Martian Bow Shock Oscillations Driven by Solar Wind Variations: Simultaneous Observations From Tianwen‐1 and MAVEN

The Martian bow shock stands as the first defense against the solar wind and shapes the Martian magnetosphere. Previous studies showed the correlation between the Martian bow shock location and solar wind parameters. Here we present direct evidence of solar wind effects on the Martian bow shock by analyzing Tianwen‐1 and MAVEN data. We examined three cases where Tianwen‐1 data show rapid oscillations of the bow shock, while MAVEN data record changes in solar wind plasma and magnetic field. The results indicate that the bow shock is rapidly compressed and then expanded during the dynamic pressure pulse in the solar wind, and is also oscillated during the IMF rotation. The superposition of variations in multiple solar wind parameters leads to more intensive bow shock oscillation. This study emphasizes the importance of joint observations by Tianwen‐1 and MAVEN for studying the real‐time response of the Martian magnetosphere to the solar wind.

ion composition boundary, and the photo electron boundary (Garnier et al., 2017;Holmberg et al., 2019;Nagy et al., 2004). The bow shock slows down and deflects the supersonic solar wind and heats up solar wind plasma in a turbulent magnetosheath. The location and global shape of the bow shock reflect the interaction between the solar wind and Martian magnetosphere, and these vary depending on solar wind and interplanetary magnetic field (IMF) conditions (Garnier et al., 2022). The effects of the solar wind and IMF on the Martian bow shock are an essential piece in comprehending the dynamics of the Martian plasma environment.
The accumulation of magnetic field and plasma data from the Mars Global Surveyor (MGS; Albee et al., 1998), Mars Express (MEX; Chicarro et al., 2004) and Mars Atmosphere and Volatile EvolutioN (MAVEN; Jakosky et al., 2015) has enabled extensive investigations of the location and shape of the Martian bow shock (Simon Wedlund et al., 2022). Variations of bow shock locations have also been widely studied. A statistical study by Vignes et al. (2002), using the data from the magnetometer (MAG) and electron reflectometer onboard MGS, found that the distance of the bow shock terminator from the planet's center is greater for large IMF cone angles (i.e., angle between the IMF vector and Mars-Sun line) than for small cone angles in the northern hemisphere, and that the quasi-parallel-region of the bow shock is closer to the planet than the quasi-perpendicular-region. Concurrent measurements from MGS and MEX (Edberg et al., 2009b) and Rosetta and MEX (Edberg et al., 2009a) revealed that a higher dynamic pressure, P dyn , causes the Martian bow shock to move inward. The result was confirmed by a statistical study using MEX data (Edberg et al., 2009a), which further revealed (a) that the IMF direction could cause the bow shock to move outward in the hemisphere with a locally upward convection electric field and (b) that an increase in solar extreme ultraviolet (EUV) flux can also cause the bow shock to move outward. Edberg et al. (2010) used the magnetosonic Mach number, M ms , measured near Earth and extrapolated to Mars during a time of approximate radial alignment, and found that an increase in M ms results in lower altitudes for the Martian bow shock. Hall et al. (2016) discovered that changes in the solar EUV flux have a greater impact on the location of the bow shock than variations in P dyn . Hall et al. (2019) also revealed the similarity between the variation in the bow shock position and solar EUV flux over solar cycle 23-24. Research based on MAVEN observations confirmed that while the EUV and M ms are the two most significant factors for the bow shock location, the solar wind P dyn also plays a role (Garnier et al., 2022;Halekas et al., 2017).
Magnetohydrodynamics simulations supported this picture of the influence of solar wind M ms and P dyn on the location of the Martian bow shock (Wang et al., 2020b). Additionally, the simulations indicated that the subsolar standoff distance and the flaring angle, which is related to the eccentricity of the bow shock, increase with the tangential IMF components to the solar wind flow direction, while the parallel IMF component has little effect on the subsolar standoff distance but influences the flaring angle.
Recently, Garnier et al. (2022) established a hypothesis on the drivers of the location of Martian bow shock, based on a statistical analysis on MEX and MAVEN data. To mitigate the effects of the cross-correlations among the multiple potential drivers, a partial correlation analysis was employed, and the relative importance of the parameters was ranked using model selection methods. They concluded that the EUV flux and M ms are the primary factors determining the shock location, with the solar wind P dyn and crustal fields as secondary drivers. Additionally, the IMF direction plays a significant role, with perpendicular shocks being positioned farther from Mars than parallel shocks.
Most of the previous studies on the impacts of solar wind on the Martian bow shock were based on statistical analyses of numerous bow shock events observed by a single orbiter. However, this approach precludes the study of the response of the bow shock to solar wind and IMF changes on short timescales. The successful deployment of the Tianwen-1 mission (Wan et al., 2020), along with the simultaneous operation of the MAVEN spacecraft, enables our study on solar wind effects on the bow shock in detail. In this study, we utilize simultaneous observations from Tianwen-1 and MAVEN to investigate the real-time response of the Martian bow shock to variations in the solar wind.

Data
We utilize data collected by the Tianwen-1 magnetometer (MOMAG; Liu et al., 2020;Wang et al., 2023;Zou et al., 2023) from 2021 November 15 to 2021 December 31. The data set provides the three components of the magnetic field in Mars Solar Orbital (MSO) coordinates, where the X-axis points from Mars to the Sun, the Z-axis toward the north ecliptic pole, and the Y-axis completes the right-handed coordinate system, sampled at 1 Hz, which was its normal mode. We also incorporate data obtained from the MAVEN mission during this period, including data acquired by the magnetometer (MAG; Connerney et al., 2015), solar wind ion analyzer (SWIA; Halekas et al., 2015) and solar extreme ultraviolet monitor (EUVM; Eparvier et al., 2015) instruments. MAVEN MAG data used in the study is at the same frequency of 1 Hz with MOMAG and in MSO coordinates. SWIA fine mode data is used to calculate the physical moments of solar wind protons, such as the number density, speed, and temperature (Halekas et al., 2017). EUVM provides the solar irradiance data in 0.1-7 nm, 17-22 nm, and 121-122 nm bands; to ensure the appropriate quality of the data, we only use observations when the instrument's boresight is directed toward the Sun and is optimal for solar observations. Figure 1 shows the orbit variations of Tianwen-1 and MAVEN spacecraft in MSO cylindrical coordinates. Both Tianwen-1 and MAVEN orbits crossed the bow shock during 2021 November and December. Tianwen-1 crossed the bow shock near the terminator and MAVEN was near the nose of the bow shock when it was located in the solar wind during this period. In this context, we find bow shock multiple-crossing cases in which Tianwen-1 recorded the shock surface oscillation while MAVEN simultaneously captured data in the solar wind upstream of the bow shock. The availability of such observations makes it possible to investigate the response of the bow shock flank to the variations in the solar wind.

Method
We identify Tianwen-1 crossings of the bow shock by the discontinuity between the solar wind and sheath, where the magnetic field strength |B| rapidly increases and becomes more disturbed from the solar wind to the sheath. While Tianwen-1 crosses the bow shock multiple times within a few minute interval, the possible drivers for the bow shock are derived from: 1. IMF strength: derived from the root-sum-squared of the three components of the magnetic field measured by the MAVEN/MAG. 2. The clock and cone angle of the IMF: the direction of the IMF is determined by the three components of the magnetic field in MSO coordinates, with the clock angle defined as tan −1 (B y /B z ) and the cone angle defined as cos −1 (−B x /|B|). 3. Solar wind magnetosonic Mach number (M ms ): M ms is determined by sw / f , with sw the proton speed from SWIA and f the fast magnetosonic speed, which is calculated by 2 = 1∕2 The Alfvén speed A is determined by = | |∕ √ 0 , where μ 0 is the vacuum magnetic permeability and the density comes from the mass and number density of the proton, ρ = m p n p . The speed of sound cs = √ ( + 5∕3 )∕ ; here we assume the same temperature of solar wind electrons, T e , and protons, T p , and take the polytropic index 1 for solar wind electrons and 5/3 for protons, considering the isothermal/adiabatic behavior of solar wind electrons/ions (Burne et al., 2021;Halekas et al., 2017). θ is the angle between the wave propagation and the magnetic field; here we use the cone angle, which results in f along the MSO X axis. 4. Solar wind dynamic pressure (P dyn ): dyn = 2 sw . 5. Angle between the bow shock normal and IMF (θ Bn ): the key parameter is the bow shock normal, which is estimated by two methods in this study. The first method is to apply the minimum variances analysis (MVA; Sonnerup & Scheible, 1998) to a series of magnetic field data taken over a 5-min time window centered on the crossing time. The shock normal is the direction along which the magnetic field varies minimally, as the magnetic field remain the shock normal should keep constant when crossing the shock surface. The second method is to utilize the shock normal from the bow shock model. When the spacecraft is close to the bow shock, we first find the point on the shock surface that is closest to the spacecraft and derive the normal at that point from the bow shock model (Schwartz, 1998; Simon Wedlund et al., 2022). EUV irradiance is also one of the primary factors affecting the location of the Martian bow shock, however, the duration of every case in this study is limited to tens of minutes, during which the EUV irradiance remained constant and we have opted not to present the EUV data in this study.
As the magnetic field measured by MOMAG and MAG are both utilized in this study, we first provide detailed comparisons of the IMF measured by the two spacecraft and the reasonability of using MAG as the monitor of upstream IMF for Tianwen-1 in Supporting Information S1.

Results
Here we looks at three case studies, where the first two are more straightforward and clean and show the result of single parameter effect, while the last case is more typical and shows the result of multiple parameters affecting the bow shock location.  Figures 2a and 2b show the magnetic field strength and vectors from Tianwen-1 MOMAG. In general, |B| decreases from ∼7 nT in the sheath to ∼2 nT in the solar wind, which is close to the IMF strength measured by MAVEN (Figure 2c). Tianwen-1 was immersed in the solar wind after 07:11UT (t 3 , marked by the third vertical dashed line), with |B| rapidly decreasing and then stabilizing. Before Tianwen-1 fully left the sheath, its |B| dropped quickly at 07:07UT (t 1 ) and then returned to the sheath level at 07:08UT (t 2 ). Between t 1 and t 2 , the value of |B| nearly decreased to the solar wind level, ∼2 nT; the IMF strength, the clock and cone angle were stable at ∼2 nT, −90° and 135° respectively, as measured by MAVEN in the upstream solar wind (Figures 2c-2e)).

Shock Oscillation Controlled by the Solar Wind Dynamic Pressure
It is noteworth that the solar wind P dyn quickly increased and stayed at high level for ∼1 min right before t 1 , which was caused by the solar wind density variation (not shown). We infer that the sudden increase of P dyn from ∼0.65 to ∼0.75 nPa compressed the bow shock at t 1 , causing Tianwen-1 to be briefly exposed to the solar wind, leading to the rapid decrease in |B|. Subsequently, when P dyn decreased to ∼0.65 nPa at t 2 , the bow shock expanded again, resulting for Tianwen-1 to be back into the sheath where |B| recovered to the sheath level. During the period of interest from 07:00 to 07:20 UT, M ms continuously fluctuated between the values of about 6 and 8. Corresponding to the peak of P dyn before t1, M ms exhibited three spikes; considering the significant impact of Mms on the shock location, the varying M ms might also play a role in this event. Figure 2j illustrates the distance along the shock normal between the shock locations at t 1 and t 3 is ∼0.07 R M . Obviously, the actual spatial oscillation is probably larger than this scale. Hence, the 0.1 nPa perturbation of P dyn in this event caused the bow shock motion at a scale >250 km along the shock normal. Overall, the locations of the bow shocks in this event are closer to the planet compared with Edberg's model, which may be due to the high M ms and the quasi-parallel shock.

Shock Oscillation Controlled by the IMF
During 03:50UT to 04:15UT on 2021 Dec 26, Tianwen-1 observed an oscillation of the bow shock that may be caused by an IMF transient with a radialward rotation. At the beginning of the event, Tianwen-1 was in the solar wind with |B| at ∼3 nT. As Tianwen-1 entered the sheath, the magnetic field became highly variable with |B| increasing at ∼03:56UT (t 1 ) and |B| increased to ∼10 nT at ∼04:00UT. At 04:07UT (t 2 ), |B| decreased rapidly back to ∼3 nT, close to the IMF strength measured by MAVEN. Then |B| increased rapidly to the sheath level again at ∼04:10UT (t 3 ).
During t 2 and t 3 , there was no significant change in the solar wind M ms and P dyn , and the IMF strength was also stable; however, the IMF direction changed considerably; the clock angle shifted from −90° to −180° (denoting a change from westward IMF to southward IMF), the cone angle shifted from 150° to 180°. Cone and clock angles both returned to their original values within ∼2.5 min. Thus, the IMF direction before and after the transient is Parker-spiral-like, while during the transient, it became radial and directed toward the Sun. The begin and end times of the transient are ∼1 min before t 2 and t 3 , respectively, well corresponding to the crossing of the bow shock. Hence, we infer that the temporarily radial IMF caused the bow shock to move inward; after the transient has passed, the bow shock may expand back toward its original position (Figure 3j).
For the Earth bow shock, Wang et al. (2020a) found that under the radial IMF condition, the dayside of the bow shock is located closer to the Earth than the average. For the Martian bow shock, Sui et al. (2023) found that the subsolar and flank regions of the Martian bow shock are situated closer to Mars under the radial IMF condition, which is consistent with our result. In addition, the varying IMF direction changes θ Bn of the shock. In this event, the local θ Bn changed from ∼90° to ∼45°, which may also cause the inward motion of the bow shock. For this event, maybe only a portion of the bow shock moves inward, since different parts of the bow shock may undergo different θ Bn changes and thus move in different directions.

Shock Oscillation Controlled by Multiple Factors
While the prior two cases demonstrated bow shock oscillations driven by P dyn pulse and IMF rotation separately, we have identified more complex events, in which Tianwen-1 observed bow shock oscillations accompanied by changes in several parameters of the solar wind measured by MAVEN. Figure 4 shows one such example, a multiple shock crossing event observed by Tianwen-1 between 00:55UT and 01:30UT on 2021 Dec 09. As |B| recorded by MOMAG fluctuates between the solar wind level (∼3 nT) and the sheath level (∼10 nT), Tianwen-1 crosses the bow shock 5 times at cadences of several minutes, entering the sheath at ∼01:11UT (t 1 , as marked by the first vertical line in Figure 4), ∼01:13UT (t 3 ), ∼01:23UT (t 5 ) and entering the solar wind at ∼01:12UT (t 2 ) and ∼01:16UT (t 4 ). Highly variable upstream solar wind conditions monitored by MAVEN may be linked to the bow shock's motion. Approximately 1 min before t 4 , the IMF strength quickly decreased from ∼4.5 to ∼3 nT, while the dynamic pressure increased from ∼1.2 to ∼1.5 nPa, returning to the previous level ∼1 min before t 5 . These changes may have contributed to the bow shock motion detected by Tianwen-1 at t 4 and t 5 . The oscillation between t 1 and t 3 may have been caused by the increasing of the IMF strength and decreasing of the dynamic pressure at ∼01:09 UT. The increase in amplitude and fluctuation of the magnetic field at ∼01:04 UT may be due to the approach of Tianwen-1 to the bow shock caused by shock expansion caused by the increasing IMF strength, rapid rotation of IMF, and the decreasing dynamic pressure at ∼01:03 UT. With the quick rotation of the IMF at ∼01:08 UT, the bow shock may have shrunk, making Tianwen-1 away from the bow shock, and causing |B| measured by MOMAG to return to the amplitude and fluctuation of the solar wind level.

Conclusions and Discussions
In this study, we provide direct evidence of solar wind effects on Martian bow shock oscillations using simultaneous observations from Tianwen-1 and MAVEN. We present three cases where Tianwen-1 crossed the bow shock multiple times within a few minutes interval, while MAVEN stayed in the upstream solar wind. During the motion of bow shock observed by Tianwen-1/MOMAG, MAVEN monitored the changes in solar wind parameters, like the IMF strength and direction, M ms and P dyn . Through these observations, we are able to establish direct connections between the bow shock oscillations and the solar wind fluctuations. The case in Section 4.1 shows direct evidence of P dyn modulations on the position of Martian bow shock. The shrinking and expanding of the bow shock may be mainly caused by the P dyn pulse. The case in Section 4.2 shows direct evidence of IMF direction modulations on the bow shock position. The shrink of the bow shock near the spacecraft may be caused by the radial IMF or by the turning from the quasi-perpendicular shock to oblique shock. The case in Section 4.3 shows the complicated modulation of various changing parameters in the solar wind on the bow   shock location. The increases of P dyn , M ms or IMF strength, or radial IMF, can compress the Martian bow shock individually. When these factors are combined at different times, their superposition make the bow shock motions more frequent and rapid.
The time delay between the time when MAVEN detected changes in the solar wind and the time when Tianwen-1 crossed the moving bow shock later is noteworthy. It may be is a function of several factors: (a) the propagation time of the solar wind from MAVEN to the bow shock, (b) the response time of the bow shock to solar wind changes, and (c) the propagation time of the bow shock from its original position to where it crossed by Tianwen-1. The first factor, the propagation time of the solar wind, can be estimated by the distance of two spacecraft in MSO X direction and the solar wind speed, which is about 10-15 s in the first and second event. Taking out the solar wind propagation time, there is still a ∼1-min time. The exact value of the response time is unknown, but must be less than 1 min. It reveals the rapid response of the bow shock to the solar wind variation, which is consistent with the simulations (Ma et al., 2014;Song et al., 2023). For the second event, if we assume that the bow shock kept static before the IMF rotation and responded to the solar wind instantaneously, after removing the propagation time of the solar wind, the ∼1-min time difference between IMF rotation and t 2 would be the time needed for the bow shock to move from bow shock location at t 1 to that at t 2 . The distance along the normal, between the two locations, is ∼0.12 R M (Figure 3j). The mean shock speed along the normal is estimated to be ∼7 km/s. If we assume that the bow shock underwent a uniformly accelerated motion, its speed at t 2 is estimated to be ∼14 km/s.