Response of Earth's Neutral Sheet to Reversals in the IMF By Component

The By component of the interplanetary magnetic field (IMF) plays an integral part in the coupling of the solar wind‐magnetosphere‐ionosphere system. In this study, we use a suite of magnetospheric spacecraft, with data spanning nearly 25 years, to statistically investigate the control of the IMF By component on the neutral sheet. Past studies have identified that this thin layer of the magnetotail, which separates the oppositely directed magnetotail lobes, responds to reversals in the IMF By component. The proposed method for driving this response is through unequal flux loading in the magnetotail lobes, and we present lobe flow data from the Cluster mission, which suggests that this is indeed the case. We find that the neutral sheet responds in a statistical fashion, with a clear twist or rotation whose orientation depends upon the polarity of the IMF By component. Additionally, under individual analyses, we find the response time of the neutral sheet to IMF By reversals is much shorter than possible through the classical dayside reconnection driven picture. We find an average response time of between 10 and 20 min with little to no dependence on distance downtail. These results suggest that the neutral sheet responds to the IMF By component on multiple timescales.


Introduction
First detected by Ness (1965), using measurements from the IMP 1 satellite, Earth's neutral sheet separates the tailward directed magnetic field in the Southern Hemisphere from the earthward field in the Northern Hemisphere. This relatively thin region of space, located within the plasma sheet, is characterized by a strong cross tail current, a minimum in the total magnetic field intensity, and a reversal in the local B x magnetic field component (Speiser & Ness, 1967).
The average location and shape of the neutral sheet has been studied extensively in the past (e.g., Fairfield, 1980;Hammond et al., 1994;Tsyganenko & Fairfield, 2004;Xiao et al., 2016), and these studies have demonstrated that the neutral sheet is not static. Its position and configuration vary with local factors, such as the dipole tilt angle, and with the external driving of the solar wind and the embedded interplanetary magnetic field (IMF). Such factors introduce a warping, bending, and twisting of the neutral sheet (Zhang et al., 2002). In this study, we focus particularly on the effect of the IMF B y component on the neutral sheet.
It is well known that the IMF B y component induces a B y component into the magnetosphere (e.g., Cowley & Hughes, 1983;Kitaev, 1991;Tenfjord et al., 2015;Wing et al., 1995) and, as such, is the source of several asymmetries throughout the magnetospheric and ionospheric systems (e.g., Grocott et al., 2007). A nonzero IMF B y component results in the site of dayside reconnection moving from the subsolar point toward the high-latitude flanks (Park et al., 2006). This, in turn, results in asymmetric flux loading of the lobes (Cowley, 1981). As described in Tenfjord et al. (2016), there are then two methods by which a B y component is induced into the closed magnetosphere.

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B y component in the closed magnetotail field lines. Specifically, intervals of B y > 0 driving should induce an anticlockwise twist (when visualized looking downtail from Earth). Later studies (e.g., Nagai, 1987;Nishida et al., 1998;Owen et al., 1995;Sibeck et al., 1985) found that this was indeed the case.
Numerous studies have looked into the timing of the induced B y , using ionospheric responses, shear flows, tail twisting, and cross-correlation studies (e.g., Browett et al., 2016;Rong et al., 2015;Tenfjord et al., 2016). However, previously, only case studies into the response time of the neutral sheet to changes in the IMF have been undertaken (e.g., McComas et al., 1986;Motoba et al., 2011;Pitkänen et al., 2016;Rong et al., 2015). We note that previous studies (e.g., Nagai, 1987;Tenfjord et al., 2016) have performed statistical analyses of the induced B y component, but these studies were restricted to the inner magnetosphere.
In this study, using nearly 25 years worth of magnetospheric magnetic field data, we undertake a statistical analysis of the response of the neutral sheet to changes in the IMF B y component orientation. Additionally, through individual event analyses, we find the response time of the neutral sheet to reversals in the IMF B y component.

Data Selection
At its simplest, the magnetotail neutral sheet is what separates the tailward orientated magnetic field, that is, negative B x (in a geocentric solar coordinate system), from the earthward directed field, that is, positive B x . Therefore, to determine its position statistically, one need only find where the direction of the x component of the magnetic field reverses (Tsyganenko et al., 1998). To do this simply requires in situ magnetic field measurements from the region of interest.
All data are resampled to 1-min cadence and are converted into the geocentric solar wind (GSW) coordinate system (Hones et al., 1986) to account for the solar wind aberration effect on the magnetotail. The GSW coordinate system is similar to the aberrated geocentric solar-magnetospheric system but differs from it by using the solar wind velocity to determine the actual aberration angle-rather than assuming a constant aberration angle of 4 ∘ . Furthermore, the location data of the spacecraft are normalized by solar wind dynamic pressure. Using the technique of Hammond et al. (1994), we attempt to account for the effect of the solar wind dynamic pressure on the size of the Earth's magnetotail and normalize the location of the spacecraft within it. As shown in equation (1), the normalization factor ( ) takes the form of a simple one-sixth power scaling with respect to a reference dynamic pressure (p r ): where p m is the measured dynamic pressure (which we compute as the average value over the previous hour). We choose the reference pressure to be the mean dynamic pressure for all solar wind data within the time period of this study, that is, 1992-2016, and we find this to be 2.10 nPa.
If the impinging dynamic pressure is stronger than the reference pressure (i.e., p m > p r ), the location of the spacecraft is scaled closer to the Earth to account for the dynamic pressure compressing the magnetosphere. Conversely, if p m < p r , the spacecraft location is scaled further away from the Earth to account for an expanded magnetosphere.
Solar wind and IMF data are collated from NASA's high-resolution (1 min) OMNIweb database (King & Papitashvili, 2005). The OMNIweb database provides a convenient source of solar wind and IMF data that has been propagated to the Earth's bow shock with a good degree of accuracy (Case & Wild, 2012). The database is an amalgamation of data from various upstream satellite missions, including WIND, ACE, and DSCOVR.
Magnetic field data collected near the neutral sheet (i.e., bounded by the region −50 ≤ X GSW < 0 R E , |Y GSW | ≤ 30 R E , and |Z GSW | ≤ 3 R E ) are selected from each of the spacecraft and combined into one large data set. Beyond 50 R E downtail data coverage is too poor for statistical analysis with this data set. The spatial coverage of the combined magnetic field data is shown in Figure 1. The amount of data in each bin is presented in days (where 1 day equates to 1,440 data points at 1-min resolution). The particularly high density region (5 < r < 15 R E ) is the result of the elliptical orbits of the four Cluster spacecraft.
We note that the data are fairly evenly distributed above and below the neutral sheet, with 51.0% of the data being recorded between 0 < Z GSW < 3R E and thus 49.0% between −3 < Z GSW ≤ 0R E . There is, however, some X dependence to this distribution, with more data located in Z GSW < 0 the further downtail it was recorded (∼60% at −40R E ).

Results and Analyses
In the following section, we investigate both the effect of the average IMF B y orientation on large-scale morphology of the neutral sheet, as well as the response time of the neutral sheet to reversals in the IMF B y orientation.

Average Morphologies
For each magnetospheric magnetic field data point located within the region of interest, the modal IMF clock angle ( ) orientation for the preceding 60 min is determined. We chose a value of 60 min as this order of response time is sufficient for a large-scale response of the tail to take place, at least for southward IMF conditions, (e.g., Browett et al., 2016) and produce the Cowley (1981) twist.
The modal values are then grouped into the following 45 ∘ wide classifications, centered on the cardinal and intercardinal directions: north ( ≥ 337.5 ∘ and < 22.5 ∘ ), northeast (67. , and northwest (377.5 ∘ > ≥ 292.5 ∘ ). So that we only include intervals where the clock angle is stable, data intervals with less than 60% agreement between individual clock angles and the modal classification are discarded.
In Figures 2 and 3, the magnetotail magnetic field data are grouped by their corresponding IMF clock angle orientation. For each orientation the associated magnetic field data are binned into 5 R E by 10 ∘ bins. The median value of the local magnetic field component in each bin determines the bin's color with the same color scale being used across all panels. Shown in Figure 2 is the local B x component and in Figure 3 is the local B y component.
Since the region of interest spans only ±3 R E in the Z GSW direction, we are in effect looking at the slice of space containing the neutral sheet. Assuming that the neutral sheet is indeed located on the equatorial plane, the median B x value should equate to zero. That is, there should be an equal amount of tailward field (negative B x ) and earthward field (positive B x ). Any deviation from this equality demonstrates nonuniformity, and, if this deviation is a systematic change from positive to negative azimuthally across the tail, it is indicative of a twisting or rotation of the neutral sheet. We note that small, short-lived, disturbances to the neutral sheet (e.g., warping and bending) will average out over such a large data set. Figure 2 demonstrates that there is a statistical preference for positive B x in the postmidnight sector, and negative B x in the premidnight sector, under eastward IMF (B y > 0, |B y | > |B z |) conditions. This trend is reversed under westward IMF (B y < 0, |B y | > |B z |) conditions. This is consistent with the idea of a neutral sheet twist. Figure 3 clearly demonstrates that the local B y orientation does indeed match that of the IMF B y component.
To test the suggestion that this preference relates to the unequal loading of IMF in the lobes (e.g., Haaland et al., 2008), we also plot the plasma convection in the lobes for eastward and westward IMF in Figure 4. The convection data, provided by the Cluster EDI instruments, are binned using the same criteria as for the magnetic field data in Figure 2. We first discard any flow velocities of >100 km/s as these are determined to be anomalous (Haaland et al., 2008). We then compute the mean V x and V y components of the convection velocity for each bin and use them to determine the magnitude and direction of V xy , where V xy = √ V x 2 + V y 2 . The length of the arrow in each bin of Figure 4 represents the magnitude of V xy and the color represents the number of data points in that bin.    . Cluster electron drift instrument velocity data, recorded from within the nightside magnetotail lobes, are sorted by interplanetary magnetic field (IMF) clock angle orientation. For both the Northern and Southern Hemispheres, the mean V xy in each bin is presented under eastward and westward IMF orientation. The mean V xy magnitude in each bin is indicated by the length of the arrow. The color of each arrow indicates the number of vectors in that bin.
sphere. As described in detail in Haaland et al. (2008), this is consistent with asymmetric flux loading from the dayside. For example, under B y > 0 conditions in the Northern Hemisphere, recently opened field lines convect dawnward under the effect of the tension force (the so-called Svalgaard-Mansurov effect, as summarized in Wilcox, 1972) and are thus deposited preferably in the dawn side of the lobe. This subsequently excites duskward flow within the lobe as the asymmetric pressure distribution is equalized between the dawn and dusk lobes (see Figure 6 in Haaland et al., 2008).
We note that there is a significant difference in the quantity of Cluster EDI data collected between the Northern and Southern Hemispheric lobes. This bias is simply due to the orbital configuration of the Cluster satellites preferentially sampling the Southern Hemisphere lobe over the Northern Hemisphere lobe. No such bias exists in Figure 2 since we sample the neutral sheet region, rather than the lobes.
To explore these relationships further and determine the statistical response time of the neutral sheet to changes in the IMF B y component, we analyze the local B x data in the neutral sheet region under intervals of IMF B y reversal.

IMF B y Reversals
To determine the response time of the neutral sheet to reversals in the IMF B y component, we first determine when the orientation of the IMF B y component reverses. To do this, we employ a method similar to Tenfjord et al. (2016). For each IMF data point, we compute a 20-and a 60-min average, both forward and backward in time. A reversal from positive to negative B y is said to have occurred if both the 20-and 60-min backward 10.1029/2018JA025712 averages are > 2 nT and both the forward averages are < −2 nT (and vice versa for negative to positive). We compute the two differing length averages to ensure a stable pretransition and posttransition period (60-min average) with a prompt transition (20-min average).
These reversal criteria were applied to the OMNI data set for years 1992-2016 and resulted in the identification of 6,825 IMF B y reversals. We then selected only those with coincident magnetotail magnetic field data, leaving 2,794 reversals. Of these, 1,377 (49.3%) were positive to negative and 1,417 (50.7%) negative to positive IMF B y reversals.

Response Time
Using the IMF B y reversals identified in section 3.2, we identified the coincident magnetic field data from the magnetotail spacecraft. The Shue et al. (1997) modeled magnetopause location was determined for each individual data point, and any data falling outside this modeled magnetopause location were discarded. Although this approach is prone to inaccuracies in the magnetopause model, it is convenient and statistically valid (e.g., Case & Wild, 2013). Additionally, the data were further restricted to the region of the magnetotail most likely to contain the neutral sheet, that is, X GSW < −5R E , |Y GSW | < 30R E , and |Z GSW | < 3R E . To increase the chances of detecting a neutral sheet crossing in the magnetospheric data, only intervals where at least one spacecraft recorded a reversal in the local B x component (i.e., passes through the neutral sheet) are kept. Intervals are four hours in length, centered around the IMF B y reversal. To ensure sufficient magnetospheric data surrounding a reversal, we require that the interval contains at least 120 data points (2 hr worth) of magnetospheric data. Intervals with fewer than 120 data points were discarded.
Using these criteria, 382 intervals of magnetotail data relating to 181 unique IMF B y reversals were identified. The data for each of these intervals were then manually inspected to determine if any neutral sheet response could be identified. We analyzed the B x component of the local magnetic field for any sudden deviations occurring near the IMF B y reversal. We required that the polarity of the local B x either switch or the strength significantly reduce/increase and remain stable after the deviation (i.e., not switching back and forth between polarities). Additionally, we required that the deviations had to be clear and be complete within 10 min. We found the deviations were often accompanied by a matching deviation in the local B y component. These criteria ensure that sudden swaps in the polarity of the local B x component are the result of the neutral sweeping over the spacecraft. Additionally, sudden increases or decreases in the magnitude of the local B x suggest that the neutral sheet has moved closer or further away from the spacecraft.
To reduce the chance of these changes occurring simply due to the spacecraft's orbit, rather than the motion of the neutral sheet, intervals where the spacecraft crossed the Y = 0 or Z = 0 axis were excluded, since one might expect a reversal in local B x in these cases anyway. Additionally, any gradual changes in B x , which is indicative of a spacecraft's orbit passing through a somewhat stationary neutral sheet, were ignored. We note, however, that in single case study events, it is difficult to be certain that the reversal in the local Bx component is due to tail twisting rather than some more localized event (e.g. warping).
An example of an IMF B y reversal with an associated abrupt change in the local B x component is shown in Figure 5. This example is of a positive to negative IMF B y reversal that took place at 07:54 UT on 28 February 1996. Plotted in the top row of Figure 5 is the trajectory of the Geotail spacecraft in the GSW X-Y, Y-Z, and X-Z planes, respectively. Also plotted is an illustration of the expected clockwise neutral sheet rotation with this type of IMF B y reversal. As noted before, the spacecraft does not cross Y = 0 or Z = 0 axes and remains in approximately the same region of space during the one hour preceding and three hours following the IMF B y reversal.
Plotted in the second row are (left) the IMF B x (red), B y (blue), and B z (green) components and (right) the AL index (Davis & Sugiura, 1966). As indicated by the vertical red line, the IMF B y component reverses direction, swapping from around +2 nT to around −2 nT at 07:54 UT. We note the time given here is approximate, with the B y component first starting to drop in magnitude a few minutes earlier. The AL index remains at fairly quiet levels until around 50 mins after the reversal has occurred, thus suggesting substorm activity, for example, is not playing a large role in this interval.
In the following rows of Figure 5, the x, y, and z components of the (left) local magnetic field and (right) perpendicular ion velocity are plotted. As indicated by the blue line, the magnetospheric spacecraft (Geotail) records a local B x component reversal at 08:20 UT, approximately 25 min after the IMF B y component reversal. The local B y component seems to match the orientation of the IMF B y component, being positive before the reversal and negative after the reversal on average. We note the local B z is steadily dropping as the spacecraft's orbit drops but remains at around +4 nT when the local B x reversal occurs. Note that the sudden reversal of the local B z (from positive to negative) earlier in the interval, at around 07:35 UT, and data from Geotail's low-energy particle instrument (not shown) is indicative of a magnetosheath flow-suggesting the spacecraft momentarily passed into the sheath.
The statistical results of these individual analyses are presented in Figure 6. Plotted in the top two panels are the locations of 120 observed sudden deviations in the local B x component for (left) positive to negative IMF B y reversals (54%) and (right) negative to positive reversals (46%). Plotted in red are events where the local B x component becomes more positive; that is, B x switches from negative to positive, or remains negative but suddenly decreases in strength, or is positive and suddenly increases in strength. Plotted in blue are events where the local B x component becomes more negative. The direction of the expected neutral sheet twist, based on the IMF B y orientation, in each case is shown by the arrows.
For the positive to negative IMF B y reversals, we expect the majority of points in the Y GSW > 0 sector to be red and the majority of points in the Y GSW < 0 to be blue, since this would be indicative of a clockwise rotation. Conversely, for the negative to positive reversals we would expect the opposite since this would be indicative of an anticlockwise rotation. Indeed, this appears to be the case, particularly beyond |Y GSW | > 5R E .
Plotted in the second row of panels (left) is a histogram of the response time, that is, the time delay between the observed IMF B y reversal and the deviation in the local B x component. We find that the median response time is 17 min with a skewed distribution to shorter response times. Both types of B x deviations share a similar distribution.

Plotted in the subsequent panels are the location of the deviations in (left
all in GSW coordinate system). Also shown in each of the plots is the Spearman correlation coefficient and the linear lines of best fit (red for more positive data, blue for more negative data, and black for all data). We find that there is a weak correlation between the response times and the location of the deviation in the X coordinate and radial distance (r) ( = −0.31 and 0.32, respectively). We note that there is significant spread in the data, which is likely due to the local effects that play a significant role in the response time of the neutral sheet to reversals in the IMF B y component (Sergeev et al., 2003).

Discussion
It is well known that Earth's magnetosphere responds to changes in the IMF orientation and, in particular, to changes in the IMF B y component. The idea of a neutral sheet responding to such changes, via a twist, was first introduced by Russell (1972) and Cowley (1981) and confirmed by numerous studies thereafter. What has been lacking until now, however, is a large-scale statistical study of the neutral sheet response, particularly its timing, to reversals in the IMF B y orientation.
The statistical response of the neutral sheet to the IMF B y orientation is demonstrated in Figures 2 and 3. By averaging the local B x and B y components over 60 min, between ±3 R E Z GSW , we find the average direction of B x and B y in the different spatial regions. A neutral sheet with no twist or rotation should average to B x = 0 across this plane with equal flux of negative (tailward) and positive (earthward) B x . The dominance of one direction of B x in one sector and the dominance of the opposite direction in the other, especially when that dominance is reversed depending upon the IMF B y orientation, illustrates a large-scale twisting of the neutral sheet. This is clearly illustrated, with a dominance of negative B x in the premidnight sector and a dominance of positive B x in the postmidnight sector for eastward IMF (B y > 0, |B y | > |B z |). This is accompanied by a complete reversal of this trend for westward IMF (B y < 0, |B y | > |B z |). Additionally, we find that the local B y component statistically matches the driving IMF conditions. This demonstrates that a positive IMF B y component twists the neutral sheet in an anticlockwise motion (when visualized looking downtail from Earth). Conversely, a negative IMF B y component twists the neutral sheet in a clockwise motion. We note that the axis of the twist appears to be a little offset from 24 MLT (i.e., Y GSW = 0), instead centered around 23 MLT, suggesting that there are some asymmetry effects also at work. Interestingly, this appears to align with the median location of substorm onset (e.g., Frey et al., 2004;Nagai, 1982).

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The twisting is most obvious during IMF B y -dominated intervals (i.e., eastward and westward) but can also be seen during intervals with a nonzero IMF B z component (e.g., southwestward). Visual inspection seems to suggest that the twist is slightly more prominent under partly northward intervals versus partly southward intervals (e.g., northwest versus southwest). This matches with previous studies, for example, Owen et al. (1995), who suggest that southward IMF results in high levels of geomagnetic activity, which restrains the twisting of the neutral sheet. Indeed, we find that under purely southward IMF the neutral sheet is extremely disturbed with substantial variance in the local B x and B y components.
The interpretation of asymmetric flux loading in the tail lobes is supported by the direction of the plasma flows in the lobes. As shown in Figure 4, we observe duskward flows in the Northern Hemisphere and dawnward flows in the Southern Hemisphere under eastward IMF. This trend is reversed under westward IMF. These results are consistent with the work of Haaland et al. (2008).
When analyzing individual response times of the neutral sheet to IMF B y reversals, we found that the responses were on much shorter timescales than the large, statistical twist. Indeed, rather than responses of the order of 60-90 min (i.e., for a Cowley, 1981,-type twist), the responses were found to be centered around 17 min. This does not, however, rule out the longer timescale response, rather just suggesting that the shorter timescale is more obvious to see in individual analyses at the locations being sampled by the spacecraft.
The neutral sheet response times we present here include the propagation time of the solar wind/IMF from the bow shock to the magnetopause. The exact timing of this propagation through the magnetosheath varies, though is approximately 4-5 min (Khan & Cowley, 1999;Wild et al., 2009), resulting in response times from the magnetopause of around 12-13 min. This result is consistent with the timescale proposed by Tenfjord et al. (2015), around 15 min from the bow shock or 10 min from the magnetopause, for pressure-induced B y induction. Further, we note that Wing et al. (2002) found that the nightside magnetic field, at geosynchronous orbit, responded to southward turnings in the IMF within 12 min. Modeling by Tenfjord et al. (2015) suggests that the rapid induction of the IMF B y component onto closed field lines is driven by fast-mode waves, which can travel at 900 km/s, carrying the magnetic pressure information into the lobes. Further investigation into this seems warranted.
Additionally, we note that, as shown in the histogram of Figure 6, some of the responses seem to occur before the IMF B y component actually reversed. Rather than indicating that the IMF was not the driver of the change, we suggest that there were perhaps inaccurate solar wind propagation delays or that there were localized features and bulges related to internal processes in the plasma sheet (e.g., substorms and reconnection events) causing local topological changes.
There appears to be little dependence on the neutral sheet response time based on the location on the sheet. Only a weak correlation was found with radial distance along the neutral sheet ( = 0.32). We suggest that this weak correlation is most likely due to the local variability inherent with the location and dynamics of the neutral sheet. Indeed, when we attempted to perform a superposed epoch analysis of the response times, we found significant variance that rendered the result inconclusive.

Conclusions
In this study, we collated magnetotail magnetic field data, spanning 25 years and from a range of magnetospheric spacecraft missions, with the aim of determining the response of the neutral sheet to changes in the IMF B y component. The magnetic field data were converted into the GSW coordinate system to account for aberration effects, filtered to our region of interest, and normalized using dynamic pressure.
As shown in Figure 2, the neutral sheet develops a twist under nonzero IMF B y conditions. Under sustained positive IMF B y conditions, the neutral sheet twists (rotates) in an anticlockwise motion (when visualized looking downtail from Earth). Conversely, sustained negative IMF B y twists the neutral sheet in a clockwise motion. We find that this is slightly more apparent under northward IMF conditions than southward. As shown in Figure 3, we also find that the local B y component strongly matches the driving IMF B y orientation.
The proposed method for introducing a neutral sheet twist is unequal loading of magnetic flux into the tail lobes (e.g., Cowley, 1981). This is supported by the plasma convection flows presented in Figure 4. We observe duskward flows in the Northern Hemisphere and dawnward flows in the Southern Hemisphere under positive IMF B y conditions. This pattern is reversed under negative IMF B y conditions.