Introduction

There is compelling observational evidence that magnetic reconnection plays a major role in the dynamics of the solar corona and the planetary magnetosphere (Parker 1963; Tsuneta 1996; Paschmann et al. 1979; Gosling et al. 1986). Large explosion events such as coronal mass ejection and magnetic reconnection in the magnetotail seem to be associated with symmetric reconnection (Tsuneta 1996; Gosling et al. 1986). On the other hand, small solar flares and flux transfer events in the dayside magnetopause are associated with asymmetric reconnection (Chen et al. 2014; Paschmann et al. 1979).

Asymmetric reconnection has been studied by a lot of researchers (Petschek and Throne 1967; Hoshino and Nishida 1983; Lin and Lee 1993; Kondoh et al. 2004; Cassak and Shay 2007). However, these studies focused on the jet region or the region around the X-point. To understand the spontaneous reconnection system, we must consider the entire reconnection system. Then, we have shown that the entire structure of the asymmetric reconnection is drastically different from the symmetric case even for slight magnetic asymmetry (Nitta et al. 2016; Nitta and Kondoh 2019, 2021, 2022). However, our previous studies have been done on the assumption of the initial isothermal condition for simplicity.

We need to set up much realistic initial conditions to verify our model. Geo-magnetopause is presently the most accessible natural plasma environment where magnetic reconnections and the consequential phenomena can be measured in situ (Archer et al. 2019; Ivchenko et al. 2000; Hasegawa et al. 2003; Phan et al. 2001; Teh and Hau 2004). Then, it is suitable that we apply our model to the asymmetric reconnection in the dayside geo-magnetopause. Phan et al. (2013) showed using THEMIS observations that the majority of reconnection events occurred for the small difference of plasma \(\beta\) on both sides of the current sheet, and the majority of reconnection events occurred over a large range of the degree of magnetic shears. Walsh et al. (2012) investigated a dawn–dusk asymmetry in plasma parameters within the geo-magnetosheath using statistical observations by the THEMIS spacecrafts. They showed the ion density and temperature are greater on the dawnside while the magnetic field strength and bulk flow speed are greater on the duskside.

The main purpose of this paper is to investigate the asymmetric reconnection environment near the ecliptic plane in the dayside magnetopause and evaluate the validation of the initial conditions in the numerical simulations. For these purposes, we identify the magnetopause crossing events by GEOTAIL satellite in the long-lasting southward IMF condition to exclude disturbed events. Then, we investigate the temporal and spatial variation of the ratio of the magnetic strength, the plasma density and the ion temperature between both sides of the magnetopause.

Dataset

We used data obtained by the low-energy particle experiment (LEP) (Mukai et al. 1994) and the magnetic field experiment (MGF) (Kokubun et al. 1994) on board GEOTAIL spacecraft from 1994 to 2019. Plasma moments such as the number density, the ion temperature, and the plasma velocity are calculated under the assumption that all ions are protons. We used 12 s (four-spin) averaged data for magnetic field vectors. In this study, GEOTAIL data were used when the spacecraft was located in the region within \(10<\textrm{MLT}<14\) and when the southward interplanetary magnetic field (IMF) data from OMNI base (https://spdf.gsfc.nasa.gov/pub/data/omni/high_res_omni) continued for at least 200 min. These OMNI data have been shifted from spacecraft positions of observation to the bow shock nose. We identified 81 complete magnetopause crossing events. Partial magnetopause crossing in which the spacecraft did not fully traverse the magnetopause is not included.

Results and discussion

Typical high magnetic asymmetry condition

We investigate a case study of a typical dayside magnetopause environment observed on 26 April 2009. Temporal variations in the IMF \(B_z\) from OMNI database and in the number density N (second panel), the ion temperature T (third panel) and the z-component of the magnetic field \(B_z\) (bottom panel) from GEOTAIL satellite between 20:30 and 23:45 UT are plotted in Fig. 1. The seven periods shown by the vertical yellow (magnetosheath side) and light blue (magnetosphere side) solid lines are identified as the magnetopause crossings by GEOTAIL satellite. The magnetopause crossings are repeatedly observed by GEOTAIL satellite in this single pass, such events are hereafter referred to as “series event” in this paper. We limit the analysis period when the southward IMF \(B_z\) at the bow shock nose continues over 200 min; therefore, the IMF \(B_z\) shown in the top panel is negative all the time in this figure. Temporal variation of the degree of asymmetry in the number density \(k_N=N_0/N_1\) (top panel), the temperature \(k_T=T_0/T_1\) (middle panel) and the z-component of the magnetic field \(k_{B_z}=B_{z0}/B_{z1}\) (bottom panel) between 20:30 and 23:45 UT from GEOTAIL satellite are plotted in Fig. 2. We averaged 5 points (1 min.) data at each line in the previous figure and the subscript 0 and 1 indicates that the value was observed in the magnetosphere and the magnetosheath, respectively. The time indicated in this figure is the observation time of the five points used for the average of the value in the magnetosheath as indicated by the yellow vertical line in Fig. 1. In this series event, \(k_N \lesssim 0.02,\ k_T\sim 10,\ \textrm{and} \ k_{B_z} \gtrsim 2.0\) all the time. This cold dense plasma condition in the magnetosheath in contrast with that in the magnetosphere is typical. It is also found that \(k_{B_z}\) gradually decreases until 22:00 and then keeps about 2.5. From only this figure, it is not impossible to determine whether this is temporal or spatial variation.

Fig. 1
figure 1

Temporal variation in the IMF \(B_z\) (top panel) from OMNI database and in the number density N (second panel), the ion temperature T (third panel) and the z-component of the magnetic field \(B_z\) (bottom panel) observed by GEOTAIL satellite on 26 April 2009. The vertical solid lines show the time when we averaged 5-point (1 min.) values in the magnetosphere (orange lines) and the magnetosheath (light blue lines), respectively

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Fig. 2
figure 2

Temporal variation in the degrees of asymmetry in the number density \(k_N=N_0/N_1\) (top panel), the ion temperature \(k_T=T_0/T_1\) (middle panel) and the z-component of the magnetic field \(k_{B_z}=B_{z0}/B_{z1}\) (bottom panel) observed by GEOTAIL satellite on 26 April 2009. The subscript 0 and 1 show the value observed in the magnetosphere and the magnetosheath, respectively

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Weak magnetic asymmetry condition

Next, we show another case study of the almost magnetically symmetric dayside magnetopause environment observed on 26 August 2015. The same parameters as in Fig. 2 between 18:00 and 21:00 UT from GEOTAIL satellite are plotted in Fig. 3. In this series event, six magnetopause crossings by GEOTAIL satellite are identified, and all of \(k_{B_z}\) in these crossings are almost 1.0. That is, the dayside magnetopause in this period was magnetically symmetric. The number density and ion temperature remain to be weakly asymmetric. \(k_N\) gradually increases after the magnetopause crossing at 19:30. From only this figure, it is also not impossible to determine whether this is a temporal or spatial variation.

Fig. 3
figure 3

Temporal variation in the degrees of asymmetry observed by GEOTAIL satellite on 26 August 2015. The format is the same as in Fig. 2

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Series events

For further investigation of the temporal and spatial variation of the series events, we plot \(k_N, k_T\), and \(k_{B_z}\) in the five series events, which are identified over five magnetopause crossings, including the above two events (plotted with filled circles) with respect to the GSM Y-position in Fig. 4. One single series event is shown by a plot set connected with solid lines. Note that GEOTAIL satellite moves toward positive y-direction. These five series events show spatial dependence, rather than temporal one. The asymmetry parameters \(k_N\) and \(k_T\) enhance in the positive y-position, while \(k_{B_z}\) in the negative y-position. The little temporal dependence in the asymmetry parameters means that the motions of the magnetopause, which allows us to observe the multiple magnetopause crossings, have little impact on the magnetopause condition.

Fig. 4
figure 4

Plot of the degree of asymmetry \(k_N, k_T\) and \(k_{B_z}\) as a function of \(y_{\textrm{GSM}}\) in five series events. The magnetopause crossings were repeatedly observed in a single pass. Such events are referred to as “series events” in this paper. The \(k_N\) is large on the dusk side, whereas the \(k_{B_z}\) on the dawn side

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All events

To confirm the above dependence, we plot the asymmetry parameters of all 81 events with respect to the y-position in Fig. 5. Every parameter does not necessarily depend on the y-position; however, the spread in the data of these parameters depends on it. Particularly, \(k_N\) significantly spread in the positive y-position, while \(k_{B_z}\) spread in the negative y-position.

Fig. 5
figure 5

Plot of the degree of asymmetry \(k_N, k_T\) and \(k_{B_z}\) as a function of \(y_{\textrm{GSM}}\) in all 81 crossings. The spread in the data of the \(k_N\) is large on the dusk side, whereas that of the \(k_{B_z}\) on the dawn side

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Next, we check the range of these degrees of asymmetry. The degrees of asymmetry in the number density shown in the top panel distribute \(0.01\le k_N \le 0.14\) on the dusk side, while \(k_N\sim 0.01\) on the dawn side. The degrees of asymmetry in ion temperature shown in the middle panel distribute \(k_T\sim 20\) in all y-position. The degrees of asymmetry in the z-component of the magnetic field shown in the bottom panel distribute \(0.5<k_{B_z}<2.5\) on the dusk side, while wide \(1.0\le k_{B_z}<4\) on the dawn side.

Relationship between asymmetry parameters

To investigate the above opposite dependency on the y-position and the relationship between \(k_N\) and \(k_{B_z}\), we show scatterplot of \(k_N\) versus \(k_{B_z}\) in Fig. 6. This scatterplot has a fixed negative correlation on a log–log scale. In the iso-thermal equilibrium condition used in our previous studies, the degree of asymmetry in the plasma density satisfies

$$\begin{aligned} k_N=\frac{\beta _0}{k_{B_z}^2(1+\beta _0)-1}k_{B_z}^2 ,\, \end{aligned}$$

where \(\beta _0\) is the plasma beta value on the low beta side. This scatter plot does not satisfy this relationship.

Fig. 6
figure 6

Scatterplot of \(k_N\) versus \(k_{B_z}\) in the all crossings on a log–log scale

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As mentioned in the introduction, Walsh et al. (2012) investigated a y-position dependency in the dayside magnetosheath and showed the ion density and temperature are greater on the dawnside while the magnetic field strength is greater on the dusk side in the magnetosheath. Then, they concluded that their results were consistent with the expected dependencies that would result from the interactions of the Parker spiral interplanetary magnetic field with the Earth’s bow shock.

Conclusions

We investigated the magnetopause environment near the ecliptic plane using the observational data from GEOTAIL satellite during the long-lasting negative IMF \(B_z\) component near the bow shock-nose. We focused on the degree of asymmetry on both sides of the current sheet in the dayside magnetopause near the sub-solar point. Our previous studies using numerical simulations showed that these asymmetries cause asymmetric magnetic reconnection and affect the global reconnection structure (Nitta et al. 2016; Nitta and Kondoh 2019, 2021, 2022). The repeated crossings of the magnetopause by GEOTAIL satellite during a single pass, which we call as “series event”, due to the oscillating motion of the magnetopause allowed us to continuously investigate these environments.

In these series events, we found a magnetically symmetric environment with (\(k_{B_z}\sim 1\)) relative to the magnetopause layer (current sheet), not only the typical cold dense plasma environment in the magnetosheath compared with that in the magnetosphere (\(k_{B_z}>1\)). Even in a single series event, the degree of asymmetry varies. This is the spatial variation, not the temporal one. This variation depends on the GSM-Y position. Every degree of asymmetry k has the spread in the data, and the spread depends on the GSM Y-position. The degree of asymmetry in the plasma density \(k_N\) has a fixed negative correlation with that in the magnetic field strength \(k_{B_z}\) on a log–log scale. In future work, we will investigate the asymmetric reconnection evolutions in these realistic degrees of asymmetry conditions.