Extremely Distant Magnetopause Locations Caused by Magnetosheath Jets

Magnetopause position is controlled mainly by the solar wind dynamic pressure and north‐south interplanetary magnetic field component and these quantities are included in different empirical magnetopause models. We have collected about 50,000 of dayside magnetopause crossings observed by THEMIS in course of 2007–2019 and compared the observed magnetopause position with model prediction. The difference between observed and predicted magnetopause radial distance, Robs − Rmod is used for quantifying the model‐observation agreement. Its median values are well predicted for cases up to Robs ≈ 12 RE for all models but higher positive deviations are found for larger magnetopause distances, mainly under a nearly radial field and low dynamic pressure. The analysis reveals their connection with transient magnetopause displacements caused by strong sunward flows in the magnetosheath. We discuss the possible origin of the observed magnetosheath flow switching in terms of the interaction of magnetosheath jets with the magnetopause.

A statistical study of extreme magnetopause locations (Grimmich et al., 2023) reveals that the high upstream Mach number, enlarged plasma β and low IMF cone angle (the angle between the IMF vector and X GSE axis) are often connected with a large magnetopause expansion.However, these parameters are not independent because prolonged intervals of a low IMF cone angle are usually connected with depressed magnetic field magnitude (Pi et al., 2014) that implies the enhanced β and Mach number and thus it is not clear which of these parameters is more important in the magnetopause location setting.
The large deviation from the model can be also connected either with a wrong prediction of upstream conditions, especially with timing of arrivals of the interplanetary shocks and other discontinuities, or with transient phenomena like hot flow anomalies (HFAs) (Jacobsen et al., 2009;Šafránková et al., 2012;Sibeck et al., 1999) that result from the interaction of IMF tangential discontinuities with bow shock (BS).Such interaction is characterized by a creation of the region of the depleted pressure in BS front leading to quick outward motions of both BS and MP.The outward BS motion can be complemented with the sunward flow in the magnetosheath (Archer et al., 2014).Plaschke et al. (2017) explain the magnetosheath sunward flow by the interaction of an intense earthward propagating magnetosheath jet with the ambient magnetosheath plasma.The magnetosheath sunward flow following the arrival of a weak IMF directional discontinuity was also reported by Shue et al. (2009).The authors suggest that the interaction leads to formation of an antisunward jet creating a dip on the MP surface that reverses the jet direction.
A comparison of observed MP locations with model predictions can serve as a proof of our understanding of the interaction between the solar wind and Earth magnetic field.Since corresponding upstream conditions are usually derived from observations at the L1 point, our knowledge on solar wind propagation and evolution on short scales are tested as well.In order to improve our understanding of the processes involved in the MP formation, the present study is devoted to the analysis of sources of large positive deviations of the MP location from the predicted positions and to the search for the conditions under which they arise.

Data Set and Motivation
We have collected more than 50,000 dayside MP crossings observed in course of the 2007-2021 years by the THEMIS spacecraft fleet (Angelopoulos, 2008).These crossings were identified by the routine based on the Jelínek et al. (2012) region identification method and partly verified by visual inspection of plots of magnetic field (Auster et al., 2008) and plasma (McFadden et al., 2008) parameters.For each of the crossings we computed the model MP position using four models (Jelínek et al., 2012;Lin et al., 2010;Petrinec & Russell, 1996;Shue et al., 1997) and the OMNI solar wind data as their input.An example of the observation-model comparison is shown in Figure 1a.The figure shows the histogram of deviations of observed MP distance from the Earth,   2010) model prediction, R mod .The red line stands for the Gaussian fit and its parameters (Center, C and Full Width at Half Maximum, FWHM) are given at the figure top.We applied the same procedure to other models and the results are very similar (C = 0.17 and FWHM = 1.32 for Shue et al. (1997); C = 0.12 and FWHM = 1.37 for Petrinec and Russell (1996); C = −0.09and FWHM = 1.66 for Jelínek et al. (2012); all values in R E units).This result is surprising because the models use very different functional forms of the MP shape and different power exponents for the dependence of R mod on upstream pressures.We select the Lin et al. (2010) model in our analysis because it exhibits the best agreement with observations.As it can be seen from the figure, the Gaussian fit describes very well the shape of distributions with the exception of a small percentage of very large positive or negative R obs − R mod values.The Gaussian core of the distribution is mostly a result of uncertainty of prediction of upstream parameters.Urbář et al. (2019) analyzed a relation between THEMIS observations in front of the BS and Wind measurements at L1 and they have shown that FWHM of the distribution of velocity ratios is as large as 0.05.The conversion of this value to the uncertainty of the subsolar MP prediction leads to FWHM of about 1.1 R E .This value is a little lower than but comparable with those characterizing the uncertainties of model predictions.
For the reasons given above, our analysis concentrates on the large deviations from the model.Figure 1b shows the plot of R obs − R mod as a function of R obs for all dayside MP crossings.The gray dots stay for individual crossings and the colored bars stand for medians in 1 R E distance bins.These medians are close to zero for distances between 8 and 12 R E for all three subsets of crossings (subsolar-green, dawn-red, dusk-blue) but systematic positive deviations are observed at larger distances.This is especially true for our subsolar subset (crossings in the 30° cone around the X axis).It should be noted that similar plots for other MP models exhibit even larger deviations.
There can be several reasons for a bad prediction of the MP location: (a) influence of an upstream parameter not included in the model, (b) wrong propagation of upstream parameters and (c) effect of an IMF discontinuity.In order to check the first item, we have plotted R obs as a function of different upstream parameters and found that the largest R obs are connected with intervals of nearly radial IMF, in agreement with findings of Grimmich et al. (2023).Other conditions like a small dynamic pressure or small IMF strength are either included in the models or follow from properties of radial IMF intervals (Pi et al., 2014(Pi et al., , 2017)).The dependence of R obs on the IMF cone angle is plotted in Figure 1c.The red bars show medians in distance bins and, despite the large spread of points, one can see a clear decreasing trend.It suggests that the addition of the cone angle to the parameters of the MP model can improve its precision (see also Dušík et al. (2010)), but this is out of the scope of the present study.However, if IMF points radially, the subsolar BS is almost parallel and the MP would be behind a strong foreshock and thus transient effects connected with foreshock fluctuations can be expected.For these reasons the next section describes several case studies that elucidate effects of the solar wind or IMF discontinuities as well as magnetosheath transients.

Magnetopause Location and Magnetosheath Transients
The first example uses observations of THEMIS B and C (THB and THC hereafter) on 2008-07-18 from 1320 to 1400 UT.THB located at (23.8, 4.7, −8.6) R E serves as the upstream monitor whereas THC at (14.9, 3.7, −5.3) R E was located close to the predicted BS location (Jeřáb et al., 2005) and finally, THD (8.4,3.3, −3.1) R E scans the MP on the magnetosphere side (no MP crossings were observed through the selected time interval).Note that we are using GSE coordinates in the paper.Figures 2a-2d (left part) show the magnetic field strength and three components, the dynamic pressure calculated from THB density and velocity measurements (d), and ion spectrogram.One can note the dynamic pressure below 0.8 nPa and almost radial IMF modulated by foreshock fluctuations caused by the high energy tail of the ion distribution visible in Figure 2c, but no notable IMF discontinuity is registered.Figures 2e-2h present the THC magnetic field, ion spectrogram, velocity components and dynamic pressure.The green line in the panel 2h shows half of the solar wind dynamic pressure because this level is usually considered for magnetosheath jet identification (Plaschke et al., 2017).The regions visited by THC are identified by color bars in the magnetic field panel (magnetosheath--blue, magnetosphere-green, solar wind-red).Figure 2i shows the model distance of the BS (blue) and MP (green) along the direction toward the THC location together with the THC radial distance (black).
Consistently with the predicted MP location, THC is located in the magnetosheath until 1332 UT when it would cross the BS according to the model prediction (Figure 2i) but it enters the magnetosphere for about 8 min, then it returns to the magnetosheath, and around 1350 UT it undergoes two BS crossings.Times of these BS crossings are reasonably predicted by the model, on the other hand, the MP crossings are very far from the prediction (3 R E for the second one).A sketch in the right part shows an approximate shape of the boundaries during the event.One can see the large but the short-time (and probably spatially limited) MP displacement, similar to that reported for interaction of the magnetosphere with HFA.However, no IMF discontinuity is observed upstream and the level of foreshock fluctuations is moderate.The only notable feature is a strong sunward flow in the magnetosheath just prior to the first MP crossing (black arrow in Figure 2g).(Šafránková et al., 2002).We observe a very quiet nearly radial IMF without any discontinuity and about constant dynamic pressure below 1 nPa.THC was again close to the predicted BS location (Figure 3l) slightly dawnward from the subsolar point.This location is consistent with observations shown in the panels c-f that reveal several solar wind/foreshock intervals characterized by large negative values of the Vx velocity component (Figure 3e) and low IMF strength (Figure 3c).However, a clear entry to the magnetosphere distinguished by green dashed vertical lines can be identified between 2217 and 2224 UT.It suggests an outward MP expansion but THE located in the magnetosphere about 1 R E inward the predicted MP position (Figure 3l, green line) enters the magnetosheath during this time interval (see color bars in Figure 3g), indicating a MP compression.As can be seen in the right-hand sketch, THC and THB observe simultaneous compression and expansion of the magnetosphere at two places separated by about 2 hr of the local time.This deformation is connected with the antisunward jet that reverses to the sunward direction just prior to the THC MP crossing.Even more clear reversal of the jet direction in the magnetosheath is observed by THE (Figure 3i, black arrow).THD that is closer to the model MP (not shown) observes similar but more pronounced features and the timing of THD-THE observations suggests that the MP distortion moves slowly dawnward.
Two examples discussed so far show the switch of the magnetosheath jet direction as an isolated phenomenon.However, Figure 4 presents observations of a series of such events, albeit only the first of them resulted in the MP deformation reaching the outbound spacecraft.The figure format follows Figure 3.The upstream parameters in Figures 4a and 4b propagated from ACE reveal again a nearly radial IMF and the dynamic pressure of about 0.8 nPa.Figures 4c-4f present the THC magnetic field, ion spectrogram, ion velocity components and dynamic pressure, respectively.THC was close to the BS and crossed it several times in course of the depicted interval (red vertical lines in Figures 4a-4f) but around 0020 UT it underwent a short excursion to the magnetosphere (green vertical lines), although it was about 4 R E upstream from its predicted position (Figure 4l).The first MP crossing is connected with a strong earthward jet that reverses its direction prior to the crossing.THB was in the magnetosheath during the THC magnetospheric interval, and it clearly shows the strong earthward jet followed by the sunward flow with the peak velocity of 200 km/s.These features resemble those shown in Figure 3 but between 0030 and 0050 UT, THB observed a series of MP crossings and nearly all of them are connected with the sunward flows (black arrows in Figure 4h).These flows are observed in the MP boundary layer and indicate a fast outward MP motion (Archer et al., 2014) but with an amplitude not sufficient to reach the THC location.

Discussion and Conclusion
The three examples shown in the previous section document observations of large outward displacements of the subsolar MP.These displacements are spatially limited and they are connected with the creation of a dip in the MP surface.The angular separation of the spacecraft observing simultaneously bump and dip was about 50° in the second and less than 30° in the third example.Such a localized MP deformation was already reported in a connection with HFAs.However, HFAs result from the interaction of the IMF tangential discontinuity with bow shock (Šafránková et al., 2012;Sibeck et al., 1999) but no such discontinuity was observed in our examples.All discussed events occur under a lower upstream pressure and nearly radial IMF.Such conditions are favorable for the creation of spontaneous HFAs (Chu et al., 2017) or magnetosheath jets (LaMoury et al., 2021), and some of them (and probably the most intensive ones) can be connected with the BS reformation as a natural part of the dynamical evolution of quasi-parallel collisionless shocks (Raptis et al., 2022).The enhanced pressure inside a jet pushes the MP inward locally, creating a dip in its surface.The dip turns the jet toward the sunward direction (Shue et al., 2009).The sunward moving jet depletes a localized region in front of the MP (Archer et al., 2014), and it thus moves sunward.This scenario prefers the creation of sunward jets leading to extreme MP displacements by mechanism described by Shue et al. (2009), as clear dips on the MP surface were documented in our second and third examples.We have also checked other possible mechanisms suggested for the sunward flow formation, like MP reconnection (Ng et al., 2021) or Kelvin-Helmholtz instability (Yan et al., 2020).Since the reconnection jets should move along the magnetic field, we have plotted the angle between the velocity and magnetic field (not shown).This angle is small in the solar wind and outer magnetosheath but it is in the range of 60 − −120° within the intervals of sunward flows and it rules out reconnection as a possible source of them.The Kelvin-Helmholtz instability is typical at the flanks because it requires a sufficient velocity shear across the MP and thus it cannot cause sunward jets in the subsolar region.On the other hand, series of less intensive sunward jets shown in our third example can result from the interaction of earthward jets with magnetosheath plasma as suggested by Plaschke et al. (2017).
Our scenario includes both the inward and outward MP displacements but the inward displacements are relatively modest (1 − 2 R E from the model position) in all cases.It is consistent with the statistics in Figure 1b because the model statistically predicts the MP rather well if it is observed closer than 12 R E from the Earth.In contrast, the outward MP displacement can exceed 4 R E from the predicted location.Nevertheless, out of 50,000 dayside crossings only about 0.5% are farther than 2 R E from the predicted locations.However, the real occurrence rate of such events is probably several times higher, because our observations demonstrate that the MP deformations are localized in space and time and only a spacecraft that is, by a chance, at the appropriate local time and sufficiently far from the Earth can register them.
A hint of the real occurrence rate of extreme MP displacements could come from detailed studies of wave processes.For example, Katsavrias et al. (2021) report significant enhancements of Pi2 pulsation activity connected with the sunward flows in the magnetosheath.A first step in this direction is a case study of different wave emissions inside and in the vicinity of jets by Krämer et al. (2023) that contributes to understanding the microphysics of the jets with motivation to gain a knowledge about their evolution and formation.
Although our study is limited to the subsolar region, Figure 1b suggests that similar effects can be probably observed along the whole dayside MP.The median values of R obs − −R mod indicate a weaker effect, but it should be taken into account that the THEMIS apogee was relatively low and the average MP position is much farther from the Earth at morning or afternoon local times and the real MP deformation magnitude thus cannot be recorded.
Last but not least, we should point out that, although preferable solar wind conditions for observations of extreme MP locations are a low cone angle and low dynamic pressure, the investigated effects are localized and transient and cannot be captured by empirical MP models.These models are frequently used in studies of the magnetosheath jets, see for examples Goncharov et al. (2020), Raptis et al. (2020), LaMoury et al. (2021), and Vuorinen et al. (2021), but our results show that their predictions should be applied with a special care in a highly disturbed magnetosheath.On the other hand, the fact that our events were observed under a nearly radial magnetic field in a combination with the aforementioned THEMIS orbital limitation probably led Merka et al. (2003) to the suggestion of a bullet like MP shape under a radial IMF.

Figure 1 .
Figure 1.(a) Distributions of R obs − R mod ; (b) R obs − R mod as a function of R obs ; and (c) R obs as a function of the cone angle; all for subsolar crossings.The Lin et al. (2010) model and OMNI database are used for R mod .The heavy broken lines in panels (b) and (c) show medians in distance bins and the thin lines stand for the first and third quartiles.

R
obs from the Lin et al. (

Figure 3
Figure 3 presents observations on 2008-08-20 around 2220 UT.Since none of the spacecraft was just upstream, Figures 3a and 3b use the ACE magnetic field and dynamic pressure propagated to the THC location by the two-step routine(Šafránková et al., 2002).We observe a very quiet nearly radial IMF without any discontinuity and about constant dynamic pressure below 1 nPa.THC was again close to the predicted BS location (Figure3l) slightly dawnward from the subsolar point.This location is consistent with observations shown in the panels c-f that reveal several solar wind/foreshock intervals characterized by large negative values of the Vx velocity component (Figure3e) and low IMF strength (Figure3c).However, a clear entry to the magnetosphere distinguished by green dashed vertical lines can be identified between 2217 and 2224 UT.It suggests an outward MP expansion but THE located in the magnetosphere about 1 R E inward the predicted MP position (Figure3l, green

Figure 2 .
Figure 2. (left) Observations of THB and THC: (a) IMF magnitude and components; (b) solar wind dynamic pressure; (c) ion spectrogram; (d) solar wind velocity; (e) THC magnetic field; (f) THC ion spectrogram; (g) THC ion velocity and its components; (h) magnetosheath dynamic pressure and a half of the upstream dynamic pressure from panel (b); and (i) predicted distance of both BS and MP from the Earth along the direction coming through THC. Green and red vertical lines mark the MP and BS crossings, the black arrow indicates the observation of the sunward flow.(right) Sketch of approximate BS and MP locations and the shapes together with spacecraft locations (see text for the description).The visited regions are marked by color bars in the magnetic field panel (magnetosheath--blue, magnetosphere-green, solar wind-red).

Figure 3 .
Figure 3. (left) Second example: (a, b) IMF components and solar wind dynamic pressure both propagated from ACE to the THC location; (c) THC magnetic field; (d) THC ion spectrogram; (e) THC proton velocity; (f) THC dynamic pressure; (g) THE magnetic field; (h) THE ion spectrogram; (i) THE proton velocity; (k) THE dynamic pressure; and (l) predicted distance of both BS and MP from the Earth along the direction coming through THC. Green and red vertical lines mark the MP and BS crossings, visited regions are marked by color bars in THC (c) and THE (f) magnetic field panels (magnetosheath--blue, magnetosphere-green, solar wind-red), the black arrow indicates the observation of the sunward flow.(right) Sketch of approximate BS and MP locations and shapes together with spacecraft positions (see text for the description).

Figure 4 .
Figure 4. (left) Third example: The same format of the data as Figure 3, only THE observations are replaced by THB.(right) Sketch of approximate BS and MP locations and shapes together with spacecraft positions (see text for the description).