Bursty magnetic reconnection at the Earth's magnetopause triggered by high-speed jets

The impact of high-speed jets -- dynamic pressure enhancements in the magnetosheath -- on the Earth's magnetopause has been observed to trigger local magnetic reconnection. We perform a three-dimensional hybrid simulation to study the magnetosheath and magnetopause under turbulent conditions using a quasi-radial southward interplanetary magnetic field (IMF). In contrast to quasi-steady reconnection with a strong southward IMF, we show that after the impact of a jet on the magnetopause, the magnetopause moves inwards, the current sheet is compressed and intensified and signatures of local magnetic reconnection are observed, showing similarities to spacecraft measurements


I. INTRODUCTION
Magnetic reconnection is a fundamental plasma process in which the topology of magnetic field lines changes, often accompanied by the conversion of magnetic energy to kinetic energy 1 . Reconnection is important in space and astrophysical environments, and has been the subject of observational, experimental and computational study 1,2 . In the Earth's magnetosphere, reconnection at the magnetopause and in the magnetotail drives global magnetospheric dynamics 3 , leading to magnetic storms 4 and substorms 5 .
Understanding how the plasma environment affects the nature of reconnection is an area of interest. Reconnection is affected by factors such as turbulence 6 , background flows 7 and driving of the plasma 8 . We focus on reconnection at the Earth's magnetopause, which depends on magnetosheath conditions 9 .
Upstream of the quasi-parallel regions of the Earth's bow shock (where the angle between the magnetic field and the shock normal is less than 45 • ), the presence of reflected ions gives rise to streaming instabilities which excite ultra-low frequency (ULF) waves 10 , which are then convected towards the bow shock. As they approach the bow shock, they can grow in amplitude and interact nonlinearly, which can lead to the formation of structures  24 . It has also been shown that jets can cause magnetopause reconnection 25,26 . In Ref. 26 it is suggested that reconnection triggered by jets may cause throat aurorae, while Ref. 25 provides in situ observational evidence that high-speed jet caused compression of the magnetopause boundary, triggering magnetopause reconnection.
Because of the importance of kinetic physics at the quasi-parallel shock, hybrid simulations (kinetic ion, fluid electrons) are an important tool for studying global processes that govern turbulent plasma dynamics in the foreshock and the magnetosheath. Compared to full particle simulations, the hybrid model captures ion kinetic effects at greatly reduced computational costs 27 . Hybrid simulations have had success in simulations of dayside processes. With respect to the quasi-parallel shock, simulations have shown the formation of kinetic structures such as diamagnetic cavities 15 , spontaneous hot-flow anomalies (SHFAs) 17, 28 and their impact on the magnetosheath. The nature and effects of magnetic reconnection at the magnetopause has also been studied under different southward IMF conditions 29-32 . Under quasi-radial IMF conditions, two dimensional simulations have found jets and reconnection in the magnetosheath downstream of the quasi-parallel shock, but reconnection at the magnetopause was not studied 33 . More recently, three dimensional simulations have shown the formation of large high-speed jets and their impact on the magnetopause and the cusp 34 .
In this work, we use a three-dimensional hybrid model to study the magnetosphere under quasi-radial IMF conditions. We focus on the interaction of high-speed jets with the magnetopause and show that signatures of local reconnection are observed after jet impact, in a manner similar to observations 25 .

II. SIMULATION SETUP
In this study we use a space-time adaptive hybrid particle-in-cell simulation code, HYPERS [34][35][36] . Ions are evolved kinetically while the electrons are treated as a chargeneutralising fluid. The magnetic field is updated using Faraday's Law and the electric field is determined by a generalised Ohm's Law. The resistivity used in this model is as follows: Here ω pe and ω pi are the electron and ion plasma frequencies respectively, n min is the cutoff (minimum) electron density allowed in the simulation, J is the current density, T e is the electron temperature and m i is the ion mass. ω ci,sw and ω pi,sw are the initial solarwind values of the respective quantities. η ch is the Chodura resistivity, which is an empirical expression previously used to model field-reversed configurations 37 . The "vacuum resistivity" The initial Alfvén Mach number is 8 (i. e. v 0 /v A = 8). The dipole strength is scaled such that the nominal magnetopause standoff distance is approximately 100 d i , which is much larger than the minimum distance required to simulate an earthlike magnetosphere (≈ 20d i ) 38 .
The inner boundary is a hemisphere of radius 50 d i with absorbing boundary conditions for particles and perfectly conducting boundaries for fields. We note that distances are scaled down for computational feasibility such that R E ∼ 12d i rather than realistically ∼ 60d i .
Unless otherwise mentioned, in the rest of the paper, ρ = en e and | B| are normalised by their upstream values, v is normalised by the upstream Alfvén speed and lengths are normalised by the ion inertial length d i . The current density J is normalised by en 0 c, and Ω ci is the ion cyclotron frequency calculated using the IMF.

III. RESULTS
In the following analysis, we use the Geocentric Solar Magnetospheric (GSM) coordinate system, where the x-axis points from the Earth towards the Sun, the y axis is in the dawn- dusk direction and the z-axis completes the right hand system.
An overview of the system after the magnetosphere has developed is shown in Fig. 1.
This shows the density in a subset of the x-z midplane at y = 0.5. Upstream of the quasiparallel shock there are density perturbations caused by the waves in the foreshock, which are convected towards the bow shock as described in other hybrid simulations 15,17,33 . The quasiparallel region of the bow shock is highly dynamic, with a rippled structure and no clear shock normal. Kinetic structures such as cavitons 15,16 and spontaneous hot-flow anomalies (SHFA, one example is shown in Fig. 1) 17 are also observed in this region as expected. As can be seen at the different times, the structure of the magnetosheath is dynamic in both space and time.
The first time interval we study is tΩ ci = 231-247, during which a high-speed jet impacts the magnetopause, producing signatures of magnetic reconnection. An illustration of the jet just before its arrival at the magnetopause is shown in Fig. 2, in which the dynamic pressure ρv 2 x at tΩ ci = 238 is plotted. Here a region of the enhanced dynamic pressure ρv 2 x , which is used to identify the jet in the magnetosheath (e.g. Refs. 18, 34, and 39), can be seen where the planes intersect. The approximate locations of the magnetopause and bow shock are marked by the white lines, which are contours of ρ = 2. The maximum dynamic pressure associated with the jet is approximately 180, compared to 64 for the solar wind. The evolution of the jet and its effect on the magnetopause can be seen in Fig. 3, which shows the dynamic pressure ρv 2 x and current density J y at y = 27.5 during the time interval considered. The dynamic pressure threshold value ρv 2 x = 0.5ρ 0 v 2 0 is used to highlight the jet location relative to the magnetopause, and is plotted as black contours in the lower panels.
Here the jet can be seen in the region with 0 < ∼ z < ∼ 25. Following the impact of the jet, there is an inward perturbation of the magnetopause and an intensification of the current density, as can be seen in the region with z > 0.

A. Magnetopause reconnection
During this time interval, signatures of magnetic reconnection are observed. This can be seen in Fig. 3, in which the evolution of B z and ηJ y is shown. We note that finite ηJ y is a necessary but not sufficient condition for magnetopause reconnection to take place. As As with the previous event, there is a quasi-steady reconnection region at negative z, and the arrival of a jet leads to the development of a reconnection region around z = 20. In this instance the x-line is oriented approximately 10 • from the negative y-axis in the +z direction and there is a guide field B g ∼ 0.4|B 0 |. The reconnection event here lasts until approximately tΩ ci = 384, for an interval of 6/Ω ci or approximately 30/Ω ci,ms (note that the upstream magnetosheath field is slightly weaker than in the previous event).
To illustrate the reconnection geometry, we use the four-field junction method, identifying In Fig. 6 we show a three-dimensional view with slices of ηJ y at tΩ ci = 238, 247 and 378.
There are field lines of four different topologies where ηJ y is enhanced, which is consistent with magnetic reconnection taking place. These figures illustrate the three different reconnection regions discussed earlier. At tΩ ci = 247, the inward dent in the magnetopause can also be seen in the x-y plane, and has a width of approximately 30 d i (∼ 2.5R E ).
A flux rope, a signature of reconnection, is illustrated in Fig. 7 at tΩ ci = 238 approximately 5d i below the lower reconnection site. Here the twisting of the field lines is right- There are inflows in the x direction and outflows in the positive and negative z directions which are not evident in the two-dimensional slices because these flows are not co-planar.
The large negative values of v x visible in the magnetosheath are due to the bulk flow, but the velocity is less negative immediately upstream to the reconnection region, with magnitude < 0.1 of the outflow speed.
In asymmetric reconnection, the predicted reconnection rate can be calculated using the . The discrepancies may be due to the inhomogeneities in the upstream parameters, and the measured outflow speeds being smaller than the model's asymmetric outflow used in the rate calculation.

B. Magnetopause motion and magnetosheath fluctuations
A detailed view of the evolution of relevant physical quantities for the event at tΩ ci = 247 can be seen in Fig. 9. It shows the one-dimensional structure of the magnetosheath and magnetopause at y = 27.5, z = 18.5 where the jet-triggered reconnection site is. The inward perturbation of the magnetopause can be tracked using the density and B z plots, showing a displacement of approximately 6 d i (∼ 0.5R E ). The approach of the jet towards the magnetopause can be seen in the bottom panel, which shows the evolution of the dynamic pressure. Along this cut, the peak dynamic pressure is at tΩ ci = 241, but the jet still continues to approach the magnetopause after. This can also be seen in Fig. 3. The evolution is qualitatively similar during the second jet triggered event (not shown).
Reconnection signatures can also be seen in these traces. As B z evolves, the field reversal layer at the magnetopause becomes narrower, and the peak negative B z increases. Because of this, the current density and ηJ y at the magnetopause both increase, reaching maxima at tΩ ci = 247. We note that it is the thinning of the current sheet caused by the jet which leads to reconnection, in this case taking place after the inward motion of the magnetopause has stopped.
The fluctuations with the oscillating B z structures may be related to the transmission of foreshock waves. This is similar to the propagating "wavefronts" seen in earlier twodimensional hybrid simulations at the quasi-parallel region of the bow shock 33

C. Discussion
As mentioned in the introduction, there have been observations of high-speed jets causing R E scale indentations [20][21][22] , and triggering reconnection 25 . The events we study in our simulation show similarities with some features of these observations. The indentation we find at the magnetopause after the jet arrives has a scale size (2.5R E ) similar to these observations.
After the jets arrive, the field reversal region becomes narrower, and signatures of transient local reconnection are seen. These aspects are consistent with the observations.
While there is magnetopause motion associated with the jet impact, the cause of reconnection in the observations was attributed to the compression of the current sheet, and reconnection was observed during the outward phase of the magnetopause motion 25 . In the simulation, the peak current density also occurs at the end of the time interval shown when the current sheet is thinner, after the jet arrives and the motion of the magnetopause begins to reverse, which can be seen most clearly in the density trace of Fig. 9.
In the simulation there are additional effects that may contribute to the transient magne- the locations of reconnection sites due to the geometry alone are expected to be displaced south of the subsolar point. This is confirmed in our simulations, in which quasi-steady reconnection events are found in the z < 0 regions. The jet-triggered reconnection events in our simulation, however are found at z > 0, away from the typical reconnection regions.

IV. SUMMARY
We have performed a 3D hybrid simulation with a steady quasi-radial southward IMF, focusing on establishing the relationship between magnetosheath jets and bursty reconnection at the magnetopause, in contrast to the quasi-steady reconnection commonly observed under strong southward IMF conditions. We find that high-speed jets compress the magnetopause and reduce the width of the current layer. This leads to local magnetic reconnection with visible plasma outflows. The simulation results may explain the observations of jet-triggered magnetopause reconnection 25 . We also note the presence of strong negative B z structures convected towards the magnetopause which can potentially contribute to inducing recon-nection events.