Pitkänen et al. Geosci. Lett. (2021) 8:3 https://doi.org/10.1186/s40562-020-00171-7

RESEARCH LETTER Open Access Asymmetry in the Earth’s magnetotail neutral sheet rotation due to IMF By sign? Timo Pitkänen1,2,3* , Anita Kullen4, Lei Cai4, Jong‑Sun Park1, Heikki Vanhamäki3, Maria Hamrin2, Anita T. Aikio3, G. Siung Chong2, Alexandre De Spiegeleer2 and Quanqi Shi1

Abstract

Evidence suggests that a non-zero dawn–dusk interplanetary magnetic feld (IMF By ) can cause a rotation of the cross-tail current sheet/neutral sheet around its axis aligned with the Sun–Earth line in Earth’s magnetotail. We use Geotail, THEMIS and Cluster data to statistically investigate how the rotation of the neutral sheet depends on the sign and magnitude of IMF By . In our dataset, we fnd that in the tail range of −30 < XGSM < −15 RE , the degree of the neutral sheet rotation is clearly smaller, there appears no signifcant rotation or even, the rotation is clearly to an unexpected direction for negative IMF By , compared to positive IMF By . Comparison to a model by Tsyganenko et al. (2015, doi:10.5194/angeo-33-1-2015) suggests that this asymmetry in the neutral sheet rotation between positive and negative IMF By conditions is too large to be explained only by the currently known factors. The possible cause of the asymmetry remains unclear. Keywords: Solar wind–magnetosphere interaction, Magnetosphere confguration, Magnetotail, Plasma sheet, Neutral sheet

Introduction Xiao et al. 2016, and references therein). Te hinging Te two magnetic hemispheres in the Earth’s magneto- efect shifts the neutral sheet northward and southward tail are separated by a dawn-to-dusk-directed cross-tail with respect to the Sun–Earth line when the geomagnetic current sheet. Within the current sheet, the boundary dipole tilt angle is positive (generally northern hemi- between the magnetic hemispheres is usually defned sphere summer) and negative (northern hemisphere win- as a surface at which the X component (along the Sun– ter), respectively. Te warping efect is also dependent Bx Earth line) of the tail magnetic feld reverses ( = 0). It on the dipole tilt angle: for positive dipole tilt angle, the is called the neutral sheet (Ness 1965). warped neutral sheet appears in the tail cross-sectional Te position of the tail neutral sheet is often subjected plane as a southward opening curve (see e.g., Tsyganenko to dynamical motion in the north–south Z direction et al. 2015, their Figure 9). For negative dipole tilt angle, termed as fapping (e.g., Speiser and Ness 1967; Lui et al. the warped neutral sheet opens northward. Te twisting 1978; Sergeev et al. 1998, 2004; Zhang et al. 2002, 2005; or rotation efect depends strongly on the dawn–dusk Gao et al. 2018). In general, the position of the neutral component of the interplanetary magnetic feld (IMF By ). 0 sheet is afected by three major causes: hinging, warp- For duskward, IMF By > , the neutral sheet is rotated ing and twisting (or rotation) (Tsyganenko et al. 1998; counter-clockwise in the tail cross-sectional plane when Tsyganenko and Fairfeld 2004; Tsyganenko et al. 2015; looking from Earth toward the tail. For dawnward, IMF 0 By < , the rotation is clockwise. *Correspondence: [email protected] In one scenario, the rotation of the neutral sheet is 1 Shandong Provincial Key Laboratory of Optical Astronomy caused by the following sequence of events: a non-zero and Solar‑Terrestrial Environment, Institute of Space Sciences, Shandong IMF By drives an asymmetric magnetic reconnection on University, Weihai, China Full list of author information is available at the end of the article the dayside magnetopause. Te magnetic tension force

© The Author(s) 2021. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativeco​ ​ mmons.org/licen​ ses/by/4.0/​ . Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 2 of 11

defects the newly opened feld lines (southward IMF) or negative IMF By , when the range of the IMF By magni- the feld lines remaining open (northward IMF) to oppo- tude was from 3 to 8 nT. Precisely taken, a slightly larger site dawn–dusk directions in the two hemispheres, which rotation was inferred for negative IMF By . When sepa- leads to an asymmetric accumulation of magnetic fux rating the northward and southward IMF, the diference in the tail lobes (e.g., Tenford et al. 2015; Tenford et al. between positive and negative IMF By in the rotation 2018). Tis generates an excess of magnetic pressure on became clearer, but the characteristics of larger rotation the dawnside of one and duskside of the other tail lobe for negative IMF By remained in both cases. so that a torque is exerted on the plasma sheet. Te mag- In this letter, we investigate possible asymmetric netotail then reaches a new equilibrium state by rotat- responses in the tail neutral sheet rotation to difer- ing the plasma sheet as well as the neutral sheet. Also, it ent IMF directions. In the analysis approach, which is has been suggested that the tangential stress on the tail based on the identifcation of the measured neutral sheet magnetopause by the defecting open feld lines exerts a crossings, we make use of the neutral sheet model by torque on the lobes, which can subsequently lead to the Tsyganenko et al. (2015). A major advance compared to rotation of the neutral sheet (Cowley 1981). the study by Kaymaz et al. (1994) is that we distinguish Several statistical studies suggest that the neutral sheet positive and negative IMF Bz conditions. In addition, we rotation increases with tailward distance from Earth as distinguish small and large IMF By magnitudes, which well as with increasing IMF By magnitude, and is gen- has been done neither by Kaymaz et al. (1994) nor Xiao erally stronger during northward compared to during et al. (2016). southward IMF ( Tsyganenko et al. 1998; Tsyganenko and Fairfeld 2004; Tsyganenko et al. 2015). Te same IMF By Data and methods and Bz dependence of the neutral sheet rotation appears Data also in MHD simulations (e.g., Kullen and Janhunen We use magnetotail data from the Geotail, Time History 2004, and references therein). of Events and Macroscale Interactions during Substorms While semi-empirical neutral sheet models (e.g., (THEMIS) and Cluster missions. Geotail data consist of Tsyganenko et al. 2015) assume that the degree of the the spin-averaged (3 s) magnetic feld measurements rotation is independent of the sign of IMF By , the statisti- from the MaGnetic Field experiment (MGF) (Kokubun cal results by Kaymaz et al. (1994) and Owen et al. (1995) et al. 1994) and the 12-s ion moments from the Low suggest a possibility that this would not be the case, Energy Particle experiment (LEP) (Mukai et al. 1994) although this is not explicitly discussed in their respec- measured over the years 1995–2006. Te THEMIS data tive papers. Using IMP-8 magnetic feld measurements are the spin-averaged (3 s) magnetic feld observations − − in the range of 40 < XGSM < 25 RE (GSM, geocentric from the FluxGate Magnetometer (FGM) (Auster et al. solar magnetospheric), Kaymaz et al. (1994) statistically 2008) and the ion moments computed onboard from inferred that the degree of the neutral sheet rotation in the measurements by the ElectroStatic Analyzer (ESA) their dataset is slightly weaker for negative IMF By than (McFadden et al. 2008). We use THEMIS data from the for positive IMF By . Notably, the results by Kaymaz et al. THEMIS-B and THEMIS-C satellites. For THEMIS-B (1994) showed signatures of nonlinear rotation, which the data coverage is from November 2007 till December weakens the inference of the rotation angle. Owen et al. 2009. THEMIS-C data cover August 2007–December (1995) investigated statistically the orientation of the 2009. From Cluster, we use spin-averaged (4 s) magnetic edge of the plasma sheet boundary layer (PSBL) using feld measurements from the FluxGate Magnetometer particle measurements by ISEE-3 satellite from a large (FGM) (Balogh et al. 2001) and the ion moments from range of distances, between -240 and 0 RE XGSM. Tey the Hot Ion Analyzer (HIA) detector of the Cluster found that the average PSBL edge tilt angle was smaller Ion Spectrometry (CIS) instrument (Rème et al. 2001) for negative than for positive IMF By . Owen et al. (1995) from the Cluster 3 spacecraft. Te Cluster data cover the concluded that the tail is generally more twisted around years 2001–2009. its axis for positive IMF By . However, their results show For the solar wind data, we use the 1-min OMNI data very large scattering in the individual PSBL edge tilt propagated to the nominal bow shock nose (http:// angles and the method gives only indirect evidence of the omniw​eb.gsfc.nasa.gov/) (King and Papitashvili 2005). In neutral sheet rotation. addition, we use 1-min SYM-H geomagnetic index data Xiao et al. (2016), on the other hand, studied the aver- provided by the World Data Center for Geomagnetism, age shape and position of the tail neutral sheet using data Kyoto, Japan, which are also retrieved through the OMNI from multiple missions. Tey inferred◦ that at low dipole database. Te geocentric solar magnetospheric (GSM) tilt angles (absolute value less than 5 ), the degree of the coordinate system is used for all spacecraft data through- neutral sheet rotation was comparable for positive and out the study. Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 3 of 11

− − Tsyganenko et al. (2015) neutral sheet model crossings in the tail region 30 < XGSM < 15RE and − + In this study, we have utilized the semi-empirical neu- 25 < YGSM < 25RE as reversals in the magnetic feld −30 tral sheet model by Tsyganenko et al. (2015), hereafter Bx component in the 5-min data. Te tail range of < − denoted as the T15 neutral sheet model. Here, we briefy XGSM < 15RE was chosen to only include clearly tail- present the main features of the model. For a detailed like distances and it is limited in the far side by the apo- description, the reader is referred to Tsyganenko et al. gees of the satellite trajectories. (2015). A crossing was accepted to the neutral sheet crossing Te T15 model describes the global shape of the unper- dataset if the following conditions were fulflled: (1) the = 2 + 2 turbed magnetospheric equatorial current sheet (neu- ion speed V⊥xy V⊥x V⊥y < 100 km/s in the XY tral sheet) at all local times as a function of geomagnetic P plane for the 5-min data samples right before and after dipole tilt angle ( ), solar wind dynamic pressure ( dyn ), the crossing. Tis is expected to efciently remove high- By Bz IMF and IMF . It has been derived from a vast data speed fows, which can perturb the neutral sheet, and pool of magnetic feld measurements from Polar, Cluster, tailward magnetosheath fows in the magnetotail fanks Geotail and THEMIS missions between 1995 and 2013. from the dataset. (2) Te IMF magnitude B < 10 nT, the 0.1 ≤ ≤ 10 In the solar magnetic (SM) cylindrical coordinates, the solar wind dynamic pressure Pdyn nPa and Zs − ≤ ≤ position of the model neutral sheet in the Z axis, , is 100 SYM-H 30 nT (Tsyganenko et al. 2015). Tus, determined by the form the most extreme solar wind and magnetospheric condi- B α 1/α tions were excluded. IMF was computed as a 40-min = − + ρ Zs RH tan � 1 1 average over a time interval from 35 min prior to the  RH    neutral sheet crossing until 5 min after the crossing. Tis β (1) By ρ × a0 + a1 cos φ + T sin φ. the same averaging window used by Tsyganenko et al.   By0 ρ0  (2015). Notably, Case et al. (2018) suggest a time scale of 10–20 min for the response of the neutral sheet to the Te frst two terms describe the hinging and warping and IMF By reversals, which is within the averaging window the last third term determines the rotation of the neutral of Tsyganenko et al. (2015) and the present study. Pdyn sheet. In the formula RH is the hinging distance, which and SYM-H were computed as averages over the 10-min depends on Pdyn , IMF Bz and the longitude√ φ for which period centered at the crossing. Tsyganenko et al. (2015) tan = = 2 + 2 φ Y /X . is the dipole tilt angle, ρ X Y , a0 used a 5-min average and the instantaneous 1-min value and a1 are Fourier coefcients, which depend on Pdyn and for Pdyn and SYM-H, respectively. We argue that 10-min IMF Bz . Te magnitude coefcient T depends on Pdyn averages describe better the general conditions around B and the power index α depends on φ , Pdyn and IMF Bz . the crossing times. In the computation of IMF and Pdyn , = 5 Te power index β depends only on IMF Bz . By0 nT total missing data up to 30% in the averaging time inter- = 10 and ρ0 RE are numerical scaling factors. vals were allowed. (3) Te measured neutral sheet cross- Te source code (Fortran) for the T15 neutral sheet ing position difers no more than 4 RE in the ZGSM model with input and output in GSM coordinates is pro- direction from the model neutral sheet by Tsyganenko vided at http://geo.phys.spbu.ru/~tsyganenko/modeling. et al. (2015). Tis removes outliers caused by the most html. extreme neutral sheet perturbations from the dataset in the same way as has been done in the study by Methods Tsyganenko et al. (2015). We have statistically investigated the rotation of the neu- In total, 2963 neutral sheet crossings were obtained tral sheet. Our approach is based on the identifcation of for the dataset. Using the T15 neutral sheet model, we the neutral sheet positions and an investigation of their removed the contributions of the hinging and warping to distribution. To identify the positions of the neutral sheet the position for each neutral sheet crossing in this data- crossings in the magnetotail plasma sheet from the data, set. Tis was done by computing a new neutral sheet we have utilized the following procedure. First, the mag- ZGSM position using the T15 model (equation (1)) with- netospheric data were averaged to a 5-min time resolu- out the rotation term, i.e., without the last term of equa- tion. Small data gaps were allowed so that > 80% (= 4 tion (1), and subtracting the result from the observed min) of data must be available. For the data point to be ZGSM position for each data point of the dataset. As a included in the database, we required average plasma ion result, one gets an estimate for the neutral sheet ZGSM ≥ β 0.1 for the 5-min interval. Te threshold for ion β , position caused by the rotation efect only (referred to as which is the ratio between ion thermal pressure and mag- dataset O). When using the T15 neutral sheet model in netic pressure, was used to exclude measurements from this study, we assume that it represents the nominal neu- the low-β lobes. Ten, we identifed the neutral sheet tral sheet position in the absence of perturbations, such Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 4 of 11

as north–south fappings. As input for the T15 model, parameters, on the magnitude of IMF By . Te magni- IMF and Pdyn values were used that are averaged in the tude of the angle α is also slightly larger for positive . same way as described above. For comparison, we also IMF By compared to negative IMF By But in general, computed the T15 model neutral sheet ZGSM posi- the degrees of the rotation are comparable between the tions caused by the rotation efect only. Tis was done two IMF By signs. Since the T15 neutral sheet model by subtracting the T15 model neutral sheet ZGSM posi- does not distinguish between positive and negative IMF tion computed without rotation from the full T15 model, By in the degree of the rotation, this means that any dif- which is equivalent to computing the ZGSM position ferences seen in the model dataset M for positive and with the T15 rotation term only (referred to as dataset negative IMF By can only come from the diferences in M). In the computation, the XGSM and YGSM positions the distributions of the model input parameters and the and the IMF and Pdyn that are associated with the actual XY positions of the neutral sheet crossings. measured neutral sheet crossings were used. Te magnitude of the rotation angle increases with We sorted the neutral sheet crossings in eight diferent the distance in the X direction in the T15 neutral sheet categories: those observed during northward and south- model (Tsyganenko et al. 2015). However, the scatter ward IMF conditions and further, those with positive and of the modeled data points from the regression line in 3 0 negative IMF By with large (> nT) and small ( < IMF each category are small, as also indicated by the high 3 By < nT) magnitudes. Ten we investigated the degree r-squared values. Terefore, we conclude that the dis- of the rotation in each of the categories in the two data- tributions of the crossings in XGSM (Fig. 1) do not sets M (model) and O (observations). Te locations of afect the determination of the rotation angle. the neutral sheet crossings in each category projected to When looking at the observations (dataset O, Fig. 2b, the GSM XY plane are shown in Fig. 1. Te relative num- d, f, h), the scattering of the data points with respect to bers of the removed outliers in each IMF category varied the regression line is signifcantly larger if compared to between 1 and 9% of the numbers of the included neutral the model. Tis is understandable, because other efects sheet crossings. such as fapping contribute to the measured positions of the neutral sheet. In the model, these efects are Results absent. Generally, the magnitudes of the rotation angles Figure 2 displays the results for the northward IMF con- are smaller for the data than for the model, except for 0 By ditions (IMF Bz > ), for dataset M (T15 model) on the low-magnitude positive IMF (Fig. 2f). left panels and for dataset O (Data) on the right panels. Te striking diference between the data (dataset O) Shown are the positions of the neutral sheet crossings in and the model (dataset M) is the strong rotation asym- metry between positive and negative IMF By in dataset the GSM YZ plane for each IMF category (when look- |α| ing from Earth tailward). In each category, we have ft- O. For the model (dataset M), for positive and nega- By ted a line of best ft of linear least squares sense to the tive IMF are comparable, both in the case of large By data points to statistically estimate the neutral sheet rota- (Fig. 2a and c) and small IMF magnitudes (Fig. 2e α and g). For the data (dataset O), for large IMF By mag- tion. Te rotation is measured by the angle between the | | nitudes (Fig. 2b and d), α is clearly smaller for negative YGSM axis and the regression line and it is increasing ◦ ◦ By 1.80 ± 0.39 5.48 ± 0.30 anti-clockwise from the positive YGSM axis. Te angle α IMF , , compared to for posi- tive IMF By . For small IMF By magnitudes, a clear rota- is computed as a gradient of the best-ftted line. Te given ◦ By 4.17 ± 0.25 error estimate for α is the standard error. Note that in the tion can be deduced for positive IMF ( , Fig. 2f), but no signifcant rotation for negative IMF T15 model, the curve describing the neutral sheet in each ◦ By 0.25 ± 0.29 tail cross-sectional plane due to the rotation, is precisely ( , Fig. 2h). In fact, in the latter case the sense of the rotation is in an unexpected direction taken nonlinear. Tis is because the rotation term in the α>0 T15 model is dependent on the sinus of the longitude ( ), but the rotation angle stays within the error φ , i.e., the rotation in one tail cross-section increases limits. towards the fanks (see equation (1) and Tsyganenko Figure 3 displays the results for the southward IMF Bz < 0 et al. 2015, their Figure 10). A linear ft is, however, suf- (IMF ). From the model results (dataset M), we see cient for our purpose, since we are interested in quantify- that similar to the northward IMF, the degree of the rota- ing the degree of the rotation at general level. tion is a couple of degrees larger for large than for small IMF By magnitudes (Fig. 3a,c,e,g). For large IMF By mag- By intercomparing the model results (dataset M, | | nitudes, α is almost the same for positive and negative Fig. 2a,c,e,g), we see that the degree of the rotation | | | | By By α ( α ) is clearly a few degrees larger for large than for IMF (Fig. 3a and c). For small IMF magnitudes, By small IMF By magnitudes. Tis is expected, as the rota- is slightly larger for positive IMF but still comparable tion angle in the T15 model depends, among other (Fig. 3e and g). Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 5 of 11

Fig. 1 Locations of the neutral sheet crossings in the GSM XY plane for the diferent IMF categories

When looking at the observations (Fig. 3b, d, f, h), angle is slightly positive, i.e., in the unexpected direc- | | we again observe large diferences in α between posi- tion, but within the error limits. At small IMF By mag- tive and negative IMF By as in the case of the north- nitudes, similarly, a clear rotation appears for positive 2.68 ± 0.21◦ ward IMF. At large IMF By magnitudes, a clear IMF By ( , Fig. 3f) (which notably has larger 2.85 ± 0.30◦ rotation can be seen for positive IMF By ( , α than the model, Fig. 3e). But contrary to what are Fig. 3b), but no signifcant rotation for negative IMF By expected, the rotation angle for negative IMF By is ± ◦ ± ◦ ( 0.27 0.39 , Fig. 3d). In the latter case, the rotation clearly opposite, positive (1.26 0.28 , Fig. 3h). Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 6 of 11

Fig. 2 Locations of the neutral sheet crossings in the GSM YZ plane for IMF Bz > 0 conditions and diferent IMF By conditions after removal of the hinging and warping efects according to the T15 neutral sheet model. Left: T15 model (dataset M). Right: data (dataset O). GT Geotail, TB = = THEMIS-B, TC THEMIS-C and C3 Cluster 3. In each panel, N marks the number of the neutral sheet crossings, the blue line a linear regression and = = the angle α the angle between the YGSM axis and the regression line indicating the rotation of the neutral sheet (increases from the positive YGSM axis toward the positive ZGSM axis). r2 is the quality indicator of the regression (square of the Pearson’s correlation coefcient). The ZGSM scale has been zoomed in to magnify the rotation Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 7 of 11

Fig. 3 Same as Fig. 2, but for IMF Bz < 0

Generally, the degree of the neutral sheet rotation is Discussion larger for northward than southward IMF conditions, Te observational results (dataset O) presented in Figs. 2 which is consistent with previous studies (e.g., Owen and 3 indicate diferences in the degree of the neutral et al. 1995; Tsyganenko et al. 2015). sheet rotation between positive and negative IMF By Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 8 of 11

conditions. Comparison to the model (dataset M) implies happen, this second crossing would still be observed in that these diferences are so large that they cannot be the quadrant, which is in accordance with the IMF By > explained by the distributions of model input parameters 0 condition (dusk and ZGSM > 0) because the satellite and spatial XY positions of the neutral sheet crossings. position practically remains unchanged. If the separa- Te tail neutral sheet crossings are generally measured tion of the crossing times were long enough, the averaged when the neutral sheet moves fast, i.e., faps in the north– IMF By value would be negative and the crossing would south direction and passes the satellite position rather appear in the unexpected quadrant for IMF By < 0. Tis than the satellite moves across a static neutral sheet. would subsequently increase the scattering in the corre- From the large scattering of the crossings in dataset O, it sponding IMF By < 0 category. is clear that the fapping afects the estimates of the rota- We have investigated the possible infuence of IMF By tion angle. However, it has been deduced that the typi- reversals occurring prior to the crossings on the results. ∼ cal amplitudes of the fapping motion are on the order of We computed 1-h average (60 min prior to until 5 min 1–2 RE (Sergeev et al. 2006). Because we obtain a clear after a crossing) of IMF and compared this 1-h IMF By positive rotation angle α for positive IMF By in all cat- direction to the assigned (35 min prior to until 5 min egories, we argue that the scattering caused by the fap- after a crossing) IMF By direction. One can assume that if ping cannot explain (i) the small magnitude of negative α these are collinear, no signifcant reversal took place. We in Fig. 2d, (ii) the very small opposite rotation in Figs. 2h fnd that for the categories of large IMF By magnitudes, and 3d, and (iii) the clear opposite rotation direction there appear only 0–2 neutral sheet crossings in each in Fig. 3h, for negative IMF By (the rotation is counter- category for which the 1-h IMF By direction is opposite clockwise as for positive IMF By while clockwise rotation to the assigned IMF By direction. Tus, IMF By reversals is expected for negative IMF By ). It might explain the dif- do not afect the results in these categories. In the case of ference, if fapping would be more signifcant for negative small magnitude IMF By categories, the relative number % IMF By , but this is fully speculative. of the IMF By reversal crossings vary from 5 to 12 and Another cause for the scattering could arise from the the efects to the neutral sheet rotation angle are small, % −3 0 response of the neutral sheet to IMF By reversals (Case 4–5 , except for northward IMF Bz and < IMF By < et al. 2018). Assume that a neutral sheet crossing is nT-category (Fig. 2h). While in this category, the contri- detected in the dusk and ZGSM > 0 quadrant in the YZ bution of the neutral sheet crossings associated with the plane when IMF By > 0 has been prevailing for a longer IMF By reversal leads to a relatively high increase of the time. Te crossing is detected either as the neutral sheet rotation angle to the unexpected direction, in percent- ∼ faps or the positive rotation increases. Te crossing is age ◦ 733%, the◦ absolute◦ increase in the angle is only thus observed in the expected quadrant in the corre- 0.22 (from 0.03 to 0.25 ). All the deviations in the neu- sponding IMF By > 0 category (the expected quadrant tral sheet rotation angle caused by the IMF By reversals is the quadrant one expects the neutral sheet to rotate are within the error limits. Terefore, we argue that IMF into, based on the prevailing IMF By conditions). Ten By reversals cannot explain the large diferences in the IMF By suddenly reverses to IMF By < 0, and a second degree of the rotation. crossing is detected if the neutral sheet responds to the Te distributions of the IMF By magnitudes inside IMF By reversal and rotates to a new (opposite) angle each category could also afect the results. If the dis- corresponding to the IMF By < 0 condition. If this would tribution of the IMF By magnitudes would be biased

Table 1 Mean and median of IMF By and IMF Bz tagged to the neutral sheet crossings in each of the IMF categories (in nT)

IMF Bz > 0 Mean IMF By Median IMF By Mean IMF Bz Median IMF Bz

IMF By > 3 nT 4.5 4.2 2.2 1.7 IMF By < −3 nT 4.6 4.2 2.2 1.7 − − 0 < IMF By < 3 nT 1.4 1.4 1.8 1.4 −3 nT < IMF By < 0 1.5 1.5 1.6 1.3 − − IMF Bz < 0 Mean IMF By Median IMF By Mean IMF Bz Median IMF Bz

IMF By > 3 nT 4.5 4.0 1.7 1.5 − − IMF By < −3 nT 4.4 3.9 1.9 1.7 − − − − 0 < IMF By < 3 nT 1.6 1.6 1.3 1.0 − − −3 nT < IMF By < 0 1.5 1.5 1.6 1.1 − − − − Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 9 of 11

toward larger magnitudes for positive and toward the results of the present study and with the results by smaller magnitudes for negative IMF By , that might Kaymaz et al. (1994) and Owen et al. (1995). explain at least partly the larger degree of the rota- Te diferences in the results, specifcally between the tion for positive IMF By . However, by comparing the present study (larger rotation for positive IMF By ) and distributions for positive and negative IMF By , we do the study by Xiao et al. (2016) (larger rotation for nega- not fnd any signifcant diferences between them and tive IMF By ) are difcult to explain. Te two studies use thus exclude that as the potential cause. Te mean and data from approximately similar time intervals for almost median of IMF By (and IMF Bz ) in each IMF category the same satellites, although Xiao et al. (2016) are using are shown in Table 1. more data with one additional mission, TC-1 (Carr et al. Te observational results that the degree of the neutral 2005). sheet rotation is larger for positive IMF By are in accord- Te diference could arise from the diferent methods ance with the results by Kaymaz et al. (1994). Notably, used. In our method, the individual neutral sheet cross- Kaymaz et al. (1994) found in their dataset a quite clear ings are identifed and the T15 neutral sheet model is rotation also for negative IMF By , whereas in our dataset used to remove the hinging and warping efects from the the rotation is clear and in the expected direction for neg- neutral sheet positions. Ten a line is ftted to the data- −3 ative IMF By only for northward IMF and IMF By < points in the YZ plane to extract the rotation. In the Xiao nT (Fig. 2d). In their dataset, Kaymaz et al. (1994) used et al. (2016) method, tail Bx measurements are binned to | | | | only data for which IMF By > Bz and did not distin- squares in the YZ plane and the majority of the Bx meas- guish between northward and southward IMF. We have urement samples in a bin determines whether the bin is checked subsets of data using the same condition, but the assigned by positive or negative Bx bin. A line is then ft- diferences in the results are relatively small. Te rotation ted to the position points that separate the positive and angles (without error estimates, which have the similar negative Bx regions to get the rotation angle. Tis is done magnitudes as in Figs. 2 and 3) in the same order as the for the data with low dipole tilt angles (absolute value 5◦ IMF By categories in Figs. 2 and 3 are for northward IMF less than ) to minimize the hinging and warping. We 5.28◦ −2.32◦ 4.70◦ 0.02◦ Bz : , , and . For southward IMF Bz have checked the neutral sheet rotation in each IMF cat- 2.81◦ 0.20◦ 3.04◦ 1.26◦ the rotation angles are: , , and . egory for a subset of our dataset using the same range for Owen et al. (1995) found that the average PSBL edge the low dipole tilt angle as Xiao et al. (2016). While the tilt angle was smaller for negative than positive IMF By . number of neutral sheet crossings in each category are Owen et al. (1995) further distinguished northward and much smaller indicating weaker statistics, the asymmetry southward IMF Bz and found that the magnitudes of the between the positive and negative IMF By remains (data PSBL tilt angles were clearly larger for northward than not shown). southward IMF. If one assumes that the PSBL tilt angle Our method is likely to have larger scattering of the refects the rotation of the neutral sheet, our results agree datapoints that construct the ft, because all the data- with this aspect with the results by Owen et al. (1995). points in the particular IMF category are included in the Also, the T15 neutral sheet model gives larger rota- ft. While not explicitly stated by Xiao et al. (2016), we tion for northward than for southward IMF, but it does assume that in the method by Xiao et al. (2016), only the not distinguish between positive and negative IMF By position data assigned by white color (in their Figures 10 (Tsyganenko et al. 2015). and 11) are included in the ft. Tis means that for each Te results that the rotation of the neutral sheet is spatial Y bin, only one position is taken to the ftting pro- weaker for negative than for positive IMF By raises a cess, and the scattering of these datapoints is generally question of a possible intrinsic degree of the rotation much smaller. However, generally, the scattering from = 0 when IMF By . In a hypothetical scenario, the tail the ftted line in our method does not vary signifcantly neutral sheet is always slightly rotated with a small posi- between the IMF By categories (Figs. 2 and 3). tive α under zero IMF By condition. Terefore, one would Te diference in the degree of the neutral sheet rota- need a small negative IMF By to rotate α to zero. How- tion could be caused by diferences in the asymmetric ever, the results by Xiao et al. (2016) do not support this accumulation of magnetic fux into the tail lobes in case scenario. Xiao et al. (2016) also studied the neutral sheet the accumulation would not be an exact mirror process −1 1 rotation at low dipole tilt angles for < IMF By < nT, for positive and negative IMF By . It is also possible that so approximately for zero IMF By . Tey found no indica- there exists another still unidentifed mechanism that is tion of intrinsic rotation. Furthermore, Xiao et al. (2016) more efcient under one IMF By direction. Tese ques- found a slightly larger rotation for clearly negative IMF tions require further investigation. As a future work, −8 −3 By ( < IMF By < nT) than for clearly positive IMF the infuence of IMF By on the neutral sheet rotation 3 8 By ( < IMF By < nT). Tis is not in accordance with should be studied using numerical global magnetosphere Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 10 of 11

models. It should be tested whether the present mod- Open Access This article is distributed under the terms of the Creative Commons Attribu‑ els produce the diference in the degree of the rota- tion 4.0 International License (http://creat​iveco​mmons​.org/licen​ses/by/4.0/), tion between positive and negative IMF By , and if yes, which permits unrestricted use, distribution, and reproduction in any medium, then investigated the physical process(es) behind the provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were asymmetry. made.

Authors’ contributions TP was responsible for the data analysis and drafting the manuscript. AK, LC, Summary J-SP and HV contributed to the data analysis. All authors contributed to the We have used Geotail, THEMIS and Cluster data from interpretation of the results and/or drafting the manuscript. All authors read 1995 to 2009 to statistically investigate the rotation of and approved the fnal manuscript. the neutral sheet under the infuence of non-zero IMF Funding By in the Earth’s magnetotail. With help of T15 neutral The work was supported by the Swedish National Space Agency (SNSA) sheet model (Tsyganenko et al. 2015), we fnd in the tail Grants 118/17 (T.P. and A.K.), 105/14 (A.D.S.), 81/17 (G.S.C.) and 271/14 (M.H.), the National Natural Science Foundation of China (NSFC) Grants 41750110486 −30 < < −15 E range of XGSM R , the degree of the neu- (T.P.) and 41850410495 (J.-S.P.) and the Academy of Finland Grant 314664 (H.V.). tral sheet rotation is clearly smaller, there appears no signifcant rotation or the rotation is even clearly in an Availability of data and materials The Geotail and THEMIS data were accessed through https​://cdawe​b.sci.gsfc. opposite direction to what is expected for negative IMF nasa.gov/index​.html/. The Cluster data were accessed through https​://www. By By By cosmo​s.esa.int/web/csa. The solar wind and SYM-H index data are available compared to positive IMF . For positive◦ IMF ◦ , the inferred rotation angle varies between 2.68 5.48 through http://omniw​eb.gsfc.nasa.gov/. The source codes (Fortran) for the and and Geopack 08 and the T15 neutral sheet model used in the data analysis are for negative IMF By , the rotation angle gets values from − ◦ ◦ provided at http://geo.phys.spbu.ru/~tsyga​nenko​/model​ing.html 1.80 to 1.26 . A comparison to the T15 model sug- Competing interests gests that this asymmetry in the neutral sheet rotation The authors declare that they have no competing interests. between positive and negative IMF By conditions is too large to be explained only by an uneven distribution of Author details 1 the neutral sheet crossings or other solar wind condi Shandong Provincial Key Laboratory of Optical Astronomy and Solar‑Terres‑ - trial Environment, Institute of Space Sciences, Shandong University, Weihai, tions at the observed neutral sheet crossings, which have China. 2 Department of Physics, Umeå University, Umeå, Sweden. 3 Space been deduced to contribute to the position of the neutral Physics and Astronomy Research Unit, University of Oulu, Oulu, Finland. 4 sheet. Space and Plasma Physics, School of Electrical Engineering and Computer Science, Royal Institute of Technology, Stockholm, Sweden. Te possible physical mechanism remains unclear. Te discrepancy between the results from diferent studies Received: 5 October 2020 Accepted: 15 December 2020 indicate that more research is needed to understand the IMF By infuence on the rotation of the neutral sheet. Diferent approaches are desired to fnd out all related aspects. While numerical modeling, such as global References Auster HU, Glassmeier KH, Magnes W, Aydogar O, Baumjohann W, Constan‑ magnetosphere models, can be used in investigations, tinescu D, Fischer D, Fornacon KH, Georgescu E, Harvey P, Hillenmaier they cannot replace observational studies. Based on the O, Kroth R, Ludlam M, Narita Y, Nakamura R, Okrafka K, Plaschke F, results of the present study, we suggest that in the future, Richter I, Schwarzl H, Stoll B, Valavanoglou A, Wiedemann M (2008) The THEMIS fuxgate magnetometer. Space Sci Rev 141:235–264. https​://doi. magnetospheric models such as semi-empirical neutral org/10.1007/s1121​4-008-9365-9 sheet models, should be parameterized so that asymmet- Balogh A, Carr CM, Acuña MH, Dunlop MW, Beek TJ, Brown P, Fornaçon K-H, ric efects due to the IMF By direction are allowed for. Georgescu E, Glassmeier K-H, Harris J, Musmann G, Oddy T, Schwing‑ B enschuh K (2001) The cluster magnetic feld investigation: overview of Te asymmetries related to the IMF y sign are not in-fight performance and initial results. Annales Geophysicae 19:1207– limited to the neutral sheet rotation. Recent studies have 1217. https​://doi.org/10.5194/angeo​-19-1207-2001 found IMF By sign-related asymmetries for instance in Carr C, Brown P, Zhang TL, Gloag J, Horbury T, Lucek E, Magnes W, O’Brien H, Oddy T, Auster U, Austin P, Aydogar O, Balogh A, Baumjohann W, Beek T, the high-latitude geomagnetic activity (Holappa and Eichelberger H, Fornacon K-H, Georgescu E, Glassmeier K-H, Ludlam M, Mursula 2018) and in the polar cap size (Reistad et al. Nakamura R, Richter I (2005) The Double Star magnetic feld investigation: 2020). instrument design, performance and highlights of the frst year’s obser‑ vations. Annales Geophysicae 23(8):2713–2732. https​://doi.org/10.5194/ Acknowledgements angeo​-23-2713-2005 The authors thank the Geotail mission PI, Geotail LEP and MGF instrument PIs Case NA, Grocott A, Haaland S, Martin CJ, Nagai T (2018) Response of Earth’s and teams for the Geotail data, and the THEMIS FGM, ESA and SST instrument Neutral Sheet to Reversals in the IMF By Component. J Geophys Res PIs and teams as well as the PI of the THEMIS mission for the THEMIS data. In Space Phys 123:8206–8218. https​://doi.org/10.1029/2018J​A0257​12 addition, we thank the Cluster mission PI, Cluster CIS and FGM instrument PIs Cowley SWH (1981) Magnetospheric asymmetries associated with the and teams for the Cluster data. Furthermore, we acknowledge GSFC SPDF/ y-component of the IMF. Planet Space Sci 29(1):79–96. https​://doi. OMNIWeb and WDC for Geomagnetism, Kyoto, Japan, for the solar wind and org/10.1016/0032-0633(81)90141​-0 SYM-H index data. Gao JW, Rong ZJ, Cai YH, Lui ATY, Petrukovich AA, Shen C, Dunlop MW, Wei Y, Wan WX (2018) The distribution of two fapping types of magnetotail Pitkänen et al. Geosci. Lett. (2021) 8:3 Page 11 of 11

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