Exploring the Properties of the Electron Strahl at 1 AU as an Indicator of the Quality of the Magnetic Connection Between the Earth and the Sun

In this report some properties of the electron strahl at 1 AU are examined to assess the strahl at 272 eV as an indicator of the quality of the magnetic connection of the near-Earth solar wind to the Sun. The absence of a strahl has been taken to represent either a lack of magnetic connection to the corona or the strahl not surviving to 1 AU owing to scattering. Solar-energetic-electron (SEE) events can be used as indicators of good magnetic connection: examination of 216 impulsive SEE events finds that they are all characterized by strong strahls. The strahl intensity at 1 AU is statistically examined for various types of solar-wind plasma: it is found that the strahl is characteristically weak in sector-reversal-region plasma. In sector-reversal-region plasma and other slow wind, temporal changes in the strahl intensity at 1 AU are examined with 64 s resolution measurements and the statistical relationships of strahl changes to simultaneous plasma-property changes are established. The strahl-intensity changes are co-located with current sheets (directional discontinuities) with strong changes in the magnetic-field direction. The strahl-intensity changes at 1 AU are positively correlated with changes in the proton specific entropy, the proton temperature, and the magnetic-field strength; the strahl-intensity changes are anti-correlated with changes in the proton number density, the angle of the magnetic field with respect to the Parker-spiral direction, and the alpha-to-proton number-density ratio. Reductions in the strahl intensity are not consistent with expectations for a simple model of whistler-turbulence scattering. Reductions in the strahl intensity are mildly consistent with expectations for Coulomb scattering, however the strongest-observed plasma-change correlations are unrelated to Coulomb scattering and whistler scattering. The implications of the strahl-intensity-change analysis are that the change in the magnetic-field direction at a strahl change represents a change in the magnetic connection to the corona, resulting in a different strahl intensity and different plasma properties. An outstanding question is: Does an absence of an electron strahl represent a magnetic disconnection from the Sun or a poor strahl source in some region of the corona?


INTRODUCTION
Knowing the magnetic connectivity between the Earth and the Sun is desirable for several reasons: e.g., 1) to gain a global understanding of the heliospheric magnetic structure, (e.g. McComas et al., 1989;Crooker et al., 2002;Crooker and Pagel, 2008;Crooker and Owens, 2012;Lockwood, 2013;Viall and Borovsky, 2020), 2) for understanding solar energetic particle (proton and electron) events and particle transport (Mazur et al., 2000;Chollet and Giacalone, 2011;Trenchi et al., 2013), and 3) for assessing the likelihood that Earth will or will not undergo an energetic-particle event.
One promising method to assess the magnetic connectivity between the near-Earth solar wind and the Sun is to interpret observations of the electron strahl in the near-Earth solar wind. The electron strahl is a beam of magnetic-field-aligned electrons originating from the solar corona that propagate away from the Sun (Feldman et al., 1976;Pilipp et al., 1987;Maksimovic et al., 2005). A robust strahl is a signature of a good magnetic connection to the Sun; an absence of a strahl has been historically interpreted as an indication of either 1) no magnetic connection to the Sun (McComas et al., 1989;Gosling et al., 2005) or 2) a strahl that does not survive from the Sun to the observer (Pagel et al., 2005a;Crooker and Pagel, 2008;Chollet et al., 2010).
In the present study the intensity of the electron strahl at 272 eV is measured. Lin and Kahler (1992) examined a number of events that were judged to be magnetic-disconnection events by an absence of a low-energy strahl and found the presence of higher-energy (2 keV-8.5 keV) strahls, calling into question whether the absence of a lower-energy strahl is an indication of a magnetic disconnection from the Sun. However, Gosling et al., (2005) examined cases of reconnection-exhause magnetic disconnections and found that electron-halo intermixing could give the impression of a higher-energy strahl, even though those magnetic-field lines were definitely disconnected from the Sun (See also the analysis of Crooker and Pagel (2008).).
At a distance of 1 AU from the Sun, the intensity of the electron strahl varies on multiple timescales, with sudden jumps in strahl intensity that are observed to be co-located with strong current sheets (magnetic directional discontinuities) (Gosling et al., 2004a;Borovsky, 2020a,b). Hence, temporal jumps in the strahl intensity are associated with sudden changes in the magnetic-field orientation.
This report explores some properties of the electron strahl that impact the ability to assess the magnetic connection between Earth and the Sun using observations of the strahl in the near-Earth solar wind. In The Electron Strahl and the Types of Solar Wind Plasma the relationship of the strahl intensity to the type of solar-wind plasma is investigated. In Impulsive SEE Events, the Electron Strahl, and the Type of Plasma the intensity of the electron strahl at 1 AU is examined during impulsive solarenergetic-electron (SEE) events, which are times when there must be a good magnetic connection between the Earth and the Sun. In Strahl Analysis sudden changes in the intensity of the electron strahl at 1 AU are statistically examined in relation to sudden changes in other plasma parameters and the statistical results are discussed in relation to ideas about strahl destruction by Coloumb scattering and whistler-turbulence scattering are tested. Discussion: Interpretation of Strahl-Intensity Changes, Assessing the Sun-Earth Connection, and the Future contains discussions of 1) the interpretations of strahl-intensity changes, 2) an assessment of the ability to determine the Sun-Earth magnetic connection, and 3) suggestions for future research.

THE ELECTRON STRAHL AND THE TYPES OF SOLAR WIND PLASMA
Various types of solar-wind plasma are emitted into the heliosphere from various types of regions on the rotating Sun. These various types of plasma have systematically differing parameters at 1 AU, (e.g. proton specific entropy, speed, heavy-ion charge-state ratios, Alfven velocity, etc.), which allows the solar wind to be categorized into the various types of plasmas (cf. Neugebauer et al., 2003Neugebauer et al., , 2016Reisenfeld et al., 2003;Zhao et al., 2009;Xu and Borovsky, 2015;Camporeale et al., 2017;Veselovsky et al., 2018;Li et al., 2020;Amaya et al., 2020;Heidrich-Meisner et al., 2020;Bloch et al., 2020). One characteristic difference between the various types of plasma at 1 AU is the intensity of the electron strahl (Borovsky, 2018). In Figure 1 the hourly averaged intensity of the electron strahl as measured by the SWEPAM instrument (McComas et al., 1998) on the ACE spacecraft at L1 upstream of the Earth is binned for the four types of solar-wind plasma in the Xu and Borovsky (2015) plasma-categorization scheme. I 272 is the base-10 logarithm of the phase-space density f 272 (in units of s 2 cm −5 ) of the electron strahl in the dominant (parallel-to-B or antiparallel-to-B) direction at an energy of 272 eV, as measured by ACE SWEPAM (See Borovsky. (2017) for a discussion of the creation of an hourly averaged index of I 272 .). In Figure 1 the gray dashed curve is the occurrence distribution of the hourly averaged strahl intensity I 272 for all data in the years 1998-2013. The other four curves in Figure 1 are the occurrence distributions of hourly averaged strahl intensity in four types of solar-wind plasma: coronal-hole-origin plasma (red), streamer-belt-origin plasma (green), sector-reversalregion plasma (purple), and ejecta (blue). Ejecta plasma (blue) has a systematically more-intense strahl and sector-reversalregion plasma (purple) has a systematically weaker strahl, with coronal-hole-origin plasma (red) and streamer-belt-origin plasma (green) have more-typical values of the strahl intensity.
Because of the robust strahl intensities in Figure 1, (e.g. greater than ∼ -29.75), it can be assumed that coronal-hole-origin, streamer-belt-origin, and ejecta plasmas at 1 AU are, in general, well connected magnetically to the Sun. This can't be assumed for sector-reversal-region plasmas, which has a range of strahl intensities in Figure 1 that can be quite weak, (e.g. less than -29.75). Two sources of sector-reversal-region plasma are discussed in the literature. The first is disconnection of magnetic field caused by reconnection between open flux on either side of a streamer stalk (Wang et al., 1999;Sanchez-Diaz et al., 2019;Lavraud et al., 2020), resulting in the emission of blobs of plasma in the streamer-stalk region. Disconnections will certainly result in a decreased strahl intensity. The second source is interchange reconnection between open field lines and closed loops of streamers (Wang et al., 2000;Crooker et al., 2004;Rouillard et al., 2020). Individual interchange reconnection events, which change the magnetic connection into loops of different heights and electron temperatures, will almost certainly result in a change in the strahl intensity. Sectorreversal-region plasma contains such features as streamer-stalk blobs and puffs (Wang et al., 2000;Bemporad et al., 2005;Sheeley et al., 2009;Rouillard et al., 2010;Sheeley and Rouillard, 2010;Foullon et al., 2011) and periodic density structures (Viall et al., 2010;Viall and Vourlidas, 2015) that are of interest for their impact on Earth (Kepko and Spence, 2003;Viall et al., 2009;Kepko and Viall, 2019). These plasma structures in the sectorreversal-region plasma can be associated with magnetic disconnections from the Sun (Wang et al., 1999;Kepko et al., 2016). There are also reconnection-disconnection events in the vicinity of the heliospheric current sheet in the sector-reversalregion plasma, (e.g. Gosling et al., 2005;Lavraud et al., 2009Lavraud et al., , 2020Sanchez-Diaz et al., 2019). Based on the weaker strahl, streamerbelt-origin plasma is the most likely solar-wind type to be poorly connected to the Sun.
Another possible indicator of magnetic connection to the Sun is whether or not the magnetic-field in a plasma has a Parkerspiral orientation. Plasma that is steadily emitted from a spot on the Sun will have an approximately Parker-spiral oriented magnetic field (Parker, 1958;Fisk, 2001;Georgieva et al., 2005); plasma that is impulsively emitted, which can include magnetic disconnections, need not have a Parker-spiral-oriented magnetic field. Even for steadily emitted solar wind, there can be underwinding, (e.g. Gosling and Skoug, 2002;Murphy et al., 2002;Riley and Gosling, 2007) or overwinding, (e.g. Smith and Bieber, 1991;Bruno and Bavassano, 1997) of the Parker spiral caused by large-scale compressions and rarefactions, and there are always large fluctuations of the magnetic-field direction about the Parker-spiral direction (Ness and Wilcox, 1966;Forsyth et al., 1996;Burlaga and Ness, 1997;Borovsky, 2010). In Figure 2 the hourly averaged angle between the magnetic-field-line orientation in the solar wind at Earth and the Parker-spiral direction is binned, with the Parker-spiral direction calculated every hour using the hourly averaged speed of the solar wind (This field-line orientation does not account for the sign of B nor does it consider the sign of B relative to the toward or away sector structure.) The OMNI data set (King and Papitashvili, 2005) for the years 1963-2013 was used. In Figure 2 the distribution of coronal-hole-origin values (red curve) is the most Parker-spiral aligned and the distribution of sector-reversal-region values (purple curve) is the least Parker-spiral aligned. Note that owing to fluctuations in the direction of the magnetic field about the mean Parker-spiral direction, the instantaneous magnetic-field direction (and the hourly averaged field direction) is rarely exactly Parker-spiral aligned (Borovsky, 2010). The facts 1) that the magnetic field is less-Parker-spiral oriented in sector-reversal-region plasma and 2) that the strahl intensity is less intense in sector-reversal-region plasma enforce the notion that the strahl intensity and the field orientation can be indicators of good or poor magnetic connection to the Sun. As will be seen in Strahl Analysis, the strahl intensity and the angle of the magnetic field from the Parker spiral are weakly anticorrelated in the solar wind at 1 AU.

IMPULSIVE SEE EVENTS, THE ELECTRON STRAHL, AND THE TYPE OF PLASMA
Impulsive solar energetic electron (SEE) events at 1 AU are associated with solar x-ray flares, (e.g. Kallenrode and Svestka, 1994;Cliver and Ling, 2007) or near-Sun events (Li et al., 2013) and electrons accelerated near the Sun traveling along the solarwind magnetic field out to a measuring spacecraft at 1 AU. If one can assume that impulsive SEE events are good indicators of magnetic connectivity to the Sun, then examining the strahl intensity during the early times in impulsive SEE events vs. the strahl intensity when SEE events are not seen could be a test of the viability of using the strahl intensity as a gauge of magnetic connectivity to the Sun. Good connectivity to the Sun may be a valid assumption for impusive SEE events (cf. Figure 2.3b of Reames (1999)) or it might not be a valid assumption (cf. Figure 6 of Wibberenz and Cane (2006)).
Assuming SEE events are well connected to the Sun at early times, to explore other conditions of good magnetic connection 216 impulsive SEE events from the near-Earth catalog of Wang et al., (2012) are used: specifically, the 216 events in the catalog that had peak electron kinetic energies of 310 keV or higher.
In Figure 3 the distribution of the 216 SEE events vs. time is plotted as the red bars, along with the monthly sunspot number (blue) and the daily averaged F10.7 flux (green). As could be expected, since the SEE events are associated with solar flares, the occurrence of the SEE events is concentrated during solar maximum.
In Figure 4 the occurrence distribution of electron-strahl intensities at Earth during the 216 SEE events is plotted as the red curve using hourly averaged values of the strahl intensities from ACE SWEPAM. The black dashed curve plots the distribution of strahl intensities for the years 1998-2013 and the blue curve plots the distribution for the solar-maximum interval 1998-2004 (which is also plotted in Figure 1). Hence, it is probably not the case that there are SEE events at Earth that are missed because the Earth was not magnetically connected to the Sun: it would appear that the Earth tends to have good magnetic connections during solar maximum. As can be seen in Figure 4 the strahl intensities for the 216 SEE events are robust in comparison with the black distribution for all times during the years 1998-2013. One might think that the electron strahl should be intense when solar energetic electrons are present because they are two energies out of the same electron distribution function, but that is not the case: the strahl is a representation of the coronal electron temperature (Bercic et al., 2020;Boldyrev et al., 2020) and the solar energetic electrons are produced by specific temporal acceleration processes (Kallenrode and Svestka, 1994;Cliver and Ling, 2007;Li et al., 2013). Also, for the early times of impulsive SSE events, the 272 eV electrons of the observed strahl at 1 AU left the Sun more than 4.3 h before the flare occurred.   Using the Xu and Borovsky (2015) categorization scheme, the type of solar-wind plasma that the Earth is in when each of the 216 SEE events were seen is binned as the red bars in Figure 5; also binned is the plasma categorization for the 1998-2004 solar maximum interval (blue bars, right) and for the entire 1963-2017 OMNI2 solar-wind data base (black bars, left). With poor statistics having divided the 216 SEE events into four bins, the occurrence distribution of plasma types for the 216 SEE events (red) is not inconsistent with the occurrence distribution of plasma types for solar maximum (blue): the SEE occurrence distribution is a little higher on ejecta and a little lower on coronal-hole-origin plasma.

STRAHL ANALYSIS
Magnetic disconnections from the Sun have been indicated by heat-flux dropouts (an absence of an electron strahl), although it has been argued that not all heat-flux dropouts are magnetic disconnections (cf. Lin and Kahler, 1992;Pagel et al., 2005a;Crooker and Pagel, 2008;Chollet et al., 2010). It is of interest to interpret whether the presence or absence of an electron strahl at 1 AU indicates the presence or absence of a magnetic connection to the Sun, or whether the absence of a strahl is caused by the scattering of the strahl between the Sun and 1 AU. To inform this, sudden changes in the intensity of the electron strahl at 1 AU are examined and compared with other simultaneous changes to determine whether the strahl-intensity changes at 1 AU might be associated with changes in the amount of strahl scattering. In the present study the focus of the strahl-change analysis will be on sector-reversal-region plasma with its generally weak strahl intensity; changes of strahl intensity in fast solar wind, (i.e. coronal-hole-origin plasma), (e.g. Hammond et al., 1996;Pagel et al., 2005b;Louarn et al., 2009;Borovsky, 2016) where the strahl intensity stays robust (cf. Figure 1), indicating always a magnetic connection to the corona, are not examined since those variations may not provide information about magnetic disconnections (A  future study of the strahl-intensity changes in the coronal-holeorigin solar wind could, however, provide additional information about how to interpret strahl changes.) Using the 64-sec-resolution ACE plasma SWEPAM and magnetic-field MAG (Smith et al., 1998) Figures 6 and 7. The first change, in Figure 6, was a sudden decrease in the strahl intensity at ACE at 1:24 UT on April 4 (Day 94) of 2005. In the top panel the strahl phase space density f 272 at 272 eV is plotted in red, the phase-space density in the opposite direction (anti-strahl) is plotted in blue, and the electron phase-space density at 272 eV perpendicular to the magnetic-field direction is plotted in green. The drop in strahl intensity by a factor of about two is denoted by the vertical black dashed line. In the middle panel of Figure 6 a number of plasma parameters are plotted: the proton number density n p (green), the proton temperature T p (purple), the proton specific entropy S p T p /n p 2/3 (red), the alpha-toproton number-density ratio α/p (orange), and magnetic-field strength B mag (blue). Note that simultaneously for this drop in the strahl intensity there is a drop in the proton specific entropy S p and a drop in the proton temperature T p . In the bottom panel of Figure 6 some information about the direction of the solar-wind magnetic field is plotted: Δθ (red) is the angular change in the magnetic-field direction every 64 s, θ PS 3-D (green) is the angle between the magnetic field and the Parker-spiral direction, and θ PS eq (blue) is the angle between the equatorial projection of the magnetic field and the Parker-spiral direction. A large value of Δθ is an indication of a crossing of a strong current sheet: as can be seen in the plot of Δθ, there is a strong current sheet co-located with the change in the strahl intensity (See also Borovsky (2020a) for a statistical study of the co-locations of strahl-intensity changes with strong current sheets.). Note in the bottom panel of Figure 6 that as the strahl intensity decreases, the two calculated angles θ PS indicate that the solar-wind magnetic field makes a transition from Parker-spiral aligned to not-Parker-spiral aligned. Figure 7 is similar to Figure 6, where an increase in the strahl intensity occurs in the top panel of Figure 7 at 2:54 UT on October 29 (Day 302) of 2005. That increase is marked by a vertical black dashed line. In the middle panel of Figure 7 the increase in the strahl intensity is accompanied by an increase the proton temperature T p (purple) and the proton specific entropy S p (red) and by a decrease in the alpha-to-proton number-density ratio α/p (orange). The bottom panel of Figure 7 indicates the presence of a strong current sheet at the location of the strahl change (the red Δθ curve) and the solar-wind magnetic field makes a transition from a non-Parker-spiral orientation to a more-Parker-spiral orientation.

data at L1, two examples of strahl changes appear in
Two causes of scattering for the electron strahl that have been well explored in the literature are Coulomb scattering (Scudder and Olbert, 1979;Lemons and Feldman, 1983;Boldyrev et al., 2020) and scattering by whistler waves (Gary et al., 1975;Saito and Gary, 2007;Viñas et al., 2010). The different mechanisms can cause scattering of the strahl at different electron energies. The rate of fast-electron angular scattering by Coulomb collisions S Coulomb is proportional to the background number density n of the plasma (cf. eq. (6.4.10) of Krall and Trivelpiece (1973) or Sect.
Using the 64-sec-resolution ACE plasma SWEPAM and magnetic-field MAG data for the year 2005, 528 strong changes in the intensity of the electron strahl at 1 AU were analyzed: 282 of those 528 strahl changes occurred when the solar-wind plasma was categorized as sector-reversal-region plasma and 246 of the strahl changes occurred in wind with v sw < 460 km/s that was categorized as either ejecta or streamerbelt-origin plasma. This list of jumps collected in 2005 is by no means exhaustive. Only 528 jumps were collected owing to the restrictions 1) that the jumps must occur in sector-reversal-region plasma or in the slow wind surrounding sector-reversal-region plasma, 2) a jump must represent an increase or a decrease in the strahl intensity that is a change in the intensity of about 50% or greater in the timescale of 1 or two data points, 3) that there must be a clear persistence in the strahl intensity for a few minutes both before and after the jump, and 4) there must be strahl and plasma measurements free of nearby data dropouts. This latter restriction was the strongest because validated ACE SWEPAM protonplasma measurements are typically absent when the solar-wind speed goes very low, as it tends to do in sector-reversal-region plasma. The statistical analysis of the 528 strahl-intensity changes from the year 2005 is summarized in Table 1 and graphically represented in Figure 8.
For the strong changes in the intensity of the electron strahl, attention was paid to the sign of simultaneous changes in the magnetic-field strength B mag , the proton number density n p , the proton temperature T p , the proton specific entropy S p T p /n p 2/3 , the alpha-to-proton number-density ratio α/p, and the change in the angle θ PS between the magnetic-field orientation and the Parker-spiral direction. A change in each of the parameters was only recorded 1) if the parameter exhibited a simultaneous shift (jump) in its magnitude and 2) if the shift change was larger than the fluctuation levels of that parameter prior to and after the change. A change in θ PS was only recorded if the field direction strongly changed from an orientation that would definitely be categorized as Parker-spiral-oriented to an orientation that would definitely be categorized as not-Parker-spiral-oriented (a positive change) or if the direction strongly changed from definitely not-Parker-spiral-oriented to definitely Parker-spiral-oriented (a negative change) (These are typically angular changes by greater than 45 o ). For all 528 changes in the strahl intensity, the statistics of simultaneous changes in those other quantities are collected into Table 1. The first three data columns of Table 1 contain the fraction of time that the change was in the same direction as the strahl-intensity change, (i.e. both simultaneously increasing or both simultaneously decreasing), the fraction of time that the changes were in the opposite directions, and the fraction of time that there was a change in the strahl intensity but no change in the other quantity that was larger than the noise level in the measurements. Each set of three rows in Table 1 represents the statistics for all of the 528 strahl changes, the statistics for the 282 strahl changes in sector-reversal-region plasma, and the statistics for the 246 strahl changes in other slow solar-wind types. Note for each variable that the statistical numbers in Table 1 are similar for each of the three rows: the similarity in the statistics of the 282 sector-reversal-region plasma strahl changes and of the 246 other strahl changes indicates that the statistical results are robust since similar values are obtained for two independent sets of events. For "All 528" rows of Table 1, the first three columns are graphically represented in Figure 8, with green corresponding to changes of the same sign (correlation), red corresponding to changes of the opposite sign (anti-correlation), and gray representing no clear changes observed. The second from the last column of Table 1 is the fraction of strahl-change events that had observed changes in the other quantity of interest. In Table 1 the strongest connections with strahl-intensity changes are for the variables S p and T p , with 58% and 56% of the strahl changes being accompanied by changes in these two variables, respectively. Note that only 35.6% of the strahl changes have B mag changes accompanying them; further, since the B mag measurements in the ACE 64-sec data set have very low noise, it is easier to find a B mag change if it occurs than it is with the other plasma variables. Still only 35.6% of the strahl-intensity changes had B mag changes: hence the connection of B mag changes to strahl changes is considerably weaker than the connection of other plasma variables to strahl changes. Note also that changes in the angle θ PS between the magnetic-field orientation and the Parkerspiral direction are only counted as nonzero if the angle change is very strong, (e.g. going between a very low angle to something greater than 45 o or vice versa); hence, in reality the connection of strahl-intensity changes to the transition between Parker-spiral aligned and not Parker-spiral aligned is probably greater than the ∼31 o recorded in Table 1.
The final column of Table 1 contains the ratio of the number of changes that were of the same sign as the strahl-intensity change to the number of changes that were of the opposite sign as the strahl-intensity change. Changes in the strahl-intensity were positively correlated with changes in S p , T p , and B mag and changes in the strahl intensity were anti-correlated with changes in n p , α/p, and θ PS . The strongest connections to the strahl change were for S p and T p . For all of the 528 strahl changes, S p changes that were of the same sign as the strahl-intensity changes were 4.47 times as likely to be found as S p changes that were of the opposite sign as the strahl change. Hence, same-sign changes are FIGURE 8 | For all 528 strahl-intensity changes examined, this is a graphic representation of the data of Table 1 showing the frequency that a variable change was the same sign as the strahl-intensity change (green) and the frequency that a variable change was the opposite sign to the strahlintensity change (red). Gray represents the per cent of the 528 strahl-intensity changes wherein no substantial change in the other variable was observed.
Frontiers in Astronomy and Space Sciences | www.frontiersin.org March 2021 | Volume 8 | Article 646443 greatly preferred. For T p that ratio in Table 1 is 3.20 to 1. B mag changes were 3.0 times as likely to be of the same sign of the strahl-intensity changes than to be of the opposite sign, but B mag changes were only observed for 35.6% of the strahl changes. Overall, changes in the alpha-to-proton number-density ratio α/p are poorly connected to strahl-intensity changes, with only 29.3% of the strahl changes having clearly identified changes in α/p, and the number of changes of α/p that were of the same sign as the strahl changes was about equal to the number of α/p changes that were of the opposite sign.
For changes in the strahl intensity caused by changes in the amount of whistler-turbulence scattering of the strahl (with the strength of the scattering going approximately as S whistler ∝ B 2 / n 1/2 ), one would expect the strahl intensity to increase when B mag decreases and/or when n p increases: however, Table 1 indicates that the opposite tends to occur for both B mag and n p .
For changes in the strahl intensity caused by changes in the amount of Coulomb scattering or in the amount of kinetic-Alfvenwave turbulence scattering (with S Coulomb ∝ n and with S kineticAlfven ∝ n), one would expect the strahl intensity to increase when the number density n p decreases, which is seen in Table 1 strahl-change association between the strahl intensity and n p . However, n p changes are only seen for 43.0% of the strahl-intensity changes and the changes with T p and with S p are stronger than the changes with n p . Table 1 yields weak support for strahl scattering by Coulomb collisions or by kinetic Alfven waves.
In the associations of Table 1 there is modest support for the notion that transfers from Parker-spiral-oriented plasma to non-Parker-spiral-oriented plasma result in a decrease in the intensity of the strahl, and that transfers from non-Parker-spiral-oriented plasma to Parker-spiral-oriented plasma result in an increase in the intensity of the strahl.
Note that the relations between changes in the strahl intensity at 1 AU and changes in the plasma properties at 1 AU are examined via Table 1 and interpretations are made; however, the changes across these same strahl-intensity boundaries closer to the Sun than 1 AU may differ in nature from the changes observed at 1 AU across the boundaries.
Further information about the strahl intensity is provided by Tables 2 and 3, which contain the Pearson linear correlation coefficients between the hourly averages of the logarithm of the strahl intensity I 272 Log 10 (f 272 ) at Earth and hourly averages of various solar-wind parameters at Earth. The correlations of I 272 with solar-wind parameters listed in Tables 2 and 3 are also graphically represented in Figure 9. Tables 2 and 3 also provide information about the intercorrelations among the solar-wind variables. Note that the logarithms of some variables are used in the correlations: for some variables (e.g. n p , S p , T p , and B mag ) this keeps outlier values from strongly affecting the correlation coefficients and other variables are ratios (e.g. C 6+ /C 4+ , C 6+ / C 5+ , O 7+ /O 6+ , and Fe/O) and using the logarithm of the ratio gives more weight in the correlations to extremely small values of the ratio; in other words, the logarithms of these variables are closer to Gaussian distributed. Table 2 pertains to all solar-wind data and Table 3 pertains to times when the solar wind is categorized as sector-reversal-region plasma. The strahlcorrelation information of Tables 2 and 3 is related to, but not exactly the same as, the information in Table 1. The information of Table 1 addresses the question: when the strahl-intensity changes, does a particular plasma quantity X make a change in the same direction? The information of Tables 2 and 3 addresses the question: how well can the value of I 272 be predicted if there is a knowledge of the value of the plasma quantity X? Tables 2 and 3 also address the question: are large values of X related to large values of I 272 and are small values of X related to small values of I 272 ? Tables 2 and 3 utilize hourly averaged values of the electron strahl from ACE SWEPAM, hourly averaged values of the solar-wind plasma and field parameters from OMNI2, and hourly averaged heavy-ion measurements from ACE SWICS (Gloeckler et al., 1998)   amplitude of the vector magnetic-field fluctuations in each hour of data and δB vec /B mag is the amplitude of the wiggle angle (in radians) of the solar-wind magnetic-field vector during each hour. In Tables 2 and 3 the angle θ PS between the magnetic-field direction and the Parker-spiral direction is calculated two ways: 1) the direction of the equatorial projection of the magnetic field from the Parker-spiral direction and 2) the full 3-D direction of the field with respect to the Parker-spiral direction. The latter includes the B z (or B n ) component of the field. For the sake of correlation coefficients it does not matter, but the logarithms are base-10 logarithms. The statistical noise in the correlation coefficients of Tables 2 and 3 is very low. For N points correlated, the statistical noise level on the correlation coefficient is 2/(N+1) 1/2 (Beyer, 1966;Bendat and Piersol, 1971).
In Table 2 there are N 127,130 data points for I 272 yielding a statistical noise level of ±0.006 for the correlation coefficients and in Table 3 there are N 25,569 data points for I 272 yielding a statistical noise level of ±0.013 for the correlation coefficients.
Between the all-solar-wind Table 2 and the sector-reversalregion-plasma Table 3 there are often substantial variations of the correlation coefficients between solar-wind variables. In the all-solar-wind correlations of Table 2, many of the correlations and anti-correlations are set up 1) by largescale compressions and rarefactions of the solar-wind plasma owing to large variations in the solar-wind speed and 2) by solar-rotation-driven sequential switching between plasma types that have systematic differences in their parameters (cf. Borovsky, 2018). In the sector-reversalregion plasma correlations of Table 3, neither of those two mechanisms operate since 1) the range of sector-reversalregion-plasma velocities is quite limited and 2) there is only one type of solar-wind plasma. In general, since the data used in Table 3 is a subset of the data used in Table 2, and since that subset is chosen by restricting the range of some of the solarwind parameters, the correlation coefficients in Table 3 are expected to be of a lower magnitude than the coefficients in Table 2. Noticeable correlations with I 272 that are actually higher in the sector-reversal-region-plasma Table 3 than in the all-wind Table 2 are the correlations of I 272 with Log (n p ), with v sw , and with Log (O 7+ /O 6+ ) (see also Figure 9).
In Table 3 the strongest correlations of I 272 are with Log (B mag ). If the field-aligned flux of the electron strahl is conserved, then a positive correlation between I 272 and B mag is expected, (e.g. in Tables 1-3 and Figure 9); this is very clearly seen in CIR compressions and trailing-edge rarefactions where the magneticfield lines are squeezed together or expanded apart and the strahlintensity pattern tracks the magnetic-field-strength pattern Borovsky, 2016). The next strongest I 272 correlations in Table 3 are with Log (0 7+ /O 6+ ), δB vec , and Log (T p ) (with δB vec being strongly correlated with B mag ). Comparing  Table 2) and the purple bars are for sectorreversal-region plasma ( Table 3).
Frontiers in Astronomy and Space Sciences | www.frontiersin.org March 2021 | Volume 8 | Article 646443 9 the I 272 correlations of Table 3 with the strahl-change findings of Table 1, the correlations of Table 3 support the positive correlations of strahl-intensity changes with changes in S p , T p , and B mag and the correlations of Table 3 support the anticorrelations of strahl-intensity changes with changes in θ PS . The positive correlations of I 272 with n p and α/p in Table 3 are counter to Table 1 findings of anti-correlations between changes in the strahl intensity and changes in n p and α/p. Of course, in using the correlations of Table 3 as support or not support of the strahl-change trends of Table 1, it must be realized that the factors that drive the large-scale correlation with strahl intensity ( Table 3) may not be the same factors that drive the sudden ∼50% strahl-intensity changes of Table 1.

DISCUSSION: INTERPRETATION OF STRAHL-INTENSITY CHANGES, ASSESSING THE SUN-EARTH CONNECTION, AND THE FUTURE
Being aware that different mechanisms can act on different energy electrons in the strahl, examining 272 eV strahlintensity changes in sector-reversal-region plasma and other slow solar wind ( Table 1) found that increases or decreases of the strahl intensity are positively correlated with S p , T p , and B mag increases or decreases and that strahl-intensity increases or decreases are anti-correlated with n p , θ PS , and α/p increases or decreases. Relevant to the B mag and α/p anti-correlations, note that 1) most (64.4%) strahl-intensity changes do not show B mag changes and 2) the association of α/p changes with strahl changes is weak.
The results of the 272 eV strahl-change analysis are inconsistent with a constant-amplitude model for whistlerturbulence scattering of the strahl as the reason for the strahlintensity changes; for whistler scattering the changes in the strahl intensity should be correlated with n p changes and anti-correlated with B mag changes and the opposite correlations are observed. The 272 eV strahl-change analysis weakly supports Coulomb scattering and/or kinetic-Alfven-wave scattering as the cause of strahl-intensity changes; the support is only weak because the expected strahl-intensity-change anti-correlation with n p is not the strongest association with strahl changes (Further ,  Table 3 solar-wind correlations show that the strahl intensity positively correlates with n p .). The strongest connection of strahlintensity changes is with changes in T p and S p , which are not involved in the Coulomb-scatting, whistler-scattering, or kinetic-Alfven-wave scattering scenarios.
The strongest associations with strahl-intensity changes are the positive correlations with changes in S p and T p ( Table 1). The factors that govern the values of S p and T p in the solar wind are not well understood. The value of the proton specific entropy S p of the solar wind at 1 AU is a strong indicator of the plasma type (cf. Figure 3 of Xu and Borovsky (2015)). Excluding ejecta plasma, the proton temperature T p of the solar wind at 1 AU is strongly associated with v sw (cf. Figure 1 of Lopez and Freeman (1986), Figure 12 of Borovsky and Steinberg (2006), Figures. 4 and 5 of Elliott et al., (2012)). The proton specific entropy S p is also strongly positively correlated with v sw (cf . Tables 2 and 3).
In the slower solar wind (such as sector-reversal-region plasma) it is well known that the observed solar-wind velocity v sw systematically increases with distance from the Sun beyond 0.3 AU (Schwenn et al., 1981;Arya and Freeman, 1991): this could be the result of a hot-electron-driven interplanetary ambipolar electric potential accelerating the solar-wind protons away from the Sun (Jockers, 1970;Lemaire, 2010;Pierrard, 2012;Borovsky and Gary, 2014). The strahl-change ( Table 1) and strahl-correlation ( Table 3) data indicates that weaker sector-reversal-region-plasma strahls are related to weaker proton temperatures and weaker proton specific entropies and the correlation data indicates that weaker strahls are associated with slower solar wind at 1 AU. These correlations could be consistent with weaker electron-driven interplanetary electric field owing to poor magnetic connection to the corona or to connections that produce poor strahl. Note however that the correlation coefficients in Table 3 are weak, indicating that strahl intensity is not the dominant driver of the proton values.
In the all-solar-wind data set ( Table 2) S p is strongly anticorrelated with the heavy-ion charge state ratios C 6+ /C 4+ , C 6+ / C 5+ , and O 7+ /O 6+ , but in sector-reversal-region plasma ( Table 3) these correlations become complicated with S p being anticorrelated with C 6+ /C 4+ and C 6+ /C 5+ and positively correlated with O 7+ /O 6+ . The oxygen-charge-state relation to the carboncharge states differs in sector-reversal-region plasma (and ejecta) from its relation in coronal-hole-origin plasma and streamerbelt-origin plasma (cf. Figures. 10 and 12 of Xu and Borovsky (2015) and Figure 1 of Zhao et al., (2016)); Xu and Borovsky (2015) speculated that this carbon-oxygen charge-state relation is an indicator of impulsive vs. steady emission of plasma from the corona, with sector-reversal-region plasma being impulsive at times.
The strahl-change analysis also finds an anti-correlation between changes in the strahl intensity and changes in the angle θ PS of the magnetic field from the Parker-spiral direction: this is consistent with stronger strahl in Parkerspiral plasma (continuously emitted with open magnetic flux from the corona) vs. non-Parker-spiral plasma (impulsively emitted, perhaps with magnetic disconnections). There may, however, be magnetic-pathlength differences between Parkerspiral fields and non-Parker-spiral fields that might also be playing a role in the 1-AU strahl intensity.
Examining the sudden changes in the intensity of the electron strahl at 1 AU accompanied by sudden changes in the magnetic-field direction, Gosling et al., (2004A,B) speculated that abrupt changes in the strahl intensity are the manifestations of abrupt changes in the mapping of the solar-wind magnetic field back to the corona. In the strahl-change statistics of Table 1, strong changes in the field direction from Parker-spiral oriented to non-Parker-spiral oriented could account for ∼25% of the strahl changes. This change in connection to the corona is also supported by the plasma-property changes found to accompany strahl-intensity changes ( Table 1) (However in Table 1 the weakest connection of strahl change is with α/p, which should change with magnetic connection to the corona.) Further, this change-in-magnetic-connection picture is supported by the above-the-corona MHD simulations of Burkholder et al., (2019) where current sheets in the plasma represent topological changes in the magnetic mapping back to the photosphere.
Sector-reversal-region plasma at 1 AU is characterized by a wide range of low strahl intensities and by sudden changes in the strahl intensity. Analysis of the strahl-intensity changes at 1 AU imply that the changes in the strahl intensity are caused by changes in the magnetic connection to the corona. When the strahl-intensities change to low values a question is: Which low values represent a lack of magnetic connection to the Sun and which low values are caused by something else? A related question is: Why is the strahl intensity so low if it is still magnetically connected to the corona?
Analysis of strahl intensity during impulsive SEE events was used to test the idea that strahl presence or absence could be used to assess the magnetic connection to the Sun. This test was based on the assumption that SEE events at Earth can only occur when the Earth is well connected magnetically to the Sun. The SEE test was not helpful in making the assessment: SEE event occur during solar maximum and the analysis found that the strahl is almost always strong during solar maximum.
To assess the quality of the magnetic connection between the near-Earth solar wind and the Sun, three tools have been explored: 1) using the strahl intensity, 2) using the orientation θ PS of the solar-wind magnetic field with respect to the Parkerspiral direction, and 3) using the type of solar-wind plasma. Using the strahl intensity is the most promising, although questions remain when the strahl intensity at 1 AU is low: 1) is the magnetic field disconnected from the Sun, 2) is the magnetic field connected to a region of the corona that is producing poor strahl, or 3) has the strahl been destroyed between the Sun and 1 AU? Using the magnetic-field orientation θ PS , along with an observation of the strahl intensity, provides more indication of whether or not the magnetic field is disconnected from the Sun. Using the plasma categorization "sector-reversalregion plasma" (with the categorization made using only proton measurements and the magnetic-field strength (Xu and Borovsky, 2015)) gives an indication of generally weak and intermittent strahl and the probability of an in-general poor or intermittent magnetic connection to the Sun.
Five suggestions are given for future research, mostly focused on the changes in strahl-intensity. 1) An examination is needed of the connection between strahl-intensity changes and the heavyion charge-state ratios of the solar-wind plasma. Such information is important in determining the nature of the change in the magnetic connection into the corona that may be occurring when there is a change in the strahl intensity and a change in the magnetic-field orientation. Such an examination has been recently enabled by the heavy-ion measurements onboard Solar Orbiter with ≤30-s time resolution (Owen et al., 2020), measurements that are an order of magnitude faster than on previous solar-wind missions. 2) Examination of strahl changes on spacecraft closer to the Sun is important for a better determination of the interpretation of strahl-intensity changes. An analysis with Parker Solar Probe in particular will be helpful, especially after a substantial data base is collected. 3) Often at 1 AU a sudden change is seen in the intensity of the antistrahl: this change can be simultaneous with a change in the strahl or it can occur without a change in the strahl (An example of this can be seen at 3.37 UT in the blue curve the top panel of Figure 7.) A statistical examination of anti-strahl intensity changes might provide insight into the physics of strahl changes. It is also a method of exploring the magnetic topology beyond 1 AU. 4) The connection of strahl-intensity changes to whistler scattering made in the present study are based on a model of whistler scattering in the heliosphere that does not account for factors that could control the whistler-turbulence amplitude in the solar wind. Improvements in the prediction of the solar-wind parameters that control the amplitude of whistler turbulence in the solar wind and the resulting electron scattering are needed for an improved assessment of the role of whistlers in the observed strahl-intensity changes. 5) Another possible reason why a strahl may not be detected at 1 AU is because of plasma-wave instabilities that may have disrupted the strahl, (e.g. Gary and Saito, 2007;Kuzichev et al., 2019;Lopez et al., 2019;Vasko et al., 2019;Versharen et al., 2019;Jeong et al., 2020;Micera et al., 2020). Parameterization of instability thresholds is needed and then a matching of strahlchange locations with plasma-parameter changes is needed to test the instability possibility.

DATA AVAILABILITY STATEMENT
Publicly available datasets were analyzed in this study. This data can be found here: http://www.srl.caltech.edu/ace/ASC/.

AUTHOR CONTRIBUTIONS
The author confirms being the sole contributor of this work and has approved it for publication.

FUNDING
This work was supported by the NSF SHINE program via grant AGS-1723416, by the NASA Heliophysics Guest Investigator Program via award NNX17AB71G, by the NSF GEM Program via grant AGS-2027569, and by the NASA Heliophysics LWS program via award NNX16AB75G.