality, as is typically observed inthe northern hemisphere (e.g. Martin 1998).The driving speed peaks at about 30 km s − in a stripalong the PIL, but drops to ≈ − in the return-flow region away from the PIL. The peak speed is highlysub-Alfv´enic and subsonic, so free energy is injectedquasi-statically. The time profile for f ( t ) is chosen sothat the driving is ramped up to its maximum speedover 500 s, held constant for a time, and then is rampeddown to zero over another 500 s once the eruption isunderway. For convenience, henceforth we will define t = 0 as corresponding to the start of the driving. Rela-tive to this, the driving is stopped at t = 98 ,
000 s (27 hrs13 min). Figure 4(d) and (e) show field lines in the filamentchannel 15 hrs 50 min into the driving. The magentafield lines in the filament channel form a classic sigmoidshape. Blue field lines show the approximate position ofthe spines of NP1, the outer spine of which has openedby this time (see § .
29 R s (203 Mm above the surface), although it rises furtheras the filament channel continues to form. Figure 4(c)shows that two hooked, J-shaped, high- Q lines form inassociation with the sigmoidal field lines (e.g. D´emoulinet al. 1996; Janvier et al. 2013). It also shows a slightshift in the pseudostreamer separatrix dome footprint,indicating that a small amount of strapping field has re-connected, along with a retreat of the adjacent helmet-streamer boundary, which now has a snub-nosed ratherthan tapered appearance. The snub-nosed shape is a sig-nature that the helmet streamer is no longer connectedto NP2 on this side. Moreover, an extremely thin cor-ridor of open flux has formed to connect the equatorialand polar coronal holes: the widening of the thin cor-ridor at its ends, where the open flux of the corridormeets the open flux of the coronal hole, is responsiblefor the shape of the boundary. Corridor formation alsois consistent with the observed shift of the outer spine ofNP1 into the open field. A similar switch from taperedto snub-nosed shape can be seen in the helmet-streamerboundary footprint of Titov et al. (2011) (see their Fig-ures 5 and 6), although not explicitly noted by them intext, when a singularly thin corridor formed during anidentical topological evolution. PRE-ERUPTION CHANGESThroughout the slow driving phase prior to erup-tion initiation, the magnetic shear continually increaseswithin the filament channel. The strong gradient in thedriving profile adjacent to the PIL forms a concentratedvolumetric current distribution along the PIL within thefilament channel. Slow tether-cutting (or slipping) re-connection (Moore et al. 2001; Aulanier et al. 2012) in-side this current distribution gradually converts someof the sigmoid-shaped, sheared-arcade field lines into asmall flux rope suspended above the PIL. For simplicity,we refer to this current concentration as the flare cur-rent sheet, although the flare reconnection begins muchlater in the evolution, during the explosive eruption andoccurs in the lower corona below the growing flux rope.We emphasize that, at this early stage, the evolution isquasi-static and the current concentration forms entirelydue to the driving profile. The flux rope begins to formabout 21 hrs into the driving. (c)(b) 30 hrs 17 min 31 hrs 57 min(a) 26 hrs 23 min(d) (e) (f)(g) (i)(h) -400-2000200400 v r k m / s -300-1500150300 v k m / s -1.4-0.9-0.40.12.1 l o g ( J ) BCS BCS FCS FlareArcade
Figure 6.
Low-coronal eruption evolution. (a)-(c) Log of the current-density magnitude (statamp cm − ). (d)-(f) Radialvelocity, v r . (g)-(i) Line-of-sight velocity, v φ . BCS = breakout current sheet, FCS = flare current sheet. An animation of panels(a) to (c) is available online showing the evolution. The animation duration is 6 s. Concurrent with the formation of the flux rope isthe continued expansion of the strapping field abovethe filament channel. This expansion stresses the pseu-dostreamer topology, lengthening the weak current sheetalready present around NP1 following the relaxation.About t = 23 hrs 30 min into this gradual phase, sys-tematic reconnection of the strapping field begins andfeeds back upon the expansion of the filament chan-nel, allowing the channel and embedded flux rope torise faster. We designate this time as the onset of thebreakout reconnection phase, and we denote the currentsheet around NP1 as the breakout current sheet fromthis point onward. Figure 5(a) shows relevant field lines within andaround the filament channel and the two current sheetsat 24 hrs 10 min into the driving, shortly after break-out reconnection begins. The open lobe and the exter-nal field lines reside in the polar and equatorial coronalholes, respectively. The volumetric current distributionwithin the filament channel shows that the formation ofthe flux rope has transformed the channel flux surfacesfrom semi-circular to inverse-teardrop shaped. Mean-while, the strengthening of the overlying breakout cur-rent sheet creates the characteristic cusp shape at thetop of the closed-lobe region (e.g. Kumar et al. 2021;Wang & Hess 2018).0Recently, Kumar et al. (2021) identified observed EUVdimmings above the breakout current sheet as a new di-agnostic signaling the onset of breakout reconnection.The dimming occurs due to depletion of plasma in thesurrounding volume as external field sweeps into thebreakout sheet, reconnects, and flows out along thesheet as reconnection exhaust. Figure 5(b) shows a syn-thetic EUV base-difference image of our simulation atthis time, revealing this dimming as well as the en-hanced density in the reconnection outflow along thepseudostreamer spire. The subtracted base image istaken from time t = 22 hrs 30 min, about an hour beforebreakout-reconnection onset.The presence of the flux rope makes it difficult to beunambiguous about the precise mechanism that triggersthe continued rise of the flux rope towards eruption fromthis time onward. Breakout reconnection certainly is keyto maintaining the eruption once the flux rope is risingrapidly. However, it is possible that an ideal rise of theflux rope due to torus instability couples to the breakoutreconnection, to tip the evolution into a self-sustainingfeedback. A similar coupling associated with ideal kinkinstability recently was shown to occur in simulations ofactive-region periphery jets (Wyper et al. 2019). Com-parisons of our results with those from a perfectly ideal-MHD model (e.g. Pariat et al. 2009; Rachmeler et al.2010), which is well beyond the scope of the currentinvestigation, would be required to address this issuedefinitively. However, it is clear from the fast evolu-tion following onset of reconnection of the flux rope andfrom the energy plots (both described in detail below)that ideal instability of the flux rope is not the dominantprocess once the eruption is underway. LOW-CORONAL EVOLUTION4.1.
Eruption Kinematics
Initially, the pseudostreamer eruption closely followsthe evolution of a mini-filament jet, but on a much largerscale. Once the breakout reconnection gets underway,the strapping field above the flux rope begins to be re-moved and the flux rope continues its rise, slowly atfirst. Figure 6(a) shows the same field lines from Figure5 2 hrs 13 min later. The field lines are traced from fixed(un-driven) points on the surface. The closing down ofthe red external field lines and the opening up of thecyan strapping field lines show the progression of thebreakout reconnection.As the reconnection continues, the breakout currentsheet moves southward as the external field (red fieldlines) sequentially reconnects. This orients the currentsheet radially and positions it directly above the now-expanded (with reconnected flux) south lobe of the pseu- (a) (b)(c) (d)30 hrs 43 min30 hrs 17 min 30 hrs 30 min30 hrs 56 min Flare ArcadesFlare Reconnection
Figure 7.
Reconnection of the flux rope. See text in § dostreamer, Figure 6(b). As the last of the strappingflux is exhausted, the rising flux rope becomes bent to-wards the breakout current sheet over the top of thesouth lobe, Figure 6(b). This bending of the filament-channel field, with or without filament/prominence ma-terial, is a typical feature of pseudostreamer eruptions(e.g. Panasenco et al. 2011; Kumar et al. 2018, 2021).In addition to bending, the flux rope accumulates moreflux, as the reconnection in the flare current sheet is en-hanced by the stretching of the sheet as the flux roperises.When the flux rope reaches the breakout currentsheet, the system departs from its previously quasi-2Devolution and enters a fully 3D phase, described below,in which the flux rope reconnects and a large fractionof the twist within the flux rope is liberated. Exactlyanalogous to mini-filament jets, this transfer of twistlaunches an untwisting plasma jet characterised by a fastradial velocity component (Fig. 6(f)) and oppositely di-rected line-of-sight velocity components on either side of,and extended along, the jet axis; see Figure 6(i). Thisshows that the low-coronal evolution of our simulatederuption is essentially that of a large-scale coronal jet.4.2. Flux-Rope Reconnection
The reconnection of the flux rope is inherently three-dimensional, and cannot be described adequately bytwo-dimensional models. Figure 7 shows field lines in theflux rope before, during, and after the reconnection. Ma-genta field lines are traced from positive-polarity foot-1 J BCSFCS
BCS -2.6-1.301.32.6 J r (a)(b) Figure 8.
Isosurface of current-density magnitude ( J =2 . − ), shaded by the radial component of thecurrent vector ( J r ), at t = 30 hrs 30 min. BCS = breakoutcurrent sheet, FCS = flare current sheet. (a) Side view. (b)Top view. Green arrows show the direction of the current. points, whilst silver field lines are traced from the con-jugate footpoints in the negative polarity. As the fluxrope begins to reconnect, some of the magenta field linesopen up whilst their counterpart silver field lines be-come part of the southern lobe of the pseudostreamer,Figure 7(b). Figure 8 shows the current density mag-nitude at this time, shaded by the radial component ofthe current density vector. At this crucial moment, thebreakout current sheet curving around the outer edge ofthe flux rope and the flare current sheet following be-hind it combine, forming one long current sheet. Thedirection of the current is indicated in Figure 8(b) bythe green arrows. This marks the instant when the nullpoint within the breakout layer (NP1) begins to slidearound the separatrix dome into the flare current sheet E m ( e r g s ) E k ( e r g s ) breakoutbegins flux ropereconnection relaxation Figure 9.
Energy plots showing E m (blue) and E k (red)with the different eruption stages annotated. behind the flux rope ( § § ENERGETICSThe evolution of the total kinetic and magnetic ener-gies of the system further confirm the jet-like nature ofthe eruption. We define the free magnetic and kineticenergies as E k = (cid:90) (cid:90) (cid:90) V ρu dV − (cid:18)(cid:90) (cid:90) (cid:90) V ρu dV (cid:19) t =0 , (14) E m = (cid:90) (cid:90) (cid:90) V π B dV − (cid:18)(cid:90) (cid:90) (cid:90) V π B dV (cid:19) t =0 , (15)where t = 0 corresponds to the start of the driving. Al-though some residual fluctuations occur in the relaxed2 (d)(a) (b)(c) t = 29 hrs 43 min t = 32 hrs 30 min t = 36 hrs 57 min t = 41 hrs 57 min FP1FP3FP2
Figure 10.
Blowout of the helmet streamer. An animation of this figure is available online showing the evolution. Theanimation duration is 6 s. state, they are small compared to the energy stored andreleased by the eruption. Therefore, the above quan-tities provide a reasonable approximation to the ac-tual magnetic energy stored and kinetic energy liber-ated by the eruption. Both curves are shown in Figure9. The timing of the different phases of the eruptionare marked with dashed lines. The kink in E m shortlyafter t = 27 hrs coincides with the time the driving isstopped. Once the breakout reconnection is initiated( t ≈
23 hrs 30 min), there is a gradual rise in kinetic en-ergy, accompanied by a gradual reduction in the mag-netic energy after the driving ceases. However, the ma- jor magnetic energy release occurs when the flux ropereaches the breakout current sheet and reconnects at t ≈
30 hrs 30 min, whereupon the kinetic energy rapidlyincreases as the eruption is launched. The rapid changesin both energies are short-lived and slow down afterabout an hour, thereafter entering a more gradual relax-ation phase. We found an almost identical qualitativebehaviour in our previous jet simulations (Wyper et al.2017, 2018), although the kinetic energy continues torise once the CME is launched in the present case withsolar wind. COUPLED HELMET-STREAMER BLOWOUT3We have seen that the low-coronal behaviour of thepseudostreamer eruption resembles that of a large-scalejet; however, the dynamics of the global topology resultsin a clear CME, which we now show is bubble-like. Thepseudostreamer is in sufficiently close proximity to theopen-closed separatrix of the helmet streamer that thehelmet streamer participates in the ejection of the fluxrope, as discussed further in §
7. Consequently, ratherthan transferring twist entirely onto open field lines asin a simple coronal-hole jet, a significant portion is in-jected into the closed field beneath the adjacent helmetstreamer. This twist blows out the top of the streamerwhen it reaches the streamer apex.Figure 10(a) shows three representative sets of fieldlines prior to the eruption. The positive footpoint ofthe erupting flux rope is shown in magenta, as in Fig-ure 6. A bundle of cyan field lines that initially formpart of the strapping field, traced from positive foot-points slightly north of the magenta field lines. Yellowfield lines with footpoints in the southern hemispherethat form high-reaching arches that pass both near thetop of the helmet streamer and close to the edge of thepseudostreamer. Figure 10(b) shows the twist gainedby the high-reaching yellow field lines, which are in theprocess of lifting off from the top of the helmet streamer(see also the accompanying animation). The figure alsoshows that the CME has three footpoint regions. Thefirst, labeled FP1, is near the positive footpoint of theerupting flux rope. The second, labeled FP2, is southof the pseudostreamer and forms when field lines withinthe CME connecting to FP1 are drawn into the flarecurrent sheet. The resulting interchange-like flare recon-nection shifts these CME footpoints from FP1 to FP2.The final footpoint region is FP3, consisting of the re-mote footpoints of the flux blown out from the helmetstreamer.Figure 10(c) shows the completely blown-out top ofthe helmet streamer several hours later. Several hourslater still, Figure 10(d) shows the reformation of thehelmet streamer. The helmet streamer reforms as anew section of heliospheric current sheet forms followingthe upward stretching of the blown-out helmet streamerflux. This is exactly analogous to the process by whichslow streamer-puff, or stealth, CMEs are thought toform except that in this case the magnetic stress wasinjected into the helmet streamer flux completely in thecorona rather than at the photosphere (e.g. Lynch et al.2016). SURFACE CONNECTIVITY AND NULLEVOLUTION A great deal of insight into this event can be gained bystudying the surface connectivity of the magnetic field,which essentially maps the complex 3D evolution of theeruption onto a 2D plane. All the key changes of theglobal magnetic evolution are captured thereby. At thesame time, the connectivity maps are not always in-tuitive to work with and require some interpretation,which we now provide.In Figure 11(a) we show the connectivity prior tobreakout initiation. As before, the open-field coronalholes are shown in yellow, magnetically closed regionsin white, and log( Q ) in grey scale. In addition to theconnectivity, we also located the null points in the lowcorona (below 3 R s ) using the tri-linear method (Haynes& Parnell 2007; Wyper & DeVore 2016). The positionsof the nulls identified at each time are projected radiallyonto the surface and shown with diamonds.As mentioned previously in § Q are highlighted (Q1 to Q4) that are associated withthe fan separatrix footprint of NP1 (Q1 and Q3) and theinner and outer fan of NP2 (Q2 and Q4, respectively).Figure 11(b) shows the connectivity well into thebreakout phase. In 2D, the progression of breakout re-connection is followed by the motion of the footpointsof separatrices on either side of the filament channel to-wards each other as strapping field is removed. Mean-while, the footpoints outlining the lobe regions moveapart as strapping field is added (e.g. Lynch et al. 2008).The same progression is evident here in 3D: Q1 and Q2move towards one another as Q2 and Q3 move apart. Atthis time, NP1 has migrated back towards the left flankof the pseudostreamer. This shift of the null, which isa natural consequence of the round trip it makes as itmoves from the breakout to flare current sheets and backto the center of the pseudostreamer, is the crucial ingre-dient that leads to the blowout of the helmet streamer.As NP1 moves to the flank, the helmet streamer be-4 t = 16 hrs 57 min t = 28 hrs 37 mint = 30 hrs 50min t = 38 hrs 3 min(a) (b)(c) (d) Opened FluxNewly Closed FluxFR Opening Mixed Open/ClosedFluxCME FootpointsParallelFlare Ribbons NP2NP1HSFlux FP3 FP2 FP1Q1Q2 Q3Snub nosedHSB TaperedHSBSnub nosedHSBTaperedHSB FR foot pointQ4Remote RibbonSemi-circularRibbon
Figure 11.
Connectivity evolution of the coronal magnetic field. Grey shading shows log( Q ); open and closed fields are shadedyellow and white, respectively; the dashed line shows the PIL; and projected positions of the null points are shown with purplediamonds. HSB = helmet streamer boundary, HS flux = helmet streamer flux, FR = flux rope, FP = CME footpoints. Ananimation of this figure is available showing the evolution. The animation duration is 12 s. comes draped over the pseudostreamer once more andconnects to the middle null (NP2). This manifests inthe connectivity plot as a return to a tapered, ratherthan snub-nosed, end to the northern helmet-streamerboundary. The twist liberated by the reconnection ofthe flux rope is now able to access closed field beneaththe helmet streamer.Figure 11(c) shows the connectivity as the flux ropereconnects. The northern footpoint of the flux rope hasnow moved outside the pseudostreamer separatrix andconnects to a mixture of open coronal-hole field andclosed helmet-streamer flux that was draped over thepseudostreamer. At the moment of flux-rope opening,a burst of explosive reconnection is initiated at NP1.Bright local and remote ribbons would be expected toform near the inner and outer spines at Q2 and Q4, as well as along the semi-circular ribbon where the fanplane meets the surface, highlighted in Figure 11(c).The ribbon is semi-circular rather than a closed loop inthis case due to the multiple nulls in the pseudostreamertopology. Similar ribbon structures have been observedby, e.g., Kumar et al. (2021). Immediately after theflux rope opens and fast flare reconnection is under-way, Q1 and Q2 then outline the positions of the mainparallel flare ribbons. Subsequently, Q1 and Q2 moveapart as NP1 moves back towards the center of the pseu-dostreamer and into the open-field region, Figure 11(c)and (d).The above description reveals that the two key in-gredients that lead to the sympathetic blowout of thehelmet streamer are (1) the proximity of the edge ofthe helmet streamer to the edge of the pseudostreamer5 v ( k m / s ) l o g ( J ) (a) (b)(c) (d) Figure 12. (a) Selected CME field lines at t = 36 hrs 23 min. (b) & (d) Log of current density (statamp cm − ) and plasmavelocity in a plane across the CME flux rope. (c) Base difference (from t = 0) of scattered white light using the method employedby Lynch et al. (2016). An animation of panel (d) is available online showing the evolution. The animation duration is 6 s. and (2) the round-trip evolution of the null point as theflux rope reconnects. The shift of NP1 into and backout of the closed field under the helmet streamer seemsto be a consequence of both reconnection at the null,as described by Edmondson et al. (2009), and a shiftof the helmet streamer itself driven by interchange re-connection along its flank, similar to that shown by e.g.Higginson et al. (2017).Finally, the connectivity map also highlights the threeCME footpoints, Figure 11(d). This makes it immedi- ately clear that the southern footpoint FP3 forms nextto the original footpoint of the outer spine of NP1. Aswas highlighted by the field-line evolution in Figs. 6and 10, the northern footpoint of the flux rope discon-nects from the CME as it is swept up by the flare re-connection, to reside back in the closed field beneaththe pseudostreamer. As can be seen in the animationaccompanying Figure 11, FP2 forms when the northernflare ribbon (Q1) sweeps over the positive footpoint ofthe pre-eruption flux rope. This is the surface signature6 Figure 13. (a)-(c) Base-difference images (from t = 0) of scattered white light. (d) Height-time plot using running differenceimages. The dashed line in (a) shows the slit for the height-time plot. An animation of this figure is available online showingthe evolution. The animation duration is 4 s. of the interchange-like flare reconnection that occursabove, shifting some of the CME field-line footpointsfrom FP1 to FP2. The remaining sheared strappingfield adjacent to the pre-eruption flux rope also opensbut is not swept over by Q1, thereby forming FP1 atlater times (see also Fig. 10, cyan field lines). CORONAL MASS EJECTIONThe CME that results is a mixture of twisted/kinkedopen field lines from the coronal holes and closed fieldlines blown out from the helmet streamer. They arecombined within two main propagating magnetic struc-tures that form the CME. The first is the blown-outhelmet-streamer flux, which has footpoints predomi- nantly at FP1 and FP3. Figure 12(a) shows that fieldlines traced from FP3 (yellow) and FP1 (cyan) wraparound one another producing what normally would beidentified as the CME flux rope; we will designate it assuch from now on. However, the analysis of the pre-vious sections has shown that this flux rope is not thesame flux rope that originally erupted, but rather formslater in the evolution. The original flux rope due to thefilament channel was ejected as the pseudostreamer jet;this later flux rope forms from the coupling with the hel-met streamer field and erupts as a CME. When viewedfrom the side, this CME flux rope appears circular de-spite being composed of a mixture of open and closedfield lines, Figure 12(b). This circular feature is embed-7 t = 16 hrs 57min t = 28 hrs 37mint = 31 hrs 23min t = 38 hrs 3min(a)(c) (d)
Opened FluxFR Opening (b)
CME Flux Rope Open FieldSheath
Figure 14.
Connectivity evolution of the arc at 30 R s . Grey scale: log( Q ). White: open coronal-hole field. Yellow: disconnectedfield lines. The dashed red line shows the reversal in B r within the heliospheric current sheet. FR = flux rope. An animationof this figure is available online showing the evolution. The animation duration is 12 s. ded within kinked/twisted field lines that form the restof the CME and have footpoints predominantly at FP2,shown with red field lines in Figure 12(b). To more di-rectly compare the structure to observations, a syntheticwhite-light base-difference image produced at the sameviewing angle as the simulation cut is shown in Figure12(c). A bubble-like circular feature is indeed embeddedwithin the broader body of the CME; see also the movieaccompanying Figure 13.Kumar et al. (2021) reported a series of observationsshowing that, ahead of the CMEs produced by pseu-dostreamer eruptions, a small jet-like puff first appears,associated with the opening of the strapping field bybreakout reconnection shortly before the eruption. InFigure 13(a)-(c) we show a series of synthetic corona-graph images from the same viewpoint, just prior tothe CME and as it propagates outward. As in the ob- servations, a puff formed by the breakout reconnectionoutflow and the opening of the strapping flux precedesthe main CME.Aside from the shock, the CME has a relatively nar-row angular extent of about 40 ◦ . Additionally, the CMEis deflected towards the heliospheric current sheet as itpropagates outward, as shown by the curved shape ofthe CME in Figure 13(b). Such a deflection is to beexpected, given that the jet straddles the open-closedhelmet-streamer boundary and, therefore, is guided to-wards its apex. We note that this deflection is not the re-sult of magnetic pressure gradients acting on the erupt-ing structure in the low corona, as has been proposedto account for CME deflections in some observed events(e.g. Shen et al. 2011; Kay et al. 2013). In that sce-nario the erupting magnetic structure is presumed to bea flux rope connected at both ends to the photosphere8with an axis at its apex that is roughly perpendicularto the ambient field it encounters. Here the eruptingstructure propagates along field lines in the low corona.The circular feature in the synthetic white-light imagesappears only after the disturbance reaches the helmetstreamer apex; when the CME flux rope forms and thehelmet streamer blows out. Prior to this the evolutionis more jet-like. Based on the location of the circularfeature in Figure 13(c) compared with the initial radialtrajectory of the jet, we estimate an apparent deflectionof around 30 ◦ .Figure 13(d) shows a time/distance plot (J-map) cre-ated from running different images evaluated along theline shown in Figure 13(a). We chose this non-radialline to capture both the puff and nose of the CME onceit is deflected. The pre-eruption puff is simply advectedby the ambient wind and follows a slowly acceleratingprofile. The CME, once launched, quickly overtakes thepuff before stabilizing at a roughly constant speed ofabout 600 km s − . Similar CME speeds and accelera-tion profiles have been measured for CMEs from pseu-dostreamers (e.g. Wang & Hess 2018). S-WEB CONNECTIVITY & IMPULSIVE SEPSThe mixture of open and closed flux within the CMEprovides a natural avenue of escape for impulsive SEPsproduced by the flare. Although a full investigation ofthe expected SEP signatures of this simulation is wellbeyond the scope of this investigation, we can still makesome preliminary remarks based on the connectivity ofthe CME. There are two potential scenarios where wemight expect SEPs to be impulsively accelerated and re-leased in this eruption. The first is the scenario exploredby Masson et al. (2013, 2019), whereby flare reconnec-tion prior to reconnection of the filament channel fluxrope stores high energy particles within the flux rope.These are then promptly released when the flux ropeis opened by reconnection with external field, in thiscase when the flux rope reaches the breakout currentlayer. The second is that once the flux rope opens theflare reconnection transitions to interchange-like recon-nection at NP1, directly accessing open field lines alongwhich SEPs could escape in a manner similar to a jet.These two scenarios overlap at the moment the flux ropeopens, but the latter would continue beyond the initialflux rope reconnection making them potentially distin-guishable observationally.Figure 14 shows log( Q ) at 30 R s at various stagesthroughout the eruption. The times are matched tothose in Figure 11 for comparison. Regions of discon-nected flux within the heliospheric current layer areshown in yellow. Broadly speaking, the open field af- fected by the eruption is localised around the left halfof the S-Web arc, the section which resided above thefilament channel. This is a useful result in itself andprovides a predictive tool for where impulsively accel-erated particles and subsequently the CME itself couldbe measured in-situ for CMEs originating from pseu-dostreamers.More specifically, throughout the breakout phase theaffected section of S-Web arc moves steadily southwardas strapping field is opened, Figure 14(b). The openingof the flux rope is shown in Figure 14(c) by the complexregion of high Q , which stretches almost to the middleof the arc. Both SEP scenarios would be expected tolaunch SEPs into this region. This shows that impulsiveSEPs could potentially reach far from the heliosphericcurrent sheet, in this case reaching around 30 ◦ from it inlatitude and covering a range of around 70 ◦ in longitude,due to the rapidly varying connectivity along the arc.Future work using for example test particles would berequired to test this claim definitively.Finally, for completeness Figure 14(d) shows the con-nectivity once the helmet streamer has blown out andthe CME is fully developed. The circular region corre-sponds to the open field lines that wrap into the CMEflux rope (cyan field lines, Fig. 12). This is bordered onone side by disconnected field (yellow) within the helio-spheric current sheet, and a semi-circular sheath of openfield corresponding to the rest of the kinked field lineswithin the CME (red field lines, Fig. 12). DISCUSSION AND CONCLUSIONSIn addition to observations of SEPs, our resultspresented here on coupled pseudostreamer/helmet-streamer eruptions have clear implications for under-standing solar eruptions. First, we emphasize that theassumed magnetic configuration of a pseudostreamerclose to the helmet streamer, Figure 3, is quite com-mon on the Sun. The coronal hole pattern of Figure2 in which a small coronal hole extension is separatedfrom the main coronal hole by a large parasitic polar-ity region can be seen frequently in source surface mapsand is reflected in S-Web maps (e.g. Antiochos et al.2011; Wang et al. 2012; Crooker et al. 2012; Titov et al.2012). Furthermore, filament channels are very oftenobserved to form over the PIL of the parasitic region,leading to a jet-like eruption (e.g. Filippov et al. 2013,2015; Yang et al. 2015; Wang & Hess 2018; Kumar et al.2021), so the scenario described in this paper shouldbe readily observed. We note that our scenario sharessome general features with streamer blowouts driven byeruptions beneath the streamer, but near its edge (e.g.Moore & Sterling 2007; Lugaz et al. 2011; Panesar et al.92016). The key difference is that in our scenario thepseudostreamer has a substantial presence outside thestreamer, within the coronal hole.Another key point is that our jet eruption is some-what special from a theoretical viewpoint in that it oc-curs in a 3D system with multiple nulls and separatorlines. There have been many simulations of jets andCMEs in the ubiquitous topology of a single null, butto our knowledge, this is the first simulation of a fila-ment channel driven eruption in a multi-null/separatortopology. This topology allows for more copious recon-nection, because the breakout current sheet now corre-sponds to a deformed line segment rather than a de-formed point. As argued in Antiochos et al. (1999),the breakout mechanism requires reconnection to oper-ate, but the reconnection must not be too “easy” if thesystem is to be explosive. Our simulation verifies thatbreakout can produce explosive eruption even in a gen-eral pseudostreamer topology.The eruption from the actual pseudostreamer, how-ever, is clearly a jet rather than a CME. We do not seeclosed pseudostreamer flux expanding outward into theheliosphere. This results holds even though the pseu-dostreamer of Figure 2 is quite large and, as discussedabove, the breakout reconnection is extended, more eas-ily allowing a flux rope to escape. Instead, the pseu-dostreamer flux rope is completely destroyed by inter-change reconnection either with the open field or thehelmet streamer field. We conjecture that this, in fact,is the general result for an eruption from a unipolarbackground as in a pseudostreamer or jet. The reasonsfor this are that first, a plasmoid in a unipolar back-ground must have its twist component anti-parallel tothe background field on one side or the other, so thatreconnection is inevitable. Second, the amount of fluxin the pseudostreamer rope is limited by the flux of theparasitic polarity, which is generally small compared tothe background. However, if the flux rope can surviveout to the Alfv´en radius ∼ R s , then any interchangebeyond this point has no effect on the amount of escap-ing flux, because a closed field line will still not retractback down to the corona. Depending on the balancebetween gas dynamic pressure and magnetic tension,this result may hold even at somewhat lower radii, say5 R s or so. These arguments imply that in order for apseudostreamer eruption to produce a CME when thepseudostreamer is deep within a coronal hole, the para-sitic polarity must have an exceptionally large amountof flux and the eruption must develop a high speed earlyon, which requires that the filament channel be highlysheared. Further simulations are required in order toquantify the fluxes and speeds required for an isolated pseudostreamer CME, if even possible, and observationsof pseudostreamer eruptions far from helmet streamersare needed to test the conclusions.The situation is very different for a helmet-streamereruption. In this case the background field is bidirec-tional and parallel to the plasmoid on both sides. Asa result, interchange reconnection does not occur and aplasmoid is free to propagate outward so that even smallplasmoids can survive indefinitely in the heliosphericcurrent sheet (Higginson & Lynch 2018). Evidence forthis behavior can be gleaned from our simulation in Fig-ures 10 and 12 and their associated animations, in whichtwisted, closed helmet-streamer field lines are swept upin the CME and expand outwards within or adjacentto the field reversal that defines the heliospheric currentsheet. A key conclusion from these figures and anima-tions is that not only does the field of the CME consist ofa mixture of closed and open flux, but the plasma as wellconsists of a mixture of material that was in the largeouter loops of the helmet streamer and the small innerloops of the parasitic polarity. This result has importantconsequences for in-situ measurements of plasma com-position. Even in the outer layers of a streamer-blowoutevent, the plasma may have originated from the smallclosed loops of a decayed active region, with a differ-ent FIP bias and freeze-in temperature from the helmetstreamer. Again, this result requires definitive testingagainst data.This work also has important implications for under-standing S-web dynamics. The bulk of the S-Web con-sists of high- Q arcs that start and end on the helio-spheric current sheet, as in Figure 14. All these arcsare due to large parasitic polarity regions that producenarrow or singular connections between coronal holes(Antiochos et al. 2011; Titov et al. 2012; Scott et al.2018, 2019). These polarity regions have PILs, whichwill invariably become sheared with time; consequently,the type of eruption that we calculated above is boundto be a frequent driver of the S-Web. Our results showthat the S-web is intrinsically coupled, in that strongdynamics at one location are likely to lead to dynam-ics elsewhere with the subsequent mixing of plasma andfield lines. This conclusion may help explain the long-standing puzzle of flare SEPs with large longitudinalextent (e.g. Dresing et al. 2012; Richardson et al. 2014)although further work is required to confirm this.Perhaps the most important and far-reaching conclu-sions from this new type of coupled eruption are for un-derstanding the interplay between solar eruptions andthe global coronal magnetic field. Taken alongside pre-vious work, our results suggest that CMEs originatingnearby the helmet streamer separatrix, be it beneath0the helmet streamer or adjacent to it in a coronal hole,should be expected to be deflected, have a more com-plex morphology and to involve a mixture of open andclosed magnetic field lines. Whereas eruptions from deepwithin the closed field will form classic CMEs and if ourconjecture is correct those from pseudostreamers deepwithin coronal holes will form jets. Accurate global fieldmodeling, supported by further simulation studies of thecoupling between eruptions and the global coronal field,is clearly then crucial to predicting and interpreting thein-situ and remote-sensing observations being made bycurrent and future solar missions.ACKNOWLEDGMENTSIt is a pleasure to thank Sophie Masson andAleida Higginson for useful discussions regarding pseu-dostreamers and the solar wind. PFW was supportedin this work by the award of an RAS fellowship andPROBA2 Guest Investigator grant. PFW thanks MatWest for supplying the SWAP image and MarilenaMierla for support during his visit to ROB. BJL, PK,JTK, CRD and SKA were supported by NASA’s H-ISFM, H-LWS, and H-SR programs. Computer re-sources for the numerical calculations were provided toCRD by NASA’s High-End Computing program at theNASA Center for Climate Simulation. REFERENCES Antiochos, S. K. 1990, MemSAI, 61, 369Antiochos, S. K., DeVore, C. R., & Klimchuk, J. A. 1999,ApJ, 510, 485Antiochos, S. K., Miki´c, Z., Titov, V. S., Lionello, R., &Linker, J. A. 2011, ApJ, 731, 112Asai, A., Shibata, K., Hara, H., & Nitta, N. V. 2008, ApJ,673, 1188Aulanier, G., Janvier, M., & Schmieder, B. 2012, A&A,543, A110Chen, Y., Du, G., Zhao, D., et al. 2016, ApJL, 820, L37Crooker, N. U., Antiochos, S. K., Zhao, X., & Neugebauer,M. 2012, JGRA, 117, A04104Dahlin, J. T., Antiochos, S. K., & DeVore, C. R. 2019, ApJ,879, 96D´emoulin, P., Priest, E. R., & Lonie, D. P. 1996, JGRA,101, 7631DeVore, C. R. 1991, JCoPh, 92, 142Dresing, N., G´omez-Herrero, R., Klassen, A., et al. 2012,SoPh, 281, 281Edmondson, J. K., Lynch, B. J., Antiochos, S. K., De Vore,C. R., & Zurbuchen, T. H. 2009, ApJ, 707, 1427 Filippov, B., Koutchmy, S., & Tavabi, E. 2013, SoPh, 286,143Filippov, B., Srivastava, A. K., Dwivedi, B. N., et al. 2015,MNRAS, 451, 1117Haynes, A. L., & Parnell, C. E. 2007, PhPl, 14, 082107Higginson, A. K., Antiochos, S. K., DeVore, C. R., Wyper,P. F., & Zurbuchen, T. H. 2017, ApJ, 837, 113Higginson, A. K., & Lynch, B. J. 2018, ApJ, 859, 6Howard, R., & Labonte, B. J. 1981, SoPh, 74, 131Janvier, M., Aulanier, G., Pariat, E., & D´emoulin, P. 2013,A&A, 555, A77Jin, M., Schrijver, C. J., Cheung, M. C. M., et al. 2016,ApJ, 820, 16Karpen, J. T., Antiochos, S. K., & DeVore, C. R. 2012,ApJ, 760, 81Kay, C., Opher, M., & Evans, R. M. 2013, ApJ, 775, 5Kumar, P., Karpen, J. T., Antiochos, S. K., et al. 2018,ApJ, 854, 155—. 2019, ApJ, 873, 93—. 2021, ApJ, in press1