We investigate the large scale evolution of a relativistic magnetic reconnection in an electron-positron pair plasma by a relativistic two-fluid magnetohydrodynamic (MHD) code. We introduce an inter-species friction force as an effective resistivity to dissipate magnetic fields. We demonstrate that magnetic reconnection successfully occurs in our two-fluid system, and that it involves Petschek-type bifurcated current layers in later stage. We further observe a quasi-steady evolution thanks to an open boundary condition, and find that the Petschek-type structure is stable over the long time period. Simulation results and theoretical analyses exhibit that the Petschek outflow channel becomes narrower when the reconnection inflow contains more magnetic energy, as previously claimed. Meanwhile, we find that the reconnection rate goes up to ~1 in extreme cases, which is faster than previously thought. The role of the resistivity, implications for reconnection models in the magnetically dominated limit, and relevance to kinetic reconnection works are discussed.
Resistive relativistic magnetohydrodynamic (RRMHD) simulations are applied to investigate the system evolution of relativistic magnetic reconnection. A time-split Harten--Lan--van Leer method is employed. Under a localized resistivity, the system exhibits a fast reconnection jet with an Alfvénic Lorentz factor inside a narrow Petschek-type exhaust. Various shock structures are resolved in and around the plasmoid such as the post-plasmoid vertical shocks and the "diamond-chain" structure due to multiple shock reflections. Under a uniform resistivity, Sweet--Parker-type reconnection slowly evolv…
Magnetic reconnection with a 0.1 rate: Effective resistivity in general relativistic magnetohydrodynamics
Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；Department of Physics, University of Toronto（多伦多大学物理系）；David A. Dunlap Department of Astronomy & Astrophysics, University of Toronto（多伦多大学大卫·邓拉普天文与天体物理系）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Astronomy, Columbia University（哥伦比亚大学天文学系）；Center for Computational Astrophysics, Flatiron Institute（平顿研究所计算天体物理学中心）；Department of Physics, University of Maryland（马里兰大学物理系）；Princeton Center for Theoretical Science and Department of Astrophysical Sciences, Princeton University（普林斯顿大学理论科学中心和天体物理科学系）；Anton Pannekoek Institute（安东·潘内克研究所）
Axion magnetohydrodynamics and reconnection-driven axion bursts
Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa（里斯本高等工程学院，里斯本理工学院）；GoLP/Instituto de Plasmas e Fusão Nuclear, Instituto Superior Técnico, Universidade de Lisboa（等离子体与核聚变研究所，里斯本技术学院，里斯本大学）
The magnetic fields can change their topology through a process known as magnetic reconnection. This process in not only important for understanding the origin and evolution of the large-scale magnetic field, but is seen as a possibly efficient particle accelerator producing cosmic rays mainly through the first order Fermi process. In this work we study the properties of particle acceleration in reconnection zones and show that the velocity component parallel to the magnetic field of test particles inserted in nearly non-resistive magnetohydrodynamic (MHD) domains of reconnection without inclu…
Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on magnetic reconnection is determined by a complex behavior with quasi-singular forming current layers enriched by their associated small scale magnetic islands called plasmoids. A new code for the solution of two dimensional dissipative magnetohydrodynamics (MHD) equations in cartesian geometry specifically developed to this end is thus presented. A current-vorticity formulation representative of an inco…
We develop a first-principles model for the relativistic magnetic reconnection rate in strongly magnetized pair plasmas. By considering the energy budget and required current density near the x-line, we analytically show that in the magnetically-dominated relativistic regime, the x-line thermal pressure is significantly lower than the upstream magnetic pressure due to the extreme energy needed to sustain the current density, consistent with kinetic simulations. This causes the upstream magnetic field lines to collapse in, producing the open outflow geometry which enables fast reconnection. The…
We apply the general relativistic resistive magnetohydrodynamics code {\tt BHAC} to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski spacetime. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly nonlinear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and non-uniform res…
Magnetic reconnection in strongly magnetized astrophysical plasma environments is believed to be the primary process for fast energy release and particle energization. Currently there is strong interest in relativistic magnetic reconnection, in that it may provide a new explanation for high-energy particle acceleration and radiation in strongly magnetized astrophysical systems. We review recent advances in particle acceleration and reconnection physics in the magnetically-dominated regime. More discussion is focused on the physics of particle acceleration, power-law formation as well as the re…
Comparison of magnetic diffusion and reconnection in ideal and resistive relativistic magnetohydrodynamics, ideal magnetodynamics, and resistive force-free electrodynamics
Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfvénic timescales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributi…
Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of l…
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysi…
The nonlinear evolution of relativistic magnetic reconnection in sheared magnetic configuration (with a guide field) is investigated by using two-dimensional relativistic two-fluid simulations. Relativistic guide field reconnection features the charge separation and the guide field compression in and around the outflow channel. As the guide field increases, the composition of the outgoing energy changes from enthalpy-dominated to Poynting-dominated. The inertial effects of the two-fluid model play an important role to sustain magnetic reconnection. Implications for the single fluid magnetohydr…
The magnetic reconnection process is studied in relativistic pair plasmas when the thermal and inertial properties of the magnetohydrodynamical fluid are included. We find that in both Sweet-Parker and Petschek relativistic scenarios there is an increase of the reconnection rate owing to the thermal-inertial effects, both satisfying causality. To characterize the new effects we define a thermal-inertial number which is independent of the relativistic Lundquist number, implying that reconnection can be achieved even for vanishing resistivity as a result of only thermal-inertial effects. The cur…
We present a new theoretical picture of magnetically dominated, decaying turbulence in the absence of a mean magnetic field. We demonstrate that such turbulence is governed by the reconnection of magnetic structures, and not by ideal dynamics, as has previously been assumed. We obtain predictions for the magnetic-energy decay laws by proposing that turbulence decays on reconnection timescales, while respecting the conservation of certain integral invariants representing topological constraints satisfied by the reconnecting magnetic field. As is well known, the magnetic helicity is such an inva…
We report turbulence effects on magnetic reconnection in relativistic plasmas using 3-dimensional relativistic resistive magnetohydrodynamics simulations. We found reconnection rate became independent of the plasma resistivity due to turbulence effects similarly to non-relativistic cases. We also found compressible turbulence effects modified the turbulent reconnection rate predicted in non-relativistic incompressible plasmas; The reconnection rate saturates and even decays as the injected velocity approaches to the Alfvén velocity. Our results indicate the compressibility cannot be neglected …
The fluid-scale evolution of relativistic magnetic reconnection is investigated by using two-fluid and magnetofluid simulation models. Relativistic two-fluid simulations demonstrate the meso-scale evolution beyond the kinetic scales, and exhibit quasi-steady Petschek-type reconnection. Resistive relativistic MHD simulations further show new shock structures in and around the downstream magnetic island (plasmoid). General discussions on these models are presented.
Magnetohydrodynamic turbulence and magnetic reconnection are ubiquitous in astrophysical environments. In most situations, these processes do not occur in isolation, but interact with each other. This renders a comprehensive theory of these processes highly challenging. Here, we propose a theory of magnetohydrodynamic turbulence driven at large scale that self-consistently accounts for the mutual interplay with magnetic reconnection occurring at smaller scales. Magnetic reconnection produces plasmoids that grow from turbulence-generated noise and eventually disrupt the sheet-like structures in…
Relativistic Sweet-Parker type magnetic reconnection is investigated by relativistic resistive magnetohydrodynamic (RRMHD) simulations. As an initial setting, we assume anti-parallel magnetic fields and a spatially uniform resistivity. A perturbation imposed on the magnetic fields triggers magnetic reconnection around a current sheet, and the plasma inflows into the reconnection region. The inflows are then heated due to ohmic dissipation in the diffusion region, and finally become relativistically hot outflows. The outflows are not accelerated to ultra-relativistic speeds (i.e., Lorentz facto…
Recently, magnetic reconnection, where a relativistically hot plasma is confined by a strong magnetic field, has received great attention in relation to astrophysical objects (e.g., pulsar magnetosphere and magnetar). However, reconnection with relativistic high-speed drift current in the plasma sheet has not been investigated yet. Thus, from both the theoretical and computational points of view, we studied the growth rate of relativistic reconnection for the high-speed drift current in a relativistically hot plasma sheet. Consequently, we argue that, contrary to the conventional understanding…
During magnetically dominated relativistic reconnection, inflowing plasma depletes the initial relativistic pressure at the x-line and collisionless plasma heating inside the diffusion region is insufficient to overcome this loss. The resulting pressure drop causes a collapse at the x-line, essentially a localization mechanism of the diffusion region necessary for fast reconnection. The extension of this low-pressure region further explains the bursty nature of anti-parallel reconnection because a once opened outflow exhaust can also collapse, which repeatedly triggers secondary tearing island…
Particle acceleration in the magnetic reconnection of electron-positron plasmas is studied by using a particle-in-cell simulation. It is found that a significantly large number of nonthermal particles are generated by the inductive electric fields around an X-type neutral line when the reconnection outflow velocity, which is known to be an Alfvén velocity, is on the order of the speed of light. In such a relativistic reconnection regime, we also find that electrons and positrons form a power-law-like energy distribution through their drift along the reconnection electric field under the relati…
Magnetic reconnection associated to the double tearing mode (DTM) is investigated by means of resistive relativistic magnetohydrodynamic (RRMHD) simulations. A linearly unstable double current sheet system in two dimensional cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the nonlinear evolution of the magnetic islands. The latter reconnection phase and time scale appear to weakly depend on the plasma resistivity and magnetization parameter. We …
Magnetic reconnection in relativistic collisionless plasmas can accelerate particles and power high-energy emission in various astrophysical systems. Whereas most previous studies focused on relativistic reconnection in pair plasmas, less attention has been paid to electron-ion plasma reconnection, expected in black hole accretion flows and relativistic jets. We report a comprehensive particle-in-cell numerical investigation of reconnection in an electron-ion plasma, spanning a wide range of ambient ion magnetizations $σ_i$, from the semirelativistic regime (ultrarelativistic electrons but non…
This review discusses the physics of magnetic reconnection, a process in which the magnetic field topology changes and magnetic energy is converted to kinetic energy, in pair plasmas in the relativistic regime. We focus on recent progress in the field driven by theory advances and the maturity of particle-in-cell codes. This work shows that fragmentation instabilities at the current sheet can play a critical role in setting the reconnection speed and affect the resulting particle acceleration, anisotropy, bulk flows, and radiation. Then, we discuss how this novel understanding of relativistic …
We investigate the saturation of particle acceleration in relativistic reconnection using two-dimensional particle-in-cell simulations at various magnetizations σ. We find that the particle energy spectrum produced in reconnection quickly saturates as a hard power law that cuts off at γ~4σ, confirming previous work. Using particle tracing, we find that particle acceleration by the reconnection electric field in X-points determines the shape of the particle energy spectrum. By analyzing the current sheet structure, we show that physical cause of saturation is the spontaneous formation of second…
We derive basic scaling equations for relativistic magnetic reconnection in the general case of asymmetric inflow conditions and obtain predictions for the outflow Lorentz factor and the reconnection rate. Kinetic Particle-in-Cell simulations show that the outflow speeds as well as the nonthermal spectral index are constrained by the inflowing plasma with the weaker magnetic energy per particle, in agreement with the scaling predictions. These results are significant for understanding non-thermal emission from reconnection in magnetically-dominated, astrophysical systems, many of which may be …
We present large scale 3D particle-in-cell (PIC) simulations to examine particle energization in magnetic reconnection of relativistic electron-positron (pair) plasmas. The initial configuration is set up as a relativistic Harris equilibrium without a guide field. These simulations are large enough to accommodate a sufficient number of tearing and kink modes. Contrary to the non-relativistic limit, the linear tearing instability is faster than the linear kink instability, at least in our specific parameters. We find that the magnetic energy dissipation is first facilitated by the tearing insta…
Magnetic reconnection is believed to be the driver of many explosive phenomena in Astrophysics, from solar to gamma-ray flares in magnetars and in the Crab nebula. However, reconnection rates from classic MHD models are far too slow to explain such observations. Recently, it was realized that when a current sheet gets sufficiently thin, the reconnection rate of the tearing instability becomes "ideal", in the sense that the current sheet destabilizes on the "macroscopic" Alfvénic timescales, regardless of the Lundquist number of the plasma. Here we present 2D compressible MHD simulations in the…
A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid pha…
Relativistic magnetic reconnection events can widely exist in magnetized plasmas in astrophysical systems. During this process, oppositely directed magnetic field lines reconnect and release magnetic energy, efficiently accelerating nonthermal particles. However, so far there is little clear observational signatures of relativistic magnetic reconnection events in astrophysical systems. Blazars are relativistic magnetized plasma outflows from supermassive black holes. Their multi-wavelength flares may be powered by relativistic magnetic reconnection. The highly variable radiation and polarizati…
Ultra-high energy cosmic rays (UHECRs) may be produced in active galactic nuclei (AGN) or gamma-ray burst (GRB) jets. I argue that magnetic reconnection in jets can accelerate UHECRs rather independently of physical processes in the magnetic dissipation region. First order Fermi acceleration can efficiently take place in the region where the unreconnected (upstream) magnetized fluid converges into the reconnection layer. I find that protons can reach energies up to E~10^{20} eV in GRB and powerful AGN jets while iron nuclei can reach similar energies in AGN jets of more moderate luminosity.
Using two-dimensional particle-in-cell simulations, we characterize the energy spectra of particles accelerated by relativistic magnetic reconnection (without guide field) in collisionless electron-positron plasmas, for a wide range of upstream magnetizations $σ$ and system sizes $L$. The particle spectra are well-represented by a power law $γ^{-α}$, with a combination of exponential and super-exponential high-energy cutoffs, proportional to $σ$ and $L$, respectively. For large $L$ and $σ$, the power-law index $α$ approaches about 1.2.
While a growing body of research indicates that relativistic magnetic reconnection is a prodigious source of particle acceleration in high-energy astrophysical systems, the dominant acceleration mechanism remains controversial. Using a combination of fully kinetic simulations and theoretical analysis, we demonstrate that Fermi-type acceleration within the large-scale motional electric fields dominates over direct acceleration from non-ideal electric fields within small-scale diffusion regions. This result has profound implications for modeling particle acceleration in large-scale astrophysical…
Basic properties of relativistic magnetic reconnection in electron-positron pair plasmas are investigated by using a particle-in-cell (PIC) simulation. We first revisit a problem by Hesse & Zenitani (2007), who examined the kinetic Ohm's law across the X line. We formulate a relativistic Ohm's law by decomposing the stress-energy tensor. Then, the role of the new term, called the heat-flow inertial term, is examined in the PIC simulation data. We further evaluate the energy balance in the reconnection system. These analyses demonstrate physically transparent ways to diagnose relativistic kinet…
Using fully kinetic simulations, we study the scaling of the inflow speed of collisionless magnetic reconnection from the non-relativistic to ultra-relativistic limit. In the anti-parallel configuration, the inflow speed increases with the upstream magnetization parameter $σ$ and approaches the light speed when $σ> O(100)$, leading to an enhanced reconnection rate. In all regimes, the divergence of pressure tensor is the dominant term responsible for breaking the frozen-in condition at the x-line. The observed scaling agrees well with a simple model that accounts for the Lorentz contraction of…
Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two- and three-dimensional kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron-positron plasmas starting with a magnetically dominated, force-free current sheet ($σ\equiv B^2/(4πn_e m_e c^2) \gg 1$). For this limit, we demonstrate that relativis…
By means of two- and three-dimensional particle-in-cell simulations, we investigate the process of driven magnetic reconnection at the termination shock of relativistic striped flows. In pulsar winds and in magnetar-powered relativistic jets, the flow consists of stripes of alternating magnetic field polarity, separated by current sheets of hot plasma. At the wind termination shock, the flow compresses and the alternating fields annihilate by driven magnetic reconnection. Irrespective of the stripe wavelength "lambda" or the wind magnetization "sigma" (in the regime sigma>>1 of magnetically-do…
Powerful flares from blazars with short ($\sim$ min) variability timescales are challenging for current models of blazar emission. Here, we present a physically motivated ab initio model for blazar flares based on the results of recent particle-in-cell (PIC) simulations of relativistic magnetic reconnection. PIC simulations demonstrate that quasi-spherical plasmoids filled with high-energy particles and magnetic fields are a self-consistent by-product of the reconnection process. By coupling our PIC-based results (i.e., plasmoid growth, acceleration profile, particle and magnetic content) with…
We performed numerical simulations of general relativistic magnetohydrodynamics with uniform resistivity to investigatethe occurrence of magnetic reconnection in a split-monopole magnetic field around a Schwarzschild black hole. We found that magnetic reconnection happens near the black hole at its equatorial plane. The magnetic reconnection has a point-like reconnection region and slow shock waves, as in the Petschek reconnection model. The magnetic reconnection rate decreases as the resistivity becomes smaller. When the global magnetic Reynolds number is $10^4$ or larger, the magnetic reconn…
Particle acceleration by magnetic reconnection is now recognized as an important process in magnetically dominated regions of galactic and extragalactic black hole sources. This process helps to solve current puzzles specially related to the origin of the very high energy flare emission in these sources. In this review, we discuss this acceleration mechanism and show recent analytical studies and multidimensional numerical SRMHD and GRMHD (special and general relativistic magnetohydrodynamical) simulations with the injection of test particles, which help us to understand this process both in r…
The concept of magnetic connections is extended to non-ideal relativistic magnetohydrodynamical plasmas. Adopting a general set of equations for relativistic magnetohydrodynamics including thermal-inertial, thermal electromotive, Hall and current-inertia effects, we derive a new covariant connection equation showing the existence of generalized magnetofluid connections that are preserved during the dissipationless plasma dynamics. These connections are intimately linked to a general antisymmetric tensor that unifies the electromagnetic and fluid fields, allowing the extension of the magnetic c…
Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density $σ\equiv B^2/(4 πn m_ec^2) > 1$ and when the system size is sufficiently large. In the limit $σ\gg 1$, the spectral ind…
The magnetic reconnection process is analyzed for relativistic magnetohydrodynamical plasmas around rotating black holes. A simple generalization of the Sweet-Parker model is used as a first approximation to the problem. The reconnection rate, as well as other important properties of the reconnection layer, have been calculated taking into account the effect of spacetime curvature. Azimuthal and radial current sheet configurations in the equatorial plane of the black hole have been studied, and the case of small black hole rotation rate has been analyzed. For the azimuthal configuration, it is…
Relativistic effects in the oscillatory damping of magnetic disturbances near two-dimensional X-points are investigated. By taking into account displacement current, we study new features of extremely magnetized systems, in which the Alfvén velocity is almost the speed of light. The frequencies of the least-damped mode are calculated using linearized relativistic MHD equations for wide ranges of the Lundquist number S and the magnetization parameter $σ$. These timescales approach constant values in the large resistive limit: the oscillation time becomes a few times the light crossing time, irr…
Magnetohydrodynamic instabilities play an important role in accretion disks systems. Besides the well-known effects of the magnetorotational instability (MRI), the Parker-Rayleigh-Taylor instability (PRTI) also arises as an important mechanism to help in the formation of the coronal region around an accretion disk and in the production of magnetic reconnection events similar to those occurring in the solar corona. In this work, we have performed three-dimensional magnetohydrodynamical (3D-MHD) shearing-box numerical simulations of accretion disks with an initial stratified density distribution…
The unusually short durations, high luminosities, and high photon energies of the Crab Nebula gamma-ray flares require relativistic bulk motion of the emitting plasma. We explain the Crab flares as the result of randomly oriented relativistic "minijets" originating from reconnection events in a magnetically dominated plasma. We develop a statistical model of the emission from Doppler boosted reconnection minijets and find analytical expressions for the moments of the resulting nebula light curve (e.g. time average, variance, skewness). The light curve has a flat power spectrum that transitions…
The energy dissipation mechanism within Gamma-Ray Burst (GRB) outflows, driving their extremely luminous prompt $γ$-ray emission is still uncertain. The leading candidates are internal shocks and magnetic reconnection. While the emission from internal shocks has been extensively studied, that from reconnection still has few quantitative predictions. We study the expected prompt-GRB emission from magnetic reconnection and compare its temporal and spectral properties to observations. The main difference from internal shocks is that for reconnection one expects relativistic bulk motions with Lore…
A model of global magnetic reconnection rate in relativistic collisionless plasmas is developed and validated by the fully kinetic simulation. Through considering the force balance at the upstream and downstream of the diffusion region, we show that the global rate is bounded by a value $\sim 0.3$ even when the local rate goes up to $\sim O(1)$ and the local inflow speed approaches the speed of light in strongly magnetized plasmas. The derived model is general and can be applied to magnetic reconnection under widely different circumstances.
Electron acceleration during magnetic reconnection is thought to play a key role in time-variable high-energy emission from astrophysical systems. By means of particle-in-cell simulations of trans-relativistic reconnection, we investigate electron injection and acceleration mechanisms in low-$β$ electron-proton plasmas. We set up a diversity of density and field structures (e.g., X-points and plasmoids) by varying the guide field strength and choosing whether to trigger reconnection or let it spontaneously evolve. We show that the number of X-points and plasmoids controls the efficiency of ele…
Blazars are relativistic magnetized plasma outflows from supermassive black holes that point very close to our line of sight. Their emission is nonthermal dominated and highly variable across the entire electromagnetic spectrum. Relativistic magnetic reconnection has been proposed as the driver of particle acceleration during blazar flares. While recent particle-in-cell simulations have self-consistently studied the evolution of magnetic reconnection and particle acceleration therein, the resulting radiation signatures have not been systematically explored. In particular, the polarization sign…
