Transition from collisional to kinetic regimes in large-scale reconnection layers

Multispecies Ion Acceleration in 3D Magnetic Reconnection with Hybrid-Kinetic Simulations

Magnetic reconnection drives multispecies particle acceleration broadly in space and astrophysics. We perform the first 3D hybrid simulations (fluid electrons, kinetic ions) that contain sufficient scale separation to produce nonthermal heavy-ion acceleration, with fragmented flux ropes critical for accelerating all species. We demonstrate the acceleration of all ion species (up to Fe) into power-law spectra with similar indices, by a common Fermi acceleration mechanism. The upstream ion velocities influence the first Fermi reflection for injection. The subsequent onsets of Fermi acceleration are delayed for ions with lower charge-mass ratios (Q/M), until growing flux ropes magnetize them. This leads to a species-dependent maximum energy/nucleon ∝(Q/M)^{α}. These findings are consistent with in situ observations in reconnection regions, suggesting Fermi acceleration as the dominant multispecies ion acceleration mechanism.

Experimental Evidence of Plasmoids in High-β Magnetic Reconnection

Magnetic reconnection is a ubiquitous and fundamental process in plasmas by which magnetic fields change their topology and release magnetic energy. Despite decades of research, the physics governing the reconnection process in many parameter regimes remains controversial. Contemporary reconnection theories predict that long, narrow current sheets are susceptible to the tearing instability and split into isolated magnetic islands (or plasmoids), resulting in an enhanced reconnection rate. While several experimental observations of plasmoids in the regime of low-to-intermediate β (where β is the ratio of plasma thermal pressure to magnetic pressure) have been made, there is a relative lack of experimental evidence for plasmoids in the high-β reconnection environments which are typical in many space and astrophysical contexts. Here, we report strong experimental evidence for plasmoid formation in laser-driven high-β reconnection experiments.

Interchange reconnection as the source of the fast solar wind within coronal holes

The fast solar wind that fills the heliosphere originates from deep within regions of open magnetic field on the Sun called 'coronal holes'. The energy source responsible for accelerating the plasma is widely debated; however, there is evidence that it is ultimately magnetic in nature, with candidate mechanisms including wave heating^1,2 and interchange reconnection^3-5. The coronal magnetic field near the solar surface is structured on scales associated with 'supergranulation' convection cells, whereby descending flows create intense fields. The energy density in these 'network' magnetic field bundles is a candidate energy source for the wind. Here we report measurements of fast solar wind streams from the Parker Solar Probe (PSP) spacecraft⁶ that provide strong evidence for the interchange reconnection mechanism. We show that the supergranulation structure at the coronal base remains imprinted in the near-Sun solar wind, resulting in asymmetric patches of magnetic 'switchbacks'^7,8 and bursty wind streams with power-law-like energetic ion spectra to beyond 100 keV. Computer simulations of interchange reconnection support key features of the observations, including the ion spectra. Important characteristics of interchange reconnection in the low corona are inferred from the data, including that the reconnection is collisionless and that the energy release rate is sufficient to power the fast wind. In this scenario, magnetic reconnection is continuous and the wind is driven by both the resulting plasma pressure and the radial Alfvénic flow bursts.

Marginally stable current sheets in collisionless magnetic reconnection

Noncollisional current sheets that form during the nonlinear development of spontaneous magnetic reconnection are characterized by a small thickness, of the order of the electron skin depth. They can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. In this work, we investigate the marginal stability conditions for the development of plasmoids when the forming current sheet is purely collisionless and in the presence of a strong guide field. We analyze the geometry that characterizes the reconnecting current sheet, and what promotes its elongation. Once the reconnecting current sheet is formed, we identify the regimes for which it is plasmoid unstable. Our study shows that plasmoids can be obtained, in this context, from current sheets with an aspect ratio much smaller than in the collisional regime, and that the plasma flow channel of the marginally stable current layers maintains an inverse aspect ratio of 0.1.

Energized Oxygen in the Magnetotail: Onset and Evolution of Magnetic Reconnection

Oxygen ions are a major constituent of magnetospheric plasma, yet the role of oxygen in processes such as magnetic reconnection continues to be poorly understood. Observations show that significant amounts of energized O⁺ can be present in a magnetotail current sheet (CS). A population of thermal O⁺ only has a relatively minor effect on magnetic reconnection. Despite this, published studies have so far only concentrated on the role of the low-energy thermal O⁺. We present a study of magnetic reconnection in a thinning CS with energized O⁺ present. Well-established, three-species, 2.5D particle-in-cell (PIC) kinetic simulations are used. Simulations of thermal H⁺ and thermal O⁺ validate our setup against published results. We then energize a thermal background O⁺ based on published in situ measurements. A range of energization is applied to the background O⁺. We discuss the effects of energized O⁺ on CS thinning and the onset and evolution of magnetic reconnection. The presence of energized O⁺ causes a two-regime onset response in a thinning CS. As energization increases in the lower-regime, reconnection develops at a single primary X-line, increases time-to-onset, and suppresses the rate of evolution. As energization continues to increase in the higher-regime, reconnection develops at multiple X-lines, forming a stochastic plasmoid chain; decreases time-to-onset; and enhances evolution via a plasmoid instability. Energized O⁺ drives a depletion of the background H⁺ around the central CS. As the energization increases, the CS thinning begins to slow and eventually reverses.

Relativistic Nonthermal Particle Acceleration in Two-Dimensional Collisionless Magnetic Reconnection

Magnetic reconnection, especially in the relativistic regime, provides an efficient mechanism for accelerating relativistic particles and thus offers an attractive physical explanation for nonthermal high-energy emission from various astrophysical sources. I present a simple analytical model that elucidates key physical processes responsible for reconnection-driven relativistic nonthermal particle acceleration (NTPA) in the large-system, plasmoid-dominated regime in two dimensions. The model aims to explain the numerically-observed dependencies of the power-law index p and high-energy cutoff γ_c of the resulting nonthermal particle energy spectrum f(γ) on the ambient plasma magnetization σ, and (for γ_c ) on the system size L. In this self-similar model, energetic particles are continuously accelerated by the out-of-plane reconnection electric field E _rec until they become magnetized by the reconnected magnetic field and eventually trapped in plasmoids large enough to confine them. The model also includes diffusive Fermi acceleration by particle bouncing off rapidly moving plasmoids. I argue that the balance between electric acceleration and magnetization controls the power-law index, while trapping in plasmoids governs the cutoff, thus tying the particle energy spectrum to the plasmoid distribution.

Efficient Nonthermal Ion and Electron Acceleration Enabled by the Flux-Rope Kink Instability in 3D Nonrelativistic Magnetic Reconnection

The relaxation of field-line tension during magnetic reconnection gives rise to a universal Fermi acceleration process involving the curvature drift of particles. However, the efficiency of this mechanism is limited by the trapping of energetic particles within flux ropes. Using 3D fully kinetic simulations, we demonstrate that the flux-rope kink instability leads to strong field-line chaos in weak-guide-field regimes where the Fermi mechanism is most efficient, thus allowing particles to transport out of flux ropes and undergo further acceleration. As a consequence, both ions and electrons develop clear power-law energy spectra that contain a significant fraction of the released energy. The low-energy bounds are determined by the injection physics, while the high-energy cutoffs are limited only by the system size. These results have strong relevance to observations of nonthermal particle acceleration in space and astrophysics.

Thermodynamic Phase Transition in Magnetic Reconnection

By examining the entropy production in fully kinetic simulations of collisional plasmas, it is shown that the transition from collisional Sweet-Parker reconnection to collisionless Hall reconnection may be viewed as a thermodynamic phase transition. The phase transition occurs when the reconnection electric field satisfies E=E_{D}sqrt[m_{e}/m_{i}], where m_{e}/m_{i} is the electron-to-ion mass ratio and E_{D} is the Dreicer electric field. This condition applies for all m_{i}/m_{e}, including m_{i}/m_{e}=1, where the Hall regime vanishes and a direct phase transition from the collisional to the kinetic regime occurs. In the limit m_{e}/m_{i}→0, this condition is equivalent to there being a critical electron temperature T_{e}≈m_{i}Ω_{i}^{2}δ^{2}, where Ω_{i} is the ion cyclotron frequency and δ is the current sheet half-thickness. The heat capacity of the current sheet changes discontinuously across the phase transition, and a critical power law is identified in an effective heat capacity. A model for the time-dependent evolution of an isolated current sheet in the collisional regime is derived.

Comparative Analysis of the Vlasiator Simulations and MMS Observations of Multiple X-Line Reconnection and Flux Transfer Events

The Vlasiator hybrid-Vlasov code was developed to investigate global magnetospheric dynamics at ion-kinetic scales. Here we focus on the role of magnetic reconnection in the formation and evolution of magnetic islands at the low-latitude magnetopause, under southward interplanetary magnetic field conditions. The simulation results indicate that (1) the magnetic reconnection ion kinetics, including the Earthward pointing Larmor electric field on the magnetospheric side of an X-point and anisotropic ion distributions, are well-captured by Vlasiator, thus enabling the study of reconnection-driven magnetic island evolution processes, (2) magnetic islands evolve due to continuous reconnection at adjacent X-points, "coalescence" which refers to the merging of neighboring islands to create a larger island, "erosion" during which an island loses magnetic flux due to reconnection, and "division" which involves the splitting of an island into smaller islands, and (3) continuous reconnection at adjacent X-points is the dominant source of magnetic flux and plasma to the outer layers of magnetic islands resulting in cross-sectional growth rates up to + 0.3 RE 2/min. The simulation results are compared to the Magnetospheric Multiscale (MMS) measurements of a chain of ion-scale flux transfer events (FTEs) sandwiched between two dominant X-lines. The MMS measurements similarly reveal (1) anisotropic ion populations and (2) normalized reconnection rate ~0.18, in agreement with theory and the Vlasiator predictions. Based on the simulation results and the MMS measurements, it is estimated that the observed ion-scale FTEs may grow Earth-sized within ~10 min, which is comparable to the average transport time for FTEs formed in the subsolar region to the high-latitude magnetopause. Future simulations shall revisit reconnection-driven island evolution processes with improved spatial resolutions.

Magnetic reconnection in partially ionized plasmas

Magnetic reconnection has been intensively studied in fully ionized plasmas. However, plasmas are often partially ionized in astrophysical environments. The interactions between the neutral particles and ionized plasmas might strongly affect the reconnection mechanisms. We review magnetic reconnection in partially ionized plasmas in different environments from theoretical, numerical, observational and experimental points of view. We focus on mechanisms which make magnetic reconnection fast enough to compare with observations, especially on the reconnection events in the low solar atmosphere. The heating mechanisms and the related observational evidence of the reconnection process in the partially ionized low solar atmosphere are also discussed. We describe magnetic reconnection in weakly ionized astrophysical environments, including the interstellar medium and protostellar discs. We present recent achievements about fast reconnection in laboratory experiments for partially ionized plasmas.

Why does Steady-State Magnetic Reconnection have a Maximum Local Rate of Order 0.1?

Simulations suggest collisionless steady-state magnetic reconnection of Harris-type current sheets proceeds with a rate of order 0.1, independent of dissipation mechanism. We argue this long-standing puzzle is a result of constraints at the magnetohydrodynamic (MHD) scale. We predict the reconnection rate as a function of the opening angle made by the upstream magnetic fields, finding a maximum reconnection rate close to 0.2. The predictions compare favorably to particle-in-cell simulations of relativistic electron-positron and nonrelativistic electron-proton reconnection. The fact that simulated reconnection rates are close to the predicted maximum suggests reconnection proceeds near the most efficient state allowed at the MHD scale. The rate near the maximum is relatively insensitive to the opening angle, potentially explaining why reconnection has a similar fast rate in differing models.

Perspectives on magnetic reconnection

Magnetic reconnection is a topological rearrangement of magnetic field that occurs on time scales much faster than the global magnetic diffusion time. Since the field lines break on microscopic scales but energy is stored and the field is driven on macroscopic scales, reconnection is an inherently multi-scale process that often involves both magnetohydrodynamic (MHD) and kinetic phenomena. In this article, we begin with the MHD point of view and then describe the dynamics and energetics of reconnection using a two-fluid formulation. We also focus on the respective roles of global and local processes and how they are coupled. We conclude that the triggers for reconnection are mostly global, that the key energy conversion and dissipation processes are either local or global, and that the presence of a continuum of scales coupled from microscopic to macroscopic may be the most likely path to fast reconnection.

Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment

The formation of an elongated Sweet-Parker current sheet and a transition to plasmoid instability has for the first time been predicted by simulations in a large-scale toroidal fusion plasma in the absence of any preexisting instability. Plasmoid instability is demonstrated through resistive MHD simulations of transient coaxial helicity injection experiments in the National Spherical Torus Experiment (NSTX). Consistent with the theory, fundamental characteristics of the plasmoid instability, including fast reconnection rate, have been observed in these realistic simulations. Motivated by the simulations, experimental camera images have been revisited and suggest the existence of reconnecting plasmoids in NSTX. Global, system-size plasmoid formation observed here should also have strong implications for astrophysical reconnection, such as rapid eruptive solar events.

Turbulent reconnection and its implications

Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes happening in magnetized plasmas. In most astrophysical environments, the Reynolds numbers corresponding to plasma flows are large and therefore the transition to turbulence is inevitable. This turbulence, which can be pre-existing or driven by magnetic reconnection itself, must be taken into account for any theory of magnetic reconnection that attempts to describe the process in the aforementioned environments. This necessity is obvious as three-dimensional high-resolution numerical simulations show the transition to the turbulence state of initially laminar reconnecting magnetic fields. We discuss ideas of how turbulence can modify reconnection with the focus on the Lazarian & Vishniac (Lazarian & Vishniac 1999 Astrophys. J. 517, 700-718 (doi:10.1086/307233)) reconnection model. We present numerical evidence supporting the model and demonstrate that it is closely connected to the experimentally proven concept of Richardson dispersion/diffusion as well as to more recent advances in understanding of the Lagrangian dynamics of magnetized fluids. We point out that the generalized Ohm's law that accounts for turbulent motion predicts the subdominance of the microphysical plasma effects for reconnection for realistically turbulent media. We show that one of the most dramatic consequences of turbulence is the violation of the generally accepted notion of magnetic flux freezing. This notion is a cornerstone of most theories dealing with magnetized plasmas, and therefore its change induces fundamental shifts in accepted paradigms, for instance, turbulent reconnection entails reconnection diffusion process that is essential for understanding star formation. We argue that at sufficiently high Reynolds numbers the process of tearing reconnection should transfer to turbulent reconnection. We discuss flares that are predicted by turbulent reconnection and relate this process to solar flares and γ-ray bursts. With reference to experiments, we analyse solar observations in situ as measurements in the solar wind or heliospheric current sheet and show the correspondence of data with turbulent reconnection predictions. Finally, we discuss first-order Fermi acceleration of particles that is a natural consequence of the turbulent reconnection.

Plasma physics of extreme astrophysical environments

Among the incredibly diverse variety of astrophysical objects, there are some that are characterized by very extreme physical conditions not encountered anywhere else in the Universe. Of special interest are ultra-magnetized systems that possess magnetic fields exceeding the critical quantum field of about 44 TG. There are basically only two classes of such objects: magnetars, whose magnetic activity is manifested, e.g., via their very short but intense gamma-ray flares, and central engines of supernovae (SNe) and gamma-ray bursts (GRBs)--the most powerful explosions in the modern Universe. Figuring out how these complex systems work necessarily requires understanding various plasma processes, both small-scale kinetic and large-scale magnetohydrodynamic (MHD), that govern their behavior. However, the presence of an ultra-strong magnetic field modifies the underlying basic physics to such a great extent that relying on conventional, classical plasma physics is often not justified. Instead, plasma-physical problems relevant to these extreme astrophysical environments call for constructing relativistic quantum plasma (RQP) physics based on quantum electrodynamics (QED). In this review, after briefly describing the astrophysical systems of interest and identifying some of the key plasma-physical problems important to them, we survey the recent progress in the development of such a theory. We first discuss the ways in which the presence of a super-critical field modifies the properties of vacuum and matter and then outline the basic theoretical framework for describing both non-relativistic and RQPs. We then turn to some specific astrophysical applications of relativistic QED plasma physics relevant to magnetar magnetospheres and to central engines of core-collapse SNe and long GRBs. Specifically, we discuss the propagation of light through a magnetar magnetosphere; large-scale MHD processes driving magnetar activity and responsible for jet launching and propagation in GRBs; energy-transport processes governing the thermodynamics of extreme plasma environments; micro-scale kinetic plasma processes important in the interaction of intense electric currents flowing through a magnetar magnetosphere with the neutron star surface; and magnetic reconnection of ultra-strong magnetic fields. Finally, we point out that future progress in applying RQP physics to real astrophysical problems will require the development of suitable numerical modeling capabilities.

Plasmoid and Kelvin-Helmholtz instabilities in Sweet-Parker current sheets

A two-dimensional (2D) linear theory of the instability of Sweet-Parker (SP) current sheets is developed in the framework of reduced magnetohydrodynamics. A local analysis is performed taking into account the dependence of a generic equilibrium profile on the outflow coordinate. The plasmoid instability [Loureiro et al., Phys. Plasmas 14, 100703 (2007)] is recovered, i.e., current sheets are unstable to the formation of a large-wave-number chain of plasmoids (k(max)L(CS)~S(3/8), where k(max) is the wave number of fastest growing mode, S=L(CS)V(A)/η is the Lundquist number, L(CS) is the length of the sheet, V(A) is the Alfvén speed, and η is the plasma resistivity), which grows super Alfvénically fast (γ(max)τ(A)~S(1/4), where γ(max) is the maximum growth rate, and τ(A)=L(CS)/V(A)). For typical background profiles, the growth rate and the wave number are found to increase in the outflow direction. This is due to the presence of another mode, the Kelvin-Helmholtz (KH) instability, which is triggered at the periphery of the layer, where the outflow velocity exceeds the Alfvén speed associated with the upstream magnetic field. The KH instability grows even faster than the plasmoid instability γ(max)τ(A)~k(max)L(CS)~S(1/2). The effect of viscosity (ν) on the plasmoid instability is also addressed. In the limit of large magnetic Prandtl numbers Pm=ν/η, it is found that γ(max)~S(1/4)Pm(-5/8) and k(max)L(CS)~S(3/8)Pm(-3/16), leading to the prediction that the critical Lundquist number for plasmoid instability in the Pm>>1 regime is S(crit)~10(4)Pm(1/2). These results are verified via direct numerical simulation of the linearized equations, using an analytical 2D SP equilibrium solution.

Distribution of plasmoids in high-Lundquist-number magnetic reconnection

The distribution function f(ψ) of magnetic flux ψ in plasmoids formed in high-Lundquist-number current sheets is studied by means of an analytic phenomenological model and direct numerical simulations. The distribution function is shown to follow a power law f(ψ)∼ψ(-1), which differs from other recent theoretical predictions. Physical explanations are given for the discrepant predictions of other theoretical models.

Demonstration of anisotropic fluid closure capturing the kinetic structure of magnetic reconnection

Collisionless magnetic reconnection in high-temperature plasmas has been widely studied through fluid-based models. Here, we present results of fluid simulation implementing new equations of state for guide-field reconnection. The new fluid closure accurately accounts for the anisotropic electron pressure that builds in the reconnection region due to electric and magnetic trapping of electrons. In contrast to previous fluid models, our fluid simulation reproduces the detailed reconnection region as observed in fully kinetic simulations. We hereby demonstrate that the new fluid closure self-consistently captures all the physics relevant to the structure of the reconnection region, providing a gateway to a renewed and deeper theoretical understanding of reconnection in weakly collisional regimes.

Theory of magnetic reconnection in solar and astrophysical plasmas

Magnetic reconnection is a fundamental process in a plasma that facilitates the release of energy stored in the magnetic field by permitting a change in the magnetic topology. In this paper, we present a review of the current state of understanding of magnetic reconnection. We discuss theoretical results regarding the formation of current sheets in complex three-dimensional magnetic fields and describe the fundamental differences between reconnection in two and three dimensions. We go on to outline recent developments in modelling of reconnection with kinetic theory, as well as in the magnetohydrodynamic framework where a number of new three-dimensional reconnection regimes have been identified. We discuss evidence from observations and simulations of Solar System plasmas that support this theory and summarize some prominent locations in which this new reconnection theory is relevant in astrophysical plasmas.

Secondary magnetic islands generated by the Kelvin-Helmholtz instability in a reconnecting current sheet

Magnetic islands or flux ropes produced by magnetic reconnection have been observed on the magnetopause, in the magnetotail, and in coronal current sheets. Particle-in-cell simulations of magnetic reconnection with a guide field produce elongated electron current layers that spontaneously produce secondary islands. Here, we explore the seed mechanism that gives birth to these islands. The most commonly suggested theory for island formation is the tearing instability. We demonstrate that in our simulations these structures typically start out, not as magnetic islands, but as electron flow vortices within the electron current sheet. When some of these vortices first form, they do not coincide with closed magnetic field lines, as would be the case if they were islands. Only after they have grown larger than the electron skin depth do they couple to the magnetic field and seed the growth of finite-sized islands. The streaming of electrons along the magnetic separatrix produces the flow shear necessary to drive an electron Kelvin-Helmholtz instability and produce the initial vortices. The conditions under which this instability is the dominant mechanism for seeding magnetic islands are explored.

Plasmoid ejection and secondary current sheet generation from magnetic reconnection in laser-plasma interaction

Reconnection of the self-generated magnetic fields in laser-plasma interaction was first investigated experimentally by Nilson et al. [Phys. Rev. Lett. 97, 255001 (2006)] by shining two laser pulses a distance apart on a solid target layer. An elongated current sheet (CS) was observed in the plasma between the two laser spots. In order to more closely model magnetotail reconnection, here two side-by-side thin target layers, instead of a single one, are used. It is found that at one end of the elongated CS a fanlike electron outflow region including three well-collimated electron jets appears. The (>1 MeV) tail of the jet energy distribution exhibits a power-law scaling. The enhanced electron acceleration is attributed to the intense inductive electric field in the narrow electron dominated reconnection region, as well as additional acceleration as they are trapped inside the rapidly moving plasmoid formed in and ejected from the CS. The ejection also induces a secondary CS.

Flux pileup in collisionless magnetic reconnection: bursty interaction of large flux ropes

Using fully kinetic simulations of the island coalescence problem for a range of system sizes greatly exceeding kinetic scales, the phenomenon of flux pileup in the collisionless regime is demonstrated. While small islands on the scale of λ ≤ 5 ion inertial length (d(i)) coalesce rapidly and do not support significant flux pileup, coalescence of larger islands is characterized by large flux pileup and a weaker time averaged reconnection rate that scales as √(d(i)/λ) while the peak rate remains nearly independent of island size. For the largest islands (λ = 100d(i)), reconnection is bursty and nearly shuts off after the first bounce, reconnecting ~20% of the available flux.

Fast magnetic reconnection in the plasmoid-dominated regime

A conceptual model of resistive magnetic reconnection via a stochastic plasmoid chain is proposed. The global reconnection rate is shown to be independent of the Lundquist number. The distribution of fluxes in the plasmoids is shown to be an inverse-square law. It is argued that there is a finite probability of emergence of abnormally large plasmoids, which can disrupt the chain (and may be responsible for observable large abrupt events in solar flares and sawtooth crashes). A criterion for the transition from the resistive magnetohydrodynamic to the collisionless regime is provided.

Comparison of secondary islands in collisional reconnection to Hall reconnection

Large-scale resistive Hall-magnetohydrodynamic simulations of the transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic reconnection are presented; the first to separate secondary islands from collisionless effects. Three main results are described. There exists a regime with secondary islands but without collisionless effects, and the reconnection rate is faster than Sweet-Parker, but significantly slower than Hall reconnection. This implies that secondary islands do not cause the fastest reconnection rates. The onset of Hall reconnection ejects secondary islands from the vicinity of the X line, implying that energy is released more rapidly during Hall reconnection. Coronal applications are discussed.

In situ observations of a secondary magnetic island in an ion diffusion region and associated energetic electrons

Numerical simulations have predicted that an extended current sheet may be unstable to secondary magnetic islands in the vicinity of the X line, and these islands can dramatically influence the reconnection rate. In this Letter, we present the first evidence of such a secondary island near the center of an ion diffusion region, which is consistent with the action of the secondary island instability occurring in the vicinity of the X line. The island is squashed in the z direction with a strong core magnetic field. Energetic electrons with anisotropic or field-aligned bidirectional fluxes are found in the ion diffusion region, and the enhancement of energetic electron fluxes is more obvious inside the secondary island.