Dayside Pc2 Waves Associated With Flux Transfer Events in a 3D Hybrid‐Vlasov Simulation

Flux transfer events (FTEs) are transient magnetic flux ropes at Earth's dayside magnetopause formed due to magnetic reconnection. As they move across the magnetopause surface, they can generate disturbances in the ultralow frequency (ULF) range, which then propagate into the magnetosphere. This study provides evidence of ULF waves in the Pc2 wave frequency range (>0.1 Hz) caused by FTEs during dayside reconnection using a global 3D hybrid‐Vlasov simulation (Vlasiator). These waves resulted from FTE formation and propagation at the magnetopause are particularly associated with large, rapidly moving FTEs. The wave power is stronger in the morning than afternoon, showing local time asymmetry. In the pre and postnoon equatorial regions, significant poloidal and toroidal components are present alongside the compressional component. The noon sector, with fewer FTEs, has lower wave power and limited magnetospheric propagation.

• Dayside Pc2 waves (>0.1 Hz) have been detected in a 3D hybrid-Vlasov simulation • These waves exhibit lower intensity within the magnetosphere at noon, compared to the prenoon and postnoon sectors • Pc2 waves observed in the simulation are associated with largest and fast moving flux transfer events initiated by subsolar reconnection

Supporting Information:
Supporting Information may be found in the online version of this article.
Several observational and numerical studies have demonstrated that dayside reconnection can occur in either bursty and patchy patterns or in a continuous or quasi-steady manner with multiple reconnection points or separator lines occurring sequentially (e.g., Fear et al., 2008;Guo et al., 2021;Hasegawa et al., 2006Hasegawa et al., , 2010;;Hoilijoki et al., 2017;Pfau-Kempf et al., 2020;Tan et al., 2011;Trattner et al., 2021;Walsh et al., 2017;H. Wang et al., 2019).This deforms the magnetopause, creating recurring FTEs that are often accompanied by ULF pulsations at the magnetopause (Yagodkina & Vorobjev, 1997).Measurements from off-equatorial magnetospheric regions (Y.H. Liu et al., 2012) and research based on indirect observations (Arnoldy et al., 1988;Kokubun et al., 1988;Yagodkina & Vorobjev, 1997) have speculated that FTEs could also generate waves in the Pc1-2 frequency range.However, the direct link between waves in the frequency range above Pc3 and FTEs has not been made.This paper establishes the first direct link between Pc2 waves and the propagation and formation of FTEs on the dayside, utilizing a 3D hybrid-Vlasov simulation.

Model
In this study, we used the Vlasiator simulation (Palmroth et al., 2023), a global hybrid-Vlasov model described in Von Alfthan et al. ( 2014), Palmroth et al. (2018), and Ganse et al. (2023).Vlasiator self-consistently models the global ion dynamics using a 6D phase space (3D in physical space and 3D in velocity space) while electrons are treated as a charge-neutralizing fluid.The Ohm's law includes the convective, Hall, and electron pressure terms assuming an adiabatic electron fluid.Further implementation details of Vlasiator can be found in Palmroth et al. (2018).
The simulation was carried out in a domain defined by the boundaries −57.8, 57.8] R E , with R E corresponding to the Earth's radius of 6,371 km, encompassing the near-Earth solar wind, the dayside magnetosphere and an extended magnetotail and based on Geocentric Solar Ecliptic coordinate system.The inner boundary was a near-ideal conducting sphere at a distance of 4.7 R E , and the simulation employed adaptive mesh refinement with three levels of spatial resolution, the highest resolution (0.16 R E ) around the magnetopause and magnetotail current sheet (Ganse et al., 2023).The simulation setup incorporated constant and homogeneous solar wind conditions, with the solar wind velocity of 750 km s −1 along the -x direction, a purely southward interplanetary magnetic field of 5 nT, a solar wind density of n sw = 1 cm −3 , a solar wind temperature of T sw = 5 × 10 5 K, and an Alfvénic Mach number of M = 6.9.
Vlasiator's capability to resolve kinetic physics in detail results, among others, in its capability to reproduce the velocity distribution function in detail, as many of the kinetic physics and waves arise from the higher energy populations that are well resolved both in space and in velocity space (see Palmroth et al., 2023).Vlasiator has been shown to capture various ion kinetic phenomena (Hoilijoki et al., 2017;Pfau-Kempf et al., 2018, 2020).

Results
In this section, we present findings from the simulation described above, conducted for a duration of 1,506 s.Our analysis considers data collected after the initialization phase, 662 s of the simulation.To characterize Pc2 waves in the simulation, we remove the background magnetic field by subtracting a moving average calculated over an interval much longer than the period of the ULF waves of interest.In this work we are interested in the frequency range above 0.1 Hz.Thus, the window for the moving average is set to 100 s, which can also capyure ULF waves with frequencies down to 0.006 Hz including those in the Pc4 range.We denote this magnetic field variation vector, with the background subtracted, as δB.All field parameters are transformed into local magnetic field-aligned coordinates (FAC) following the method outlined in Regi et al. (2017).The FAC system has three axes: one axis aligned with the local magnetic field direction (δB p ) and two axes perpendicular to it, along the radial (δB r ) and azimuthal directions (δB a ).In addition to the FAC system we also used the LMN coordinate system and the contouring method described in Alho et al. (2023) to identify FTE axes and their distributions.In this coordinate system L is along the maximum local variation of the magnetic field, N is orthogonal to L and approximately normal to the magnetopause current sheet, and M completes the right-handed orthonormal system.We also used the gradient of the normal magnetic field around the magnetopause as a proxy to determine the size of FTEs.

ULF Waves Near the Magnetopause
To investigate the generation of Pc2 waves near passing FTEs, in Figure 1 we present a case study involving a virtual satellite situated at coordinates [x = 8.95, y = −3.5, z = 1.57]R E within the magnetosphere (indicated by a blue star).This virtual satellite observes magnetic field pulsations, and Figures 1b and 1c depict the variations of the parallel magnetic field component (δB p ) and its wavelet power spectrum calculated using Morlet wavelet (Torrence & Compo, 1998).The wavelet power spectrum shows enhanced wave power in two distinct frequency bands: one localized in the frequency range between 0.1 and 0.3 Hz with a peak of 0.125 Hz (corresponding to Pc2 waves with an 8-s period), and another between 5 and 20 mHz with a peak at 10 mHz, corresponding to Pc4 waves.Our focus in this study is on the Pc2 waves.We also present a movie of these waves on three planes which are associated with prenoon, noon and postnoon periods (see Movie S1).In the movie, Pc2 waves represented by δB p are shown on planes at y = 3.5 R E (postnoon), y = 0 R E (noon), and y = −3.5 R E .The waves are originated from the magnetopause and propagating into the magnetosphere, and are more prominent in the post and prenoon planes.
In the Earth's magnetosphere, ULF waves typically exhibit a combination of polarizations, including compressional, toroidal, and poloidal modes (Lee & Lysak, 1989;McPherron, 2005).Figures 1d-1f displays the three polarization components (compressional, toroidal, and poloidal) after filtering using a fifth order band-pass Butterworth filter within the frequency range of [0.1 to −0.5] Hz.The poloidal mode involves radial magnetic field pulsations and azimuthal electric field fluctuations, while the toroidal mode features variations in azimuthal magnetic field and radial electric field.The compressional mode is associated with oscillations mainly in the parallel magnetic field component and azimuthal electric field.Notably, there is significant interaction between compressional and poloidal oscillations, as both involve field line oscillations in the radial direction (Lee & Lysak, 1989).From all the three panels, starting around 870 s into the simulation, significant pulsation amplitudes occur periodically.To further investigate the spatial distribution of Pc2 waves depicted in Figure 1c, Figure 2 presents the distribution of wave power, averaged over the higher frequency band ([0.1-0.5]Hz) and during the entire simulation period with a similar approach used in Turc, Zhou, et al. (2022).This distribution is shown across three distinct planes in the dayside magnetosphere, with data collected after 800 s into the simulation when Pc2 waves first become apparent in the magnetosphere.The three polarization components (δB p , δB a , and δB r ) were extracted from planes at y = 3.5 R E (postnoon), y = 0 R E (noon), and y = −3.5 R E (prenoon).In the magnetosheath, the noon sector exhibits considerably higher compressional and poloidal mean wave power than the other sectors.In contrast, within the magnetosphere, the prenoon sector shows the highest values for all polarization components, followed by the postnoon sector.Compressional wave modes dominate over toroidal and poloidal Pc2 ULF waves in the pre-and postnoon sectors, with the latter showing lower wave power, as demonstrated in Figures 2b, 2c, 2h, and 2i.The poloidal and toroidal modes were not detected deep within the magnetosphere near the magnetospheric equatorial plane.Additionally, the mean wave power significantly decreases as we go toward the cusp in both hemispheres.Despite the higher values of all components in the noon sector of the magnetosheath, the noon sector within the magnetosphere lacks significant wave power.Overall, the poloidal and toroidal components are restricted within the region between magnetopause and x = 8 R E , however, the compressional mode is seen beyond x = 8 R E into the magnetosphere, especially in the prenoon sector (Y = −3.5 R E plane).

Origin of Pc2 Waves
To investigate the origin of the Pc2 waves depicted in Figure 2, in Figure 3 we demonstrate a correspondence between the FTEs along the magnetopause surface and the waves.We identified FTEs at a virtual spacecraft location approximately one Earth radius away in the x direction from where the waves are depicted in Figure 1a (blue star), near the magnetopause surface at coordinates [x = 10.05,y = −3.5, z = 1.57]R E .FTEs are typically recognized by the presence of a bipolar variation in the magnetic field component that is locally perpendicular to the magnetopause (Paschmann et al., 1982;Russell & Elphic, 1979).However, additional indicators, such as an increase in magnetic field strength on the magnetosheath side of the FTE or a decrease on the magnetosphere side, elevated total pressure, and an increase in plasma bulk velocity in the z direction, have also been used to identify FTEs (Paschmann et al., 1982;Sun et al., 2019;Teh et al., 2017;Zhang et al., 2011).
In Figures 3a-3d, the combination of the FTE-related parameters, including the magnetic field magnitude, the radial and normal components of the magnetic field, plasma density and pressure, the z-component of plasma velocity, and the derivative of the local normal magnetic field along the L direction are used to indicate the presence of FTEs (marked with vertical dashed lines).The variations in magnetic field magnitude, the bipolarity of B r and B N , along with peak pressure and density, collectively suggest the existence of FTEs.In panel (e) of this figure, we present the gradient of B N along the local magnetic field direction (L) to indirectly infer the size of the passing FTE.The significant variation and bipolarity of this gradient, after 900 s, around 1,100 s, and before 1,300 s, are observed near the wave packets shown in the last panel of Figure 3, indicating the presence of large FTEs passing by.
Upon comparing Figure 3f with the Movie S1, it becomes evident that FTEs, as they move along the magnetopause surface, give rise to the Pc2 waves.These waves are initiated during FTEs characterized by a significantly higher  stack plot along a curve parallel to the magnetopause surface and inside the magnetosphere that includes the blue star shown in Figure 1a.In addition, contour lines of X and O points are superimposed as described in Alho et al. (2023).Figure 5c shows a similar panel from Figure 1d.
Examining Figures 5b and 5c, we note that the first two wave packets observed during the time periods 900-1,060 and 1,100-1,200 in panel (c) are accompanied by reconnection events (X points) occurring around the sub-solar point (within 1 R E ), as well as one or more FTEs occurring away from this region, which is clearly visible in Movie S1.The subsequent wave packet observed after 1,300 s originates from the reconnection region, as no O points are observed during this time period and around the sub-solar point.It is also worth highlighting that the time periods before 750 s and after 1,400 s lack X points around the sub-solar point.The absence of waves between 700 and 800 s in Figure 4b is possibly due to the figure is taken from a surface parallel to the magnetopause surface, which is significantly further away from the magnetopause surface (small magnitude of fluctuation is seen in Figure 3f around this period), where the waves didn't propagate deep into the magnetosphere.To provide a schematic illustrating the scenario we propose to explain the observations throughout the entire simulation, we have included a schematic representation in Figure 5d.This illustration shows three source regions: one at the leading edge of the diverging FTEs, another at the reconnection region, and potentially the trailing edge of the two FTEs.During the entire simulation period (see Movie S1), the Pc2 waves observed originate from either of these three sources or a combination thereof.

Discussion
In this study, we have shown direct evidence of a previously speculated source of Pc2 waves which are associated with the formation and passage of FTEs along the magnetopause surface.Using a hybrid-Vlasov simulation, we demonstrated that these waves exhibit large wave power in the compressional, toroidal, and poloidal components with the compressional component being notably more dominant near the magnetospheric equator in close proximity to the magnetopause.Furthermore, we establish a strong connection between the presence of Pc2 waves and the occurrence of large, high-velocity FTEs initiated through a sub-solar reconnection.
In our simulation, despite the steady southward IMF, the reconnection process appears to be dynamic, as previously reported in 2D and 3D hybrid-Vlasov simulations by Hoilijoki et al. (2017) and Pfau-Kempf et al. (2020), as shown in Movie S1.Consequently, FTEs are continuously generated and propagate along the magnetopause.
It is important to note that all the solar wind parameters remain constant throughout the simulation period, ruling out the possibility of attributing the Pc2 waves observed in our study to solar wind variations (Usanova et al., 2012).While KHI can also generate ULF waves, their efficiency and persistence are notably enhanced when the IMF orientation is northward (Hwang, 2015;Kavosi & Raeder, 2015), which is not the case in our simulation.KHI also exist during southward IMF, however, they are thought to drive Pc4-5 waves (Kronberg et al., 2021;C. P. Wang et al., 2017).In addition, the process of ULF waves originating from foreshock-generated sources and propagating across the magnetopause (Turc, Roberts, et al., 2022) is excluded due to the strictly southward orientation of the IMF, preventing the formation of the foreshock in front of the magnetopause nose.Thus, we conclude that the origin of the observed waves in the vicinity of the magnetopause in our simulation is attributed to magnetic reconnection and FTE propagation at the magnetopause surface.We have also clearly demonstrated this direct connection between FTEs and their propagation during active sub-solar reconnection.
Using spectral analysis of magnetic field component fluctuations, we have demonstrated that Pc2 waves display significant wave power within a region of 3 R E distance from the magnetopause (Figure 2).In addition, we have 10.1029/2023GL106756 8 of 10 observed that the wave power in the magnetosphere is highest in the prenoon sector in all three polarization components followed by the postnoon and noon sectors.The magnetic local time occurrence of waves (between 0.1 and 2 Hz) in the vicinity of the magnetopause reported by Grison et al. (2021) showed similar characteristics to what we observed in our simulation.Additionally, Anderson et al. (1992) conducted a statistical analysis, revealing a higher occurrence rate of dayside Pc1-2 pulsations in the outer magnetosphere (L > 7) compared to the inner magnetosphere (L < 5), coinciding with the same region where we observe Pc2 waves in our simulation.Yagodkina and Vorobjev (1997) also reported magnetic pulsations associated with FTEs in the 6 to −8 s period (Pc2 range), exhibiting magnitudes ranging from 0.1 to 0.2 nT.These pulsations share a comparable frequency range and magnitude with those observed in our simulation.
The majority of investigations into ULF waves within the frequency range discussed in this article (referred to as Pc2) have typically associated their driving mechanisms with variations in solar wind parameters or temperature anisotropy resulting from the interaction between hot ions moving from the nighttime to the daytime side and the cold ions in the plasmasphere (Remya et al., 2018;Tetrick et al., 2017;Usanova et al., 2012).The absence of both the plasmasphere in the simulation and temperature anisotropy around the magnetopause (not shown here) strongly implies that this mechanism is not responsible for the formation of the waves.However, this research suggests that Pc2 waves may originate locally from the formation and propagation of FTEs.While this paper does not delve into the processes underlying the formation and the most suitable model for describing the FTEs observed in the simulation, Figure 5 and the accompanying video showcase numerous instances of multiple reconnection X-lines.These X-lines are particularly prevalent in the region where high wave power was detected (Figure 5).Whether these reconnection sites or the motion of FTEs serve as the dominant sources of the waves remains an unanswered question within the scope of this study, emphasizing the need for further investigations.

Summary
This study utilizes a hybrid-Vlasov simulation to investigate dayside Pc2 waves in the outer magnetosphere when a purely southward IMF and steady fast solar wind hits the Earth's magnetosphere.The study found Pc2 waves above 0.1 Hz frequency linked to the formation and passage of FTEs across the dayside magnetopause.
We established a direct link between these waves and the presence of large, rapidly moving FTEs generated during sub-solar reconnection.Moreover, the study identified a significant asymmetry in MLT wave power, with the prenoon sector exhibiting a greater dominance of Pc2 waves compared to the noon and postnoon sectors.Substantial wave polarization components in the poloidal and toroidal ULF modes were also detected in the off-equatorial regions of the magnetosphere.

Figure 1 .
Figure 1.(a) Variation of B in the parallel direction on Y = −3.5 R E plane at t = 956 s.(b) Its time evolution from a virtual spacecraft located at [x = 8.95, y = −3.5, z = 1.57]RE the blue asterisk in (a), (c) Morlet wavelet transform of (b), shaded area is the cone of influence and the dashed red line is the ion local gyrofrequency.The lower three panels (d-f) consist of polarization components (compressional, toroidal, and poloidal, respectively) of the magnetic field filtered in the Pc2 wave, [0.1, 0.5] Hz, frequency range.
z-direction plasma bulk velocity (panel (d)) and are notably absent when the velocity drops below 100 km/s.This distinction is particularly pronounced before the 900-s mark and during the period between 1,200 and 1,300 s.In addition, a visual comparison of FTE occurrences, distribution of O points from Alho et al. (2023) method, in the three planes presented in the Figure S4 reveals a significant difference in the distribution of O points between the Y = −3.5 R E or Y = 3.5 R E plane and the noon-midnight plane.This occurrence pattern mirrors the Pc2 wave power illustrated in Figure 2. The majority of FTE formations shown in Figure 4 are localized within the range of Z = ±4 R E on the three planes (refer to the Movie S1).It should be noted that the distribution of O point counts shown in Figure 4 is used to qualitatively compare the three planes.In Figure 5, we further illustrate the link between the FTE motion and the wave patterns presented on the plane Y = −3.5RE (see Movie S1). Figure 5a is a stacked plot representing the z-component of plasma bulk velocity along the northern hemisphere of the magnetopause surface.In panel (b) of this Figure we present the Pc2 wave

Figure 2 .
Figure 2. Spatial distribution of mean wave power in Pc2 range of compressional, toroidal, and poloidal components at the cross-sectional plane in the postnoon (top row), noon (mid row), and prenoon (bottom row) sectors, using the parallel, azimuthal, and radial component of the magnetic field.The cyan curve shows the approximate location of the magnetopause (β* = 1.2) according to Brenner et al. (2021).The light gray magnetic field lines represent the magnetosphere condition at t = 1,112 s into the simulation.

Figure 3 .
Figure 3. (a) Magnitude of magnetic field at the virtual spacecraft in the vicinity of the magnetopause at [x = 10.05,y = −3.5, z = 1.57]R E , (b) radial and local normal N component of magnetic field, (c) proton density and pressure, (d) the z-component of proton velocity, and (e) the gradient of the local normal magnetic field in the local magnetic field direction.The vertical dashed lines mark the center of flux transfer events at the virtual spacecraft location based on pressure peaks.The last panel shows the compressional ultralow frequency pulsation in the Pc2 frequency range from a virtual spacecraft at the same location as Figure 1a.

Figure 5 .
Figure 5. (a) A stacked plot showcasing the plasma bulk velocity from a curve along the Z-direction along the magnetopause surface, ranging from Z = 0 R E to Z = 5 R E on the plane Y = −3.5 R E , (b) a similar stacked plot but for the Pc2 wave resulting from pulsations in the parallel component of the magnetic field, occurring on a surface parallel to the magnetopause and situated inside the magnetosphere including the blue star at Z = 1.57R E shown in Figures 1a and 1c a replication of the panel as displayed in Figures 3f and 3d a cartoon illustrating different sources of waves discussed, as depicted in the accompanying video (Movie S1), X denotes the reconnection point.The contour lines in (a) and (b) are the X points (black) and O points (cyan).