The Inhomogeneity of Composition along the Magnetic Cloud Axis

It is generally accepted that CMEs result from eruptions of magnetic flux ropes, which are dubbed as magnetic clouds in interplanetary space. The composition (including the ionic charge states and elemental abundances) is determined prior to and/or during CME eruptions in the solar atmosphere, and does not alter during magnetic cloud propagation to 1 AU and beyond. It has been known that the composition is not uniform within a cross section perpendicular to magnetic cloud axis, and the distribution of ionic charge states within a cross section provides us an important clue to investigate the formation and eruption processes of flux ropes due to the freeze-in effect. The flux rope is a three dimensional magnetic structure intrinsically, and it remains unclear whether the composition is uniform along the flux rope axis as most magnetic clouds are only detected by one spacecraft. In this paper we report a magnetic cloud that was observed by ACE near 1 AU on 1998 March 4--6 and Ulysses near 5.4 AU on March 24--28 sequentially. At these times, both spacecraft were located around the ecliptic plane, and the latitudinal and longitudinal separations between them were $\sim$2.2$^{\circ}$ and $\sim$5.5$^{\circ}$, respectively. It provides us an excellent opportunity to explore the axial inhomogeneity of flux rope composition, as both spacecraft almost intersected the cloud center at different sites along its axis. Our study shows that the average values of ionic charge states exhibit significant difference along the axis for carbon, and the differences are relatively slight but still obvious for charge states of oxygen and iron, as well as the elemental abundances of iron and helium. Besides the means, the composition profiles within the cloud measured by both spacecraft also exhibit some discrepancies. We conclude that the inhomogeneity of composition exists along the cloud axis.


INTRODUCTION
Coronal mass ejections (CMEs) are an energetic explosive phenomenon in the solar atmosphere [1,2,3,4], and they are called interplanetary coronal mass ejections (ICMEs) after leaving the corona. When ICMEs interact with the Earth's magnetosphere, they can cause geomagnetic storms [5,6,7] and influence the normal work of high-tech equipments, such as the satellites, power grids and GPS navigation systems [8,9]. Therefore, it is of great significance to grasp the trigger mechanisms and eruption processes of CMEs.
The researchers of solar physics community have reached a consensus that CMEs result from eruptions of magnetic flux ropes (MFRs), which refer to a volumetric current channel with the helical magnetic field lines wrapping around the central axial field [e.g., 10,11]. In whitelight coronagraph images, CMEs often exhibit a three-part structure, i.e., a bright front, a dark cavity and a bright core [12]. The cavity and core have been considered as the MFR cross section and erupted filament, respectively, for several decades. However, recent studies clearly demonstrate that both the filaments and hotchannel MFRs can appear as the bright core [13,14,15,16]. The hot channels are first revealed through extreme-ultraviolet passbands sensitive to high temperatures (e.g., 131 and 94Å) [17], and they can also be observed in hard X-ray [18] and microwave [19] images. Researchers also suggest that the dark cavity corresponds to a low-density region with sheared magnetic field in the early eruption stage [16].
Both theoretical and observational studies reveal that MFRs can form prior to [20,21,17,22,23] and during [24,25,26,27,28] solar eruptions, while they might exist before eruptions in more events [29]. The numerical simulations demonstrate that the repetitive magnetic reconnections could play an important role during the MFR evolution [30]. The remote-sensing observations have been widely used to investigate the MFR formation process [26,31,32]. The charge states within ICMEs are frozen-in near the Sun [33] and the relative abundances of elements with different first ionization potentials (FIPs) are different obviously in the corona and photosphere [34,35]. As the composition does not alter during CME propagation to 1 AU and beyond [36], the in situ data are also employed to analyze the MFR formation [37,28,38] and plasma origin [39,40] of CMEs. So far the most complete composition data of ICMEs are provided by the solar wind ion composition spectrometer (SWICS) aboard the advanced composition explorer (ACE) and Ulysses, which can provide the charge states and elemental abundances of ∼10 elements [41].
When an ICME has its nose pass through a spacecraft, the MFR will be detected as a magnetic cloud (MC) [42,43,44]. This is schematically shown in Figure 1(a) (also see [45,46] for a similar cartoon), where the purple arrow depicts a spacecraft trajectory crossing one ICME through its nose portion as marked with the blue rectangle. Figure 1(b) displays the MFR within the rectangle, and the green dots represent the center of each cross section. The black, blue and red arrows depict three different trajectories.
Several statistical studies have been conducted on ICME composition. Huang et al. [47] analyzed the composition inside 124 MCs and reported that fast MCs have higher charge states and relative elemental abundances (except the C/O) than slow ones. Owens [48] analyzed the charge states of carbon, oxygen, and iron within 215 ICMEs, including 97 MCs and 118 non-cloud events, and found that MCs exhibit higher ionic charge states than non-cloud events. Zurbuchen et al. [49] performed a comprehensive analysis of the elemental abundances of 310 ICMEs from 1998 March to 2011 August. They reported that the abundances of low-FIP elements within ICMEs exhibit a systematic increase compared to the solar wind, and the ICMEs with elevated iron charge states possess higher FIP fractionation than the other ICMEs. Very recently, Song et al. [50] reported that all the ICME compositions possess the solar cycle dependence.
In the meantime, some attentions are paid on the composition distribution inside each MC. Song et al. [37] found that the average values of iron charge states (<Q F e >) can present four regular profiles along the spacecraft trajectories throughout MCs, i.e., (i) a bimodal profile with both peaks higher than 12+, (ii) a unimodal profile with peak higher than 12+, (iii) and (iv) the <Q F e > profile remains beyond and below 12+ throughout the spacecraft trajectory inside an MC, respectively. Their studies demonstrated that the charge states can be nonuniform within the cross section of a specified MC, and suggested that the above profiles are tightly correlated with both the impact factor of spacecraft trajectories and the formation process of MFRs. For example, the bimodal profile implies that the MFR exists prior to eruption, see Figure 8 in [37] for more details. In addition, the elemental abundances are not uniform within one cross section either [39]. Therefore, a spacecraft can detect different composition profiles when it cross one MC along the blue and black arrows as shown in Figure 1(b), which are located in the same cross section perpendicular to the axis but with different impact factors. However, whether the inhomogeneity of composition exists along the MC axis remains unclear because most MCs are detected only by either ACE or Ulysses. Given the MC is a three-dimensional (3D) structure intrinsically, the axial distribution of composition can reveal whether different portions along the MFR axis experience different eruption processes in the corona.
In this paper, we report an intriguing event, in which an MC was observed by both ACE on 1998 March 4-6 and Ulysses on March 24-28. At these times, both spacecraft were located around the ecliptic plane, and the latitudinal and longitudinal separations between them were ∼2.2 • and ∼5.5 • , respectively. The Grad-Shafranov (GS) reconstruction [51,52] demonstrated that the MC axis oriented in an approximate east-west direction with the axis direction at Ulysses being titled slightly away from that at ACE, and both spacecraft almost intersected the MC center [53].
This implies that the two spacecraft crosses the MC along two trajectories resembling the black and red arrows in Figure 1(b), respectively, and provides us an excellent opportunity to explore whether the composition is uniform along the axis. We introduce the data in Section 2, and give the observations in Section 3. Section 4 presents the conclusion and discussion.

DATA
The data used in this paper are provided by several payloads on board the ACE and Ulysses spacecraft. ACE is in a halo orbit around the first Lagrangian point between the Earth and the Sun since it was launched in 1997. Ulysses was launched in 1990 and entered an elliptical and heliocentric orbit with an aphelion at ∼5.4 AU from the Sun and a perihelion distance of ∼1.34 AU. Magnetic field data are provided by the ACE/MAG [54] and Ulysses/Magnetic field [55] instruments. The bulk solar wind properties and the helium abundances are from the Solar Wind Electron Proton Alpha Monitor (SWEPAM) [56] on board ACE and the Solar Wind Observations Over the Poles of the Sun (SWOOPS) [57] on board Ulysses. The SWICS instruments on board both spacecraft [58,59] offer the composition of heavy ions.

OBSERVATIONS
The criteria used to identify MCs near 1 AU mainly include the enhanced magnetic field strength, smoothly changing of magnetic-field direction, declining profile of solar-wind velocity, low proton temperature (or low plasma β), and elevated He 2+ /H + ratio [42,60,61]. ACE detected an MC on 1998 March 4-6 as shown in Figure 2. The purple vertical dashed line denotes the shock driven by the ICME, and the two purple dashdotted lines demarcate the MC boundaries. Figure 2(a) shows the total magnetic field strength and its three components in RTN coordinate, where the X-axis (R) points from Sun center to spacecraft, the Y-axis (T) is the cross product of solar rotational axis and X axis, lying in the solar equatorial plane towards the west limb, and the Z-axis (N) is the cross product of X and Y axes. The total magnetic field strength (black) increased obviously compared to the background solar wind and the Bn component (blue) changed its direction gradually within the MC, which are the typical features of MCs. Figures 2(b)-(d) present the velocity, density, and temperature of the ICME sequentially. The declining profile of velocity indicates that the MFR is expanding.
Ulysses detected an MC on March 24-28 [62] as shown in Figure 3, where the magnetic field, velocity, density, and temperature are presented from top to bottom panels sequentially. The velocity profile in Figure 3(b) shows that the MC keeps expansion during the propagation to 5.4 AU. Due to the continuous expansion, the total magnetic field intensity within this MC decreased obviously near 5.4 AU compared to ∼1 AU, see Figures 2(a) and 3(a). A shock exists within the MC as depicted with the red arrows in Figures  3(a) and 3(b), and the MC rear boundary can be identified through the He 2+ /H + ratio and the plasma β value [53]. Note that the shock does not influence our analyses about the ionic charge states and elemental abundances.
Previous studies [63,53] have confirmed that the MC displayed in Figure (3) corresponds to that in Figure (2). Skoug et al. [63] fitted both MCs using a force-free model of magnetic field [64], and found that their central speed and cloud axis direction were very similar. The increase in MC diameter between 1 and 5.4 AU was also consistent with an expanding MC. Besides, both MCs had lefthanded field structure and contained the similar magnetic fluxes, which were further confirmed by Du et al. [53] with the GS reconstruction technique. In addition, Du et al. [53] input the plasma and magnetic field data observed by ACE to their magnetohydrodynamic model to simulate the MC propagation and evolution to the Ulysses location. They compared the model predictions and the Ulysses observations, and identified further that Ulysses and ACE observed the same MC. As mentioned, the ACE (at ∼1 AU) and Ulysses (at ∼5.4 AU) were located near the ecliptic plane with a latitudinal separation of ∼2.2 • and a longitudinal separation of ∼5.5 • when they detected the MC. The GS reconstruction showed that the MC axis oriented in an approximate east-west direction, and both spacecraft almost intersected the MC center [53], which support that ACE and Ulysses crossed the MC at different sites along its axis and provide us an excellent opportunity to explore whether the axial composition is uniform.
We compare the composition measured by both spacecraft in Figure 4 Our study shows that the average values of composition within an MC can possess significant differences along the axis. For example, the C 6+ /C 5+ ratio measured by Ulysses (3.04) is 12 times higher than that by ACE (0.23). In the meantime, the differences could be relatively slight for some compositions. For example, the O 7+ /O 6+ ratio measured by Ulysses (0.41) is higher than ACE (0.34) by ∼21%. The means of <Q F e > detected by both spacecraft are nearly identical (∼10). As to the elemental abundance, the Fe/O ratio by ACE (0.17) is ∼42% higher than that by Ulysses (0.12), and the He 2+ /H + ratio of ACE (0.093) is higher than Ulysses (0.053) by ∼75%.
Besides the average values, the composition profiles measured by both spacecraft also exhibit discrepancy. Figure 4(a) shows that the C 6+ /C 5+ of Ulysses elevated at the MC center, while the ACE profile did not exhibit the central peak.
The O 7+ /O 6+ of Ulysses presented a multi-peak profile, while ACE did not detect obvious peaks as shown in Figure 4(b). The He 2+ /H + of ACE elevated in the second half as displayed in Figure  4(e), different from the profile of Ulysses that did not have large variation along the whole path. These can rule out the possibility that the inhomogeneity of composition is induced by the erosion [66] completely during propagation from 1 AU to 5.4 AU. Moreover, the erosion effect should be small for this event as both MCs have the similar magnetic fluxes as mentioned. The profiles of <Q F e > and Fe/O measured by both spacecraft also exhibit some different fluctuation characteristics as displayed in Figures 4(c) and 4(d). The above results prove that the composition is inhomogeneous along the MC axis.

CONCLUSION AND DISCUSSION
An MC was detected by ACE at ∼1 AU and Ulysses at ∼5.4 AU sequentially during March 1998, when both spacecraft were located around the ecliptic plane. The latitudinal and longitudinal separations between them were ∼2.2 • and ∼5.5 • , respectively. The GS reconstruction [53] showed that the axis oriented in an approximate east-west direction, and both spacecraft almost intersected the MC center, which provided an excellent opportunity to explore whether the composition is uniform along the axis. We compared the ionic charge states of carbon, oxygen, and iron (C 6+ /C 5+ , O 7+ /O 6+ , and <Q F e >), as well as the elemental abundances of iron and helium (Fe/O and He 2+ /H + ) along the two trajectories. The results showed that the average values of C 6+ /C 5+ exhibit significant difference along the axis, while the differences are relatively slight but still obvious for O 7+ /O 6+ , <Q F e >, Fe/O, and He 2+ /H + . Besides the means, the composition profiles within the MC measured by both spacecraft also exhibit obvious discrepancies. We conclude that the inhomogeneity of composition exists along the MC axis.
The magnetic field within the MC measured by Ulysses did not exhibit the obvious changing of direction compared with the measurements of ACE, see Figures 2(a) and 3(a). This might indicate that Ulysses passed through the ICME along a path a little far from the MC center than ACE. Figure  4(a) showed that Ulysses detected high C 6+ /C 5+ at its central portion, which should also be observed by ACE if the composition is uniform along the MC axis. However, the C 6+ /C 5+ profile of ACE did not present the elevated center. Therefore, if assuming there were some uncertainties about the spacecraft path in the GS reconstruction, it will not change our conclusion about the axial inhomogeneity of MC composition.
The charge states of carbon, oxygen and iron are frozen-in sequentially in the corona, i.e., the frozen-in altitudes of carbon and iron are the lowest and highest, respectively, in these three elements. For example, the carbon are frozenin below 1.5 solar radii [67,68], while the iron around 3-4 solar radii [69,70]. Therefore, the obvious differences of C 6+ /C 5+ along the MC axis imply that the different portions of MFR along the axis experience eruption processes with different physical parameters (e.g., temperature, density, and velocity) in the low corona. The similar values of <Q F e > indicate that the physical parameters along the axis approached in the high corona. These should be taken into account in 3D simulations of CMEs. The axial inhomogeneity of elemental abundances implies that the abundances are not uniform throughout the MC source region on the Sun.
Our study demonstrated that the axial composition is nonuniform inside an MC, while we can not conclude that this large inhomogeneity exists within each MC. More events are necessary to investigate the inhomogeneity of composition along the MC axis, which needs a CME being detected by several spacecraft sequentially or simultaneously at different locations. This becomes more realizable as Solar Orbiter was launched in 2020 [71]. Besides, Chinese solar physicists are proposing several space missions [72] to explore the Sun and solar eruption further. The Lay a Finger on the Sun [73] will launch a spacecraft to explore the solar eruption near the Sun, thus it will provide more MC cases that are measured sequentially near the Sun and around 1 AU combined with other spacecraft. The Solar Ring [74] plans to deploy six spacecraft, grouped in three pairs, on a sub-AU orbit around the Sun. The two spacecraft in each group are separated by ∼30 • and every two groups by ∼120 • , which can provide more cases that are measured simultaneously by two or more spacecraft around the ecliptic plane. All of these missions will facilitate the studies of solar eruptions and other related issues.

CONFLICT OF INTEREST STATEMENT
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

AUTHOR CONTRIBUTIONS
HS led the analysis and drafted the manuscript. QH contributed to further understand the GS reconstruction results in [53]. XC, JZ, LL, and AZ provided suggestions to improve the research. BW helped to plot Figure 1. RZ and YC contributed to improve the manuscript.

FUNDING
This work is supported by the CAS grants XDA-17040507 and the NSFC grants U2031109, 11790303 (11790300) and 12073042. Hongqiang Song is also supported by the open research program of the CAS Key Laboratory of Solar Activity KLSA202107.

ACKNOWLEDGMENTS
We thank the referees for their constructive comments and suggestions which helped to improve the original manuscript considerably. We acknowledge the use of data provided by ACE and Ulysses missions. Hongqiang Song thanks Dr. Ying D. Liu for the helpful discussions.

DATA AVAILABILITY STATEMENT
The plasma and magnetic field data of both ACE and Ulysses are publicly available at the ACE science center (http://www.srl.caltech. edu/ACE/ASC/level2/index.html) and the Ulysses Final Archive (http://ufa.esac. esa.int/ufa/), respectively. Figure 1. Schematic drawing of the spacecraft trajectory crossing an ICME. The black dashed and solid lines represent the shock and MFR, respectively. The red dotted lines delineate the MFR axis. The ICME nose portion is marked with the blue rectangle in Panel (a), which is enlarged for details in Panel (b). The blue, black, and red arrows describe the different trajectories of spacecraft, and the green dots denote the MC center.