Multi Satellite Observation of a Foreshock Bubble Causing an Extreme Magnetopause Expansion

The interaction of a solar wind discontinuity with the backstreaming particles of the Earth’s ion foreshock can generate hot, tenuous plasma transients such as foreshock bubbles (FB) and hot flow anomalies (HFA). These transients are known to have strong effects on the magnetosphere, distorting the magnetopause (MP), either locally during HFAs or globally during FBs. However, previous studies on the global impact of FBs have not been able to determine whether the response stems directly from the transverse scale size of the phenomenon or its fast motion over the magnetosphere. Here we present the observation of an FB and its impact on the magnetosphere from different spacecraft scattered over the dayside magnetosphere. We are able to constrain the size of the transverse scale of an FB from direct observations to be about 10 RE. We go on to discuss how the magnetosphere responds to this transient, which seems to have a similar scale across the dayside.


Introduction
Earth's bow shock (BS) mainly decelerates and diverts the incoming solar wind around the magnetosphere.However, a fraction of the solar wind particles are reflected at the BS and stream along the interplanetary magnetic field (IMF) back into the solar wind.The interactions between this back streaming and the solar wind particles excite plasma waves in the so called foreshock region (Eastwood et al., 2005;Wilson, 2016).
The foreshock is a highly dynamical region, hosting different kinds of intrinsic and externally-driven kinetic transients.These include structures resulting from solar wind discontinuities interacting with the foreshock, such as hot-flow anomalies (HFAs, Schwartz et al., 1985) and foreshock bubbles (FBs, Turner et al., 2013).The core of these transients is characterized by hot, tenuous plasma regions, in which flow deflection and reduction of the total pressure occur.An impact of this pressure "hole" in the foreshock on the BS leads to an expansion of the magnetosphere followed by a compression (e.g., Archer et al., 2014Archer et al., , 2015;;Jacobsen et al., 2009;Sibeck et al., 1999;Sibeck et al., 2000;Turner et al., 2011;Šafránková et al., 2012).These impacts can also generate field-aligned currents and ultralow frequency (ULF) waves in the magnetosphere and auroral brightening (Hartinger et al., 2013;Zhao et al., 2017;Wang et al., 2018;Liu et al., 2022).
The spatial scale at which phenomena such as HFAs and FBs can have an impact on the magnetosphere is not yet fully understood and remains an open question (see Zhang et al., 2022, and references therein).However, several observations of these phenomena suggest that, in particular, magnetopause (MP) responses may occur at different scales.
HFAs form when a solar wind discontinuity connects with the BS.The convective electric field has to point toward the discontinuity plane, accumulating back streaming foreshock particles on one or both sides of the discontinuity (e.g., Schwartz et al., 2000).The core of the HFAs typically reaches transverse scale sizes of 1-2 R E (Schwartz, 1995).As the core is convected with the discontinuity across the BS, the MP is distorted on a local scale (e.g., Turner et al., 2011).However, for example, the study by Sibeck et al. (1999) reports on a large-scale distortion and thus hinting at a more global impact.
The cores of FBs form due to the concentration of foreshock ions upstream of discontinuities in the IMF (Liu et al., 2015;Liu, An, et al., 2020).Simulation results suggest that FBs can reach scale sizes similar to the entire foreshock region, that is, up to 10 R E (Omidi et al., 2010(Omidi et al., , 2020)).Spacecraft observations have confirmed that at least along the x-direction this is true (e.g., Liu, Turner, et al., 2016;Turner et al., 2020;Vu et al., 2022).These core sizes suggest a more global impact on the MP.Archer et al. (2015) showed in a multi satellite case study, that FBs have indeed a global impact and lead to a large scale expansion of the MP across a transverse scale of ∼20 R E (inferred from ground magnetometer data).However, Archer et al. (2015) could not infer whether the global expansion was due to the FB's transverse scale size or the fast transit of a rarefaction (surface) wave down the magnetopause, initiated by the arrival of the transient.Vu et al. (2022) reported on a FB-like transient structure and inferred a scale size ∼5 R E across the BS surface.Although Vu et al. (2022) did not investigate what effect their FB-like transient had on the magnetosphere and the MP, the smaller scale of this event suggests that the MP may not be affected on the scales reported by Archer et al. (2015) solely due to its transverse scale size.Further studies are therefore needed to understand the transverse scale of foreshock transients and how they affect the magnetosphere.
In this paper we present recent observations of a large FB by the Magnetospheric Multi Scale (MMS) mission (Burch et al., 2016).The FB occurred on 23 December 2020 around 00:55 UT.Due to the conjunction with the three spacecraft of the Time History of Events and Macro-scale Interactions during Substorms (THEMIS) mission (Angelopoulos, 2008), the SOSMAG (Constantinescu et al., 2020;Magnes et al., 2020) magnetometer onboard the Geostationary-Korea Multi-Purpose Satellite-2A (GEO-KOMPSAT-2A) and one of the Geostationary Operational Environmental Satellites (GOES) at the geostationary orbit (GEO), we could study the FB and its impact at multiple locations in the magnetospheric system.We reevaluate the findings of Archer et al. (2015) and Vu et al. (2022) in regard to the transverse scale size of the FB, giving new constraints in multiple dimensions.

Data and Methods
For our analysis, we utilize a wide range of different spacecraft data: Magnetometer data with a 1 s cadence from the Advanced Composition Explorer (ACE, Stone et al., 1998;Smith et al., 1998) located far upstream at L1 around [217.57, 9.17, 17.16] R E and time-shifted high resolution OMNI data with a cadence of 1 min (King & Papitashvili, 2005) are used to monitor upstream conditions of the solar wind.Burst mode data from the Fluxgate Magnetometer (MMS-FGM, Russell et al., 2016), the Fast Plasma Investigation (FPI, Pollock et al., 2016) experiment and the Fly's Eye Energetic Particle Spectrometer (FEEPS, Blake et al., 2016) on board of the MMS spacecraft are used for the analysis of the foreshock transient.We study the motion of the BS and MP with the Fluxgate Magnetometer data (TH-FGM, Auster et al., 2008) and particle data from the Electrostatic Analyzer (ESA, McFadden et al., 2008) of the three THEMIS spacecraft THA, THD, and THE.FGM and ESA data are used in the spin-resolution (FGM) and reduced mode (ESA) with cadences of about 3-4 s.We also utilize low resolution (fgl, 0.0625 s) FGM data from THA and THD for the whole event.Magnetic field data from SOSMAG (Constantinescu et al., 2020;Magnes et al., 2020) and GOES-17 (Loto'aniu et al., 2019) both with a data rate of 1 s are used to investigate the magnetospheric response.
All vector data are presented and analyzed in the geocentric solar ecliptic (GSE) coordinate system.We assume that the positions of all spacecraft in these coordinates are quasi-stationary for the duration of the event, since the spacecraft are only moving at a few km/s, that is, the distance traveled by the spacecraft is much smaller than the scale of the transient, since the event is only observed over a period of 30 min.
For the classification of the foreshock transient in Section 3.1 we use the criteria given by Turner et al. (2013Turner et al. ( , 2020) ) to distinguish between FB and HFA.We look at the boundaries, motion and trigger of the transient.
Similar to the method presented by Vu et al. (2022), we use a combination of minimum variance analysis (MVA, Sonnerup & Scheible, 1998) and the multi-spacecraft-timing method (e.g., Equation (10.20) in Schwartz, 1998) to analyze the different boundaries of the FB and the magnetosphere.First we calculate normal directions with the MVA in a size varying window, which is slid across the whole event.We only consider normals for which the intermediate-to-minimum eigenvalue ratios are greater than 5 and time intervals capturing boundary or shock crossings entirely.For these preselected intervals and suitable spacecraft configurations (i.e., only for MMS), we also calculate the normals and boundary velocities with the MST method, and only consider normals which deviate less then 15°from the MVA results.The final normals are than calculated as a mean from all suitable intervals and given a standard deviation error.
We choose the sign of all calculated normal directions to point always in the upstream direction (i.e., with a positive x component) and adjust the sign of the boundary velocity accordingly (only necessary for timing results).The time differences between spacecraft observations required for the timing method is calculated using cross correlation between each magnetic field components and calculating the mean from the three different time lags.Additionally, we also utilize the conservation of mass flux (Equation (10.29) in Schwartz, 1998) to calculate boundary velocities from the THEMIS and MMS MVA results to compare them, if applicable, with the timing velocities.
To determine the expansion speed v exp of the transient and its core size in the direction of the solar wind flow S core (see Figure 1), we follow Liu, Turner, et al. (2016) and Turner et al. (2020): S core = |v dwn ⋅ n trail |Δt core . (2) We compare the results with the equations given by Vu et al. (2022): Here, v dwn is the downstream velocity vector measured by MMS, Δt core is the amount of time (in s) that the spacecraft has spent in the transient core and the normal vectors n and boundary velocities v of the upstream shock, the leading inner boundary and the trailing inner boundary are denoted by n shk and v shk , n lead and v lead and n trail and v trail , respectively.Figure 1 visualizes the different regions, boundaries and vectors necessary for our analysis in a schematic depiction of a foreshock transient in the x z-plane.
Assuming that the boundary planes of the transient are planar and extend beyond the observation points, we can calculate a point where the transient core should close as the intersection of the trailing and leading edge planes (similar to the estimation method of Vu et al., 2022).The transverse scale L core of the transient core can then be estimated from the distance between the intersection and the MMS position during the observation of the trailing boundary.

Observations
In Figure 2 [3.22, 5.61, 1.33] R E .This configuration allows us to observe the transient event on a global scale across the dayside magnetosphere.

Solar Wind and Foreshock -MMS Observations
In Figure 3 we present magnetic field and particle data of MMS1 sampled to a common cadence of 0.25 s.Additionally, we show the magnetometer data from ACE, time shifted by 44 min, which is roughly the time delay between the ACE and MMS positions.This timeshift will be justified later.
At 00:46:30 MMS crossed from a fast traveling solar wind (v MMS,dwn = [ 553.36,41.99,4.04]km/s) into the foreshock region of the Earth.Between 00:51 and 00:56, MMS encountered two strong flow deflections with v x near and above 0 km/s.Accompanying these deflections are temperatures up to 10 times higher and ion densities noticeably lower than in the ambient solar wind.Upstream of the deflection, the spacecraft enters a region with high ion densities around 17 cm 3 and a strong pressure up to 25 nPa.After 00:58:30 the spacecraft is again located in the undisturbed solar wind.This signature clearly belongs to foreshock transients like an HFA or FB, characterized by a core region of hot tenuous plasma in which flow deflection and pressure reduction occur, bound by plasma sheath and an upstream shock (Turner et al., 2013).
Further evidence therefore comes from the FEEPS data.Both in the high energy electron and ion intensities (panels ( 8) and ( 9) of Figure 3) we see spikes up to a energy regime of 200 keV limited to the core region of the transient between 00:54:00 and 00:56:00.Additionally, we also see high energy ions upstream of the event directly after the bounding upstream shock around 01:00:00.Highly energized particles are common in the core and upstream regions of transients, as they act as efficient particle accelerators (e.g., Liu et al., 2019;Turner et al., 2018;Wilson et al., 2016).Note that the energetic particles are not visible in the FPI data as they are obscured by the noise level of the instrument.
We propose that at least the signature between 00:54:00 and 00:58:30 belongs to an FB.In the following, we point out a few clear indicators that support our assumption, and we raise some points that may help to identify the first transient: 1) The MMS spacecraft does not observe any features of a compression region (i.e., increased density and magnetic field strength) upon entry into either of the transient structures at 00:50:30 and 00:53:35 respectively.Such a compression region on the downstream side would be an clear indicator for HFAs.
2) The second transient shows an extended sheath region between its trailing inner boundary at 00:56 and the upstream shock front around 00:58:30.The foot of this shock shows large amplitude waves, which is common for transients (e.g., Turner et al., 2020).The normal for the upstream shock calculated with the sliding MVA window with size varying between 4 and 8 s yields [0.99, 0.05, 0.06] ± 0.51°.The normal calculated from the timing in the same intervals yields [0.99, 0.01, 0.14] ± 2.10°with a shock velocity v shk in the spacecraft frame of 311.61 km/s roughly consistent with the results of 362.11 km/s from the conservation of mass flux method.These normals show a very strong x component consistent for a FB shock expanding in sunward direction.The shock of a FB is usually a fast mode shock, that is, the magnetic field should be coplanar across the shock and the MVA may not be reliable.Thus we also calculate a coplanarity estimate of the shock normal (see chapter 10.4.2 in Schwartz, 1998).This yields a normal of [0.94, 0.19, 0.20] ± 14.98°which agrees within 11.32°with the timing results.3) Analyzing the burst mode data with regard to the arrival time of the second transient at the four MMS spacecraft, we can infer that this transient convects in negative x gse direction, that is, with the solar wind flow.4) Foreshock transients typically form around or upstream of rotational (RD) or tangential (TD) discontinuities.
However, the signature of the discontinuity in the spacecraft data (MMS) is often obscured by the foreshock transient signature.Therefore we look at the ACE data: We can identify multiple discontinuities in the ACE data, using the partial variance of increments method (PVI, Greco et al., 2018) with a threshold of 2 (see panel (1) in Figure 4).MVA with a window of width of 4-60 s is performed on the discontinuities.With these normals we calculated a time delay of 35-40 min between observations at L1 and the arrival of the discontinuities at the MMS position using the method of Weimer et al. (2003).Still, this time shift give us only a rough estimate for the delay, thus we compared the timeshifted ACE data with solar wind data from MMS (see Figure 4).We can identify similar structures in these two time series, suggesting an additional timeshift of 4 min.Therefore, we suppose that the total timeshift should be 44 min.This time delay motivates the shift in the ACE data presented in Figure 3.However, we want to point out, that each discontinuity has a unique time delay due to its orientation, and the presented timeshift should be viewed as an educated guess.
Due to the additional timeshift, it is possible to associate the arrival of a discontinuity (the magenta shaded area in Figures 3 and 4) at the MMS location with the occurrence of the first transient.The analysis of this discontinuity in the ACE magnetic field data yield a normal of [0.26, 0.97, 0.02] ± 1.13°.Figure 2 shows the discontinuity orientation derived from these calculated normal.According to Liu, Turner, et al. (2016), we can classify discontinuities utilizing the ratio of the normal component to the field magnitude (B n /B).However, the magenta discontinuity yields B n /B = 0.67 and cannot be clearly classified as either an RD type or a TD type, so we can only refer to it as a directional discontinuity (DD).Since the PVI results do not show a clear second discontinuity, we try to compare the MMS ϑ cone and ϑ clock downstream and upstream of the second transients with the ACE angles after the DD (see shaded areas in panels ( 4)-( 7) of Figure 4).As there seems to be only a rough similarity between the angles, we decided not to associate any features in the ACE data with the occurrence of the second transient.However, we can see clear changes in the MMS cone angle, indicating the presence of another discontinuity reaching the foreshock region, driving the second transient.

5)
We calculate the solar wind convection electric fields downstream and upstream of the transients from the MMS burst mode data.This yields electric fields of [0.10, 1.23, 0.65] mV/m downstream and [ 0.13, 1.57, 0.97] mV/m upstream.Both vectors seem to point back at the discontinuity plane of the upstream ACE DD we suspect to be responsible for the first transient.We have inferred this from the angles between the electric field vectors and the normal direction of the ACE discontinuity, yielding 28.42°and 31.99°for the downstream and the upstream side, respectively.For the second transient, since we do not know the orientation of the driver discontinuity, we cannot make a definitive statement.6) From the orientation of the DD and the local BS model we can conclude that the discontinuity responsible for the first transients connects with the BS in the x-y-plane at [11.4, 8.3] R E .A connection between the driving discontinuity and the BS is mandatory for the formation of a HFA.
Table 1 summarizes the points raised by our identification process.The first transient seems to be a HFA-like transient, especially according to points ( 5) and ( 6), while the second transient shows characteristics which are more likely to be associated with an FB than of an HFA, particularly those listed under (1) and (2).

Bow Shock and Magnetopause -THEMIS Observations
In Figure 5 we present TH-FGM and ESA data from the three THEMIS spacecraft.Shortly after MMS enters the core of the first transient (see yellow markers in Figure 5), all THEMIS spacecraft cross the BS and encounter a strong sunward plasma flow in the magnetosheath between 00:50:30 and 00:52:30 (visible in THD and THA), indicating an outward moving BS. MVA on fgl magnetic field data during the crossing yields [0.77, 0.54, 0.34] ± 2.02°for THA and [0.94, 0.05, 0.33] ± 1.00°for THD, while coplanarity estimates yields [0.83, 0.15, 0.53] ± 4.40°for THA and [0.85, 0.31, 0.36] ± 15.42°for THD.These results are within 30.1°of each other.However, as mentioned above, MVA results are not necessarily reliable for fast mode shocks like the BS.Therefore, we only use the coplanarity results for further analysis.The coplanarity estimate differs by 28.34°f or THA and 23.10°for THD from the local BS model normal of Chao et al. (2002), suggesting a small deformation of the BS surface at the THEMIS location.
Starting with THE at 00:58:30 the spacecraft encounter a magnetopause crossing (MPC) and enter the magnetosphere, that is, the magnetosphere expanded drastically such that the BS and MP both swept across the THEMIS spacecraft.We calculate an equivalent stand-off distance R 0,sc during this crossing using the Shue et al. (1998) MP model formula identical to the calculation done in Grimmich et al. (2023): R 0,sc is 12.95 R E for the innermost probe, which is a deviation of 3.12 R E to the prediction of the Shue et al. (1998) MP model (using OMNI data), confirming the extreme expansion.From MVA we get [0.80,0.56, 0.20] ± 5.22°(THA), [0.91, 0.22, 0.33] ± 3.84°(THD) and [0.98, 0.16, 0.12] ± 0.52°(THE) as normal directions.All of the normals show a strong x component, indicating that there is no local deformation, but rather a global motion of the MP.The associated boundary velocities from the conservation of mass flux method are 100.16km/s (THA) and 81.89 km/s (THD).For the velocity data is not useable, thus we cannot calculate boundary velocities.However, they should be similar to THD's results as these two spacecraft are very close to each other.
After roughly 1 min all spacecraft cross back into the magnetosheath.Here, the MVA on the MPCs yields [0.88, 0.45, 0.11] ± 4.73°(THA), [0.79, 0.51, 0.33] ± 2.84°(THD) and [0.82, 0.45, 0.34] ± 2.45°(THE) with velocities from the conservation of mass flux method of 24.03 km/s (THA) and 74.19 km/s (THD).These values fit with an inward moving MP which seems to have an equilibrium position just inside the THEMIS orbits, as the boundary velocity drops from THD to THA.
Additionally, we can observe that for both magnetosphere incursions the plasma velocity has a strong sunward component during the first MPC and a more anti sunward component during or shortly after the second MPC.This observation also suggest an outward motion followed by a inward motion of the MP.
We also see that, between 01:02:20 and 01:04:00, all three spacecraft encounter a sheath region which looks very similar to parts of the sheath region of the FB (marked in purple in Figure 5).Correlation analysis of the total magnetic field from MMS1 and THEMIS reveals a correlation coefficient of 0.73 for THA and THD and a coefficient of 0.83 for THE in this sheath region.Thus, we can infer that THEMIS encountered the sheath region of the FB and then crossed into the pristine solar wind.Additionally the calculated MVA normals for the fgl data of THD and THA of the upstream shock of the sheath are [0.92,0.05, 0.39] ± 3.08°and [0.96, 0.08, 0.25] ± 4.55°for THA and THD.These normals lie within 15.31°of the normal we calculated for the upstream shock of the FB on MMS data.Again, we used the coplanarity estimate for the normal direction as a more reliable estimate of the shock normal yielding [0.92, 0.26, 0.27] ± 8.71°and [0.89, 0.40, 0.21] ± 4.93°for THA and THD, respectively.These results agree roughly within 22.44°with the MVA results and within 23.6°with the estimates of the MMS observation.In the fgl data (not shown) a shock foot with large amplitude waves similar to the MMS observations is visible as well.The conservation of mass flux method yields 289.50 km/s (THA) and 307.40 km/s (THE) for the shock velocity in the spacecraft frame.

Magnetospheric Response -GEO Observations
The total magnetic field of the SOSMAG and GOES observations is displayed in Figure 6.We subtract the magnitude of the IGRF model (Alken et al., 2021) at both spacecraft locations to better visualize the variations in the magnetospheric field.Both time series show a clear decrease in the magnitude over several minutes followed by a strong increase of the field.The signature is first observed at GOES-17 and a few minutes later also by SOSMAG.However, the signature in the SOSMAG data is much clearer and stronger, and we can see a short increase of the field preceding the decrease.These signatures are fitting for a large expansion followed by a compression of the magnetosphere, as magnetic field strength should decrease in an expansion and increase when the magnetic field is more compressed.The first magnetic field increase in the SOSMAG data also hints at a compression preceding the expansion, at least in the vicinity of SOSMAG.
We also checked the Disturbance Storm-Time Index D st (Nose et al., 2015).This index provides information on geomagnetic activity associated with horizontal magnetic field deviations.In general, negative values indicate ring current activity, while positive values indicate magnetospheric compression.During the event the hourly D st index is 3 nT, i. e., no strong ring current activity is responsible for the observed deviation in the magnetic field.

Discussion
From the MMS observation, we could clearly identify the transient signatures as an FB, preceded by probably a HFA-like transient forming around a solar wind discontinuity.This first transient is likely to be an early-stage transient, as neither edge shows the compression region associated with late-stage FB and HFA-like transients (e.g., Chu et al., 2017;Zhang et al., 2010).Further investigation is required to more clearly identify this transient.In the following we focus more on the FB and its impact on the magnetospheric system.
For the estimate of the FB size we calculate normal directions and boundary velocities for the leading and the trailing inner edges of the FB at 00:54:00 and 00:56:00, respectively.For the leading edge, MVA yields [0.28, 0.90, 0.34] ± 0.46°with a velocity from the conservation of mass flux method of 194.32 km/s, while timing in the same interval yields [0.37, 0.89, 0.26] ± 2.41°with a velocity estimate of 212.30 km/s.For the trailing edge, MVA yields [0.89, 0.46, 0.11] ± 0.40°with a velocity from conservation of mass flux method of 266.79 km/s, while timing in the same interval yields [0.96, 0.25, 0.11] ± 2.52°with a velocity estimate of 250.50 km/s.3) and ( 4) we calculate an expansion speed for the FB core of 224.68 km/s and a size S core along the solar wind flow of 10.39 R E .Equations ( 1) and ( 2) yield an expansion speed of 234.30 km/s and a core size of 11.91 R E .These results are in agreement with previously reported expansion speeds and sizes of FBs (Liu, Turner, et al., 2016;Turner et al., 2020;Vu et al., 2022).
Our estimation for the transverse scale yields L core = 7.58 R E using the distance from MMS to the intersection point of the edge planes.Since the FB is basically a 2D structure in the x-z plane that extends in the y direction, this estimation is done in the y = 0 plane.This transverse scale estimation is clearly a lower limit, since the FB can be extended beyond the observation point MMS and close at another location.
Interestingly, the sheath of this FB seems to be very large, as MMS is inside this region for multiple minutes (00:56:00 to 00:58:30).The reason for this large sheath region could be the age of the FB which we estimate to be roughly 4 min by dividing the core size by the expansion speed (Liu, Turner, et al., 2016;Turner et al., 2020).Hence, the FB probably formed 21 R E upstream of MMS and is in its late stage of expansion when MMS observes its features.
The path taken by the MMS through the bubble and the orientation of the FB could be another explanation.If the FB boundaries were more parallel to the path of the MMS, it would take longer to cross the sheath region and lead to the signature we observed.According to the normal direction of the FB boundaries, the flow direction of the bubble (solar wind flow) deviated from the boundary normal by 72.37°when entering the bubble and by 9.82°w hen leaving the sheath.These angles seem to indicate that MMS did not take the shortest path through the FB sheath.So the geometry does clearly has some influence on the long observation time of the sheath.
The expansion speed in the spacecraft frame, which we calculated earlier, could also be an indication of the thickness of the sheath.If the FB is expanding very rapidly toward the Sun, so that in the spacecraft frame the FB sheath/shock has a very small speed toward the Earth, we would observe a long duration for the sheath in measurements.Our calculated expansion speed of about 230 km/s appears to be comparable to reported mean values (Turner et al., 2020;Vu et al., 2022) and thus cannot fully explain the long sheath observation due to a thicker sheath resulting from a very fast expansion speed.
At the time MMS observes the HFA-like transient (00:51:00), THEMIS enters the magnetosheath (see Figure 5) and observes a distortion of the BS.Since we expect the BS to respond immediately to a connected region of lower density like a transient core (e.g., Otto & Zhang, 2021;Zhou et al., 2022), the HFA-like transients cause this BS distortion because it is likely connected to the BS via the IMF discontinuity (see orientation of the DD in Figure 2).This scenario is supported by the calculated normal directions of the BS, as the orientation suggests an outward distortion of the BS toward the dusk and north, that is, toward the MMS/transients location (see Figures 7a and 7b).Shortly after the interaction between the HFA-like transient, the FB is likely to have also touched the BS, probably at the time MMS observed the FB shock front (00:58:30).As the connection of the FB core erodes the original BS over the size of the core (e.g., Wang et al., 2020), strong pressure gradients are created in the magnetosheath, leading to a sudden expansion of the MP (Archer et al., 2015).This can be seen in the short time between the first MP encounter in the THEMIS data and the observation of the shock front by MMS (see vertical lines in Figure 5).The shock front of the FB is then incorporated into a new BS forming upstream of the FB (see Figures 7c and 7d)), as can be seen from observations of the FB's sheath and shock front during re-entry of THEMIS spacecraft into the solar wind around 01:03:50 when the new BS returns to its nominal position (see Figures 7e and 7f).
It is very likely that the low total pressure in either the HFA-like or FB core causes the magnetosphere to expand rapidly.For an estimation of the equivalent stand-off distance of the MP R 0,eq in the equilibrium position, we use the simple pressure balance formula (e.g., Baumjohann & Treumann, 1997) Here, the Earth's dipole coefficient is g 0 1 = 30,000 nT and κ = 0.88.With a total pressure inside the transient cores in the range of 0.3-1.5 nPa, R 0,eq yields 10.12 to 13.26 R E agreeing nicely with the derived equivalent stand-off distance of 12.95 R E for the MPCs, and our assumption.The Shue et al. (1998) model prediction for the stand-off Journal of Geophysical Research: Space Physics 10.1029/2023JA032052 distance of 9.75 R E also agrees roughly with the results from Equation (5) yielding 8.48 R E when using p tot values from MMS solar wind observations before the event.
The observed multiple MPCs in response to the foreshock transients may have several causes: The boundary velocity estimates during the MPCs suggest a fast moving MP in response to the transient, overshooting the actual equilibrium position and then leading to an oscillation of the MP around it.During the first entry into the magnetosheath, the boundary velocity is between 80 km/s and 100 km/s, while for the exit we see lower velocities that decrease between spacecraft.The boundary velocity during re-entry 1 minute later is much lower (about 10 km/s) than the initial outward motion, supporting oscillatory motion.Similar oscillations in response to extreme and sudden changes ahead of the MP have been suggested before (e.g., Desai et al., 2021).
Another explanation could be, that the first MP incursion stems from the response to the HFA-like transient, while the second incursion stems from the FB core.In particular, the total pressure would support this assumption, as the pressure inside the HFA-like transient is much lower (0.3 nPa) than the pressure inside the FB (1.5 nPa), which would lead to an initial larger MP expansion followed by a smaller one, as we observed.Finally, if we assume that only the FB causes the response of the MP, changes in pressure within the core could also be responsible for the observed movement of the MP.The pressure profile inside the FB core supports this, as we see the lowest pressure immediately after entry, followed by a slight increase and then a dip to lower pressure before entering the sheath region (see panel (6) of Figure 3).
Overall, we can summarize that one of or both of the transients observed by MMS led to a massive MP displacement of more than 3 R E , which is to our knowledge the largest reported displacement of the MP caused by foreshock transients.
The timing between the observations of MMS and THEMIS also allows us to give another estimate for the transverse scale of the FB.While THEMIS observes the first MPC (i.e., the FB has reached the THEMIS position), MMS encounters the upstream shock front of the FB.Thus, the FB has to cover at least the distance between the two spacecraft constellations, and δr projected on the FB shock plane can be used as a low limit estimate for the transverse scale size of this event.This would lead to an estimate of roughly 7.94 R E .
Additionally, we can infer more constraints in regard to the expansion of the FB during this event.As predicted by Omidi et al. (2010) the FB shock front becomes the new BS, when hitting the original BS.We can verify this, as THEMIS observed basically the shock front of the FB after the last MPCs instead of a normal BS before entering the solar wind.Using the conservation of mass flux we calculate shock velocities for THA and THD for the FB shock and find 289.50km/s and 307.40 km/s, respectively.With Equation (1) these boundary velocities lead to expansion speeds of 219.28 km/s (THA) and 225.32 km/s (THD) for the FB.These expansion speeds are clearly similar to the ones observed at MMS reaffirming that both constellations observed the same shock at different locations.These results also suggest that the expansion of the FB seems to be constant over the 5 min which lie between the MMS and THEMIS observations.However, as we already mentioned, the BS and the FB's shock merge together, thus the expansion speeds might not be solely stemming from the FB expansion and could also already contain parts of the BS motion.
MMS also sees energetic ions upstream of the FB.Based on the pitch angle spectra (not shown), those ions move sunward away from the FB shock, which could hint at a foreshock region associated with the FB (Liu, Hietala, et al., 2016).Following the method used in Liu, Hietala, et al. (2016), we can estimate the velocity of the reflected ion beam: We utilize the upstream solar wind velocity v up = [ 541.97, 28.30, 4.54] km/s and the IMF vector 68, 2.16, 1.78] nT from MMS observations at 01:01:00 to calculate the Hoffmann-Teller velocity for the FB shock: Subsequently, the reflected ion beam of the FB foreshock can be estimated with v r,FB = v up + 2(v shk + v HT ). ( 7) Equation ( 7) yields a velocity of [127.03, 297.73, 287.10] km/s.From the FEEPS data we estimate that the FB foreshock is roughly observed for 2.5 min.Thus, the size of the foreshock along the FB shock surface direction n shk should be roughly 10.19 R E , stemming from reflected ion beam velocity and the observation time.The size of the foreshock also indicates typically the shock surface size, that is, the transverse scale of the FB.Hence, we have another estimate for this scale which roughly agrees with our previous estimates.
All together, we can constrain the size if this FB to be 10-12 R E in x and 7-10 R E in the transverse (y z) direction.
As far as we know, this is the largest estimate of an FB size in the y or z GSE dimensions.Previous studies only have given constraints in the x dimension (Turner et al., 2020) or found only values up to 5.1 R E (Vu et al., 2022).
Our estimates together with constraints given for the x dimension fully support the original predictions of Omidi et al. (2010), namely that the size of the FB is ∼10 R E in the x and y dimensions.Grimmich et al. (2023) suggested that favorable conditions for large deviations between modeled and observed MP, such as those investigated here, are for example, high solar wind velocity with large Alfvén Mach numbers M A .During the transients encounter the solar wind velocity was 550 km/s with an very high M A of 15 (OMNI data).These conditions are also often associated with the occurrence of foreshock transients (Zhang et al., 2022).
In particular, the high value of M A may be responsible for the growth of the FB to the observed large size.Results from Turc et al. (2018) suggest that the suprathermal ion density in the foreshock increases with M A .This high density could lead to a large source of ions that can accumulate in a FB core, accelerating the growth of the FB.Indeed, Liu et al. (2023) showed that there is a clear relationship between the expansion rate of FBs and the foreshock ion density and velocity, supporting growth to large sizes under high M A .
From the magnetic field observations at GEO, we can deduce how and to what extent the two transients affect the magnetosphere.Both transients were first observed by MMS on the dusk flank of the magnetosphere, which at GEO is covered by GOES17 (see Figure 2).Subsequently, the magnetosphere begins to expand at the GOES location shortly after the encounter with the HFA-like transient (Figure 6).This suggests that the HFA-like transient probably led to an initial local expansion on the dusk side toward the HFA-like transient core.As the transient moves across the BS, the local expansion would also move, leading to the dawn expansion of the magnetosphere observed by SOSMAG a few minutes later.While moving, the transient would certainly grow and develop compressional boundaries on either side of the core, leading to compression signatures before and after the expansion signature in the magnetosphere.Indeed, we can see such a signature in the SOSMAG observation, which lends plausibility to this theory.
However, based on similar observations with THEMIS and MMS, we have determined that the FB must cover a large part of the dayside magnetosphere.Thus, after initial local expansion of the magnetosphere, the FB may lead to more global expansion.As THEMIS enters the magnetosphere for the first time and MMS leaves the FB, we see the beginning of the magnetospheric expansion in the SOSMAG data on the dawn flank, while it also appears to be still expanding on the dusk side.This could mean that the magnetosphere is expanding globally on a scale of almost 10 R E (fitting with the size of the FB) in response to the transients.Of course, due to the short time between the arrival of the transients at the BS, both suggested scenarios could occur almost simultaneously.
Another explanation could be that the signatures observed at GEOS17 and SOSMAG are independent of each other.If this is the case, it is likely that GOES observed the response to the FB with only one compression after the expansion which could be associated with the FB shock, whereas SOSMAG observes the delayed responses to the moving and growing HFA-like transient with two compression regions.
Overall, it is difficult to clearly indicate whether the magnetosphere is responding on a global scale.Although the almost simultaneous observation of an expansion or incipient expansions at GOES, THEMIS and SOSMAG strongly suggest a large-scale distortion due to the transients and the FB in particular, in line with previous predictions (Omidi et al., 2010) and observations (Archer et al., 2015).Furthermore, even if the large-scale distortion is initially confined to the dayside, it is possible that the magnetospheric system is further disturbed on the flanks after the event.As suggested by Archer et al. (2015), it is possible that the transients have resulted in surface waves on the MP that propagate along the flanks, further distorting the system.In addition, it has been reported that both FB-and HFA-like transients can propagate along the flanks to the nightside, leading to displacements of the MP and BS (e.g., Liu, Wang, et al., 2020;Wang et al., 2020).However, further investigation would be required to determine whether this is the case here.
Journal of Geophysical Research: Space Physics 10.1029/2023JA032052

Summary and Conclusions
We report the impact of a large foreshock transient on the magnetospheric system on 23 December 2020.Different spacecraft either observed this transient directly or the response of the magnetosphere to it.We identify this transient as a large and also quite matured foreshock bubble preceded by an HFA-like transient at an early stage.
The scattered spacecraft allow us to determine the transverse scale of the foreshock bubble in different ways, which lies probably between 7 and 10 R E .This observational estimates agrees well with predictions from simulations and exceeds previous estimates for this scale size.
We can also infer that the transients lead to a more than 3 R E displaced magnetopause and, together with the HFAlike transient, triggers an almost simultaneous large scale response in the magnetospheric field of roughly 10 R E across the dayside magnetosphere, similar to the size of the FB.
In a statistical analysis of MP locations that deviate from MP model predictions based on solar wind conditions measured at L1 (OMNI data), Grimmich et al. (2023) found that favorable solar wind conditions for extreme MP locations are similar to the conditions associated with the occurrence of foreshock transients (high solar wind speeds with large Alfvén Mach numbers), suggesting that these transients may be a reason for the deviation from model predictions.Indeed, this study shows that foreshock transients such as the FB here are a possible source of large deviations between MP observations and model predictions.It also confirms that solar wind conditions affecting the magnetosphere can be different from those measured at L1, particularly due to the development of the foreshock region and the occurrence of transient events.
In addition, as we have pointed out, we see only one clear discontinuity as a possible driver for the transients.Omidi et al. (2020) point out that a discontinuity responsible for the formation of a FB could also form a HFA.Although more research is needed to fully confirm this, our event may be one of the first in situ observations of this phenomenon.Furthermore, this event might also offer the opportunity to study the formation of a foreshock associated with the shock of the foreshock bubble in more detail in the future, as we find energetic ions upstream of the bubble.
The transient we discuss here in detail is not the only one occurring on this day; many more transients are observed in a short period of time.These might also allow to further investigate the response of the magnetosphere to the arrival of such transients.

Figure 1 .
Figure 1.Schematic representation of the foreshock transient at the time MMS crosses the upstream shock, showing all important regions and boundaries.In addition, the estimates for the different scale sizes and the angles and distances required for the calculations are marked in orange and gray respectively.

Figure 2 .
Figure 2. Spatial distribution of spacecraft on 23 December 2020 around 00:55 UT in the GSE x-y-plane (left panel) and x-zplane (right panel), respectively.Earth is symbolized by the gray semicircle.The arrows at the spacecraft locations point along the spacecraft orbits.The Shue et al. (1998) model magnetopause and the Chao et al. (2002) model bow shock for B z,IMF = 0.95 nT, p dyn = 2.55 nPa, β = 4.30 and M MS = 7.27 are shown in blue and black, respectively.One discontinuity suspected to be responsible for the initiation of the event is represented by a magenta dashed line.

Figure 3 .
Figure 3.Time series plot of ACE and MMS1 data on 23 December 2020.From top to bottom the panels display the magnetic field data from ACE (44-min timeshifted), magnetic field data from MMS, the ion velocity, the ion density, the ion temperature, the total pressure, the ion energy flux density and the high energetic ion and electron intensities.The colored region indicate the core (yellow) and the upstream sheath and shock (violet) of the foreshock bubble.The magenta shaded region indicate a discontinuity observed by ACE.

Figure 4 .
Figure 4. Time series plot of ACE and survey mode MMS1 data on 23 December 2020 in a 1 s resolution.The first panel shows PVI results and the threshold used for the identification of discontinuities.The second panel shows ACE magnetic field data timeshifted by 40 min (details in the text).The third panel shows the MMS magnetic field data.The marked features in gray in the ACE and MMS magnetic field data suggest an additional timeshift (orange arrow) of ∼4 min.The IMF cone and clock angle are shown in the four bottom panels for MMS and ACE (timeshifted with 44 min).The magenta shaded region marks a discontinuity probably responsible for one of the foreshock transients.

Figure 5 .
Figure 5.Time series plot of THEMIS data on 23 December 2020.From top to bottom the panels display the magnetic field data, ion velocity, ion density and the energy flux density for THA, THD and THE.Velocity data for THE is not available in a sufficient resolution and thus not plotted here.The black vertical lines indicate magnetopause crossings, the yellow bars in panels (1), (5) and (9) indicate the entry/exit of MMS into/from the transients and the violet shaded region highlights the sheath region of the FB.

Figure 6 .
Figure6.Time series plot of SOSMAG and GOES-17 total magnetic field data on 23 December 2020.The IGRF(Alken et al., 2021) at the spacecraft orbits is subtracted from the data.The yellow bars indicate the time of entry/exit of MMS into/ from the two transients, while the vertical black lines represent the first and last encounter of the MP at the THEMIS location.

Figure 7 .
Figure 7. Time evolution of BS and MP response to MMS observed foreshock transients.Panels (a) and (b) show the assumed response of the BS to the HFA-like transit around the discontinuity (magenta line) at 00:51:00.Panels (c) and (d) show the displacement of the MP and the reformation of the BS due to the interaction with the FB at 00:58:30.Panels (e) and (f) show the arrival of the reformed BS at the THEMIS position at 01:03:50.The spacecraft positions are the same as in Figure 2, and the solid blue and dashed black lines represent the nominal MP and BS models, respectively, while the cyan line shows the localized observed/assumed position of BS and MP.
we present the location of the different spacecraft on 23 December 2020 between 00:40 and 01:10 in GSE coordinates.We use the time-shifted OMNI data, the Shue et al. (1998) MP model and the Chao et al. (2002) BS model to calculate the shown average location and shape of the MP and BS during the event.

Table 1
Identification Criteria Adapted From Turner et al. (2013)and Observation Results From the Two Foreshock Transients GRIMMICH ET AL.