On the Contribution of Coronal Mass Ejections to the Heliospheric Magnetic Flux Budget on Different Time Scales

Coronal mass ejections (CMEs) contribute closed magnetic flux to the heliosphere while they are connected at both ends to the Sun and play a key role in adding magnetic flux to the heliosphere. Here, we discuss how the type of magnetic reconnection that opens CME field lines in the inner heliosphere, i.e., interchange (IC) and/or interplanetary (IP) reconnection, determines the length of time CMEs contribute to the heliospheric flux budget. This distinction has not been taken into account in past studies that estimate the CME flux opening timescale. We outline key criteria to aid in distinguishing IC reconnection from IP reconnection based on in situ spacecraft data and highlight these through two example events. Studying the manner in which CMEs reconnect and open in the inner heliosphere yields important insights not only into CMEs’ role in the heliospheric flux budget but also the evolution of CME complexity, connectivity, and topology.


Introduction
In this paper, we discuss two processes through which coronal mass ejections (CMEs) can play a part in the heliospheric magnetic flux budget: (1) interchange (IC) reconnection close to the Sun, and (2) interplanetary (IP) reconnection (or erosion).In what follows, we argue that a large fraction of CMEs likely undergoes both types of reconnection as they propagate and expand in the heliosphere, thereby affecting the heliospheric magnetic flux budget on different timescales.
Studying CMEs (as well as their IP counterpart, ICMEs), specifically their interaction with the solar wind and other large-scale solar wind structures as well as how frequently they undergo IC reconnection, can yield important insights into the role of CMEs in the heliospheric flux budget (e.g., McComas et al. 1992;Schwadron et al. 2010).Past studies (e.g., Owens & Crooker 2006;Owens et al. 2008) have found that CMEs inject closed magnetic flux into the heliosphere, thereby temporarily adding magnetic flux to the inner heliosphere while they remain closed, and raising the heliospheric magnetic flux budget significantly during solar maximum when CMEs are most frequent.
In general, the closed magnetic flux injected by CMEs into the heliosphere raises the heliospheric magnetic flux level, unless there is a process that can remove closed magnetic flux.Two possibilities for this exist: disconnection (McComas 1995) and IC reconnection (Gosling et al. 1995;Crooker et al. 2002).To reduce the magnetic flux injected by a CME, disconnection has to entail reconnection of a closed field line on itself, thereby releasing a plasmoid.Past works have shown disconnection events to be rare (e.g., Shodhan et al. 2000;Owens & Crooker 2007;Schwadron et al. 2010).IC reconnection on the other hand, which is an open field line merging with a closed field line in one leg of a CME loop (see Figure 1(a)) that has already expanded into the heliosphere, is common (e.g., Crooker et al. 2002).The merging of the field lines opens the CME loop and occurs low enough in the solar atmosphere to return a closed loop to the solar corona (i.e., below the solar Alfvén surface, estimated to be typically around 10-20 solar radii (R S ) Kasper et al. 2021).Overall, IC reconnection does not reduce flux that was there before a CME erupted, but it does reduce the flux added by the CME back to what it was before the CME erupted, thereby nullifying the flux added by CMEs.Based on simulations that match the observed doubling in the magnetic field intensity at 1 au over the solar cycle, Owens & Crooker (2006) found that the flux catastrophe caused by CMEs (i.e., the endless buildup of heliospheric flux; McComas et al. 1992) can be avoided via an average CME flux opening timescale of ∼50 days (see further discussion below).
In this study, we invoke the Alfvén surface as the boundary between the corona and the heliosphere, below which plasma can flow both inward and outward from the Sun because the plasma is sub-Alfvénic there, while above the boundary, the plasma moves outward because it is super-Alfvénic outside of the corona. 4Thus, changes that happen above the Alfvén surface cannot propagate inward and affect the morphology and connectivity of the solar corona, while changes that happen below this boundary can.Overall, it is the magnetic flux that passes through the Alfvén surface that contributes to the heliospheric magnetic flux budget, while magnetic flux below this surface is considered part of the coronal flux.If reconnection between a closed CME loop and an open field line happens below the Alfvén surface, as in IC reconnection, the new loop that forms will stay below the Alfvén surface and therefore will not contribute to the heliospheric magnetic flux budget, thereby removing flux from the heliosphere added by CMEs.As noted in Crooker et al. (2002), IC reconnection still continues in the corona even if the leading edge of the CME is far from the Sun.On the other hand, reconnection that occurs beyond the Alfvén surface in IP space between a CME and the interplanetary magnetic field (IMF) will not cause any direct change to the heliospheric magnetic flux.This distinction is important because if a CME undergoes such IP reconnection, the newly reconnected closed loop that forms will not be returned to the solar corona, and therefore the CME in question will continue to add closed magnetic flux to the heliosphere.
Thus, for any individual CME, there are three possible scenarios at play: (a) CME undergoes only IC reconnection, (b) CME only undergoes IP reconnection, and (c) CME undergoes both IC and IP reconnection.However, it is important to note that CMEs that fall in scenarios (b) and (c) will still have an additional step in their evolution whereby they eventually fully open through IC reconnection.This is necessary in order to avoid the heliospheric magnetic flux catastrophe and also to match the measured floor in the magnetic field intensity at 1 au (Owens et al. 2008).
Figure 1 depicts the three scenarios.In scenario (a) (Figure 1 top panels, following Owens & Crooker 2006), the closed CME field line reconnects with an open field line beneath the Alfvén surface, a small closed loop forms that is returned back to the solar corona and thereby does not contribute to the heliospheric flux budget.On the other hand, in scenario (b) (Figure 1 middle panels), the closed CME loop reconnects with an open field line in IP space, above the Alfvén surface, and the large closed loop that forms, which is made up of IMF and a CME field, is not returned to the corona.As the CME propagates far from the Sun through the solar system, this surviving ejecta-associated magnetic field likely interacts with the IMF to form merged interaction regions, and it may get quite complex.However, until it opens through IC reconnection, it will have portions connected back at the Sun and therefore have flux going through the Alfvén surface, thereby continuing to contribute to the flux budget.Eventually, assuming only solar meridional motions and diffusive motions at play, the ejecta-associated flux footpoints can move into coronal holes and undergo IC reconnection, as pointed out through theoretical calculations by Fisk & Schwadron (2001) and Schwadron et al. (2010).Since the solar meridional motion speed is 10-20 m s −1 , a photospheric element moves about 1 R S on timescales (τ) of 1-2 yr, while the timescale of diffusive motion of footpoints is on the same order.We note that our estimate of the timescale for moving the CME-associated closed flux into a coronal hole is likely an upper limit, since for individual cases the distance between these regions may be shorter than a solar radius.Once in coronal holes, subsequent IC reconnection with the open field lines there would ensure the removal of the CME field from the heliospheric flux budget, but at significantly longer timescales than if it underwent just IC reconnection.
In scenario (c) (Figure 1 bottom panels), both processes are occurring on the same CME, just on different field lines.We hypothesize that scenario (c) is likely happening in the majority of CMEs, with some field lines being opened through IC reconnection on one CME leg in the corona, while different field lines are being opened directly in IP space, potentially simultaneously.Determining on average what fraction of the CME flux is opened in the corona versus in IP space is imperative to establish the overall CME flux contribution to the heliosphere.
From the perspective of contribution to the flux budget, what matters are the timescales at play.CMEs that undergo only IC reconnection (scenario a) contribute to the flux budget for the least amount of time, while ones in scenario (b) and (c) will take significantly longer (i.e., τ up to ∼1-2 yr, as discussed above) to open.There is a large body of past research that has looked at IC reconnection-related ICME flux opening timescales, with some papers suggesting that this would be on the order of months to years (Crooker et al. 2004;Riley et al. 2004), while others suggest a much shorter ICME flux opening timescale on the order of hours (Reinard & Fisk 2004).For example, Crooker et al. (2004) considered a statistical set of ICMEs at Ulysses near 5 au and found no significant differences in the fraction of bidirectional electron flows compared to a similar investigation at 1 au by Shodhan et al. (2000), suggesting the rate of IC reconnection peaks in the ∼1 day after the CME eruption and then acts at much smaller rates but over longer timescales (up to several months) to completely disconnect ICMEs from the corona.Furthermore, neither the study by Crooker et al. (2004), nor the estimated ICME flux opening timescale of ∼50 days found in Owens & Crooker (2006) (based on constant and exponential flux opening models), take into account IP reconnection, and in general, IP reconnection has not been considered in the past when estimating ICME flux opening timescales.
Ultimately, although IP reconnection does not alter the total amount of magnetic flux in the heliosphere, it matters in this context because it can prevent the efficient opening of CME closed magnetic flux through IC reconnection, thereby prolonging the length of time that CMEs contribute closed magnetic flux to the heliosphere.Overall, this implies that there is a varying timescale of the contribution of individual ICMEs to the heliospheric flux budget, with some ICMEs contributing for considerably longer than others, depending on their interactions in IP space (i.e., depending on the fraction of the ICME opened up through IP reconnection versus IC reconnection).In what follows, we showcase examples of both IC and IP reconnection occurring in separate ICMEs as measured at 1 au, and we call attention to the necessity of more such studies, especially statistical ones, to gain better insight into the duration of ICME contributions to the heliospheric flux budget.
While our paper tackles the heliospheric magnetic flux budget problem from the CME contribution perspective, it has implications for a broad range of solar and heliospheric physics research areas.Our discussion directly affects investigations on the ICME flux opening timescale (e.g., Crooker et al. 2004;Reinard & Fisk 2004;Riley et al. 2004;Owens & Crooker 2006) and ones on the evolution of the heliospheric open magnetic flux and flux floor across various timescales (ranging from different phases of the solar cycle to millennial timescales (e.g., Schwadron et al. 2008;Smith & Balogh 2008;Vieira & Solanki 2010;Lockwood & Owens 2011).Furthermore, closely related studies for which our results are highly relevant are ones aimed at distinguishing between IP and IC reconnection signatures, as well as studies investigating the connectivity and topology of ICMEs.Finally, most broadly, our results also affect investigations on the effects of open magnetic flux on galactic cosmic rays (e.g., Alanko-Huotari et al. 2006;Bazilevskaya et al. 2014).

Signatures of IC versus IP Reconnection
Successfully identifying the in situ signatures of IC reconnection is key to separating it from IP reconnection that happens past the Alfvén surface.In order to unambiguously distinguish IC reconnection from IP reconnection, ideally, one would have in situ multi-spacecraft measurements of the same CME at increasing heliocentric distances, with the first observation point being below the Alfvén surface.One of the limitations of recent studies (post-Helios and pre-Parker Solar Probe and Solar Orbiter) is the lack of solar wind and suprathermal electron measurements at <1 au, as such data have only been available near 1 au.The recent arrival of Parker Solar Probe (and crossing below the Alfvén surface on occasion; Kasper et al. 2021), Solar Orbiter, and BepiColombo to the inner heliosphere will make a difference in this regard; however, years of observations are needed before a large enough number of CME events are observed in radial alignment to be able to carry out such detailed investigations.
Past papers, including those of Crooker et al. (2002) and Crooker & Webb (2006), assumed that the main in situ signature of IC reconnection is unidirectional suprathermal electrons in a CME indicating open field lines, whereas heat flux dropouts (i.e., a complete lack of suprathermal electrons) would indicate complete disconnection of the field lines from the Sun.However, although unidirectional suprathermal electrons in a CME are a necessary condition for IC reconnection, it is not sufficient because IP reconnection can also yield unidirectional electron flows.
Other studies, such as that of Lavraud et al. (2011), used helicity and polarity information from in situ data of magnetic clouds (MCs) to determine the direction of open flux transport on the Sun due to IC reconnection and associated footpoint exchange at the legs of MCs.Ruffenach et al. (2012) distinguished between erosion (i.e., IP reconnection) and IC reconnection largely based on the location of unidirectional suprathermal electrons (i.e., whether at the center or the front/ back of the MC).Furthermore, Crooker & Webb (2006) showed that remote sensing observations of X-ray and EUV signatures can be used to identify if IC reconnection indeed occurred, and where, on the solar corona for a CME event that displayed unidirectional electrons at 1 au.
In order to maximize the chances of observing an ICME undergoing IC reconnection, we propose three additional requirements for identifying IC reconnection on top of observing extended unidirectional suprathermal electron flows: (1) unidirectional electrons found in the middle of the CME magnetic ejecta (ME; as opposed to the front or back), (2) unidirectional electrons observed flowing in the same direction (i.e., not alternating direction), and (3) a lack of in situ reconnection signatures.The reason for having requirement (1) is that signatures of reconnection, such as unidirectional electrons, at the front or back of MEs are most likely related to erosion, i.e., reconnection of the CME with open field lines in IP space as first suggested by Dasso et al. (2006) and observed by Ruffenach et al. (2012).Since then, many papers (e.g., Ruffenach et al. 2015;Scolini et al. 2022) have shown that ME erosion is common during CME propagation.Next, we have added requirement (2) in which unidirectional electrons need to be observed streaming in the same direction because this indicates that reconnection is occurring on the same CME leg, as described by Crooker et al. (2002).Lastly, requirement (3) reinforces that if reconnection is occurring below the Alfvén surface, and is thus truly IC reconnection, it should not have direct in situ signatures of reconnection in IP space.
We note that requirement (1) does not mean that IC reconnection is affecting in general the center or core of the ME only, but that it can start there and work its way outward to fully open the ICME magnetic field.This is even more likely if the ICME field line footpoints are relatively near regions of mixed polarity where the probability of reconnection is high.Thus, requirement (1) ensures that we are observing the ICME during the IC reconnection process; however, it also means that we would be missing ICMEs for which IC reconnection starts at the edges, or ones that have fully opened through IC reconnection.
To simplify efforts in identifying ICMEs that exhibit IC reconnection, we propose focusing on ICMEs that interact with high-speed streams (HSS) as more likely to have undergone IC reconnection.This is because Crooker et al. (2002) suggested that CME IC reconnection may be happening as part of the global circulation process of open magnetic field lines at the Sun, first proposed by Fisk (1996).It was suggested that the circulation is driven by differential rotation of the photosphere in coronal holes and completed in the closed streamer belt through IC reconnection.High-speed solar wind streams emanate from the open field line regions found in coronal holes at the Sun and are one of the major large-scale solar wind structures that CMEs interact with during propagation (Scolini et al. 2022).This interaction likely starts back at the Sun, where the open field lines in coronal holes can IC reconnect with the closed field lines of the CME, while the interaction also continues in IP space in situ as well.We thus propose that the most likely CME events to exhibit signatures of IC reconnection are ones that also interact with coronal holes and HSSs (for examples of such reconnection see Baker et al. 2009 andLugaz et al. 2011).
Given current observational limitations, using the three requirements outlined above allows for a reasonable degree of confidence in distinguishing IC reconnection from IP reconnection.Finally, given our hypothesis that CMEs that interact with the HSS are more likely to have undergone IC reconnection in the corona, we suggest focusing on such a subset of events when trying to identify clear IC reconnection signatures.

Example Events
In the following, we briefly showcase two examples of CME events, one of which displays signatures of IP reconnection, while the other displays signatures of IC and IP reconnection.

IP Reconnection Example
The first CME, which showcases signatures of IP reconnection, was launched from the Sun on 2011 March 16 at 19:12 UT with a second-order speed of ∼740 km s −1 at 20 R S .As can be seen from Figure 2, the IP counterpart of the CME (i.e., the ICME) shock arrived at STEREO-A on March 19 at 11:25 UT, and the ME arrived on March 19 at 23:34 UT and ended by March 21 at 1:30 UT. Figure 2 shows the magnetic field strength and components, as well as the solar wind proton speed, density, temperature, β p , and suprathermal electron pitch angle distribution (PAD) as measured by STEREO-A at this time.For the suprathermal electron PADs, similarly to Scolini et al. (2022), we integrate the fluxes among the six energy channels operating above ∼100 eV, i.e., at 1716.84, 1056.95, 650.70, 400.60, 246.62, and 151.83 eV.At each time step, PADs are normalized to the peak flux observed at that time, in order to have distributions running between 0 and 1 throughout the ICME passage period.
Within the ME (between the second and third bold magenta lines), there is a clear distinction between periods of unidirectional electrons at the front and end of the ME that also coincide with signatures of in situ IP reconnection, and a period of bidirectional electrons where no in situ reconnection signatures are present.The first period of unidirectional electrons at the beginning of the ME from the second bold magenta line to the first dashed line is accompanied by relatively high proton density, temperature, and β p compared to the period directly afterward.The combination of these plasma signatures along with the unidirectional electrons being at the front of the ME indicate that likely IP reconnection, i.e., erosion of the front of the ME, has taken place.This reconnection is most likely occurring between the B N > 0 field in the ME front and the B N < 0 field in the IMF.Immediately following this period, demarcated by the two dashed magenta lines, is the only extended period of bidirectional electrons (lasting ∼9 hr), and coincides with MC-like plasma and magnetic field signatures (except there is a lack of field rotation during this period): low variability in the magnetic field components, decreasing speed profile, low proton density, and lower (although quite variable) proton temperature, as well as β p = 1.
The remaining part of the ME from the second dashed line to the last vertical magenta line, i.e., the ME tail, is characterized by almost entirely unidirectional electrons (with only a short section of bidirectional electrons in the middle) indicating open field lines.These unidirectional electrons are in the opposite direction to the unidirectional electrons seen at the beginning of the ME.Additionally, there are signatures of in situ reconnection in this ME tail region, similar to the front of the ME, including the increased density, temperature, β p , as well as increased variability in the magnetic field compared to the MClike region.We note that both the magnetic field direction and the decreasing speed profile are consistent with the spacecraft still being inside the ME until the last vertical magenta line.Despite the increased fluctuations, on average, B R and B T are consistent from before the second dashed magenta line to after, while B N carries the rotation in the flux rope-like ME structure.Furthermore, the rotation in the field at the last magenta line marks the passage from the ME into the IMF.At the back of the ME, the reconnection/erosion is thus likely occurring between the B N < 0 field in the ME and the B N > 0 field in the IMF.
The fact that the unidirectional electrons are aligned with the magnetic field direction (at pitch angle = 0°) in the front of the ME and are antialigned with the magnetic field (pitch angle = 180°) in the back region of the ME indicates that the IP reconnection observed at the front and back of the ME occurred on different legs of the ICME.It is important to note that the strahl direction did not change during this event, which stayed at 180°throughout.Taken all together, the combination of unidirectional electrons at the front and back of the ME, prolonged bidirectional electrons at the center, as well as in situ reconnection signatures during the unidirectional electrons portions (in opposition to all three criteria for IC reconnection signatures we laid out in Section 2), are strongly suggestive of IP reconnection having taken place between the ICME and the IMF (Figure 1(b)) on opposite legs of the ICME.This IP reconnection opened the field lines at the front and back of the ME, leaving some of the center field lines still attached to the Sun.It is important to note that, based on in situ data at Venus Express and STEREO-A and ENLIL model simulations, this ICME did not interact with any large-scale structure or other transients in the solar wind during propagation from the Sun to STEREO-A (Scolini et al. 2022).Thus, IP reconnection/ erosion at the front and back of the ME must have taken place with the background IMF.

IC Reconnection Example
Next, we showcase a CME that interacted with an HSS and met all our criteria for IC reconnection as laid out in Section 3.1 above.This CME was launched from the Sun on 2012 January 2 15:13 UT with a second-order speed of ∼1100 km s −1 at 20 R S and arrived at STEREO-A on January 5 at 20:40 UT. Figure 3 shows the ICME at STEREO-A, in the same manner as Figure 2 for the previous ICME example above.The arrival of the ICME coincides with the ME as there is no sheath or shock structure present (the speed at the front of the ICME is the same as in the solar wind).The ME can be characterized as fairly pristine with clear MC signatures when looking at the magnetic field and plasma data between the first and second magenta lines (low variability magnetic field along with clear rotation, low proton density, temperature, and β p ).It is thus somewhat unexpected that there are bidirectional electrons only at the front and back of the ME, while the majority of the center of the ME is made up of unidirectional electrons antiparallel to the magnetic field.We attribute this extended unidirectional electrons period in the middle of the ME to IC reconnection given that there are multiple hours of continuous bidirectional electrons before and after this period, making it unlikely that IP reconnection could have occurred in the center of the ME, especially given the lack of in situ reconnection signatures.
On the other hand, the end boundary of the ICME is not clear: from the standpoint of the magnetic field data only, one would put the ME/ICME end somewhere near the dashed magenta line where the magnetic field magnitude returns to the background IMF level, while the plasma parameters indicate an ME end earlier, near the second bold magenta line, where β p becomes consistently >1 and the bidirectional electrons near the end of the ME turn to unidirectional electrons.It is important to note that around the second bold magenta line is also the arrival of an HSS, which can be seen from the speed and density increase.We infer that IP reconnection between the back of the ME and the HSS possibly took place between the bold and dashed magenta lines, causing the unidirectional electrons and the unclear ME rear boundary.
The interaction between the HSS and this ICME deserves a bit more investigation, specifically as it explains the speed profile observed in the ICME.Up until 04:00 UT on January 6, the ICME exhibited a typical decreasing speed profile, indicating expansion of the ME, while at 04:00 UT there is an abrupt speed increase followed by a slightly increasing speed profile until the ME rear.In front of the abrupt speed increase at 04:00 UT, there is a small bump in the density, indicating compression of the otherwise low-density ME plasma.We estimate the minimum time the interaction between the back of the ICME and the HSS must have been taking place, given that the compression propagated through to approximately the center of the ME and did not reach the front yet (and therefore the ICME did not drive a shock).We calculate that the Alfvén speed is 178 km s −1 in the ICME, and the affected ME size is 0.08 au, which yields a minimum interaction time of 19.6 hr.This is a minimum because the ME size is a lower limit given that the structure we observe is already compressed.This estimated 19.6 hr of in situ interaction of the back of the ME and the HSS is relatively short in comparison to the ∼3 days of propagation time from the Sun to STEREO-A, and cannot be the cause of the unidirectional electron flows and therefore the open field lines, especially the ones ahead of the region that was compressed.To check for further evidence of IC reconnection causing the unidirectional electrons in the majority of the ICME center, we looked at STEREO-A EUVI images of the Sun at 195 Å (Figure 4), which shows that there is a clear coronal hole within ∼10°in the latitude of the leg of the posteruptive arcade.This coronal hole, initially localized in the south polar regions, was observed in STEREO-A EUVI movies to be significantly extended toward lower latitudes during the CME eruption, suggesting reconnection with the erupted CME may have taken place in the CME's early propagation phase.Although it is not possible to retrieve information about the magnetic polarity of coronal structures from STEREO-A observations, we tracked the coronal hole a few days before, while it was observed front-sided from Earth.The CHIMERA coronal hole database (Garton et al. 2018) based on SDO observations indicates this coronal hole was characterized by a positive polarity.Unfortunately, we do not have detailed photospheric magnetic field information to conclusively determine the magnetic field direction in the southern leg of the posteruptive arcade.We further note that the in situ orientation of the CME at STEREO-A looks quite different from the posteruptive arcade approximate orientation, making inferences about the coronal configuration from in situ data unreliable.
We note that, although proximity between an active region and a coronal hole does not guarantee IC reconnection, in this case, the fact that the coronal hole opened up toward the active region during the CME eruption and based on the available in situ data at STEREO-A, we infer that the most likely scenario is that the open field lines from the coronal hole IC reconnected with the ICME while still below the Alfvén surface, causing the unidirectional electrons observed in the center of the ME.In this case, this IC reconnection was inside the CME, i.e., field lines in the center of the CME southern leg opened up through IC reconnection but other field lines on the outer edges of the CME leg remained closed at the time when the observations were made.Presumably, this IC reconnection continued to eventually fully open the ICME.Furthermore, the HSS emanating from the coronal hole also interacted with the ICME in situ during propagation between the Sun and STEREO-A, compressing the ICME and also causing the fairly short duration IP reconnection in the rear of the ME, at the ME/HSS interface.

Conclusions
The aim of this paper is to bring to the community's attention the importance of investigating whether a CME has gone through IC reconnection, IP reconnection, or both, in order to understand the duration of its contribution to the heliospheric magnetic flux budget.Those CMEs that fall in the extreme scenario of initially undergoing only IP reconnection within, for example, a benchmark heliospheric distance of 1 au, are the ones to take the longest time to fully open since they then also have to undergo IC reconnection before they no longer contribute magnetic flux to the heliospheric flux budget.On the other extreme, those that are opened up fully by IC reconnection within 1 au will contribute closed magnetic flux for the shortest amount of time.In reality, we expect the majority of CMEs to be undergoing both IC and IP reconnection simultaneously, however, this needs to be tested with large-scale statistical studies.
Assuming that the average ICME flux opening timescale of ∼50 days established by Owens & Crooker (2006) is accurate, it remains to be determined how different CME types contribute to this overall timescale.It is important to note that the Owens & Crooker (2006) estimate of the average CME flux is the least accurate estimate in their calculation of the ICME flux opening timescale, given that it relies on the result of only one study, using constant-α force-free magnetic flux rope fits to 132 CMEs by Lynch et al. (2005).This should be revisited in future studies as more recent CME flux estimates may yield that CMEs contribute quite differently to the total magnetic flux than what was assumed by Owens & Crooker (2006).
Another important area for future investigations is the relationship between a CME's flux opening timescale and the evolution of its complexity.A number of recent studies have investigated the causes and consequences of CME complexity changes during propagation from the Sun to 1 au (e.g., Winslow et al. 2016;Scolini et al. 2021;Winslow et al. 2021;Scolini et al. 2022).Scolini et al. (2022) conducted the first statistical analysis of complexity changes affecting the magnetic structure of CMEs observed by radially aligned spacecraft.They analyzed multi-spacecraft magnetic field measurements along with measurements of solar wind plasma and suprathermal electrons wherever available, for 31 CMEs from Mercury to 1 au between 2008 and 2014.By analyzing this data at the inner and outer spacecraft, Scolini et al. (2022) identified complexity changes that manifested as fundamental alterations or significant reorientations of the structures.They found that the majority of CMEs undergo complexity changes from Mercury to 1 au and that complexity tends to increase with heliocentric distance.The results also showed that the observed complexity changes are likely driven by the interaction of CMEs with one or more large-scale solar wind structures.
One of the major drivers of complexity changes in CMEs is HSSs, which emanate from the open field line regions in coronal holes at the Sun.Scolini et al. (2022) found that CMEs that interact with HSSs in situ are more likely to show complexity change than ones that interact with other large-scale solar wind structures.It is thus possible that the interaction that we see in situ away from the Sun between CMEs and solar wind disturbances, like HSSs, is, in part, a proxy for what is happening at the solar footpoint and in part direct interaction in IP space, due to the CME also interacting with the HSS in situ.
It is currently an open question if there is a relationship between a CME's complexity change and the length of time it contributes to the heliospheric flux budget.It remains to be investigated whether those CMEs that exhibit the highest degree of complexity change from the inner heliosphere to 1 au are also the ones that contribute longest to the flux budget, which is really dependent on whether reconnection (and what type of reconnection) caused the majority of the observed complexity change in the CME structures.It is possible that CMEs that have undergone both types of reconnection, IC and IP, are ones that exhibit the most extreme complexity changes, in which case their contribution would fall in the mid-range of the flux budget contribution timescale τ.Finally, we underscore that by studying CMEs, specifically their interaction with largescale solar wind structures, how frequently they undergo IC versus IP reconnection, magnetic topology changes, etc., we can gain important insights into how CMEs contribute to, and their role in, the heliospheric flux budget.

Figure 1 .
Figure 1.Cartoon showing scenarios (a)-(c), described in the main text, for an ICME.All scenarios eventually result in a zero net change to the heliospheric magnetic flux contribution, but the process and the amount of time it takes to get there differs between the scenarios.The solid circle shows the solar surface and the dashed circle, the location of the Alfvén surface.Selected magnetic field lines are represented by solid black and gray lines, with the arrows marking their polarity.Red arrows mark the direction of propagation of suprathermal electrons along magnetic field lines.The green and blue arrows mark the direction of propagation and circulation pattern of selected field lines, respectively.Magenta stars and red stars mark the locations of IC and IP reconnection, respectively.The cartoon is not to scale.Initial cartoon (panel (a)) adapted from Owens & Crooker (2006), with scenarios (b) and (c) added to this work.

Figure 2 .
Figure 2. Plasma and magnetic field data as measured by STEREO-A for the CME that arrived on 2011 March 19.IPR in the figure stands for IP reconnection.The color bar represents the normalized flux of suprathermal electrons.Vertical solid magenta lines indicate the arrival time of the shock and the arrival and end of the ME, while the dashed lines mark an extended period of bidirectional electron flows and IC-like signatures.

Figure 3 .
Figure 3. Plasma and magnetic field data as measured by STEREO-A for the CME that arrived on 2012 January 5. ICR in the figure stands for IC reconnection while IPR stands for IP reconnection.The color bar represents the normalized flux of suprathermal electrons.Vertical solid magenta lines indicate the arrival and likely end time of the ME, while the dashed line marks a possible extension to the ME time period.Just to the right of the dashed magenta line is the arrival of an HSS as can be seen from the solar wind speed shown in the second panel.

Figure 4 .
Figure 4. STEREO-A EUVI image of the Sun at 195 Å ∼7 hr after the ICME erupted on 2012 January 2. The purple arrow is pointing to the posteruptive arcade, while the red arrow is pointing to the coronal hole nearby.The separation between the southern leg of the arcade and the northern edge of the coronal hole is ∼10°.