The Earth’s magnetosphere is embedded in the solar wind and adjusts itself to the prevailing solar wind conditions. Numerous previous studies have investigated the relations between the magnetospheric phenomena and solar wind observations recorded at the L1 point. However, the solar wind plasma and interplanetary magnetic field (IMF) undergo changes at the bow shock (BS) and pass through the magnetosheath (MSH) before reaching the magnetosphere. Thus, the changes of solar wind parameters in MSH on large and small scales directly affecting the magnetosphere should be studied deeply. Despite the importance of MSH processes, relatively few large-scale statistical studies have been devoted to the situation in the entire MSH. It might be due to the continuous motion of BS and magnetopause (MP) locations, causing difficulty in the determination of the exact location of these boundaries for a particular MSH observation.

Hydrodynamic models of MSH plasma and magnetic field profiles (Spreiter et al., 1966; Spreiter and Stahara, 1980) predict that the velocity decreases from BS toward MP, whereas the density and temperature increase. Magnetohydrodynamic simulations confirm these global MSH profiles (e.g., Liu et al., 2015). However, multipoint observation studies (e.g., Zastenker et al., 2002) show that the hydrodynamic model could only predict the large-scale MSH profile. Still, it cannot reproduce the small-scale structures where values of particular plasma parameters can differ from the predicted values by a factor of 5 (Němeček et al., 2000). Such structures can be generated in MSH, and their generation processes would depend on the IMF cone angle (arccos (|B_X|/|B|)) because the hydrodynamic model predictions are less accurate when the IMF vector is aligned with a solar wind flow (Němeček et al., 2000). The follow-up study of Němeček et al. (2002) further points out that the IMF orientation strongly influences the dayside MSH radial profile of the ion flux.

Several statistical studies (Paularena et al., 2001; Longmore et al., 2005) have applied the MSH interplanetary medium reference frame (Bieber and Stone, 1979) to solve the problem of boundary locations. Their global studies have shown a dawn-dusk asymmetry in the plasma density; it is larger at the dawn side, whereas the flow speed is higher on the dusk side, and this asymmetry depends on the solar cycle. Dimmock and Nykyri (2013) applied the same method to the THEMIS data and showed the asymmetries of the magnetic field, density, and flow speed in MSH. The results also reveal that the IMF orientation plays a role in forming the MSH magnetic field strength profile. Ma et al. (2020) used more than 12 years of THEMIS data to investigate MSH and magnetospheric asymmetries and compare them with BATS-R-US simulations. The results show that the plasma density is higher at the region close to MP during northward IMF (nIMF) than southward IMF (sIMF) orientation.

One of the most critical parameters for modifying upstream solar wind parameters at BS is an angle between the IMF vector and the normal to the BS surface (ϴ_BN) (Czaykowska et al., 2000). BS influences only the components perpendicular to the shock normal; therefore, the solar wind parameters would exhibit more significant changes downstream quasi-perpendicular shocks (ϴ_BN > 45°) than downstream quasi-parallel shocks (ϴ_BN < 45°). The proton temperature is nearly isotropic downstream of the quasi-parallel shock, but the increase of the temperature anisotropy is typical for the downstream of quasi-perpendicular shocks. Temperature anisotropy can directly affect plasma instability excitation and growth rates (Gary et al., 1993), forming more waves in the downstream region of perpendicular shocks. On the other hand, reflected particles move upstream along the magnetic field line under the quasi-parallel shock topology, generating a foreshock region in front of BS. The highly disturbed solar wind in the foreshock ultimately propagates into MSH. Different kinds of transients (e.g., Xirogiannopoulou et al., 2024) are generated in the foreshock and influence the downstream structures (see Zhang et al., 2022 for a review). For example, the hot flow anomalies originating due to the interaction of an IMF tangential discontinuity substantially decrease the dynamic pressure (P_d) and cause a local MP expansion (Šafránková et al., 2012). Similar effects can result from the interaction of MP with the MSH jets (Němeček et al., 2023).

In addition to the different types of bow shock and foreshock effects, the plasma and magnetic field profiles are also influenced by the local structures in MSH, such as the depletion layer (Midgley and Davis, 1963). The depletion layer in front of MP is characterized by a strong magnetic field and low plasma density. Such structures also depend on the IMF orientations; the depletion layer usually appears when the IMF points northward because an inward flow compresses the magnetic field, and the increased magnetic pressure pushes the plasma away along the magnetic field lines, but dayside reconnection destroys the depletion layer under sIMF (e.g., Anderson and Fuselier, 1993; Šafránkova et al., 2009). On the other hand, MP reconnection occurs at the lobe region, and it creates a dense low-latitude boundary layer on the magnetospheric side of the MP and/or MSH boundary layer on the opposite side under nIMF, but these layers are missing for sIMF (Němeček et al., 2015). Zhang et al. (2019) studied the plasma parameters in MSH and their influence on the reconnection rate. They conclude that the IMF clock angle, MSH plasma β, and the solar wind sound Mach number are significant factors controlling the MP reconnection rate.

Based on the above results, we know that the IMF orientation plays an important role in the determination of the MSH environment. Aside from the south-north magnetic orientation, the radial IMF (rIMF) component is also essential because IMF points nearly radially approximately 10%–15% of the total observation time (Pi et al., 2014). RIMF shifts the foreshock toward the BS nose, and the foreshock covers almost the whole dayside magnetosphere (Blanco-Cano et al., 2009). Foreshock transients, such as spontaneous hot flow anomalies, foreshock bubbles, etc., are more likely to be generated in this huge region and influence the magnetosphere. RIMF forms a thinner MSH because of the low Mach number (Pi et al., 2014; Wang et al., 2020), and the magnetic field at the subsolar MSH would be low due to the low compression ratio at the quasi-parallel BS (Czaykowska et al., 2000). The radial (B_X) component converts into B_Y and B_Z components in MSH (Pi et al., 2016), and it leads to different B_Z orientations in the north and south hemispheres and the simultaneous appearance of subsolar and lobe reconnection locations in different hemispheres (Pi et al., 2017). This asymmetric reconnection can generate a thick MSH boundary layer (Pi et al., 2018).

Several simulation results show that the pressure profiles, including total (P_tot), dynamic (P_d), thermal (P_t), and magnetic (P_b) pressures across MSH reflect different IMF orientations (e.g., Samsonov et al., 2012; Wang et al., 2018). The simulations reveal three interesting results: 1) P_t increases with a distance from BS for sIMF, but it shows a bump in MSH for nIMF because the depletion layer decreases P_t near MP; 2) the ratio between upstream and downstream P_tot across BS changes with upstream P_d; and P_tot decreases significantly after the BS crossing for a large P_d; 3) P_tot roughly remains constant across the whole MSH for nIMF, but it decreases during the MSH pass for sIMF (see Figs. 8, 9 in Wang et al. (2018)). Samsonov et al. (2012) compare the results of isotropic and anisotropic MHD models and show that the anisotropic temperature modeling leads to a lower effective P_tot under rIMF than the nIMF orientation. These phenomena have not yet been confirmed by observations.

In summary, we know many effects of changing the incoming solar wind parameters before reaching MP, and most depend on the IMF orientation. However, the effects themselves or whether they will occur in the whole MSH still need to be quantified, especially for rIMF. Therefore, we use 4 years of THEMIS observations to study the MSH spatial profiles of the plasma parameters, magnetic field strength, and pressure components and discuss the influence of IMF orientations on them. After the introduction, section 2 describes the data used in this study, section 3 contains the data processing methods, and section 4 is devoted to the results obtained by two different approaches. The discussion and conclusions are presented in sections 5 and 6.

We use measurements from all probes of the THEMIS mission (Sibeck and Angelopoulos, 2008) from 2007 to 2010 because these probes with apogees ranging from 10 to 30 R_E provide frequent MSH observations during the selected period. The electrostatic analyzer (ESA; McFadden et al., 2008) records the plasma data continuously with a 3-s resolution. In the target region of our study, ESA often switches between the solar wind and magnetospheric modes, which could influence the statistical results. Therefore, the onboard moments (MOM) calculated from data gathered in the magnetospheric mode are selected. The fluxgate magnetometer (FGM; Auster et al., 2008) records the magnetic field vector with even higher time resolution, but all measurements mentioned above are averaged into 1-min intervals.

Each statistical MSH study faces the task of determining the distance between the MSH point of observation and MP/BS without continuously recording MP/BS locations. To solve this task, we apply two approaches and check the consistency of the results.

This study is devoted to the influence of the IMF direction on the average spatial profiles of magnetic field and plasma parameters across dayside MSH. First, let us clarify the uncertainties affecting this study. It is known that the SW speed changes in a range of 250–800 km/s; the proton density varies from a few units to two hundred cm^-3, and the temperature varies by an order of magnitude. Variations of the IMF magnitude are similar, but the IMF direction can dramatically change in seconds, and all these changes are reflected in MSH. Since the MSH parameters would be related to upstream ones, we use normalized quantities in our analysis. Unfortunately, no near upstream monitor is permanently available, and thus, we use the observations made at the L1 point and propagate them to the spacecraft location (deceleration in MSH is omitted). The propagation routines cannot take into account plasma instabilities modulating SW parameters so that the actual upstream conditions can differ from those predicted. Moreover, Urbar et al. (2019) compared the velocity measured by THEMIS upstream BS with propagated Wind data and found that THEMIS in the magnetospheric mode underestimates the velocity by a factor of 0.93, and it results in ∼15% difference in the dynamic pressure; nevertheless, the difference can be as significant as 30% in individual cases. The inter-calibration, therefore, does not allow us a direct comparison of particular values, but we believe that they cannot change the observed trends. Moreover, the width of the distribution of THEMIS/Wind velocity ratios is about ± 3%, and this uncertainty also contributes to the uncertainty of MP and BS models. The uncertainty of the Shue et al. (1997) model is around 0.8 R_E near the Sun-Earth line (Lin and Wang, 2009), and the Chao et al. (2002) model exhibits an average standard deviation of around 5.7 R_E (e.g., Dmitriev and Chao, 2003). For these reasons, we analyzed the MSH passes using superposed epoch analysis, where the boundaries were certain. This fact allows us to distinguish the MP boundary layers, but this approach still suffers from the uncertainty of estimations of upstream SW parameters. Since the number of MSH passes under a stable IMF orientation is limited, we apply the second approach—a method of the MSH coordinate. However, its results are affected by all aforementioned uncertainties, and it causes relatively huge standard deviations of our average profiles. For example, the average ion speed in MSH is 180.6 km/s with a standard deviation of 97.5 km/s under rIMF conditions.

We use the standard error of the mean as the measure of uncertainty and show it in plots. The number of points used to determine average profiles is large, and the error bars are often hidden within the line thickness. Therefore, we believe that differences between presented profiles are reliable and that they are associated with a particular IMF direction or with a value of the upstream pressure.

As noted, we try to answer three questions from simulation results (Samsonov et al., 2012; Wang et al., 2018):

(1) How does the ratio of upstream to downstream Ptot at BS change with increasing upstream Pd? Specifically, does Ptot decrease significantly after the BS crossing for large Pd (Wang et al., 2018)?

According to the simulation results by Wang et al. (2018) a large upstream pressure cause a decrease in P_tot across BS. This effect is more pronounced for nIMF but still visible for sIMF. However, our analysis (Figure 8) shows different results. The low THEMIS P_d in the upstream was already discussed and attributed to an underestimation of the ion velocity, but it would not affect the overall profiles. Nevertheless, Figure 8 shows that P_tot is maintained from the solar wind toward MP if the upstream P_d is low, and even P_tot increase in the BS vicinity is observed for higher P_d. The low MSH P_tot in the model is probably connected with an underestimation of MSH P_t that compensates the decrease of P_d. We cannot compare this feature with our analysis because it combines all IMF orientations, and thus, the higher P_t in the P_d<1 nPa set is probably connected with an enhanced portion of rIMF events in this set (Pi et al., 2014).

The influence of the IMF orientation on the pressure profiles in MSH was investigated in two ways, and their results are almost consistent (Figures 3, 5); the differences near MSH boundaries are connected with the problem of their determination in the MSH coordinate approach. The Wang et al. (2018) simulations predict constant P_tot across MSH for nIMF and its decrease toward MP for sIMF, but we do not see any notable difference between these two IMF orientations. The P_t profile in simulations rises toward MP and exhibits a bump in the MSH center for nIMF, but it is flat for all IMF orientations in observations. A much larger P_t for rIMF than for the other two orientations is consistent with calculations by Samsonov et al. (2012), but these calculations predict a gradual rise of P_t toward MP, but a decrease is observed in Figure 5C.

Figure 5 shows the distribution of P_tot and its components along the path from the SW to the magnetosphere. As could be expected, the whole system is in the pressure equilibrium because an increase in P_t and P_b for all IMF orientations balances a decrease in P_d. The only notable feature is the excess of normalized P_t for rIMF in MSH due to an increased temperature and a density peak in front of MP (Figure 4). This increase of P_t can also be related to T_ANI changes under rIMF conditions. As the V decreases, an increasing N is expected, but they are absent for nIMF and sIMF. It can be related to the draped magnetic field lines increasing the magnetic field strength, pushing the plasma away, and creating a depletion layer for nIMF. Note that subsolar reconnection also moves the solar wind flux away for sIMF.

P_d for rIMF shows a smooth change when it crosses BS. We suggest that it is related to BS non-stationarity. The simulations of the BS formation by De Stretck and Poedts (1999) reveal that BS under a field-aligned flow is an unstable structure. They conclude that the intermediate BS could form under rIMF conditions. Lin and Wang (2005) also performed a 3D simulation of BS under rIMF. Their results show that the quasi-parallel BS is nonstationary and its reformation frequently occurs. Both studies imply that BS is unstable under rIMF, and this can result in the non-sharp BS crossing in our statistics.

In order to elucidate the possible sources of differences between models and observations, we have investigated the role of fluctuations in the formation of the mean MSH profiles. The foreshock effect is a general phenomenon that can be noticed in our results because the foreshock can be found in front of BS under all IMF orientations and covers the whole dayside BS under rIMF conditions. The high fluctuation level of all parameters (Figure 7) in front of BS increases the temperature (Figure 4B) for rIMF. Figure 6C shows that T_ANI under rIMF is ∼0.5 in the foreshock region and becomes ∼1 in the first-half MSH, but Pi et al. (2022) report that T_ANI is close to 1 in SW for the rIMF events. The reason for the T_ANI decrease is the increasing T_PARA (Figure 6B) by the reflected particles in the foreshock. T_ANI jumps to around 1 in MSH for rIMF, and it is consistent with the finding of Czaykowska et al. (2000) that quasi-parallel BS is less effective in increasing T_ANI than quasi-perpendicular BS. The simulation results of Samsonov et al. (2012) also imply that T_ANI in MSH is ∼1 for rIMF (see Figure 2 in that paper). Large MSH T_ANI for nIMF and sIMF orientations maintain the level of fluctuations of all parameters through the whole MSH but nearly isotropic temperature for rIMF in the first half of MSH leads to their damping. As a result, there are no noticeable differences in fluctuation levels between different IMF orientations just in front of MP, with the exception of the magnetic field.

We used two methods to investigate the SW modification in MSH for different IMF orientations. The first approach is based on the superposed epoch analysis of complete MSH crossings recorded by THB and THC during 2007–2010. The second method applies the radial distance of the spacecraft from the model MP normalized to the MSH thickness for all THEMIS observations in the subsolar MSH. We should note that the results of both approach analyses are generally consistent, regardless of the fact that we encountered some of the above-mentioned differences.

Applications of our two analyses allow us to summarize the results as follows:

(1) We did not find any influence on the value of the upstream pressure on the mean magnetosheath profile.

All these features are associated with the preconditioning of the SW plasma and IMF in the foreshock that is present under rIMF but missing during the other IMF orientations.

Since we did not confirm the suggestions following from models (Samsonov et al., 2012; Wang et al., 2018), we plan to use the collected data for a complex comparison with local magnetosheath models like Vandas et al. (2020) in the near future.