Inner Magnetospheric Response to the Interplanetary Magnetic Field By Component: Van Allen Probes and Arase Observations

We utilize 17 years of combined Van Allen Probes and Arase data to statistically analyze the response of the inner magnetosphere to the orientation of the interplanetary magnetic field (IMF) By component. Past studies have demonstrated that the IMF By component introduces a similarly oriented By component into the magnetosphere. However, these studies have tended to focus on field lines in the magnetotail only reaching as close to the Earth as the geosynchronous orbit. By exploiting data from these inner magnetospheric spacecraft, we have been able to investigate the response at radial distances of <7RE. When subtracting the background magnetic field values, provided by the T01 and IGRF magnetic field models, we find that the IMF By component does affect the configuration of the magnetic field lines in the inner magnetosphere. This control is observed throughout the inner magnetosphere, across both hemispheres, all radial distances, and all magnetic local time sectors. The ratio of IMF By to the observed By residual, also known as the “penetration efficiency,” is found to be ∼0.33. The IMF Bz component is found to increase, or inhibit, this control depending upon its orientation.

• The influence of interplanetary magnetic field (IMF) B y is observed throughout the inner magnetosphere, using Van Allen Probes and Arase observations • The median ratio of change in the observed B y to IMF B y is ∼0.33, though a clock angle dependence is found • We find a consistent effect across both hemispheres, all magnetic local time sectors, and all radial distances Correspondence to: N. A. Case, n.case@lancaster.ac.uk

Citation:
Case, N. A., Hartley, D. P., Grocott, A., Miyoshi, Y., Matsuoka, A., Imajo, S., et al. (2021). Inner magnetospheric response to the interplanetary magnetic field B y component: Van Allen Probes and Arase observations. Journal of Geophysical Research: Space Physics, 126, e2020JA028765. https://doi. org/10.1029/2020JA028765 recent works utilize sophisticated magnetic field models to determine the background field, for example, Tsyganenko and Andreeva (2020) implemented the radial basis function model of Andreeva and Tsyganenko (2016) to determine the background field. In that work, data from an array of spacecraft missions were compared to determine the effect of IMF B y at radial distances, r > 5R E . The penetration efficiency was found to depend on both the location and the strength and orientation of IMF B z .
We note that, despite being widely used in the historical literature, the term "penetration efficiency" is likely inaccurate or, at least, not wholly appropriate. Stemming from earlier studies, such as Cowley (1981), the term implies that the change in the local field topology is a direct result of the IMF field lines themselves making their way, or "penetrating," into the magnetosphere, that is, through the Dungey Cycle (Dungey, 1961). The timescale for this process would be several hours, yet more recent results have suggested that a B y component can be imparted onto closed field lines over significantly shorter timescales (e.g., Khurana et al., 1996;Tenfjord et al., 2015Tenfjord et al., , 2017, though the issue of timing remains an open question (e.g., Case et al., 2018Case et al., , 2020. It is for this reason that later studies have tended to refer to the IMF as "inducing" or "transferring" a B y component onto the magnetospheric field lines-particularly in the region of closed field lines. In this study, we extend the historical literature to determine the response of the inner magnetosphere (r < 7R E ) to the IMF B y component. To date, the effect of the IMF B y component on the large-scale local magnetic field in this region, particularly within 5R E , has not yet been statistically documented. As described in Section 2, we utilize a multi-mission data set spanning 7 years (17 spacecraft years), as well as an empirically driven magnetic field model, to statistically analyze how the local B y component changes as a result of the IMF B y component. In Section 3, we compare the spacecraft measurements, with a model background field subtracted to the IMF B y for a range of different IMF conditions and find the average "penetration efficiency" to be 0.33 across the entire inner magnetosphere.

Data and Methodology
For the purposes of this study, data are used from the Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) fluxgate magnetometer (Kletzing et al., 2013), which is housed onboard the dual satellite NASA Van Allen Probes (formerly Radiation Belt Storm Probe [RBSP]) mission (Mauk et al., 2013). The EMFISIS triaxial fluxgate magnetometer measures the 3D magnetic field vector at a rate of 64 samples per second. This data set is available in full resolution, or with a downsampled cadence of both 1 and 4 s. The following analyses incorporate all available magnetic field observations from both the Van Allen Probes spacecraft spanning the full mission duration, from launch on August 30, 2012, to mission end on October 18, 2019 for RBSP-A, and July 19, 2019 for RBSP-B.
Also included in this study are data from the Japanese geospace exploration project Arase satellite, formerly the exploration of energization and radiation in geospace satellite (ERG) (Miyoshi, Shinohara, et al., 2018b), which was launched on December 20, 2016. The Arase magnetic field experiment (MGF; Matsuoka et al., 2018) measures the magnetic field at a sampling rate of 256 vectors per second, but data are also provided at 64 vectors per second and spin (8 s) resolution. The accuracy of the MGF data is dependent upon which sampling mode the instrument is in, with a lower accuracy for higher dynamic ranges. In this study, we utilize Arase MGF data spanning the period from March 13, 2017 to August 31, 2019, with an accuracy of at least ±1.25 nT. These data are combined with observations from the Van Allen Probes to provide high levels of data coverage across all regions of the inner magnetosphere.
Due to the statistical nature of the following analyses, and to temporally align the spacecraft data with upstream IMF conditions, all spacecraft data are resampled to a 1-min resolution. The IMF data are obtained from the high-resolution (1 min) OMNIweb database (King & Papitashvili, 2005). These data are recorded by several upstream observers and then time-shifted to the bowshock nose. Although there are inherent uncertainties in undertaking such a shifting process, especially when the upstream observer is not close to the Sun-Earth line, the approach is statistically valid (e.g., Case & Wild, 2012;Mailyan et al., 2008). Since we are investigating the magnetic field in the inner magnetosphere, spacecraft data are presented in the solar-magnetic (SM) coordinate system so that they are aligned with the Earth's magnetic dipole. IMF data are presented in the geocentric solar magnetospheric (GSM) coordinate system.
The spatial data coverage of both the Van Allen Probes and Arase missions is provided in Figure 1 in SM coordinates. Data coverage for Van Allen Probes is shown in panels (a and b), Arase in panels (c and d), and the combined data set in panels (e and f). In panels (a, c, and e), data coverage is plotted by location in the X and Y planes, and each bin is 1R E by 1 h in magnetic local time (MLT) in size. In panels (b, d, and f), data coverage is plotted by location in the XY (i.e.,  2 2 X Y ) and Z planes, and the bins are 1R E square. The bin fill color represents the total number of 1-min data points contained within it.
For both missions, data coverage is approximately homogeneous in MLT, due to the long duration of the data and the orbital precession of the spacecraft. The greatest number of observations are available between 5 and 6 R E for both satellite missions, due to their similar apogee altitude. The larger orbital inclination of Arase (31°) provides greater coverage in the Z SM direction than is possible solely from the Van Allen Probes observations (10.2° inclination). We note that the Van Allen Probes mission contributes significantly more data to this study than the Arase mission simply due to its dual-spacecraft nature and longer period of operation.

Magnetospheric Models
In the following analyses, the Van Allen Probes and Arase in situ magnetic field data are compared against modeled background field values to determine what effect the IMF B y component has on the magnetic field in the inner magnetosphere. In this region, the background field is a radially dependent combination of an internally driven component (i.e., the terrestrial quasi-dipolar field) and an externally driven component (i.e., the solar wind/IMF-shaped magnetosphere).
To determine the internal component of the background field, we utilize the latest version of the international geomagnetic reference field (IGRF 13) (Thébault et al., 2015). The IGRF is derived from magnetic field data recorded by magnetic observatories, ground surveys, and low Earth orbiting satellites and is regularly updated to account for the latest variations in the Earth's magnetic field. It is independent of any upstream solar wind or IMF conditions. The externally driven component of the background field is determined using the empirically derived T01 model of the inner magnetosphere (Tsyganenko, 2002a(Tsyganenko, , 2002b. T01 was developed using in situ observations from a range of spacecraft missions (see Figure 1 of Tsyganenko [2002b] for mission and temporal coverage) and is driven by a variety of upstream parameters, including the solar wind speed and the IMF B y and B z components, as well as their time history. We note that the Van Allen Probes and Arase missions were not part of the T01 empirical data set and so their data are independent of the modeling data.
The IMF B y component is utilized as a parameter in the T01 model in the calculation of the IMF clock angle and external magnetic pressure. IMF B y contributes, for example, to the determination of the model's penetration efficiency term-which is clock-angle-dependent (Equation 10 in Tsyganenko, 2002b). It is therefore expected that the effects of the IMF B y component on the inner magnetosphere would be hidden when comparing the in situ data with the model output. As such, we also compare the in situ observations with a version of T01 in which we set both the instantaneous and historical IMF B y to zero. This removes the IMF B y influence on the modeled B y field component but ensures that other contributions, such as spacecraft location and dipole tilt angle, are accounted for. We note that the external magnetic pressure exerted will therefore likely be underestimated, however, this is a relatively small systematic offset that does not significantly affect the responses seen (e.g., Tenfjord et al., 2017).
In the subsequent results and discussion, "model" is the modeled field calculated by the addition of the IGRF and T01 field contributions, including IMF B y as a driver, and B y(mod) is the y-component of this field. "Model*" is the modeled field calculated by the addition of the IGRF and T01, with IMF B y = 0, and By mod is the y-component of this field. The field measured by the spacecraft is referred to as the "observed" field and B y(obs) denotes the y-component of this field. Although not the primary aim of this study, comparing the "observed" data with "model" allows us to verify that the combination of models we use is working well for our data intervals. The spacecraft data are also sorted by hemisphere, i.e., on either side of the neutral sheet which separates the oppositely directed magnetic lobes. Since the neutral sheet is not necessarily located on the Z SM = 0 plane, we use both the spacecraft location and the in situ measured field to determine which hemisphere the spacecraft is located in at any given time. Data are defined as being sampled from the Northern Hemi- Conversely, data are defined as being sampled from the Southern Hemisphere when Z SM < 0 R E and B i > 0. Given the reasonably steady nature of the solar wind (e.g., Milan et al., 2010), the median IMF B y is calculated for each spacecraft data point by simply using the preceding 30 min of IMF B y data, neglecting any propagation time from the bowshock to the magnetopause or magnetospheric response time.

Results
Figure 2 shows data recorded in the Northern Hemisphere. In the top row are the median B y(obs) values per bin for (left) IMF B y ≤ 2 nT, (center) |B y | < 1 nT, and (right) B y > 2 nT. As with Figure 1, the data bins are 1R E in the radial direction and 1 h in MLT in size. The color of the bin represents the median value.
In the middle row of Figure 2   , but with a sizable collection of blue colored bins particularly around the dusk sector. We note too that the IMF |B y | < 1 nT state appears to be dominated by blue bins, suggesting an offset in which model* systematically overestimates the local B y field. The median absolute relative percentage of the IMF B y = 0 offset to the B B y obs y mod  value for the two nonzero states is 45.0%-though it does vary across MLT and radial distances. To remove this systematic offset, in the bottom row of Figure 2, we plot the median B B y obs y mod  minus the corresponding offset observed for the IMF |B y | < 1 nT state. In both the IMF B y > 2 nT and B y ≤ 2 nT cases, the previously mentioned trends become clearer across almost all radial and MLT bins once this offset is removed. To determine whether the response of the observed field is different between hemispheres, or between the dusk and dawn sectors, data are separated into the following regions: Northern Hemisphere 01-11 MLT (blue) and 13-23 MLT (red), and Southern Hemisphere 01-11 MLT (green) and 13-23 MLT (orange). The medians of all the regions combined (i.e., all data) are plotted in black. Additionally, for every region, in each panel, a line of the best fit is plotted. For the IMF B y plots (a-c) the line of best fit is linear, for the clock angle (d-f) plots the line of best fit is a third-order polynomial.
In Figures 4a and 4d, it appears that B y(obs) does not respond to the IMF B y component. As previously mentioned, however, this is simply because the background field is much larger than the IMF B y component. When we subtract the background model* field, in panels (b and e), the relationship becomes clear. .    0 33 IMF B y − 0.41 nT. We note that the negative intercept of this line of best fit is consistent with the negative (blue) offset observed in the middle panel of Figure 2.
In Figure 4e, third-order polynomial fits between the IMF clock angle and B B y obs y mod  are shown. Again, these fits are broadly similar for all MLT regions. The turning points of the various fits are all offset from θ = ±90° (i.e., IMF B z = 0). For the all data medians (black line), the maximum and minimum occur at θ = 97° and θ = −109° respectively. Both of these turning points demonstrate that while the clock angle must be dominated by the IMF B y component contribution, it must also contain a rela-tively small southward B z component to maximize the influence of the IMF B y component on the inner magnetosphere.
We note that the absolute difference between the maximum and minimum clock angles and |θ| = 90° is 7 and 19° respectively. This indicates that there is a small asymmetry between the required relative contribution of IMF B y and B z for the two IMF B y orientations. This result suggests that for IMF B y to be most effective in the inner magnetosphere for B y < 0, a more strongly negative IMF B z component is required compared with when IMF B y > 0.
In Figures 4c and 4f  To investigate any radial dependencies in the data, we split the data by the location in MLT and then the bin by the radial distance from the Earth. One representative example of this binning is shown in Figure 5, where data are sampled from the Northern Hemisphere in the 01-11 MLT sector. The lines of best fit plotted in the figure are the medians of the data from this MLT sector, binned by radial distance from the Earth.
The results in Figure 5 are very similar to those in Figure 4. There is a clear linear response at almost all radial distances when B B y obs y mod ( ) ( *)  is plotted against IMF B y , and a third-order polynomial response when plotted against the IMF clock angle. In panel (b), the gradients of the IMF B y linear fits are broadly similar as with the MLT sectors (∼0.3). The third-order polynomial fits to the clock angle (panel e) follow similar patterns as before with the maxima and minima, for all fits, occurring at θ ∼ 95° and θ ∼−110°, respectively. We note that the 6 ≤ r < 7R E bin is an exception to this, which we attribute to the relatively small number of data points in this bin-as is apparent in Figure 1e.
To determine the degree to which the IMF B y influences the observed B y component across the whole of the inner magnetosphere, we compute linear lines of best fit for B B  The color of the bins represents the gradient of the fits for the data in that bin. Gray bins indicate limited data (where there was no data for every IMF B y bin) or poor fits (where the unreduced chi-square goodnessof-fit statistic was greater than 1).
Panels (a-c) show that the fit gradients range from ∼0.2 to 0.5 throughout the inner magnetosphere, though there appears to be no particular pattern to this distribution and there is little discernible difference between hemispheres. The gray bins are predominantly due to limited data in the outer radial bins (i.e., 6 ≤ r < 7R E ).
CASE ET AL.  The result is much more mixed for panels (d-f), with gradients ranging between ±0.2, though again there is no particular pattern to this distribution.

Discussion
In this study we have collated magnetic field data from two spacecraft missions in the inner magnetosphere, namely, the Van Allen Probes and Arase. Utilizing the IGRF 13 and T01 magnetic field models to determine the "background field level," we have demonstrated how the IMF B y component affects the y-component of the magnetic field in the inner magnetosphere.
As shown in Figure 1, our data are recorded in the R XY < 7R E and |Z| < 4R E regions, in SM coordinates. The Van Allen Probes and Arase missions provide unparalleled coverage in this region, allowing us to undertake comprehensive statistical analyses of the local magnetic field in the inner magnetosphere with respect to the upstream IMF B y component.
In the top row of Figure 2, we show the median observed B y component for three IMF B y states: IMF B y ≤ 2 nT, IMF |B y | < 1 nT, and IMF B y > 2 nT. Unsurprisingly, since the total field strength in this region is several orders of magnitude larger than the IMF, there is no discernible difference between the IMF B y states when the data are presented in this way. However, when the background field (By mod ( *) ) is subtracted, as in the middle row of Figures 2 and 3, the response to the IMF B y component becomes clear. There does, however, appear to be some asymmetry in the data. The IMF B y ≤ 2 nT shows a much clearer response than the IMF B y > 2 nT state and the IMF |B y | < 1 nT state appears to be more like a weakened version of the IMF B y ≤ 2 nT state, rather than a true "neutral" (or zero) state. These results suggest that model* B y is overestimating the y-component of the magnetic field in all cases. The results from Figure 3 are broadly similar to their counterparts in Figure 2, indicating that there is little-to-no discernible difference between the two hemispheres.
In Figures 4 and 5  , and By(obs) − By(mod) as a function of (a-c) IMF B y and (d-f) IMF clock angle. In Figure 4, the data are plotted by their location in MLT and in Figure 5 by their radial location. The results of these two figures are similar, and so are discussed together.
In panels (a-c), the data are plotted as a function of IMF B y in the range of ±6 nT. We note that outside this range the amount of data drops off significantly resulting in poor fits (i.e., a large chi-square goodness-of-fit statistic). Once the background field is subtracted (panel b), the effect of the IMF B y component becomes clear. Using a linear least squares fit, we find a direct relationship between the IMF B y and the B B y obs y mod ( ) ( *)  residual. The gradients, or "penetration efficiencies," are similar for all MLT and r regions, averaging around 0.33. While the line of best fit offsets does vary, even the largest offset (Figure 5b) is, when normalized to the strength of the background field, small. Although it is interesting to note that almost all offsets are negative, even when taking into account the IMF B y component in the model (i.e., B y(obs) − B y(mod) )-which is consistent with the slightly negative local B y state observed for IMF |B y | < 1 nT in Figures 2 and 3  In Figures 4 and 5d-5f, the data are plotted as a function of the clock angle. Based on the assumption that the fits should have a maximum amplitude when IMF B y is dominant and zero amplitude when no IMF B y is present, a third-order polynomial is used to fit the data. A third-order polynomial, unlike a sine function, allows for an asymmetry in the turning points of the fit, which is particularly evident in panel (e) of both the figures. In Figure 4, for example, the maximum turning point is located at θ = 97° and the minimum turning point at θ = −109°. The clock angles for both the turning points occur when the IMF |B y | component is several times larger than the IMF |B z | component, but the IMF B z component is nonzero and negative. The maximum and minimum of the fits do not occur at the same |θ|, which demonstrates that the ratio between the IMF B y and B z components required for the maximum amplitude is different for the two opposite IMF B y directions. This result may indicate that one orientation of the IMF B y component more readily facilitates reconnection than the other or that the topology of newly opened flux increases/decreases the efficiency, for which the B y component is transferred into the inner magnetosphere. We note, however, that these differences are small and are the maximum and minimum of the fits, rather than the data themselves, and so may be prone to fitting error. Further investigation into this observed discrepancy, perhaps through magnetohydrodynamic modeling, therefore seems warranted.
When comparing the hourly averaged IMF and observed B y components in the X GSM ∼ −20 to − 30R E regions, Fairfield (1979)  . .
nT. Of course, our data are recorded in a much different region of the magnetosphere than the IMP 6 spacecraft used by Fairfield (1979) and has also had other non-IMF B y related effects removed from it through use of the T01 model. Cowley (1981) noted that, because the Fairfield (1979) result was found in both the tail lobes and the plasma sheet, it directly implied the existence of asymmetries on closed field lines. Indeed, all data used in this present study are within 7R E , that is, on closed field lines. Numerous studies that followed on from the Fairfield (1979) investigation have found the "penetration efficiency," that is, the gradient of the lines of best fit, to vary depending on the region of the magnetosphere being studied and IMF conditions (e.g., Cao et al., 2014;Cowley & Hughes, 1983;Fairfield, 1979;Lui, 1984;Kaymaz et al., 1994;Nagai, 1987;Petrukovich, 2009;Wing et al., 1995). For example, in the T01 model, which is used throughout this study, the penetration efficiency ranges from 0.068 for northward IMF to 0.622 for southward, however, it is not location dependent (Tsyganenko, 2002b). In recent work by Tsyganenko and Andreeva (2020), modeling of the neighboring regions to that in our study found similar efficiencies of between 0.2 and 0.4, with the larger efficiencies occurring during southward IMF.
The general relationship of ΔB y(obs) ∼ 0.33 ×IMFB y holds throughout the inner magnetosphere. There is, of course, some variation in the gradient of the relation by the MLT sector and by radial distance, as can be seen in Figures 4 and 5. However, the median gradient for the 1-h MLT by 1 R E bins in Figure 6 is 0.33, with an interquartile range of 0.07, suggesting that the general trend holds throughout this region. Again, this is consistent with the recent modeling work, for example, Figure 4 in Tsyganenko and Andreeva (2020).
We note that the southward IMF has resulted in higher penetration efficiency in past studies and, as discussed, we too see this effect in Figures 4e and 5e. We have, therefore, also investigated the effect of the southward IMF on our penetration efficiencies. Shown in Figure 7 are the distributions of the penetration efficiency for three clock angle states: "all data, 90° < |θ| ≤ 135°, and "other." The median penetration efficiencies for these states are 0.33, 0.40, and 0.30, respectively. This result demonstrates that the penetration is higher when the IMF B y is dominant but accompanied by a negative B z . This, presumably, is the result of southward IMF driving a larger dayside reconnection rate which, in turn, increases the amount of flux being transferred from the IMF into the magnetosphere. Given that the difference between the median values presented is quite small, we compare the two sample population distributions, using the statistical z-test, finding that the difference between the two distributions is highly significant.
Our analyses have also allowed us to compare the in situ magnetic field with the combined modeling of IGRF 13 and T01. Woodfield et al. (2007) compared T01 with 2 years of perigee Cluster data (∼4R E ) and found that the model performed very well in a global sense. Although such testing was not the main aim of this study, our results agree with this assessment. The results of the analyses undertaken, particularly those presented in Figures 4 and 5 (c and f), suggest that the T01 model accurately reflects the impact of the IMF B y on the observed B y component in the inner magnetosphere, that is, the line of best fit gradients. Although the offsets of the lines of best fit may sometimes appear large, they represent a small fraction of the total background magnetic field in this region. We note that we are able to attribute this accurate IMF B y response solely to the T01 model, since the IGRF model does not contain any solar wind/IMF inputs.
In this study, the issue of timing, that is, how long it takes the inner magnetosphere to respond to, and reconfigure based on, the IMF B y component, has not been investigated. Instead, all spacecraft data were associated with the preceding 30-min average of the IMF B y component. While the response to the IMF B y component was clearly seen on this timescale, this does not necessarily mean that it takes 30 min or less for the IMF B y component to influence the inner magnetosphere. The IMF B y component tends to have a long auto-correlation length (e.g., Milan et al., 2010) and so the IMF B y may have been stable for much longer than the averaging period used. Additionally, it does not mean that the system has completely reconfigured in this time, and so we expect our results to include a combination of fully reconfigured states as well as newly responding states. We note the work by Tenfjord et al. (2015Tenfjord et al. ( , 2017, who found that the inner magnetosphere responded to changes in IMF B y orientation on timescales of ∼30 min but took longer to fully reconfigure to the new B y state. Additionally, this was undertaken using GOES data recorded at geosynchronous orbit (r ∼ 6.6R E ). It would therefore be a worthwhile exercise to investigate the issue of timing using Van Allen Probes and Arase data to determine whether their results hold closer to the Earth. Such future work is planned by the authors.

Conclusion
Utilizing 7 years (17 spacecraft years) of data from two spacecraft missions, namely, Van Allen Probes and Arase, we have rigorously investigated the effect of the IMF B y component on the inner magnetosphere. We have shown that IMF B y influences the local field in both the hemispheres, all radial distances, and all MLT sectors.
The response of the inner magnetosphere to the IMF B y component scales linearly in the IMF range analyzed (−6 ≤ IMF B y ≤ + 6 nT). The "penetration efficiency," that is, the fraction of the IMF B y component that is imparted onto the background inner magnetospheric field is largely consistent throughout the inner magnetosphere at ∼0.33. This result is consistent with previous studies near this region, for example, Tsyganenko and Andreeva (2020).
The penetration efficiency was found to be clock-angle-dependent, specifically the maximum efficiency is observed when the clock angle is dominated by the B y component but also contains a negative B z component. Again, this is consistent with previous studies from other regions of the magnetosphere. The median penetration efficiency increased to 0.4 during favorable conditions (90° < |θ| ≤ 135°) and dropped to 0.3 during unfavorable conditions. Additionally, we have found that, in a statistical sense, the Tsyganenko (2002aTsyganenko ( , 2002b model, when combined with the IGRF 13 model (Thébault et al., 2015), accounts for the IMF B y effect well in the inner magnetosphere.