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A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions
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ScienceDirect Advances in Space Research xxx (2015) xxx–xxx www.elsevier.com/locate/asr
A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions Gilbert Pi, Jih-Hong Shue ⇑, Jong-Sun Park, Jih-Kwin Chao, Ya-Hui Yang, Chia-Hsien Lin Institute of Space Science, National Central University, Jhongli, Taiwan Received 6 July 2015; received in revised form 2 November 2015; accepted 19 November 2015
Abstract In previous studies, the magnetic field structures in the solar wind and in the magnetosheath usually have a high dependence on only the Y component. In this study, we compared the simultaneous data from OMNI database, THEMIS-B in the solar wind, and THEMISC in the magnetosheath to investigate the relationship between the magnetic field structures in the solar wind and in the magnetosheath under the radial IMF conditions. We find that Bz has a better correlation than By between the magnetic fields in the two regions, and the correlation for Bx is poor. When the magnetic field transits through the bow shock, the magnetic field will be enhanced in all components, especially in By. After that, Bx will divert to the Y and Z components, but the diversion to By will be larger than that to Bz in this case. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Radial IMF; Magnetosheath; Magnetic field structure
1. Introduction A comparison of the magnetic field structure in the interplanetary space and the magnetosheath has been widely discussed for decades. Fairfield (1967) showed some consistent results between the IMP 1 and IMP 2 data, and used the gas dynamical model to demonstrate that the Interplanetary Magnetic Field (IMF) structure frozen in the solar wind plasma can convect through the bow shock. Formisano et al. (1973) distinguished the three states of the magnetosheath structure based on different Mach numbers and plasma b in the upstream plasma. The downstream plasma is characterized by a Maxwellian distribution with a low b and magnetosonic Mach number. With higher b and Mach number and the upstream without waves, the downstream plasma is characterized by a pronounced non-Maxwellian high-energy tail in the proton velocity ⇑ Corresponding author at: Institute of Space Science, National Central University, Jhongli City, Taoyuan County 32001, Taiwan. E-mail address: [email protected] (J.-H. Shue).
distribution. For any Mach number and b, if the upstream waves are observed, the plasma parameter jumps across the discontinuity are small and not so well defined. Engebretson et al. (1991) used the ISEE 1, 2, and AMPTE data to indicate that the dayside magnetospheric Pc 3–4 pulsation activity and the low IMF cone angles are associated with increased turbulence in the subsolar magnetosheath magnetic field. Wing et al. (1995) used the GOES-6 and GOES-7 data to correlate the Y component of the geosynchronous magnetic field with the Y component of the IMF. The correlation of the geosynchronous By and the IMF By had different coefficients in the noon (0.61) and midnight (0.50) regions. Zastenker et al. (2002) showed that the magnetosheath parameter variations are an amplification of those in the solar wind in some cases, but these variations are originated in the magnetosheath itself in most of the cases. Gutynska et al. (2009) studied the fluctuations in the magnetosheath and found that the magnetic field strengths in magnetosheath are highly dependent on those of the solar wind. Sˇafra´nkova´ et al. (2009) used simultaneous observations
http://dx.doi.org/10.1016/j.asr.2015.11.012 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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to study the Bz distributions in the magnetosheath and IMF. They concluded that the probability of the observations of the same Bz sign in the solar wind and in the magnetosheath is surprisingly very low from a general point of view. The probability was found to change with the solar cycle. The solar minimum has a larger probability than the solar maximum. Antonova et al. (2012) used the THEMIS data to prove that By has a higher correlation between the magnetic fields in the magnetosheath and in the solar wind than the other two components. Pulinets et al. (2014) showed the results for a comparison of the structure between the magnetic fields in the solar wind and near the magnetopause. The results also support the previous studies. From the results of Engebretson et al. (1991), the cone angle can affect the dependence of the magnetic field in the magnetosheath on that of the solar wind. In this study, we investigate the dependence of the magnetic field in the magnetosheath on that of the solar wind during a longduration radial IMF event. The long-duration radial IMF is one of the special solar wind conditions when the orientation of the IMF is aligned with the solar wind velocity and persists over hours. The radial IMF conditions are usually associated with a low density and temperature and the fluctuations of all parameters are also weak (e.g., Pi et al., 2014). 2. Data The Time History of Events and Macroscale Interactions during Substorm (THEMIS) (Sibeck and Angelopoulos, 2008) is a mission which explores the geomagnetic environment of the magnetosphere. The THEMIS spacecraft traverses almost all regions in the magnetosphere and sometimes it also crosses the magnetopause and the bow shock at the dayside magnetopause. The mission comprises five probes with different orbits. The high-quality payloads are set up on each THEMIS probe to provide us with temporal and spatial observations
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3. Results Fig. 2 shows the magnitude of the magnetic field variations with time in the different areas. The first panel is |Bx|/|B| calculated from the OMNI database. The orientation of the IMF turned in the radial direction from 1400 to 1920
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in space. The Flux Gate Magnetometer (FGM) (Auster et al., 2008) is used to monitor the magnetic field in the magnetospheric system. In this study, we use the solar wind OMNI database (King and Papitashvili, 2005) to identify the longduration radial IMF events. The creators of the OMNI database gathered these solar wind measurements from various sources, combined them with a common calibration, and shifted the data in time to the nose of the bow shock. The current calibrated version of the OMNI database is based on that for the Wind data (Kasper et al., 2006). The criterion of long-duration radial IMF events is the one where |Bx|/|B| is larger than 0.9 (25°) and persists over 4 h. There are 52 long duration radial IMF events found during the period from 2007 to 2011. One of the events fortunately has the simultaneous THEMIS observations at both sides of the bow shock. Fig. 1 shows the positions of the THEMIS probes on 24 September 2008. The two curves denote the locations of the magnetopause and the bow shock. The locations of the magnetopause and the bow shock are calculated from the Shue et al. (1997) model and the Chao et al. (2002) model, respectively, under the average conditions of the radial IMF events (Pi et al., 2014). The THEMIS-B and THEMIS-C probes were separately located at the two sides of the bow shock. THEMIS-B was upstream of the bow shock, which provides us with the IMF structure in the solar wind. THEMIS-C was located downstream of the bow shock. This event gives us a good opportunity to investigate how the radial IMF structures are changed after crossing the bow shock.
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Fig. 1. The positions of the THEMIS probes on 24 September 2008. The two curves denote the locations of the bow shock (the dotted line) and the magnetopause (the solid line).
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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UT. The data of the second panel are for the total magnetic field from the OMNI database on 24 September 2008. The magnitude of B is maintained in a range from 3 to 4 nT during the period. The third and last panels are the B variations with time recorded by THEMIS-B in the solar wind and THEMIS-C in the magnetosheath, respectively. Distinguished by the properties of the magnetic field, the THEMIS-B probe first stayed in the solar wind region from 1400 to 1530 UT (see Fig. 2c). After 1530 UT, the variations of the magnetic field increased. This means that THEMIS-B was passing through a foreshock region. Around 1940 UT, there was a huge jump and the variations of the IMF decreased after the jump. This is in reference to the foreshock region changing with the orientation of the IMF. The foreshock region is located in the front of the quasi-parallel shock. Under the radial IMF conditions, the foreshock region almost covers all areas around the Sun–Earth line. When the IMF orientation move back to 45° as the Parker’s spiral structure, the foreshock region will suddenly change back to the dawnside. THEMIS-B probe crossed the bow shock around 2020 UT. In the magnetosheath, the magnitude of the magnetic field increases from 2 nT to 10 nT. The THEMIS-C (see Fig. 2d) was
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Fig. 3. The X component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the Bx of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
staying in the solar wind at the beginning of the event and passed the foreshock region around 1530–1630 UT. After THEMIS-C moved into the magnetosheath and changed to the region with a strong magnetic field until 2000 UT. After 2000 UT, the sharp increase in the magnitude of the magnetic field is an untypical magnetopause crossing. Figs. 3–5 are the magnetic fields observed by different satellites for each component. The magnetic fields in each figure are the OMNI database, THEMIS-B, and THEMIS-C from top to bottom. The horizontal dotted lines in each figure denote the zero line. In this study, we intend to focus on how the large scale magnetic field structures are influenced after crossing the bow shock, so we reduce the time resolution of the data to remove the turbulent fluctuation in both the foreshock region and the magnetosheath regions. To find the best time resolution to remove the fluctuation, we use the FFT technique to determine the dominant periods of the fluctuations. The periods are around 20–90 s in the foreshock region and 15–90 s in
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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Fig. 4. The Y component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the By of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The Z component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the Bx of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the magnetosheath. For this reason, we used 90 s resolution data in our analysis, as marked with the red lines in each figure. Fig. 3a shows the X component of the magnetic field variation with time. In Fig. 3a, Bx increased after 1400 UT and kept the magnitude in a range from 3 to 4 nT until 1920 UT. The Fig. 3b and c show the magnetic fields from THEMIS-B and C. The magnetic field structures between the two satellites are positively correlated. The relationships can also be found in By (Fig. 4) and Bz (Fig. 5) components. We calculated the correlation coefficient between the magnetic fields observed from THEMIS-B (Fig. 3b) and THEMIS-C (Fig. 3c). The time interval we selected is marked by the two vertical lines in Fig. 3b. We selected the interval after the THEMIS-C moved into the magnetosheath and before the end of radial IMF interval. Each component of the magnetic field from THEMIS-B are used to calculate the correlation coefficients with the THEMISC data by shifting the data points and choosing the shifted
time with the best correlation. We find that the shifted times in each component are similar. The differences of the best shifted times between each two components are less than 8 data points (less than 12 min). We applied the shifted time determined from Bz (10 min) as the shifted time for all components because of the strongest correlation between the magnetic field structures in Bz from THEMIS-B and THEMIS-C. The two vertical lines in Fig. 3c denote the corresponding region to the selected region in Fig. 3b. The scatter plots for all components of the magnetic field are shown in Fig. 6. The Bx has the weakest correlation between the magnetic field structures in the solar wind and in the magnetosheath, 0.40 for the correlation coefficient. The By has a correlation coefficient about 0.67 and Bz has the highest correlation coefficient (0.73). We also test the results base on different time resolutions data, and all the results show the highest correlation in Bz.
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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4. Discussion Sˇafra´nkova´ et al. (2009) showed that the Bz has a weak relationship between the magnetic field in the magnetosheath and in the solar wind. Antonova et al. (2012) reported that only the Y component has a good correlation between the magnetic field in the magnetosheath and in the solar wind. All previous studies were based on statistical results. Unfortunately, only one good case under the radial IMF event with simultaneous observations was found. In this case, the obtained result is different from previous studies. Under the radial IMF conditions, the correlation of the magnetic fields between the two sides of the bow shock is good in Y component, but even better in the Z component. The correlation coefficient was easily influenced by the local fluctuations even after a removal of some fluctuations by reducing their time resolution. The correlation coefficients are not high in By (0.73) and Bz (0.67), but they are relatively higher than that for Bx (0.40). We applied a linear fitting to each component of the magnetic field from THEMIS-B and a time shifted data from THEMIS-C (the blue lines in the Fig. 6). The results for Bx, By, and Bz are BX sh ¼ 2:2 BX sw 6:1, BY sh ¼ 5:0 BY sw þ 5:8, and BZsh ¼ 3:8 BZsw þ 0:7. The first character in the subscript of B denotes each component and the other two characters denote the observation from the solar wind region (sw) or the magnetosheath region (sh). The first coefficient in the linear equation shows the scaling of each component. The scaling represents the enhancement of the magnetic fields after crossing the bow shock. The By has the largest scaling of around 5.0 and Bz also has an scaling of about 3.8, but the scaling of Bx is only 2.2. This can be interpreted as that only the tangential component will be enhanced after crossing the bow shock. At the nose of the bow shock, the normal is always close to the X direction, so Bx has the smallest scaling. The second coefficient of the linear equation can be interpreted as an external factor that comes from a conversion among the
three components of the magnetic field. The negative second coefficient in the linear equation of Bx implies that a part of Bx diverts into the other components. The sum of the second coefficients for By and Bz is also close to the second coefficient of Bx (6.3 for By plus Bz, and 6.1 for Bx). It implies that the X component turns to the Y component more than to the Z component with a large second coefficient in the fitting results. A large enhancement rate and more magnetic field strength from Bx to By result in the highest correlation coefficient in Bz. For a magnetic structure moving into the magnetosheath from the solar wind, the magnetic field structure is influenced by at least two mechanisms. One is that the tangential component will be enhanced after crossing the bow shock. The other is the draping of the magnetic field around the magnetosphere, which Bx will turn into the other two components. The two mechanisms can influence each other at some point, so the first coefficient for By can be larger than the maximum enhancement ratio predicted from the Rakine– Hugoniot conditions.In Fig. 5, the IMF observed from OMNI database and observed from THEMIS-B are similar in the large structure without any time shift. Both of the Bz started with a negative value and turned to a positive value. The structures at THEMIS-B and C are also consistent, but the amplitude of the disturbances increases about 4 times (from ±5 to ±20 nT). The By (Fig. 4) has a similar variation as the Bz. The By in three different regions are always in phase. In Fig. 3 (for Bx), we cannot find a strong relationship between the OMNI database and the THEMIS-B data. The scaling of the X component from THEMIS-B to those from THEMIS-C is also not a constant. The scaling in the first half part in the two vertical lines seems to be larger than that in the second half. When magnetic field structure is close to the magnetopause, Bx will turn into By and Bz. In this case, Bx mainly turned into By because of the location of THEMIS-C was in the plane of z = 0, but far from the Sun-Earth line in the Y direction. In this location, we can expect Bx to turn the orientation into mainly in By. The
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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This work was supported by grants MOST-103-2111-M008-020 and NSC-102-2923-M-008-003 to National Central University. We thank Joe King and Natalia Papitashvili of the National Space Science Data Center (NSSDC) in the NASA/GSFC for the use of the OMNI 2 database and V. Angelopoulos for the use of data from the THEMIS mission.
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duration radial IMF event on 24 September 2009 is presented in this study. In this case, good correlations are found between the magnetic fields upstream and downstream of the bow shock in both the Y and Z components under the radial IMF condition. This result is inconsistent with the relationship from the previous studies for the nonradial IMF orientation. Its best correlation coefficient is 0.73 for Bz and 0.67 for By. The results of the linear fitting between the upstream and downstream magnetic field in each component imply that Bx turn into By more than into Bz in this case, consequently, By also has the largest scaling after a crossing of the bow shock. Therefore, Bz remains relatively unchanged, resulting in the highest correlation coefficient in Bz.
References 17:07
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Fig. 7. The ratios of the magnetic field in the magnetosheath to the corresponding field in the solar wind, (a) for the X component and (b) for the Y component. The red curves are the smoothed calculation of the ratio and the vertical dotted line denote the time when the magnetic field start to convert. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
result may change if we observe the magnetic field in a different location. Fig. 7 shows the ratios of the magnetic field in the magnetosheath to that in the solar wind. The red line is the smoothed line of the ratio. If we assume that the magnetic field can only be enhanced after crossing the bow shock, the relationship of the magnetic field in the two different region can be represented as BSH ¼ A BSW ; where A is a constant for the enhancement rate and the subscripts denote the magnetic field in the magnetosheath (SH) or that in the solar wind (SW). If there is no other mechanism, the constant A should be stable, but in Fig. 7a, we notice that the ratio of Bx decreases after 1808 UT (marked with the dotted line) and the ratio of By increase during the same period (Fig. 7b). This is the evidence for a conversion of Bx to By. This result also implies that Bx will be more likely to turn into By when the IMF is propagating closer to the magnetopause. 5. Summary The correlation between the magnetic field in the solar wind and that in the magnetosheath during the long-
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Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
ScienceDirect Advances in Space Research xxx (2015) xxx–xxx www.elsevier.com/locate/asr
A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions Gilbert Pi, Jih-Hong Shue ⇑, Jong-Sun Park, Jih-Kwin Chao, Ya-Hui Yang, Chia-Hsien Lin Institute of Space Science, National Central University, Jhongli, Taiwan Received 6 July 2015; received in revised form 2 November 2015; accepted 19 November 2015
Abstract In previous studies, the magnetic field structures in the solar wind and in the magnetosheath usually have a high dependence on only the Y component. In this study, we compared the simultaneous data from OMNI database, THEMIS-B in the solar wind, and THEMISC in the magnetosheath to investigate the relationship between the magnetic field structures in the solar wind and in the magnetosheath under the radial IMF conditions. We find that Bz has a better correlation than By between the magnetic fields in the two regions, and the correlation for Bx is poor. When the magnetic field transits through the bow shock, the magnetic field will be enhanced in all components, especially in By. After that, Bx will divert to the Y and Z components, but the diversion to By will be larger than that to Bz in this case. Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Radial IMF; Magnetosheath; Magnetic field structure
1. Introduction A comparison of the magnetic field structure in the interplanetary space and the magnetosheath has been widely discussed for decades. Fairfield (1967) showed some consistent results between the IMP 1 and IMP 2 data, and used the gas dynamical model to demonstrate that the Interplanetary Magnetic Field (IMF) structure frozen in the solar wind plasma can convect through the bow shock. Formisano et al. (1973) distinguished the three states of the magnetosheath structure based on different Mach numbers and plasma b in the upstream plasma. The downstream plasma is characterized by a Maxwellian distribution with a low b and magnetosonic Mach number. With higher b and Mach number and the upstream without waves, the downstream plasma is characterized by a pronounced non-Maxwellian high-energy tail in the proton velocity ⇑ Corresponding author at: Institute of Space Science, National Central University, Jhongli City, Taoyuan County 32001, Taiwan. E-mail address: [email protected] (J.-H. Shue).
distribution. For any Mach number and b, if the upstream waves are observed, the plasma parameter jumps across the discontinuity are small and not so well defined. Engebretson et al. (1991) used the ISEE 1, 2, and AMPTE data to indicate that the dayside magnetospheric Pc 3–4 pulsation activity and the low IMF cone angles are associated with increased turbulence in the subsolar magnetosheath magnetic field. Wing et al. (1995) used the GOES-6 and GOES-7 data to correlate the Y component of the geosynchronous magnetic field with the Y component of the IMF. The correlation of the geosynchronous By and the IMF By had different coefficients in the noon (0.61) and midnight (0.50) regions. Zastenker et al. (2002) showed that the magnetosheath parameter variations are an amplification of those in the solar wind in some cases, but these variations are originated in the magnetosheath itself in most of the cases. Gutynska et al. (2009) studied the fluctuations in the magnetosheath and found that the magnetic field strengths in magnetosheath are highly dependent on those of the solar wind. Sˇafra´nkova´ et al. (2009) used simultaneous observations
http://dx.doi.org/10.1016/j.asr.2015.11.012 0273-1177/Ó 2015 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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to study the Bz distributions in the magnetosheath and IMF. They concluded that the probability of the observations of the same Bz sign in the solar wind and in the magnetosheath is surprisingly very low from a general point of view. The probability was found to change with the solar cycle. The solar minimum has a larger probability than the solar maximum. Antonova et al. (2012) used the THEMIS data to prove that By has a higher correlation between the magnetic fields in the magnetosheath and in the solar wind than the other two components. Pulinets et al. (2014) showed the results for a comparison of the structure between the magnetic fields in the solar wind and near the magnetopause. The results also support the previous studies. From the results of Engebretson et al. (1991), the cone angle can affect the dependence of the magnetic field in the magnetosheath on that of the solar wind. In this study, we investigate the dependence of the magnetic field in the magnetosheath on that of the solar wind during a longduration radial IMF event. The long-duration radial IMF is one of the special solar wind conditions when the orientation of the IMF is aligned with the solar wind velocity and persists over hours. The radial IMF conditions are usually associated with a low density and temperature and the fluctuations of all parameters are also weak (e.g., Pi et al., 2014). 2. Data The Time History of Events and Macroscale Interactions during Substorm (THEMIS) (Sibeck and Angelopoulos, 2008) is a mission which explores the geomagnetic environment of the magnetosphere. The THEMIS spacecraft traverses almost all regions in the magnetosphere and sometimes it also crosses the magnetopause and the bow shock at the dayside magnetopause. The mission comprises five probes with different orbits. The high-quality payloads are set up on each THEMIS probe to provide us with temporal and spatial observations
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3. Results Fig. 2 shows the magnitude of the magnetic field variations with time in the different areas. The first panel is |Bx|/|B| calculated from the OMNI database. The orientation of the IMF turned in the radial direction from 1400 to 1920
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in space. The Flux Gate Magnetometer (FGM) (Auster et al., 2008) is used to monitor the magnetic field in the magnetospheric system. In this study, we use the solar wind OMNI database (King and Papitashvili, 2005) to identify the longduration radial IMF events. The creators of the OMNI database gathered these solar wind measurements from various sources, combined them with a common calibration, and shifted the data in time to the nose of the bow shock. The current calibrated version of the OMNI database is based on that for the Wind data (Kasper et al., 2006). The criterion of long-duration radial IMF events is the one where |Bx|/|B| is larger than 0.9 (25°) and persists over 4 h. There are 52 long duration radial IMF events found during the period from 2007 to 2011. One of the events fortunately has the simultaneous THEMIS observations at both sides of the bow shock. Fig. 1 shows the positions of the THEMIS probes on 24 September 2008. The two curves denote the locations of the magnetopause and the bow shock. The locations of the magnetopause and the bow shock are calculated from the Shue et al. (1997) model and the Chao et al. (2002) model, respectively, under the average conditions of the radial IMF events (Pi et al., 2014). The THEMIS-B and THEMIS-C probes were separately located at the two sides of the bow shock. THEMIS-B was upstream of the bow shock, which provides us with the IMF structure in the solar wind. THEMIS-C was located downstream of the bow shock. This event gives us a good opportunity to investigate how the radial IMF structures are changed after crossing the bow shock.
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Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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Fig. 2. The total magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the |Bx|/B, the total magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C.
UT. The data of the second panel are for the total magnetic field from the OMNI database on 24 September 2008. The magnitude of B is maintained in a range from 3 to 4 nT during the period. The third and last panels are the B variations with time recorded by THEMIS-B in the solar wind and THEMIS-C in the magnetosheath, respectively. Distinguished by the properties of the magnetic field, the THEMIS-B probe first stayed in the solar wind region from 1400 to 1530 UT (see Fig. 2c). After 1530 UT, the variations of the magnetic field increased. This means that THEMIS-B was passing through a foreshock region. Around 1940 UT, there was a huge jump and the variations of the IMF decreased after the jump. This is in reference to the foreshock region changing with the orientation of the IMF. The foreshock region is located in the front of the quasi-parallel shock. Under the radial IMF conditions, the foreshock region almost covers all areas around the Sun–Earth line. When the IMF orientation move back to 45° as the Parker’s spiral structure, the foreshock region will suddenly change back to the dawnside. THEMIS-B probe crossed the bow shock around 2020 UT. In the magnetosheath, the magnitude of the magnetic field increases from 2 nT to 10 nT. The THEMIS-C (see Fig. 2d) was
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Fig. 3. The X component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the Bx of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
staying in the solar wind at the beginning of the event and passed the foreshock region around 1530–1630 UT. After THEMIS-C moved into the magnetosheath and changed to the region with a strong magnetic field until 2000 UT. After 2000 UT, the sharp increase in the magnitude of the magnetic field is an untypical magnetopause crossing. Figs. 3–5 are the magnetic fields observed by different satellites for each component. The magnetic fields in each figure are the OMNI database, THEMIS-B, and THEMIS-C from top to bottom. The horizontal dotted lines in each figure denote the zero line. In this study, we intend to focus on how the large scale magnetic field structures are influenced after crossing the bow shock, so we reduce the time resolution of the data to remove the turbulent fluctuation in both the foreshock region and the magnetosheath regions. To find the best time resolution to remove the fluctuation, we use the FFT technique to determine the dominant periods of the fluctuations. The periods are around 20–90 s in the foreshock region and 15–90 s in
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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Fig. 4. The Y component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the By of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. The Z component of the magnetic field observed by three different satellites on 24 September 2008. From top to bottom are the Bx of the magnetic field observed from OMNI database, THEMIS-B, and THEMIS-C. The two vertical lines denote the time interval we selected to calculate the correlation coefficient. The magnetic fields are averaged in 90-s resolution, as marked with the red lines. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
the magnetosheath. For this reason, we used 90 s resolution data in our analysis, as marked with the red lines in each figure. Fig. 3a shows the X component of the magnetic field variation with time. In Fig. 3a, Bx increased after 1400 UT and kept the magnitude in a range from 3 to 4 nT until 1920 UT. The Fig. 3b and c show the magnetic fields from THEMIS-B and C. The magnetic field structures between the two satellites are positively correlated. The relationships can also be found in By (Fig. 4) and Bz (Fig. 5) components. We calculated the correlation coefficient between the magnetic fields observed from THEMIS-B (Fig. 3b) and THEMIS-C (Fig. 3c). The time interval we selected is marked by the two vertical lines in Fig. 3b. We selected the interval after the THEMIS-C moved into the magnetosheath and before the end of radial IMF interval. Each component of the magnetic field from THEMIS-B are used to calculate the correlation coefficients with the THEMISC data by shifting the data points and choosing the shifted
time with the best correlation. We find that the shifted times in each component are similar. The differences of the best shifted times between each two components are less than 8 data points (less than 12 min). We applied the shifted time determined from Bz (10 min) as the shifted time for all components because of the strongest correlation between the magnetic field structures in Bz from THEMIS-B and THEMIS-C. The two vertical lines in Fig. 3c denote the corresponding region to the selected region in Fig. 3b. The scatter plots for all components of the magnetic field are shown in Fig. 6. The Bx has the weakest correlation between the magnetic field structures in the solar wind and in the magnetosheath, 0.40 for the correlation coefficient. The By has a correlation coefficient about 0.67 and Bz has the highest correlation coefficient (0.73). We also test the results base on different time resolutions data, and all the results show the highest correlation in Bz.
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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Fig. 6. The scatter plots of all components of the magnetic fields observed in the solar wind and in the magnetosheath. The Z component has the best correlation coefficient (C.C.) between the magnetic fields in the solar wind and in the magnetosheath. The fitting lines overlapped with the data points. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
4. Discussion Sˇafra´nkova´ et al. (2009) showed that the Bz has a weak relationship between the magnetic field in the magnetosheath and in the solar wind. Antonova et al. (2012) reported that only the Y component has a good correlation between the magnetic field in the magnetosheath and in the solar wind. All previous studies were based on statistical results. Unfortunately, only one good case under the radial IMF event with simultaneous observations was found. In this case, the obtained result is different from previous studies. Under the radial IMF conditions, the correlation of the magnetic fields between the two sides of the bow shock is good in Y component, but even better in the Z component. The correlation coefficient was easily influenced by the local fluctuations even after a removal of some fluctuations by reducing their time resolution. The correlation coefficients are not high in By (0.73) and Bz (0.67), but they are relatively higher than that for Bx (0.40). We applied a linear fitting to each component of the magnetic field from THEMIS-B and a time shifted data from THEMIS-C (the blue lines in the Fig. 6). The results for Bx, By, and Bz are BX sh ¼ 2:2 BX sw 6:1, BY sh ¼ 5:0 BY sw þ 5:8, and BZsh ¼ 3:8 BZsw þ 0:7. The first character in the subscript of B denotes each component and the other two characters denote the observation from the solar wind region (sw) or the magnetosheath region (sh). The first coefficient in the linear equation shows the scaling of each component. The scaling represents the enhancement of the magnetic fields after crossing the bow shock. The By has the largest scaling of around 5.0 and Bz also has an scaling of about 3.8, but the scaling of Bx is only 2.2. This can be interpreted as that only the tangential component will be enhanced after crossing the bow shock. At the nose of the bow shock, the normal is always close to the X direction, so Bx has the smallest scaling. The second coefficient of the linear equation can be interpreted as an external factor that comes from a conversion among the
three components of the magnetic field. The negative second coefficient in the linear equation of Bx implies that a part of Bx diverts into the other components. The sum of the second coefficients for By and Bz is also close to the second coefficient of Bx (6.3 for By plus Bz, and 6.1 for Bx). It implies that the X component turns to the Y component more than to the Z component with a large second coefficient in the fitting results. A large enhancement rate and more magnetic field strength from Bx to By result in the highest correlation coefficient in Bz. For a magnetic structure moving into the magnetosheath from the solar wind, the magnetic field structure is influenced by at least two mechanisms. One is that the tangential component will be enhanced after crossing the bow shock. The other is the draping of the magnetic field around the magnetosphere, which Bx will turn into the other two components. The two mechanisms can influence each other at some point, so the first coefficient for By can be larger than the maximum enhancement ratio predicted from the Rakine– Hugoniot conditions.In Fig. 5, the IMF observed from OMNI database and observed from THEMIS-B are similar in the large structure without any time shift. Both of the Bz started with a negative value and turned to a positive value. The structures at THEMIS-B and C are also consistent, but the amplitude of the disturbances increases about 4 times (from ±5 to ±20 nT). The By (Fig. 4) has a similar variation as the Bz. The By in three different regions are always in phase. In Fig. 3 (for Bx), we cannot find a strong relationship between the OMNI database and the THEMIS-B data. The scaling of the X component from THEMIS-B to those from THEMIS-C is also not a constant. The scaling in the first half part in the two vertical lines seems to be larger than that in the second half. When magnetic field structure is close to the magnetopause, Bx will turn into By and Bz. In this case, Bx mainly turned into By because of the location of THEMIS-C was in the plane of z = 0, but far from the Sun-Earth line in the Y direction. In this location, we can expect Bx to turn the orientation into mainly in By. The
Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012
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This work was supported by grants MOST-103-2111-M008-020 and NSC-102-2923-M-008-003 to National Central University. We thank Joe King and Natalia Papitashvili of the National Space Science Data Center (NSSDC) in the NASA/GSFC for the use of the OMNI 2 database and V. Angelopoulos for the use of data from the THEMIS mission.
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duration radial IMF event on 24 September 2009 is presented in this study. In this case, good correlations are found between the magnetic fields upstream and downstream of the bow shock in both the Y and Z components under the radial IMF condition. This result is inconsistent with the relationship from the previous studies for the nonradial IMF orientation. Its best correlation coefficient is 0.73 for Bz and 0.67 for By. The results of the linear fitting between the upstream and downstream magnetic field in each component imply that Bx turn into By more than into Bz in this case, consequently, By also has the largest scaling after a crossing of the bow shock. Therefore, Bz remains relatively unchanged, resulting in the highest correlation coefficient in Bz.
References 17:07
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Fig. 7. The ratios of the magnetic field in the magnetosheath to the corresponding field in the solar wind, (a) for the X component and (b) for the Y component. The red curves are the smoothed calculation of the ratio and the vertical dotted line denote the time when the magnetic field start to convert. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
result may change if we observe the magnetic field in a different location. Fig. 7 shows the ratios of the magnetic field in the magnetosheath to that in the solar wind. The red line is the smoothed line of the ratio. If we assume that the magnetic field can only be enhanced after crossing the bow shock, the relationship of the magnetic field in the two different region can be represented as BSH ¼ A BSW ; where A is a constant for the enhancement rate and the subscripts denote the magnetic field in the magnetosheath (SH) or that in the solar wind (SW). If there is no other mechanism, the constant A should be stable, but in Fig. 7a, we notice that the ratio of Bx decreases after 1808 UT (marked with the dotted line) and the ratio of By increase during the same period (Fig. 7b). This is the evidence for a conversion of Bx to By. This result also implies that Bx will be more likely to turn into By when the IMF is propagating closer to the magnetopause. 5. Summary The correlation between the magnetic field in the solar wind and that in the magnetosheath during the long-
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Please cite this article in press as: Pi, G., et al. A comparison of the IMF structure and the magnetic field in the magnetosheath under the radial IMF conditions. Adv. Space Res. (2015), http://dx.doi.org/10.1016/j.asr.2015.11.012