Unraveling the Internal Magnetic Field Structure of the Earth-directed Interplanetary Coronal Mass Ejections During 1995 – 2015

Abstract

The magnetic field configurations associated with interplanetary coronal mass ejections (ICMEs) are the in situ manifestations of the entrained magnetic structure associated with coronal mass ejections (CMEs). We present a comprehensive study of the internal magnetic field configurations of ICMEs observed at 1 AU by the Wind mission during 1995 – 2015. The goal is to unravel the internal magnetic structure associated with the ICMEs and establish the signatures that validate a flux-rope structure. We examine the expected magnetic field signatures by simulating spacecraft trajectories within a simple flux rope, i.e., with circular–cylindrical (CC) helical magnetic field geometry. By comparing the synthetic configurations with the 353 ICME in situ observations, we find that only 152 events ($F_{r}$) display the clear signatures of an expected axial-symmetric flux rope. Two more populations exhibit possible signatures of flux rope; 58 cases ($F^{-}$) display a small rotation (${<}\,90^{\circ}$) of the magnetic field direction, interpreted as a large separation of the spacecraft from the center, and, 62 cases ($F^{+}$) exhibit larger rotations, possibly arising from more complex configuration. The categories, $C_{x}$ (14%) and $E$ events (9%), reveal signatures of complexity possibly related with evolutionary processes. We then reconstruct the flux ropes assuming CC geometry. We examine the orientation and geometrical properties during the solar activity levels at the end of Solar Cycle 22 (SC22), SC23 and part of SC24. The orientation exhibits solar cycle trends and follow the heliospheric current sheet orientation. We confirm previous studies that found a Hale cycle dependence of the poloidal field reversal. By comparing our results with the occurrence of CMEs with large angular width ($\mbox{AW}>60^{\circ}$) we find a broad correlation suggesting that such events are highly inclined CMEs. The solar cycle distribution of bipolar vs. unipolar $B_{z}$ configuration confirms that the CMEs may remove solar cycle magnetic field and helicity.

1 Introduction

The interplanetary counterparts of coronal mass ejections (ICMEs) are the main drivers of geomagnetic activity. In addition to transporting large amount of mass and magnetic flux away from the Sun, their internal magnetic field structure is prone to be coupled to the upper magnetosphere triggering magnetic reconnection processes that allow the injection of solar magnetic energy into the whole magnetospheric system. Thus, the reliable prediction of the ICME internal magnetic field structure is a requisite for developing a robust space weather forecast capability.

A breakthrough in the understanding of the ICME internal structure was reached by Burlaga et al. (1981), Klein and Burlaga (1982) with the magnetic-cloud (MC) concept. Under this definition, the authors interpreted the in situ observations as a 3D magnetic flux-rope topology confining cold plasma, i.e., increase of the magnetic field, smooth rotation in the magnetic field direction and low proton temperature. The obvious next steps were to implement known plasma physics flux-rope models (Lundquist, 1950, for instance) to techniques (Lepping, Burlaga, and Jones, 1990) to reconstruct the internal ICME magnetic configuration as observed by the magnetometers onboard satellites and to provide valuable information about the orientation, geometry, and other magnetic parameters, such as the central magnetic field, magnetic flux or chirality. Ever since, ICMEs with smooth and monotonic internal magnetic field changes have been systematically labeled MCs, irrespective of whether the in situ measurements fulfilled all the MC definition or not.

MCs are not always detected within ICMEs (see Richardson and Cane, 2004) despite the fact that flux ropes are always expected based on the CME eruption theories (see Vourlidas, 2014, and the references therein). This might result from changes during IP evolution (see Manchester et al., 2017, and the references therein), from spacecraft crossing far from the ICME core, or possibly from the topological complexity of the magnetic structure during CME initiation in the solar corona. In any case, our information about ICME internal magnetic structure is limited by a single spacecraft crossing through the large structure that leaves a considerable amount of uncertainty. This practical observational constraint is used to justify the application of flux-rope models to in situ reconstructions even when the measurements do not display the expected signatures of a flux-rope crossing.

To explain these partial flux-rope signatures, Nieves-Chinchilla et al. (2018) extended the MC definition by introducing the concept of the magnetic obstacle (MO) and compiling a catalog of MO-ICMEs observed by Wind in the period 1995 – 2015. MOs are not always characterized by a full single rotation or even a rotation, and they, therefore, cannot be fully described by the MC flux-rope configuration. These MO configurations have been variously called “magnetic-cloud-like”, “flux-rope-like” or “non-classic-MC” (see e.g. Lepping, Wu, and Berdichevsky, 2005; Wu and Lepping, 2015; Gopalswamy et al., 2015; Badruddin, Mustajab, and Derouich, 2018). The common thread is that these structures are reconstructed using flux-rope topologies. However, we understand that this approach may result in confusion rather than shed light into the magnetic nature of CME and that it is necessary to explore what are the limitations in such scenarios.

This is the motivation behind this paper. Inspired by the findings in Nieves-Chinchilla et al. (2018), we want to understand in depth what in situ magnetic field observations should be expected when a spacecraft crosses a flux rope with different trajectories. The paper comprises two parts. In the first part, we simulate the expected magnetic field signatures for a spacecraft crossing a large magnetic flux-rope structure under all possible trajectories. We then compile a guide to properly identify the magnetic flux-rope observations associated with ICMEs (Section 2). We employ the simplest geometry, i.e., the circular–cylindrical geometry based on the Nieves-Chinchilla et al. (2016) model and reconstruction techniques. By using different flux-rope orientations and impact parameters, we evaluate the effects on the in situ observations. This exercise helps us identify flux ropes in the actual observations. Thus, such events can be classified accordingly as flux ropes amenable to reconstruction, or not flux ropes that require a different analysis method (Section 3).

In Section 4, we report the output from the reconstructions solely for events displaying flux-rope signatures. The analysis extends from the end of Solar Cycle 22 (SC22), through Cycle 23 (SC23), to the maximum of Cycle 24 (SC24). Section 5 gives the summary and conclusions.

2 Simulation of Virtual Spacecraft Crossing an Axial-symmetric Flux Rope

The circular–cylindrical analytical flux-rope model (henceforth the CC model) was presented in Nieves-Chinchilla et al. (2016). The flux-rope magnetic topology was established as an axially symmetric magnetic field cylinder with a twisted magnetic field. The magnetic field components in the circular–cylindrical coordinate system are

$$\begin{aligned} B_{r} =&0, \\ B_{y} =&B_{y}^{0} \biggl[1- \biggl( \frac{r}{R} \biggr)^{2} \biggr] ,\\ B_{\varphi } =&-H\frac{B_{y}^{0}}{|C_{10}|} \biggl(\frac{r}{R} \biggr), \end{aligned}$$

(1)

where the two direct output parameters are $B_{y}^{0}$, the magnetic field at the center of the flux rope and $C_{10}$ a measure of the force-freeness with the $H$ sign ($+1$ or −1) that indicates if the flux rope is right- or left-handed. The radius of the flux-rope cross-section, $R$, is a derived parameter (see Equation 5 in Hidalgo et al., 2002) and $r$ is the radial distance that describe the spacecraft trajectory.

These equations summarize the model that describe physically the characteristics of heliospheric flux ropes by assuming a geometry with axial symmetry and circular cross-section. The reconstruction technique has been largely discussed by Nieves-Chinchilla et al. (2016), Nieves-Chinchilla (2018). The trajectory of the spacecraft is inferred by using the minimization of the $\chi ^{2}$ function (equation 13 in Nieves-Chinchilla, 2018) and therefore the orientation of the flux rope. Thus, in addition to the model parameters ($B_{y}^{0}, C_{10}$), the longitude ($\phi$), the tilt ($\theta$) and impact parameter ($y_{0}$) complete the five direct output parameters.

In this section we will simulate different flux-rope axis orientations, or spacecraft trajectories, and return the expected synthetic magnetic field observations. In these simulations, we fix the flux-rope radius, $R=0.07~\mbox{AU}$, and the flux-rope bulk velocity to $v_{\mathrm{sw}}=450~\mbox{km}\,\mbox{s}^{-1}$. The transit time (duration) of the spacecraft within the structure can be obtained from Equations 2 and 5 in Hidalgo et al. (2002). Thus,

$$ t_{s}=\frac{2}{v_{\mathrm{sw}}\sqrt{1-\sin ^{2}\phi \cos ^{2}\theta }}\sqrt{R ^{2}-y_{0}^{2}}. $$

(2)

2.1 Synthetic Magnetic Field Configurations

One of the first studies devoted to exploring flux-rope configurations was carried out by Bothmer and Schwenn (1998). In this study, the authors first classified the ICME internal configuration in terms of a magnetic quasi-cylindrical geometry, with left- (LH) or, right-handed (RH) chirality, and with the axis laying in the ecliptic plane, i.e., with very low inclination. Figure 1 shows synthetic solar wind data of a magnetometer onboard a virtual spacecraft flying through a flux-rope cylinder for four low inclined magnetic field configurations in GSE (geocentric solar ecliptic) coordinate system ($\phi=90^{\circ},270^{\circ}$, $\theta =0^{\circ }$ with left/right chirality). The configurations correspond to the leading and trailing magnetic field polarities or chirality, i.e., right-handed (RH, +) or left-handed (LH, −), and to the axis eastwards (E, $\phi =90^{\circ }$) or westwards (W, $\phi=270^{\circ }$). In the simulation, the magnetic field has been normalized to the central magnetic field, $B_{y}^{0}$ and $|C_{10}|=1$. In the north-to-south (NS) configurations, the $B_{z}^{\text{GSE}}$-component goes from positive to negative (Figure 1a, 1d) and vice versa for the south-to-north (SN) configurations (Figure 1b, 1c). Thus, Figure 1 is organized as the eastwards flux tubes with both polarities (a) NES-RH and (b) SEN-LH, and the westwards combined with both polarities in the (c) SWN-RH and (d) NWS-LH. Each combination includes (i) the expected temporal variation of the in situ magnetic field components in GSE coordinate system, (ii) the magnetic hodograms, and, (iii) the figure included the corresponding magnetic field sketch.

Figure 1

(a) In situ signatures in the GSE coordinate system and sketch representing the north-east-south, right-handed (NES-RH), (b) representing the south-east-north, left-handed (SEN-LH), (c) south-west-north, right-handed (SWN-RH), and (d) north-west-south, left-handed (NWS-LH). For each configuration is included: (i) Temporal variation, (ii) magnetic hodograms of the GSE magnetic components, and (iii) flux-rope configuration sketch.

The temporal variation of the magnetic field components (i) is within the time of the spacecraft crossing the structure, where $T_{\text{i}}$ is the first encounter of the spacecraft with the flux rope and $T_{\text{f}}$ is the last contact of the spacecraft. Then $T_{\text{f}}-T_{\text{i}}$ is the duration of the magnetic cloud (Equation 2). For these simulations, we have selected a very small impact parameter (small distance of the spacecraft to the flux-rope center) $y_{0}=0.10R$, where $R$ is the radius of the tube cross-section. This configuration was named bipolar by Mulligan, Russell, and Luhmann (1998) because of the double sign in the $B_{z}$-component. The $y$-component is aligned with the GSE-$y$-axis and therefore is positive (E, Figure 1a, 1b) or negative (W, Figure 1c, 1d), and maximum at the center. Finally, the $x$-component is close to zero since the spacecraft is crossing close to the tube center ($y_{0}$ small). The hodograms, bottom three square plots (iii), are built by combining two magnetic field components, $B_{j}^{\text{GSE}}$, with $j=(x,y,z)$. In each square plot, $T_{\mathrm{i}}$ is indicated with a red dot. In each figure, from Figure 1a to 1d, there is a full ($180^{\circ }$) rotation in the combined plot of $B_{y}^{\text{GSE}}$ vs. $B_{z}^{\text{GSE}}$.

Mulligan, Russell, and Luhmann (1998) also added four more categories (and named them unipolar since $B_{z}$ does not change sign, either positive or negative) for the flux-rope configurations that can be visualized as a highly inclined cylinder with the axis perpendicular to the ecliptic plane. In Figure 2 these four categories are shown using the same convention as Figure 1. Thus, the $B_{z}^{\text{GSE}}$ component is aligned with the local $B_{z}$ component and does not change sign, i.e., northwards or southwards and with the maximum at the center. In Figure 2a, 2b, $B_{z}$ is northwards with the two combined chirality (RH and LH), and in Figure 2c, 2d is southwards with the two combined chiralities (RH and LH). In these four scenarios the orientation is $\phi =90^{\circ }$ but the tilt ($\theta$) is $90^{\circ }$ for the northwards configuration and $-90^{\circ }$ for the southwards configuration. Note that the configuration would be the same for any $\phi$ combined with $\theta \approx [\pm ]90^{\circ }$.

Figure 2

(a) In situ signatures in the GSE coordinate system and sketch representing the west-north-east, right-handed (WNE-RH), (b) representing the east-north-west, left-handed (ENW-LH), (c) east-south-west, right-handed (ESW-RH), and (d) west-south-east, left-handed (WSE-LH). For each configuration is included: (i) Temporal variation, (ii) magnetic hodograms of the GSE magnetic components, and (iii) flux-rope configuration sketch.

For highly-inclined flux tubes, the magnetic field component profiles $B_{y}^{\text{GSE}}$ and $B_{z}^{\text{GSE}}$ are swapped compared to the low-tilted tubes. In this case, the rotation is clearly exhibited in the $y$-component and the $z$-component remains positive or negative with the maximum value at the tube center. The east-to-west configurations are the ENW-LH and ESW-RH (Figure 2b, 2c). The $B_{z}^{\text{GSE}}$ component remains positive for the northwards (N) configuration (Figure 2a, 2b) and negative for the southwards (S) configurations (Figure 2c, 2d). The $B_{x}^{\text{GSE}}$ component remains constant for all configuration as discussed in Figure 1. Again, the rotation is clearly depicted in the hodograms (ii), where the case $B_{y}^{\text{GSE}}$ vs. $B_{z}^{\text{GSE}}$ exhibits the full $180^{\circ }$ rotation.

In real observations, we cannot force the flux ropes to reach the spacecraft with a high ($|\theta |>60^{\circ }$) or low ($|\theta |<30^{ \circ }$) inclined tilt; with the tube axis completely perpendicular to the Sun–Earth line ($\phi \approx 90^{\circ }$ or $\approx 270^{ \circ }$); or, with the impact parameter close to the tube axis ($y _{0}<0.10R$). Traditionally, the threshold between unipolar or bipolar magnetic configurations has been located around $\theta =45^{\circ }$ (Huttunen et al., 2005) and called Intermediate by Palmerio et al. (2018) but there is not a study to evaluate the impact of the longitude ($\phi$) in the configuration.

Figure 3 includes the synthetic data for magnetic configurations with a more realistic longitude, tilt, and impact parameter. Figure 3a shows the case with $(\phi,\theta,y_{0})=[45^{\circ},0^{\circ },0.10R]$. In this case, the $B _{z}^{\text{GSE}}$ component maintains the bipolarity but the $B _{y}^{\text{GSE}}$ component is not aligned with the flux-rope axis and $B_{x}^{\text{GSE}}$ component will also be curved. In general, while the flux-rope axis remains in the ecliptic plane, we would still expect a complete rotation in this component if the spacecraft crosses completely the flux-rope cross-section side to side.

Figure 3

In situ signatures in the GSE coordinate system and sketch representing a combination of $\phi$ and $\theta$ angles. (a) $\phi=45^{\circ }$ and $\theta=0^{\circ }$, right-handed, (b) $\phi=90^{\circ }$ and $\theta=45^{\circ }$, left-handed, (c) $\phi=10^{\circ }$ and $\theta=45^{\circ }$, right-handed, and (d) $\phi=90^{\circ }$ and $\theta =90^{\circ }$, left-handed. This last figure include two spacecraft impact parameter, $y_{0}= 0.2$ (red), and $y_{0}=0.8$ (green). For each configuration is included: (i) Temporal variation, (ii) magnetic hodograms of the GSE magnetic components, and (iii) flux-rope configuration sketch.

Figure 3b depicts a longitude angle of $\phi =90^{ \circ }$ and a mid axis inclination of $\theta =45^{\circ }$. In this configuration the $B_{z}^{\text{GSE}}$ displays bipolarity as well as the $B_{y}^{\text{GSE}}$ component. This configuration shows a hybrid magnetic field profile between the previously described bipolar and unipolar configurations. In Figure 3c, the magnetic configuration changes with the same tilt but longitude more aligned with the Sun–Earth line ($\phi =10^{\circ }$) and higher impact parameter ($y_{0}=0.50R$) exhibits unipolar $B_{z}$.

For completeness, we have included a series of plots in the Appendix, Figure 14 with $B_{x}^{\text{GSE}}$ (red), $B_{y}^{ \text{GSE}}$ (blue) and $B_{z}^{\text{GSE}}$ (green) profiles, to serve as a guide of the different flux-rope orientations. Each plot fixes the $\phi$, $y_{0}$ and chirality and provides the component profiles for $\theta =[0^{\circ },30^{\circ },60^{\circ },90^{\circ }]$, where the line-thickness from higher to lower indicate lower tilt to higher tilt. From this figure, the reader can use Figures 1, 2 and 3 to estimate the expected magnetic signatures of different axis orientations by changing the orientation from north to south, east to west, or the chirality as discussed previously.

The configuration in Figure 3c illustrates the effect of the combination $\theta$ and $\phi$ with an impact parameter of $y_{0}=0.50R$. In this case, the rotation is displayed in, at least, two of the three hodograms. Due to the combination of the orientation and the increasing in the impact parameter, the rotation measured in the hodograms is less than $180^{\circ }$. This configuration is a transition between Figure 14a and Figure 3a.

Figure 3d also illustrates the effect of the separation of the spacecraft from the flux-rope axis. The orientation is aligned with the Sun–Earth line and had maximum tilt. Two different impact parameters are illustrated. The red dashed line (the dot indicates the start time) on the sketch is $y_{0}=0.20R$ with red lines in the hodograms and colored solid line in the temporal plot. The configuration with a high impact parameter, $y_{0}=0.80R$, is displayed with green dashed line in the sketch, green line on the hodograms and dashed colored line in the temporal plot. The separation of the spacecraft affects the magnetic field configuration of the temporal plot with a separation of the $B_{x}^{\text{GSE}}$ component from the zero level, flattening in the $B_{z}^{\text{GSE}}$ component and a lower slope in the $B_{y}^{\text{GSE}}$ component.

Figure 15 exhibits two more scenarios. In the top figures, (a) and (b), the flux-rope axis is almost perpendicular to the Sun–Earth line ($\phi =90^{\circ }$) and highly inclined ($\theta =90^{ \circ }$) but two impact parameters to evaluate the effect of the increase in the impact parameter. In this case, there is a change in the $B_{y}^{\text{GSE}}$ slope, the $B_{z}^{\text{GSE}}$ curvature and increase of the $B_{x}^{\text{GSE}}$ distance to the 0-level as the $y_{0}$ increases (Démoulin, Dasso, and Janvier, 2013). In the bottom two cases, (c) – (d) for the same longitude and impact parameter, display the effect of the change from low longitude ($\phi =30^{\circ }$) higher latitude ($\phi =60^{\circ }$). During this range of transition from $B_{z} ^{\text{GSE}}$ bipolar to unipolar and $B_{y}^{\text{GSE}}$ unipolar to bipolar, both component are partially bipolar with more o less emphasis in each polarity as the inclination changes. Thus, during this interval, the configuration displays a hybrid combination of polarity in the magnetic field components.

2.2 Threshold Between Bipolarity and Unipolar $B_{z}$ Configuration

One of the ultimate outcomes that this study provides is the range of angle combinations of the geometrical parameter that will display a bipolar $B_{z}$ configurations. As discussed previously, the tilt ($\theta$) is not the only angle to take into consideration but the axis longitude, $\phi$, also play a role. Figure 4 explores different $\phi$, $\theta$ and chirality combinations and aids to determine different ranges or intervals for the NS configuration in the GSE coordinate system. Note that the discussion above, in Section 2.1 and later in this section, can be applied to the case of RTN (Radial Tangential Normal) coordinate system just taking into account that $\phi _{\text{GSE}}=\phi _{\text{RTN}}+180^{ \circ }$. Thus, for the axis perpendicular to the Sun–Earth line, with $\phi _{\text{GSE}}=90^{\circ }$ or $270^{\circ }$, is switched to $\phi _{\text{RTN}}=270^{\circ }$ or $90^{\circ }$, and the $\phi _{\text{GSE}}=0^{\circ }$, pointed from the observer to the Sun, is $\phi _{\text{RTN}}=180^{\circ }$.

Figure 4

Combination of flux-rope axis configurations; longitude ($\phi$), tilt ($\theta$), and chirality ($H$) fixing the impact parameter, $Y_{0}=0.10R$, to obtain a bipolar $B_{z}$ configuration normalized to the central magnetic field, $B_{y}^{0}$.

Figure 4a displays the profiles ($\theta > 0^{\circ}$) of northwards tilts with the central magnetic field pointing eastwards ($\phi < 180^{\circ }$) with positive chirality or westwards ($\phi > 180^{\circ }$) with negative chirality. Figure 4b display the profiles of southwards tilts ($\theta < 0^{\circ }$) with the central magnetic field pointing eastwards ($\phi < 180^{\circ }$) with positive chirality or westwards ($\phi > 180^{\circ }$) with negative chirality. Note that the $B_{z} ^{\text{GSE}}$ profile coincides with certain eastwards or westwards angle-chirality combinations. Thus, for instance, in the boundary between northwards or southwards, with $\theta =0^{\circ }$ (black line in both figures), $\phi =90^{\circ }$ with positive chirality is eastwards and $\phi =270^{\circ }$ with negative chirality is westwards. Note that, in these cases, eastwards or westwards will determine the $B_{y}^{\text{GSE}}$ sign (see Figures 14 for illustrations). By changing the chirality in the set of combinations included in the figure, the configuration switches from NS to SN.

Following the definitions given by Lepping et al. (2015) we have considered the cases called mostly north (mostly-N) or mostly south (mostly-S). These cases will be called here as hybrid since they are in the transition between highly ($\theta >|60|^{\circ }$) and lowly ($\theta <|30|^{\circ }$) inclined axis. In Figure 4a, this transition range of mostly-N-to-NS is depicted with lines in yellow–orange–red colors ($\theta =60^{\circ }$) and purple–blue–green colors ($\theta =30^{ \circ }$). Note that we have included for each tilt three lines that define the range of longitudes ($\phi$). Thus, for the highly inclined cases, the longitude angle goes from $\phi =50^{\circ }$ and $\phi =230^{\circ }$ (combinations displayed with the upper red line) to $\phi =130^{\circ }$ and $\phi =310^{\circ }$ (combinations displayed with the bottom yellow line). In between, for the cases with the axis perpendicular to the Sun–Earth line (combination represented with orange color, $\phi =90^{\circ },270^{\circ}$), the slope of the curve is slightly steeper. In these cases, the $B_{z}$ component is ${\approx}\,90\%$ north and the transition from N-to-S occurs in the trailing time boundary, closer to $T_{f}$. The bottom range of this transition region is defined by the combinations with $\theta =30^{\circ }$ (lines in green–blue–purple colors). Note that now the $\phi$ range is larger, for instance, for the eastwards combinations, as the longitude goes from $\phi =20^{\circ }$ (upper green curve) to $\phi =170^{ \circ }$ (bottom purple curve). Therefore, it sweeps $60^{\circ }$ more. The same is the case for the westwards combinations with $\phi$ from $200^{\circ }$ to $350^{\circ }$. In these cases, the slope of the curve increases significantly when $\phi =90^{\circ }$ or $\phi =270^{ \circ }$ is reached (combination in blue line).

The same discussion can be carried out for the mostly-S combinations. In these cases the again the green–blue–purple combinations define the souther NS scenarios. They are highly inclined with the central magnetic field pointing toward the south ($\theta =-60^{\circ }$). The change in the polarity from N-to-S occurs in the first period of the flux-rope duration (${\approx}\,10\%$). The lower tilt for the mostly-S bipolar combinations are marked by the red-orange-yellow combinations. In these cases the transition occurs in the ${\approx}\,30\%$ of the time that the spacecraft is within the flux rope. Again, the slope of the $B_{z}$ curve increases as $\phi$ approaches the perpendicular to the Sun–Earth line.

In this discussion we have considered that the spacecraft is crossing close to the flux-rope center ($Y_{0}=0.10R$). The fact that it is crossing above or below the axis does not affect the $B_{z}$ rotation only the distance of the spacecraft to the flux-rope center. Thus, as $|Y_{0}|$ increases the slope decreases and the maximum $|B_{z}^{\text{GSE}}/B_{y}^{0}|$ rate also decreases. Thus, the range for $\phi$ can also be affected. For completeness, we have included the similar scenarios in Figure 16 for an impact parameter of $Y_{0}=0.50R$. Note that the range for $\phi$ decreases in $60^{\circ }$ for a tilt of $\theta=30^{\circ}$.

Here we have shown the expected magnetic field configurations and hodograms of the basic flux-rope magnetic configurations. Obviously, reality is more complex than flux-rope axis with high or low tilt, accordingly we have illustrated the hybrid case for discussion. We want to highlight an important outcome in this section: none of the simulated configuration displays a rotation of more than $180^{\circ }$. In the next section, we will compare the synthetic data with the actual Wind observations in order to investigate the internal magnetic structure of ICMEs and evaluate the appropriateness of the axial-symmetric magnetic configuration to reconstruct such structures.

3 Magnetic Obstacles Observed Within ICMEs

In this section, we revisit the ICMEs observed by Wind in the period 1995 – 2015 and reported in Nieves-Chinchilla et al. (2018) to classify them according to their magnetic configuration signatures. We reconstruct only events with magnetic signatures consistent with flux ropes to obtain their axis orientation, spacecraft impact parameter, and cross-section size.

The classification criteria are based on the results of the modeling discussed in the previous section. We visually sort the MOs into three broad categories: $F$, single flux-rope structure; $C_{x}$, complex structure with more than one rotation; and, $E$, ejecta with unclear rotations. For the $F$-events, we divide them further according to the length of their magnetic field rotations. Thus,

• $F_{r}$: Single rotation between $90^{\circ}\,\mbox{--}\,180^{\circ}$.

• $F^{-}$: Single rotation lower than $90^{\circ}$.

• $F^{+}$: Single rotation greater than $180^{\circ}$.

• $C_{x}$: Multiple rotations.

• $E$: Unclear rotation.

Figure 5 illustrates the three categories. According to our discussion, an axially symmetric model would be appropriate for the $F_{r}$ population (e.g. October 18, 1995 event in Figure 5a). Deviations from this case are the events with incomplete rotation ($F^{-}$ population) that could arise from large impact parameter ($y_{0}$) crossings (e.g. Figure 5b, September 4, 2012 event). Magnetic field rotations larger than $180^{\circ }$ ($F^{+}$ population) can be interpreted as flux ropes with significant curvature or complex topologies such as a spheromak or a double flux rope (Figure 5c, September 6, 2006 event). The remaining two categories ($C_{x}$ and $E$-populations, Figure 5d, 5e) cannot be reproduced by a flux-rope model.

Figure 5

Classification of the magnetic field configurations within the ICMEs observed by Wind. From the top: (a) a $F_{r}$ observed on October 18, 1995, (b) a $F^{-}$ observed on September 4, 2012, (c) a $F^{+}$-event observed on September 6, 2006, (d) a $C_{x}$ observed on February 7, 1995, (e) a $E$ observed on February 10, 1997.

Table 2 reviews the ICME events between 1995 – 2015 listed in Nieves-Chinchilla et al. (2018). Each one is tagged according to our classification, i.e., $F_{r}$, $F^{-}$, $F^{+}$, $C_{x}$, and $E$. Figure 6 illustrates the distribution of the categories. At the top, Figure 6a pie charts display the total ICME dataset distributions in Solar Cycle 23 (SC23) and 24 (SC24). Figure 6b shows the annual variations of the various ICME types. From top to bottom, we plot the sunspot number variation (binned to 12 days) and the change in the solar polar magnetic field to evaluate the occurrence of MOs and populations in the solar cycle. The histograms start at the top with the total number of ICME-MO events in red, $F_{r}$-events in orange, $F^{-}$-events in yellow, $F^{+}$ in green, $C_{x}$ in blue, and $E$ in purple. In general, the variation of $F_{r}$-events dominates the variation of the total, since they comprise the largest population.

Figure 6

(a) Pie chart of ICMEs with signatures of $F_{r}$, $F^{-}$, $F^{+}$, $C_{x}$ and $E$ for the total period selected (1995 – 2015), for the Solar Cycle 23 (SC23) and for Solar Cycle 24 (SC24). (b) From the top, the sunspot temporal variation (binned to 12 days) for the period selected for the analysis and solar polar field. The histograms represent the annual population of the magnetic obstacle (MO) categories and flux-rope species $F_{r}$, $F^{-}$, $F^{+}$, $C_{x}$ and $E$. Dashed vertical lines indicate the solar cycle minimum, dotted vertical lines indicate the solar cycle maximum, and red dashed vertical line indicates the same SC23 period to the SC24 period considered in this study.

Among the 353 ICME events (Table 2), 77% (272 events) exhibit flux-rope signatures, 14% (51 events) exhibit internal complex structure, and 8% (30 events) are ejectas (see Figure 6a). Similar statistics are evident when considering individual solar cycles with slightly more $F$-events and $C_{x}$-events in SC24 than in SC23 but fewer $E$-events. For the purpose of comparison, we have added the statistics of SC23 (Table 2, row SC23 short) for the same phase (June 1st, 1996 to May 31st, 2003) on SC24. For the same period we find larger number of events observed during SC23 than SC24. This result is consistent with the sunspot number that indicates stronger solar activity in SC23 than SC24. In a more detailed comparative analysis, the difference is between the number of $F$-events and $E$-events, while $C_{x}$-events maintain the same ratio. One possible explanation is that $E$ and $C_{x}$-events are the consequences of evolutionary processes and are not dependent on the spacecraft trajectory through the MO (see Riley and Richardson, 2013, for instance). This interpretation of higher ratio of F-events is based not only on the number of events but also on the fact that ICMEs during SC24 are weaker (see Gopalswamy et al., 2015; Nieves-Chinchilla et al., 2018; Jian et al., 2018, for instance), in terms of magnetic strength, expansion and bulk velocity, than events in SC23. Therefore, interaction with the ambient solar wind or with other large heliospheric structure, is weaker and has less effect on the ICME’s internal structure.

Taking a closer look on flux ropes, 43% carry classic MC signatures with large internal magnetic field rotation ($F_{r}$-population). Their percentage is slightly higher in SC24 (48%) versus SC23 ($39\%$, $41\%$ in the short period). $F^{-}$-events constitute $16\%$ of the total ranging from 15% in the SC23 to $18\%$ in the SC24. The percentage of $F^{+}$ is the same for SC23 and for total dataset at around 18% and slightly lower in SC24 (14%). Thus, in terms of flux-rope reconstruction under axial-symmetric assumptions, ${\approx}\,43\%$ of the ICME-MO events exhibit the proper signatures, while ${\approx}\,34\%$ display deviations.

The total number of ICME-MOs follows the solar cycle phase in a broad sense. As shown in Figure 6b, there are more events during max than min with a double peaks around the SC23 maximum and during the declining phase. For individual populations, only the sunspot peak in 2001 shows a corresponding $F_{r}$ peak, the $F_{r}$ minimum occurs in 2006 – 2007, not at the sunspot minimum of 2009, and $F_{r}$-events continue to be detected at a rate of 3 – 4 events/year even during the deep activity minimum of SC23. During SC24, the $F_{r}$ is clearly peaked in 2012 – 2013 although the sunspot number remains rather flat. However, by comparing the $F_{r}$ occurrence trend with the solar polar magnetic field, the maximum occurrence in the $F_{r}$-populations is consistent with the change in the solar magnetic field polarity. In fact, the minimum in the $F_{r}$ occurrence is in 2006 that corresponds to the equidistant year between the SC23 and SC24 polarity change. Thus, our results are consistent with the interpretation that flux ropes are mainly responsible for removing the Sun’s magnetic helicity and energy. This behavior is consistent with the findings recently discussed by Vourlidas and Webb (2018). They suggest that well-formed flux-rope events ($F_{r}$ category) must arise from polarity inversion lines outside of active regions and could be, therefore, associated with streamer blowout (SBOs) CMEs. This interpretation should be confirmed by a detailed analysis of pairs of CME-ICME’s.

Similar to $F^{-}$, the $F^{+}$-events represent the main contributors to the double bump in the total number of MOs. The $F^{+}$ rates show a strong increase during the rising phase of SC23, when intense flux emergence at lower latitudes and the appearance of magnetically complex active regions may be the reason. However, no such pattern is seen in SC24. Possible explanations are the lower overall eruptive activity (from ARs) and the weaker polar fields that failed to guide CMEs towards the ecliptic as was the case in SC23.

For the remaining cases, although the number of events is low, we can discern some trends. There are more $C_{x}$-events around sunspot activity peaks, which seems to be consistent with the larger number of magnetically complex ARs. Those should generate eruptions of equally complex structures that the $C_{x}$ category represents. On the other hand, only the peak of SC23 shows appreciable number of ejecta. This is consistent with the interpretation of $E$-events as a result of multi-CME pileups and/or interaction. A large number of CMEs (up to 10 within one day, in some cases) were detected during the SC23 maximum (e.g. Vourlidas et al., 2010) but this was not the case in SC24, which is consistent with the much lower $E$-event rate in SC24.

4 Analysis and Discussion

The basis of the fitting procedure and reconstruction technique has been extensively explained in Nieves-Chinchilla et al. (2016). The fitting procedure is based on a Levenberg–Marquardt algorithm to infer the trajectory of the spacecraft in an iterative transformation from the satellite coordinate system to the flux-rope local coordinate system where the model is developed. After setting some initial-guessed parameters, the algorithm has a semi-automatic fitting procedure. Table 5 shows the Earth-directed events observed by Wind in the period of 1995 – 2015. The first column lists the events sorted by year followed by the ICME start time (month/day hhmm), decimal day of year, MO start time (month/day hhmm) and MO duration. All the events are also classified as ejecta ($E$), complex ($C_{x}$), or flux rope ($F$). The flux-rope configurations are identified as $F_{r}$, $F^{-}$ and $F^{+}$ following the discussion in the previous section. The mean solar wind speed ($V_{\mathrm{sw}}$) of the MO needed for the reconstruction of the spacecraft trajectory is also included. The table also includes orientation and size for the $F$-cases; $\phi$, longitude; $\theta$, tilt; $y_{0}$, impact parameter; and $R$, cross-section radius. It also contains the goodness of fit parameters: $\chi ^{2}$, chi-square; and the correlation coefficient, $\rho$.

Figure 7 serves as an example of the fitting procedure. The event was detected on June 27 (178), 2013 at 13:51 UT by the Wind spacecraft. The data is displayed in GSE coordinate system, averaged to 15 minutes, and it lasts for 33.62 hours. The event bulk speed is $393~\mbox{km}\,\mbox{s}^{-1}$ and exhibits a very slow expansion velocity ($7~\mbox{km}\,\mbox{s}^{-1}$ as reported by Nieves-Chinchilla et al., 2018). The visual inspection of the event suggests that the configuration is similar to the synthetic data shown in Figure 2d. The magnetic field is dominated by the $B_{y}^{\text{GSE}}$-component, which implies a highly tilted structure from south to north, which means left-handedness. In the $B_{z}^{\text{GSE}}$-component there is a slight change in the polarity with ${\approx}\,10\%$ of the MO north oriented right after the spacecraft enters in the flux rope. The $B_{x}^{\text{GSE}}$-magnetic field component is not completely flat, which indicates a deviation from the perpendicular direction to the Sun–Earth line by an angle $\phi$. Because the $B_{x}^{\text{GSE}}$-component is close to 0, the impact parameters should be close to the flux-rope center.

Figure 7

In situ magnetic field strength and the GSE components (black dots) versus time with output model (pink line) overplotted. Magnetic field configuration along the tube reconstructed from the model output parameters. The magnetic field lines displayed correspond to the distances to the center of $0.20R$, $0.40R$, $0.60R$ and $0.80R$, where $R$ is the flux-rope radius.

Table 5 reports the fitting parameters for this example. In agreement with the visual analysis, the orientation of the event is $\phi=313^{\circ }$ (${\approx}\,47^{\circ }$ away from the Sun–Earth line) and $\theta =-56^{\circ }$, tilted and pointing southwards. The impact parameter is $y_{0}=0.023~\mbox{AU}$, which is 16% away from the flux-rope center ($R=0.145~\mbox{AU}$). The chirality is left-handed.

$B_{x}^{\text{GSE}}$ (Figure 7a) depicts the magnetic field strength at the top followed by the three magnetic field components ($x,y,z$ in GSE system). Overplotted with pink line is the output fitting from the reconstruction. A visual inspection of the fitting indicates that the model (pink line) agrees very well with the data, both in the magnetic field strength and the components.

Quantitatively, we report two parameters, $\rho$, and $\chi$. They are defined as

$$ \rho = \frac{\rho _{t}+\rho _{x}+\rho _{y}+\rho _{z}}{4} $$

(3)

where $\rho _{t},\rho _{x},\rho _{y},\rho _{z}$ are correlation coefficients for each normalized magnetic field dataset (magnitude and $x,y,z$-components) included in the fitting procedure, and,

$$ \chi = \sqrt{\frac{1}{N^{2}}\frac{\sum_{n=0}^{N}\sum_{i=s,x,y,z}[(B _{i}^{\text{GSE}}-B_{i}^{mdl})^{2}]_{n}}{(|B|^{\text{max}})^{2}}} $$

(4)

with $i=s$ for the magnetic field strength. In general, as $\rho$ approaches 1 the output fitting become better, and lower $\chi$ indicates better fits to the data. In the example event above the values are $\rho =0.893$ and $\chi =0.209$, which indicate that the fitting is very good/excellent verifying the visual inspection. The Wind ICME catalog includes all the events plots, fitting output parameters and reconstruction (see wind.nasa.gov/ICMEindex.php ).

4.1 Flux Ropes Orientation

Figures 8 and 9 give an overview of the distribution of the two orientation angles of the $F$-events. The angles, longitude ($\phi$) reported in Table 5 in the range from $0^{\circ }$ to $360^{\circ }$, and tilt ($\theta$) in the range from $-90^{\circ }$ to $90^{\circ }$ (Table 5), have been folded to a range from $0^{\circ }$ to $90^{\circ }$. For $\phi$, the new angle $\phi_{f}$ identifies if the flux-rope axis is aligned ($\phi_{f}=0^{\circ}$) or perpendicular ($\phi _{f}=90^{\circ }$) to the Sun–Earth line. For $\theta$, the new angle $\theta _{f}$ identifies if the flux-rope axis is highly tilted ($90^{ \circ }$) or lies in ($0^{\circ }$) the ecliptic plane. Figure 8 shows the $F_{r}$-population and Figure 9 the $F^{-}$ and $F^{+}$-populations in $15^{\circ }$ bins.

Figure 8

Occurrence of the $\phi _{f}$ (top, blue color) and $\theta_{f}$ (bottom, pink color histogram) angles in bins of $15^{\circ }$ for $F_{r}$-population. (a) and (d) display the occurrence for the total number of events, (b) and (e) during SC23, and (c) and (f) during SC24. Vertical line represents the mean value (mn) and dashed vertical line represents the median value (md). The light color in (b) and (e) indicates the comparable phase of SC23 to available phase of SC24.

Figure 9

Histograms for $\phi _{f}$ (top, blue colors) and $\theta_{f}$ (bottom, pink colors) values obtained for the two flux-rope species. The colors are grading from darker color for $F^{-}$, and light color for $F^{+}$. (a –c) display the total number of events, during SC23, and during SC24 for $\phi _{f}$. (d – f) display the total number of events, during SC23, and during SC24 for $\theta _{f}$ solid. Vertical line represents the mean value (mn) and dashed vertical line represents the median value (md) colored according to the population.

Figure 8a – 8c (dark blue color) shows the distribution of the angle $\phi _{f}$ of $F_{r}$-population. To compare between solar cycles, we have colored in light blue color the SC23 period corresponding to that of SC24 included in this study. Figure 9a – 9c exhibits the $F^{-}$- (blue) and $F^{+}$-populations (light blue). In the a-panel the total dataset is shown, in the b-panel the events in the SC23 comparable phase, and in the c-panel the events in SC24 indicated in Nieves-Chinchilla et al. (2018). None of the populations exhibit a clear preferred orientation $\phi _{f}$. Note however, in all populations and in the full dataset, the mean ($\phi_{f,\text{mn}}>45^{\circ}$) and median ($\phi _{f,\text{md}}>45^{\circ }$) values indicate a slight tendency for the axis to be more perpendicular to the Sun–Earth line (see Table 4) Table 3 also indicates that in all populations more than 50% of the events are oriented perpendicular to the Sun–Earth line. This could be a selection effect since the magnetic field rotation is better observed as the flux-rope axis becomes more perpendicular.

In Figure 8d – 8f (dark pink color) and in Figure 9d – 9f (pink and light pink colors), distributions of the $\theta _{f}$ angle for the three populations are shown. In Figure 8d – 8f, the histograms represent (d) the total dataset, (e) the SC23 and (f) SC24 dataset events. The in SC23 events falling into the shortened period corresponding to our SC24 event are colored in light pink. The majority of all populations show low tilt ($\theta_{f}<30^{\circ }$). For $F_{r}$-population (Figure 8d – 8f), 58% of the events have tilts lower than $30^{\circ}$ (Table 3), slightly more occurrence in SC24 with 61% than in SC23 with 56% of the events. The median/mean tilt of the total number of flux ropes studied is $25^{\circ }\,\mbox{--}\,30^{\circ }$, showing similar median/mean ($\theta_{f,\text{mn}}/ \theta _{f,\text{md}}$) tilt values in SC23, $23^{\circ }\,\mbox{--}\,31^{\circ }$ and in SC24 $27^{\circ}\,\mbox{--}\,30^{\circ }$. The comparative analysis between solar cycles, using a similar temporal interval (light pink in SC23), exhibits similar occurrence rate and suggests that the number of events with low tilt increases towards the declining phase in SC24 probably attributed to lower inclination of heliospheric current sheet in the declining phase.

For the other two populations, $F^{-}$ and $F^{+}$, the trend is slightly different. In the case of the $F^{-}$-population (pink color), the median/mean for the whole dataset is $15^{\circ }\,\mbox{--}\,20^{\circ }$, which is ${\approx}\,10^{\circ }$ lower than the values for the $F_{r}$-population. This difference persists during the two solar cycles. Note that ${\approx}\,80\%$ of the reconstructed events have low tilt (Table 3). In the case of the $F^{+}$-population, the median/mean values exhibit similar values to that of the $F_{r}$-population and consistently for the whole dataset and for SC23, i.e., $\theta_{f,\text{md}}\,\mbox{--}\,\theta _{f,\text{mn}}= 28^{\circ}\,\mbox{--}\,31^{\circ }$ and $\theta _{f,\text{md}}\,\mbox{--}\,\theta _{f,\text{mn}}= 24^{\circ}\,\mbox{--}\,28^{\circ }$, but slightly higher for SC24 with $\theta _{f,\text{md}}\,\mbox{--}\,\theta _{f,\text{mn}}= 41^{\circ}\,\mbox{--}\,36^{\circ}$.

Figure 10 exhibits the annual normalized occurrence of events with $\phi _{f}>45^{\circ }$ and ${<}\,45^{\circ }$ in the top two panels with blue colors and $\theta _{f}>30^{\circ}$ and $\theta _{f}<30^{\circ }$ in the two bottom panels with pink colors. The three set of panels (a – c) represent the three populations: (a) with dark blue/pink for the $F_{r}$-population, (b) with blue/pink for the $F^{-}$-population, and (c) with light blue/pink color for the $F^{+}$-population. For each population the temporal variation of the sunspots is included in two panels (red or blue color line) to help evaluate the trend relative to the solar cycle variation. Between the top two and bottom two panels, we have also included the heliospheric current sheet (HCS) tilt in order to evaluate the effect of the large scale magnetic field in the flux-rope orientation.

Figure 10

Annual normalized angular occurrence for the three populations: (a) $F_{r}$-population, (b) $F^{-}$-population, and (c) $F^{+}$-population. From the top, the occurrence of events with $\phi _{f}>45^{\circ }$ at the top, occurrence of events with $\phi _{f}<45^{\circ }$, latitude of heliospheric current sheet, occurrence of events with $\theta _{f}>30^{\circ }$, and, at the bottom, occurrence of events with $\theta _{f}<30^{\circ }$.

Based on visual inspection of the figure, the $F_{r}$-population shows solar cycle trend vs. the other two populations in both angle orientations, $\phi _{f}$ and $\theta _{f}$. In the case of $\phi _{f}$, (top panel of Figure 10a) the occurrence rate of flux ropes with a perpendicular axis to the Sun–Earth line increases during the rising phase of solar cycles. An occurrence decrease in the second panel can be identified for the same period. The effect is most significant during the SC22 minimum and SC23 rising phase. Near solar maximum and in the early declining phase in SC23 (2000 – 2005), the top panel exhibits lower occurrence rate probably because solar wind disturbances.

Previous studies have explored the solar cycle dependency of the magnetic field polarity within MCs (Mulligan, Russell, and Luhmann, 1998; Li et al., 2011, 2014; Li, Luhmann, and Lynch, 2018). In these studies the identification of the high or low inclined flux ropes was based on visual inspection and they did not attempt to measure the MC flux-rope inclination angle. We have plotted the $\theta _{f}$ angle (pink color) in the two bottom panels of Figure 10. Our analysis shows that there is a clear flux-rope inclination dependence with respect to the solar cycle in the $F_{r}$-population (Figure 10a, two bottom panels, pink bar plots) and no clear dependence in the other two populations (Figure 10b, 10c). Pink bars show the annual occurrence of the events with tilt ${>}\,30^{\circ }$. Each bar is divided into cases with $30^{\circ }<\theta _{f}<60^{\circ }$ with pink color and crowning each bar is the occurrence of events with higher inclination, i.e., $\theta >60^{\circ }$ (white bar). The $\theta _{f}>60^{\circ}$ cases are the most probable and exhibit north or south polarity under a certain combination with $\phi$ while the $30^{\circ}<\theta _{f}<60^{\circ }$ cases display bipolarity. Over plotted, with blue line, is the SSN to follow the solar cycle trend and in between the longitude and tilt is plotted the HCS tilt angle obtained by WSO of Stanford based on a potential-field source-surface (PFSS) model. The highly tilted events reach a frequency of ${\approx}\,80\%$ during 2003 and 2014, in the early declining phase of SC23 and SC24.

In the bottom panel the annual occurrence of low-tilted events ($\theta_{f}<30^{\circ }$) colored with pink color is shown. These are the cases where the $B_{z}^{\text{GSE}}$-component will display a double sign or bipolarity, i.e., NS or SN, unless the axis is aligned with the Sun–Earth line. They show solar cycle dependency with minimum occurrence around the maximum in both solar cycles for the $F_{r}$-population. It is important to note that, in contrast to the high inclined events, the occurrence of low-tilted events are more frequent with a systematic ${\approx}\,20\%$ of the cases observed during the maximum solar cycles periods studied.

Finally, we want to explore if there is any remote sensing signature of the CME inclination. Figure 11a shows the not stacked barplot with the normalized occurrence of CMEs with angular width (AW) larger than $60^{\circ }$. The set includes 1185 events from the dual-viewpoint CME catalog based on COR2 data (Vourlidas et al., 2017). All events are treated equally, i.e., no distinction regarding their apparent morphology in the coronagraph images is made. The angular widths are projected measurements based on single viewpoint images. The proportion of CMEs exhibiting AW larger than $60^{\circ }$ clearly varies with the solar cycle. Wide CMEs ($\mbox{AW} > 60^{\circ }$) dominate at times of solar maxima, increasing the occurrence as the global configuration of the Sun’s magnetic field becomes more complex. Balmaceda et al. (2018) reports that CMEs with clear signatures of flux ropes (presence of a cavity, three-part structure, etc.) exhibit typical widths of ${\approx}\,50^{\circ }$, in agreement with previous results on the average CME width (Yashiro et al., 2004; Vourlidas et al., 2010). Loop CMEs, on the other hand show an average width almost $2\times$ larger (${\approx}\,90^{\circ}$) and are interpreted as flux-rope CMEs seen face-on. Thus, an interpretation is that around the maximum more CMEs exhibit larger inclinations and therefore they are seen projected on the plane of sky as wide structures. By comparing this result with our analysis for the same period of time (Figure 11b) they broadly correlate with systematic increases of wide CME and high inclined flux ropes around the maximum. However, the number of CMEs with $\mbox{AW}>60^{\circ }$ increases during the years 2010 – 2012 and slightly decreases afterwards. In the case of the flux ropes, the highly inclined increases more after 2012. We interpret this comparative result as an effect of an evolutionary process; the highly inclined CMEs are accommodated to the HCS tilt suffering deflections or rotations in the journey at 1 AU. In any case, this finding leads us to questions such as how, when and why some flux ropes are affected by the surrounding magnetic field configurations, and if it is related to the source region, by initial stages or by propagation processes.

Figure 11

Comparative analysis of the normalized occurrence during 2007 – 2014 of CMEs with angular width (AW) greater than $60^{\circ }$ and the high tilted flux ropes with $\theta >30^{\circ }$. The CMEs AW measurements are taken from the CME catalog based on COR2.

4.2 Magnetic Bipolar or Unipolar Configuration

Figure 12 displays the annual normalized occurrence of bipolar or unipolar magnetic configuration of the $F$-events and the solar polar magnetic field. The SN or NS classification has been done according to the discussion and definition given in Figure 4 and Table 1. The figure is crowned by the solar polar magnetic field and SSN to follow the change in the solar magnetic field polarity and solar cycle trend. Among the 272 $F$-events, 103 events (38%) are NS, 106 events (38%) are SN, 24 events (9%) are N and 39 events (14%) are S. The identified NS and SN bipolar events include the mostly S or N events since the dataset is not large enough to evaluate the different configurations. Thus, during the 21 years of data, almost two solar cycles, we have found almost an even number of opposite bipolar configurations and opposite unipolar configurations.

Figure 12

From the top. (a) Annual distribution of the sunspot number in red and polar magnetic field. (b) Annual normalized occurrence of the NS (positive) and SN (negative) configurations. (c) Annual normalized occurrence of the N (positive) and S (negative) configurations. (d) Annual normalized occurrence of the right-handed (positive) and left-handed (negative) configurations.

Table 1 Ranking the polarity.

Table 2 Occurrence of events by category. The statistics include the total dataset, the Solar Cycle 23 (SC23, from June 1, 1996 to December 31, 2008) and Solar Cycle 24 (SC24, from 2009 to 2015). SC23 [short] includes the statistic of a SC23 subset data (from June 1, 1996 to May 31, 2003).

Table 3 Statistics of the Direct output parameters.

Table 4 Mean (mn) and median (md) values of the flux-rope orientation for the total dataset, Solar Cycle 23 (SC23), and Solar Cycle 24 (SC24).

A visual inspection of Figure 12b reveals a smooth change in the polarity in the bipolar flux-rope configurations. The flux-rope polarity changes from SN in the rising phase of the SC23 towards NS in the declining phase to dominate during the SC24 rising phase. Around the solar cycle minima the configurations, either SN (SC23) or NS (SC24), almost exclusively dominate. The number of events with N or S configuration increases around the solar cycle maximum and declining phase consistently with the number of events with tilt ${>}\,30^{\circ }$ (Figure 10). These results confirm the findings of Li et al. (2011, 2014), Li, Luhmann, and Lynch (2018) based on visual identification of the flux-rope polarity. There is a cyclic reversal of the bipolar MC poloidal field on the same time scale of the solar magnetic cycle. These results suggest that CMEs could remove the latest solar cycle magnetic field and helicity (Low, 2001; Gopalswamy et al., 2003).

In Figure 12d, the annual normalized occurrence of the chirality is shown. The positive values indicate the right-handed events and negative values left-handed and visual inspection of the plot does not reveal a clear solar cycle trend. This result suggests that the bipolarity is only due to the orientation of the flux rope.

4.3 Spacecraft Impact Parameter and Cross-Section Size

Figure 13 displays the normalized occurrence of impact parameter ($y_{0}/R$) (a) for $F_{r}$-population (first column), (b) $F^{-}$-population (second column) and (c) $F^{+}$-population (third column). The bin size of the histogram is 0.2 of the radius from the flux-rope center. Thus, at 0 the spacecraft crosses through the flux-rope center, while at 1 the spacecraft crosses through the flux rope edge. In the case of the $F_{r}$-population, Figure 13a, the occurrence of the impact parameter is distributed along all possibilities with a slight increases (${\approx}\,25\%$) around the flux rope center (0 – 0.2) and flux rope edge (0.8 – 1.0). In the case of $F^{-}$-population, Figure 13b, the results are consistent with the initial hypothesis that the $F^{-}$-events are flux ropes crossed by the spacecraft with high impact parameter. However, in the case of the $F^{+}$ population, the model interprets that the spacecraft is crossing closer to the flux-rope axis. These results does not shed any light to the debate between Lepping and Wu (2010) and Démoulin, Dasso, and Janvier (2013). The first authors found a progressive decrease of the identified MCs as the impact parameter increases. The second group demonstrated mathematically that there is not a fundamental basis for such result.

Figure 13

Percentage of the impact parameter ($y_{0}/R$) occurrence for (a) $F_{r}$-population, (b) $F^{-}$-population, and (c) $F^{+}$-population. The impact parameter ($Y_{0}$) has been scaled to the flux-rope size ($R$). Percentage of the size ($R$) occurrence for (d) $F_{r}$-population, (e) $F^{-}$-population, and (f) $F^{+}$-population.

Finally, the bottom panel in Figure 13b shows the normalized occurrence of flux-rope radius ($R$). This is a derived quantity from the reconstruction. In all cases, the range of values vary between 0 – 0.2 AU on average, however, the mean/median values of each population show different values. While the $F_{r}$-events show a mean/median value of 0.11 AU, the $F^{-}$ population is smaller with values of ${\approx}\,0.07\mbox{/}0.09~\mbox{AU}$ and the $F^{+}$ population is larger with a value of ${\approx}\,0.15~\mbox{AU}$.

5 Summary, Conclusions and Final Remarks

The understanding of the magnetic field configuration in CMEs is primarily based on the assumption that their internal structure are flux ropes. In this paper, we conduct a study to better understand the internal magnetic field structure of ICMEs and analyze the intrinsic properties of the magnetic obstacles at 1 AU. We undertook a comprehensive study of events observed by Wind in the period of 1995 – 2015. These events are characterized by periods of increased magnetic field strength, smooth internal change in the magnetic field direction and the existence of plasma cooler than the surrounding solar wind. We defined these structures as low-$\beta$ magnetic obstacles (MOs).

As reported by Nieves-Chinchilla et al. (2018), the expected configuration of the internal ICME magnetic flux-rope structures do not always exhibit the rotation in magnetic field direction. Such structures with unclear flux-rope signatures are variously defined in the literature as “magnetic-cloud-like”, “flux-rope-like” or “non-classic-magnetic-cloud”. The MO term is introduced to reduce confusion as a unifying replacement for all these terms.

In the first part of this paper, we simulate the magnetic configurations for various flys through a circular–cylindrical flux-rope structure. We create and analyze synthetic data based on the circular–cylindrical flux-rope model and 3D reconstruction of Nieves-Chinchilla et al. (2016). The free parameters in the simulation are the longitude ($\phi$), tilt ($\theta$), impact parameter ($y_{0}$) and chirality ($H=+$ or $H=-$) of the flux rope. We compile and discuss various magnetic field configurations (unipolar, bipolar or hybrid) and the in situ signatures observed for different spacecraft crossings. We discuss the effect of large impact parameters on the chirality or handedness.

With an eye to space weather needs, we study in detail (Section 2.2) the flux-rope orientations resulting in bipolarity in the $B_{z}$ component. We define intervals for a pure bipolar configuration when $B_{z}$ is 30% to 70% positive/negative during the first half of the spacecraft transit through the flux rope and 70% to $30\%$ negative/positive in the second half. In this configuration the $B_{y}$ component is mostly positive (negative) when the flux rope is eastwards (westwards), respectively. We define mostly-north or mostly-south bipolar configuration when the $B_{z}$ component changes polarity but remains for most of the time (70% – 90% of the crossing duration) positive (mostly-north) or negative (mostly-south). Most of these cases are within the previously hybrid configurations where both the $B_{z}$ and $B_{y}$ display bipolarity. One important conclusion from this analysis is the longitude of the flux-rope axis plays a significant role and should be taken into account to predict the critical $B_{z}$ bipolarity.

In the second half of the paper, we conduct a detailed classification of the observed patterns in MOs by comparing the 353 ICMEs observed by Wind to the synthetic observations, we sort the ICME samples in three broad categories based on the magnetic field rotation pattern. Namely, as shown in Figure 5, we identify events without obvious rotation ($E$), events with single magnetic field rotation ($F$), and events with more than one magnetic field rotation ($C_{x}$). In other words, the $F$ types are events closely following the expectations from a magnetic flux rope.

We further subdivide the $F$-population in three groups based on the angular span of the magnetic field rotation: i) $F_{r}$-events exhibit rotation between $90\,\mbox{--}\,180^{\circ}$; cases most amenable to reconstruction with axially symmetric flux-rope geometries; ii) $F^{-}$ types exhibit shorter rotations and are primarily cases with large impact parameters; iii) $F^{+}$ types that exhibit rotations ${>}\,180^{\circ }$ and obviously deviate from an axially symmetric geometry. The $F^{+}$-events may represent events with significant curvature or distortion (Nieves-Chinchilla et al., 2018). It would be interesting to explore whether other magnetic structures such as spheromak or double flux ropes give rise to such structures.

In the analysis of the internal magnetic field configuration we find that:

• From the 353 ICMEs with MOs, 272 are $F$ type (${\approx}\,77\%$ of the total) and can be associated with flux-rope structure. The remaining 23% exhibit internal complexity ($C_{x}$ and $E$). There are more complex events around sunspot activity peaks, which seems consistent with the larger number of magnetically complex ARs. Complex events are more prevalent during the peak of SC23. This suggests that complexity arises as the result of multi-CME pileups and/or interaction. A large number of CMEs (up to 10 in a single day) were detected during the SC23 maximum (e.g. Vourlidas et al., 2010) but this was not the case in SC24, which is consistent with the much lower complexity rate in SC24. Thus, evolutionary processes, such as interaction or erosion, can be the main cause of difference between coherent flux-rope structures and complex, but also, it should be important for future studies to take into account the solar source and initiation processes of such CMEs.

• Within the non-flux-rope events, we find 51 $C_{x}$ cases (14%) and 30 $E$ cases (9%) that display different intrinsic complex signatures. This statistics is basically consistent in the solar cycles. In the first group, the internal magnetic configuration displays magnetic substructures that could be reproduced by a more complex model than a single-flux-rope model. The second group does not show any coherent or systematic signatures.

• Of the $F$ types, the $F_{r}$ cases (152 events, ${\approx}\,43\%$) display the expected signatures of a flux rope with axial-symmetric geometry. The other two types can also be considered flux ropes under some assumptions. The $F^{-}$ cases (16%) are considered flux ropes crossed by the spacecraft with very large impact parameter and therefore there is not a full magnetic field rotation. This assumption is also interpreted by the model in the fit with $~78\%$ of the cases with large impact parameter. The $F^{+}$ cases (18%) can be considered single flux ropes by assuming that the curvature is significant. These cases can be considered also spheromak structure but this feature needs to be further explored in future studies. Using reconstruction with the circular–cylindrical geometry, the model interprets these cases with small impact parameter, i.e., the spacecraft crosses close to the flux-rope center. In terms of the size, the model interprets that the $F^{-}$ are the smallest structures (median of the dataset ${\approx}\,0.072~\mbox{AU}$) and the $F^{+}$ are the largest (median of the dataset ${\approx}\,0.149~\mbox{AU}$). The $F_{r}$ median size is 0.111 AU.

• ICME rises and falls with the solar cycle following, in a broad sense, we have a solar cycle trend with a double small bump at the end of the declining phase of the SC23. In the case of the $F_{r}$ the minimum of occurrence corresponds to the period of stability in the middle declining phase. In the interpretation of the small increase in the number of $F^{-}$- and $F^{+}$-events around this period we could speculate that the origin and intrinsic structure of such events are different of the $F_{r}$ but to confirm this hypothesis a systematic analysis of the solar source is required.

• The $F^{+}$ rate strongly increases during the rising phase of SC23. Intense flux emergence at lower latitudes and the appearance of magnetically complex active regions may be the reason for this. No such pattern is seen in SC24. Possible reasons are the lower overall eruptive activity (from ARs) and the weaker polar fields that failed to guide CMEs towards the ecliptic as was the case in SC23.

In the analysis of the orientation of the ICMEs based on the reconstruction described by Nieves-Chinchilla et al. (2016), the main findings and conclusions can be summarized as follows:

• More than half of the $F_{r}$-events display low tilt ($\theta<30^{\circ}$) for the whole dataset and by solar cycles. This number increases significantly in the case of the $F^{-}$ type events. This inclination is more likely to display the range of bipolar $B_{z}$ configuration for almost all longitudes (more aligned with Sun–Earth line, less $B_{z}$ rotation). On the other hand, only ${\approx}\,17\%$ of the $F_{r}$-events show high inclination ($\theta >60^{\circ }$), with ensured $B_{z}$ unipolar configuration. Thus, according to our results, most of the cases are deflected at 1 AU but the $F^{-}$ are more susceptible than any other type of flux ropes.

• We find that both longitude and tilt follow the general trend of the solar cycle for the $F_{r}$ type of events. The other two populations do not show a solar cycle trend.

• In the case of the tilt ($\theta$), the $F_{r}$ follow the SSN trend and the HCS tilt, with maximum tilt (${>}\,60^{\circ }$) around the maximum in the SSN and remain high occurrence of highly tilt flux ropes (${>}\,30^{ \circ }$) during the declining solar cycle phase consistently with HCS tilt. Therefore, there is more chance to find $B_{z}$ magnetic bipolar configuration around the minimum.

• By comparing the occurrence of highly tilt flux ropes ($\theta >30^{\circ}$) with the occurrence of CME with wide angular (AW) width ($\theta >60^{\circ }$) observed remotely with STEREO during 2007 – 2014, we have found that they broadly correlate. The number of events with $\mbox{AW}>60^{ \circ }$ increases during the 2010 – 2012, years of high solar activity, and slightly decreases afterwards. In our analysis, the highly inclined flux ropes ($\theta >30^{\circ }$) increases in 2012. These results suggests two things: the solar cycle variation of the angular width could provide information about the flux-rope orientation in the early stages of the CME evolution, and, the shift between the maximum occurrence of CME with large angular width and highly tilted flux ropes could be an effect of the evolutionary processes, i.e., the highly inclined CMEs are accommodated to the HCS tilt suffering deflection or rotation in the evolution throughout the heliosphere.

• The analysis of flux-rope configurations show that the events with $B_{z}$ magnetic bipolar configuration clearly follow the solar cycle trend suggesting that the CMEs could be responsible for removing the magnetic field and helicity from the Sun. This result confirms previous studies based on visual inspection.

• The annual occurrence of the left- or right-handed chirality does not show a clear trend with the solar cycle. This result confirm that the solar cycle trend in the $B_{z}$ magnetic bipolarity is solely due to the orientation of the flux rope.

• In the case of unipolar configuration, the number of N/S configurations increases around the solar cycle maximum and declining phases consistently with the number of events with tilt ${>}\,30^{\circ }$ but shows no other strong cycle trends or privileged orientation N or S in the solar cycles.

This work is an attempt to reconcile the observations of the heliospheric flux ropes and the modeling by exploring the limitations in the models and in the observations. We are constrained to exploring the internal magnetic field structure of the CMEs by figuring out the magnetic configurations. The strong limitation of 1D in situ observations from instruments onboard satellites prevents us from complete view of the structure. Thus, we have to infer flux-rope structures based on single monotonic changes in the magnetic field in spite of that they do not always display the expected magnetic field configuration associated with flux-rope internal structure. In this paper we cannot confirm if all CMEs are flux ropes, or whether more complex structures, or evolutionary processes have affected the internal structure, it is necessary to expand the analysis with larger dataset, to combine this kind of studies with systematic multi-view, and multipoint analyses. The Parker Solar Probe mission (Fox et al., 2016) and the future Solar Orbiter mission (Müller et al., 2013) will aid to shed some light on this dilemma with conjunctions with other missions and by exploring the first stages in the evolutionary processes. Finally, another aspect to take into account in the fact that the current analytical models and in situ reconstruction techniques are limited to reproduced structures with well-organized internal magnetic field and well-defined geometry. However, a realistic and more intuitive view of the heliospheric flux ropes can be described in terms of a confined magnetized plasma within magnetic field lines wrapping around an axis in a twisting but not necessarily a monotonic way. It is important to review the current status of the models and adapt them to our current understanding of the heliospheric flux-rope topology and geometry.

Appendix: In situ Imprints of the Magnetic Field Flux-Rope Configurations

Figure 14

Internal magnetic field configurations.

Figure 15

(a) In situ signatures in the GSE coordinate system and sketch representing the west-north-east, right-handed (WNE-RH), (b) representing the east-north-west, left-handed (ENW-LH), (c) east-south-west, right-handed (ESW-RH), and (d) west-south-east, left-handed (WSE-LH). For each configuration is included: (i) Temporal variation, (ii) magnetic hodograms of the GSE magnetic components.

Figure 16

Combination of flux-rope axis configurations; longitude ($\phi$), tilt ($\theta$), and chirality ($H$) fixing the impact parameter $(Y_{0})=0.50R$ to obtain a bipolar $B_{z}$ configuration normalized to the central magnetic field, $B_{y}^{0}$.

Table 5 Catalog of ICMEs observed by Wind from 1995 to 2015. Column: (1) event number; (2) year; (3) ICME – disturbance arrival time, DOY and magnetic obstacle arrival time; (4) duration; (5) MO type; (6) MO bulk velocity (km s⁻¹); (6) magnetic field configuration; (7) longitude ($\phi$); (8) tilt ($\theta$); (9) impact parameter (Y₀); (10) radius ($R$); (11) goodness of the fitting ($\chi^{2}$); and (12) correlation coefficient ($\rho$).