THE OXYGEN CHARGE-STATE RATIO AS AN INDICATOR OF FOOTPOINT FIELD STRENGTH IN THE SOURCE REGIONS OF THE SOLAR WIND

In comparison to high-speed (≳500 km s⁻¹) solar wind from coronal holes, low-speed wind is characterized by greater temporal and spatial variability, higher ion charge-state ratios/freeze-in temperatures, greater enrichment in elements of low first-ionization potential (FIP), and helium abundances that increase from values much smaller than in the fast wind at sunspot minimum to comparable values at sunspot maximum. (For a recent comprehensive review of this topic, see Abbo et al. 2016.) These marked differences have led to the prevailing paradigm that the slow solar wind originates not from coronal holes, but from closed loops rooted inside the neighboring coronal streamers. An alternative scenario is that both fast wind and the bulk of the slow wind come from coronal holes/open-field regions, with the speed depending on the rate of flux-tube expansion, which determines the height of the energy deposition.

The ionic composition of the solar wind is generally assumed to be conserved during propagation from the corona to 1 au, and is sometimes used instead of the speed itself to distinguish different types of wind and to infer their source regions. Based on measurements of the oxygen charge-state ratio made during 1998–2008 with the Solar Wind Ion Composition Spectrometer (SWICS) on the Advanced Composition Explorer (ACE), Zhao et al. (2009) took O⁷⁺/O⁶⁺ = 0.145 as the threshold value separating coronal hole from non-coronal hole or streamer wind. As shown by Crooker & McPherron (2012), who applied a superposed epoch analysis to 258 stream interfaces identified in ACE data during 1998–2009, 0.15 also represents the mean value of the O⁷⁺/O⁶⁺ ratio at the (zero epoch) midpoint of the interface between fast and slow wind.

During the last solar minimum (here taken to extend from the beginning of 2007 to the end of 2009), the solar wind charge-state ratios, as well as the helium and heavy ion abundances, underwent a steep decrease, suggesting a corresponding decrease in the coronal temperatures (see, e.g., Kasper et al. 2012; Lepri et al. 2013; Zhao et al. 2014). Retaining their O⁷⁺/O⁶⁺ = 0.145 criterion for separating coronal hole from non-coronal hole wind, Zhao et al. (2014) attributed the solar cycle changes in the O⁷⁺/O⁶⁺ ratio to changes in the morphology (tilt and waviness) of the heliospheric current sheet (HCS).

In this paper, we point out that the oxygen charge-state ratio, unlike the wind speed itself, is a continuously varying function of the footpoint field strength, and we show that the large systematic decrease in the O⁷⁺/O⁶⁺ values during 2007–2009 closely reflects the enormous weakening of the photospheric field at that time. These results call into question the use of charge-state ratios to distinguish coronal hole from streamer wind.

As in previous studies (e.g., Wang & Sheeley 2003; Ko et al. 2014; Owens et al. 2014; Fu et al. 2015), we locate the footpoint areas of the near-Earth solar wind by applying a potential-field source-surface (PFSS) extrapolation to photospheric field measurements. This procedure maps all of the wind back to open-field regions/coronal holes, and does not take into account dynamical processes (such as interchange reconnection) that may occur at the interfaces between open and closed field regions. Additional uncertainties are introduced by the neglect of sheet currents in the outer corona and by the lack of reliable polar-field measurements, which may result in the misidentification of source regions especially near solar minimum. On the whole, however, the model reproduces surprisingly well the interplanetary sector structure and the observed configuration of coronal holes throughout the solar cycle (see, e.g., Figure 2 in Wang et al. 1996). We therefore expect the PFSS-derived footpoint locations and field strengths to be valid on a statistically averaged basis.

Let r denote heliocentric distance, L heliographic latitude, and ϕ Carrington longitude. In our version of the PFSS model, the magnetic field ${\boldsymbol{B}}$ remains current-free from the coronal base to r = R_ss = 2.5 R_⊙, at and beyond which it is constrained to be radial. At the inner boundary, B_r is matched to the photospheric field, assumed to be radially oriented at the depth where it is measured. The magnetograph data are in the form of 27.3 day synoptic maps from the Mount Wilson Observatory (MWO) and the Wilcox Solar Observatory (WSO), which have a resolution of the order of 5° in longitude. The MWO and WSO line-of-sight measurements are corrected for the saturation of the Fe i 525.0 nm line profile by multiplying by the latitude-dependent factor $(4.5\mbox{--}2.5{\sin }^{2}L)$, and are deprojected by dividing by $\cos L$ (see Wang & Sheeley 1995). An arithmetic average is then taken of both data sets. The footpoint $({R}_{\odot },{L}_{0},{\phi }_{0})$ of the field line that intersects the spacecraft is found by tracing inward from 1 au, allowing for the longitude shift due to solar rotation during the wind propagation time (taken to be inversely proportional to the measured proton velocity).

The O⁷⁺/O⁶⁺ measurements are from the ACE/SWICS 1.1 database,¹ which covers the period from 1998 February to 2011 August, spanning 180 complete Carrington rotations (CR 1933–2112). For consistency with the spatial/temporal resolution of the coronal field extrapolations, we form 8 hr averages from the hourly O⁷⁺/O⁶⁺ ratios, and interpolate to obtain values corresponding to every 5° of source-surface longitude. We omit intervals of very high O⁷⁺/O⁶⁺ (≳1) that are flagged as being associated with coronal mass ejections in the SWICS database. Corresponding 8 hr averages of the proton bulk speed v_p, the proton density n_p, and the radial component of the interplanetary magnetic field (IMF) are computed from hourly values extracted from the OMNIWeb database,² which includes observations from Wind as well as ACE.

We remark that the SWICS 1.1 data set provides measurements of other composition parameters, including C⁶⁺/C⁵⁺, which behaves very much like O⁷⁺/O⁶⁺, and Fe/O, which is an indicator of low-FIP enrichment. We focus here on O⁷⁺/O⁶⁺ because it is the most widely used of the available parameters; most of our results will also apply to C⁶⁺/C⁵⁺ and Fe/O.

To indicate quantities evaluated at the coronal base, at the source surface, and near Earth, we employ the subscripts "0," "ss," and "E," respectively. Here, the "coronal base" is defined to lie above the chromospheric–coronal transition region, so that radiative losses can be neglected. Since we are using low-resolution magnetograph data (representing an average of the photospheric field over approximately one or two supergranules), the field strength B₀ at the coronal base may be taken to be the same (by flux conservation) as that measured at the photosphere. For each Earth-directed flux tube, we also calculate the source-surface field strength, $| {B}_{\mathrm{ss}}|$, and the factor by which the flux tube expands in solid angle between the coronal base and the source surface:

$$\begin{eqnarray}&&{f}_{\mathrm{ss}}={\left(\displaystyle \frac{{R}_{\odot }}{{R}_{\mathrm{ss}}}\right)}^{2}\displaystyle \frac{{B}_{0}}{| {B}_{\mathrm{ss}}| }.\end{eqnarray} \tag{ 1 }$$

From conservation of mass along a flux tube, we may derive the proton-flux density at the coronal base as

$$\begin{eqnarray}&&{n}_{0}{v}_{0}=\left(\displaystyle \frac{{B}_{0}}{{B}_{{\rm{E}}}}\right){n}_{{\rm{E}}}{v}_{{\rm{E}}},\end{eqnarray} \tag{ 2 }$$

where n_E, v_E, and B_E are given by the OMNI measurements. Denoting by F_w the nongravitational contribution to the total energy-flux density of the solar wind, we also have from energy conservation:

$$\begin{eqnarray}&&\displaystyle \frac{{F}_{{\rm{w}}0}-{\rho }_{0}{v}_{0}({GM}/{R}_{\odot })}{{B}_{0}}\simeq \displaystyle \frac{{F}_{\mathrm{wE}}}{{B}_{{\rm{E}}}}\simeq \displaystyle \frac{{\rho }_{{\rm{E}}}{v}_{{\rm{E}}}^{3}/2}{{B}_{{\rm{E}}}},\end{eqnarray} \tag{ 3 }$$

where $\rho \simeq {n}_{{\rm{p}}}{m}_{{\rm{p}}}$ is the mass density and we have used the fact that the bulk kinetic energy provides the main contribution to F_w at 1 au. The (nongravitational) energy-flux density at the coronal base is then given by

$$\begin{eqnarray}&&{F}_{{\rm{w}}0}\simeq {\rho }_{0}{v}_{0}\left(\displaystyle \frac{{{GM}}_{\odot }}{{R}_{\odot }}+\displaystyle \frac{1}{2}{v}_{{\rm{E}}}^{2}\right).\end{eqnarray} \tag{ 4 }$$

The scatter plots in Figure 1 show the relationship between the O⁷⁺/O⁶⁺ ratio and (a) the proton bulk velocity at Earth, v_E; (b) the expansion factor at the source surface, f_ss; (c) the field strength at the coronal base, B₀; (d) the source-surface field strength, $| {B}_{\mathrm{ss}}| ;$ (e) the proton-flux density at the coronal base, ${n}_{0}{v}_{0};$ and (f) the energy-flux density at the coronal base (excluding the gravitational potential energy), F_w0. Here, a data point is plotted for every 5° of Carrington longitude, with the blue points representing the period 1998–2004 (corresponding to the maximum and early declining phases of cycle 23), and the red points representing the minimum period of 2007–2009. The transitional interval 2005–2006 has been omitted in order to emphasize the difference between the maximum and minimum periods.

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Considering first Figure 1(a), we see that the O⁷⁺/O⁶⁺ ratio decreases monotonically with increasing v_E both during 1998–2004 and during 2007–2009, but the solar minimum points are shifted systematically downward. Thus, for a given wind speed, the corresponding value of O⁷⁺/O⁶⁺ is a factor of ∼2 smaller during 2007–2009 than during 1998–2004. The median value of O⁷⁺/O⁶⁺ is 0.147 during 1998–2004, but only 0.062 during 2007–2009. It is noteworthy that almost all of the solar minimum wind lies below the O⁷⁺/O⁶⁺ = 0.145 cutoff (marked by a horizontal line) that separates coronal hole from streamer wind, according to Zhao et al. (2009). This would imply that most of the slow wind, as well as the fast wind, comes from coronal holes during 2007–2009.

Figure 1(b) shows that the O⁷⁺/O⁶⁺ ratio increases with increasing expansion factor. Again, a systematic downward shift of the O⁷⁺/O⁶⁺ values is seen in 2007–2009, as expected from the fact that the abscissas of Figures 1(a) and 1(b), v_E and f_ss, are (inversely) correlated with each other (see, e.g., Wang & Sheeley 1990; Cohen 2015; Poduval 2016).

Figure 1(c) shows that the O⁷⁺/O⁶⁺ ratio tends to increase monotonically with the footpoint field strength, with a striking separation seen between the 1998–2004 (blue) and 2007–2009 (red) domains of the plot. The median value of B₀ during 1998–2004 is 20.7 G, as compared with only 2.6 G during 2007–2009; the factor of 7.8 decrease in $\langle {B}_{0}\rangle$ corresponds to a factor of 2.4 decrease in $\langle {{\rm{O}}}^{7+}/{{\rm{O}}}^{6+}\rangle$. The large vertical spread of the points reflects the wide range of wind speeds, and hence of O⁷⁺/O⁶⁺, associated with a given value of B₀.

As expected, the source surface field was also systematically weaker during 2007–2009 than during 1998–2004 (Figure 1(d)), with the median strengths differing by a factor of 5.7. During each period, the O⁷⁺/O⁶⁺ ratio tends to increase with decreasing $| {B}_{\mathrm{ss}}|$. On the other hand, there is no dense clustering of high-O⁷⁺/O⁶⁺ points toward the left (low-$| {B}_{\mathrm{ss}}|$) edge of the scatter plot, as might be expected if such points were closely associated with the streamer belt/HCS.

Figures 1(e) and (f) show that O⁷⁺/O⁶⁺ tends to increase with the proton-flux density and the energy-flux density at the coronal base, with the median values of ${n}_{0}{v}_{0}$ and F_w0 both being a factor of ∼4 smaller during 2007–2009 than during 1998–2004. The similarity between the two plots follows from the fact that ${F}_{{\rm{w}}0}\propto {n}_{0}{v}_{0}$ (Equation (4)).

In Figures 2(a)–(d), we display scatter plots of v_E versus O⁷⁺/O⁶⁺, f_ss, B₀, and $| {B}_{\mathrm{ss}}|$. Figure 2(b) confirms the tendency for the wind speed to decrease with increasing expansion factor, as it does with increasing O⁷⁺/O⁶⁺ (Figure 2(a)). Note, however, that the v_E–f_ss relationship is independent of solar cycle phase, and does not show the vertical shift characterizing the v_E–O⁷⁺/O⁶⁺ relationship.

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From Figure 2(c), we conclude that the wind speed is poorly correlated with the footpoint field strength; a very wide range of v_E is associated with any given value of B₀. Figure 2(d) shows that the wind speed generally increases with the source-surface field strength, but with the v_E–$| {B}_{\mathrm{ss}}|$ curve shifted toward smaller $| {B}_{\mathrm{ss}}|$ during 2007–2009 than during 1998–2004. Both fast and slow wind are characterized by lower values of B₀ and $| {B}_{\mathrm{ss}}|$ at solar minimum than at solar maximum.

In Figures 2(e) and (f), ${n}_{0}{v}_{0}$ and F_w0 are plotted against B₀. The mass- and energy-flux densities at the coronal base both increase almost linearly with the footpoint field strength. This result is consistent with the idea that the underlying magnetic field is the ultimate source of the heating and acceleration of the solar wind.

Figures 1 and 2 show no evidence for two distinct types of solar wind that can be identified by the O⁷⁺/O⁶⁺ ratio, or by any of the other plotted parameters (v_E, f_ss, B₀, B_ss, ${n}_{0}{v}_{0}$, F_w0). The main significance of the ${{\rm{O}}}^{7+}/{{\rm{O}}}^{6+}\simeq 0.15$ criterion seems to be that it represents the median value of the charge-state ratio over the relatively active period 1998–2004. As indicated by Figure 1(c), however, this median value is a function of the underlying photospheric field strength, and decreased to only 0.06 during 2007–2009.

The downward shift of the O⁷⁺/O⁶⁺–v_E curve during 2007–2009 (Figure 1(a)) may be attributed to the fact that the O⁷⁺/O⁶⁺ ratio is also a function of B₀ (Figure 1(c)), which is essentially uncorrelated with v_E (Figure 2(c)). The downward shift of the O⁷⁺/O⁶⁺–f_ss curve (Figure 1(b)) may be interpreted similarly. In general, variations in O⁷⁺/O⁶⁺ reflect variations in the two independent parameters v_E and B₀, or equivalently, in f_ss and B₀.

In Figure 3, we display stackplots of the observed and PFSS-predicted IMF sector polarity, oxygen charge-state ratio, wind speed, source-surface expansion factor, and footpoint field strength during 1998–2011. Here, each row of pixels represents a 27.3 day CR (with time running from right to left); larger values of O⁷⁺/O⁶⁺, f_ss, and B₀ are represented by brighter colors, with the color scheme being reversed for v_E.

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It is apparent from Figure 3 that very high O⁷⁺/O⁶⁺ ratios (≳0.35, indicated by red pixels) were frequently recorded during the 1998–2002 sunspot maximum, when the footpoint field strengths were also at their peak. Conversely, O⁷⁺/O⁶⁺ ratios smaller than 0.06 (indicated by blue pixels) occurred inside high-speed streams (including those in 1999–2000, 2003–2004, and 2005–2008), as well as outside such streams at sunspot minimum, when B₀ fell to its lowest values. The predominance of very slow wind (${v}_{{\rm{E}}}\lt 325$ km s⁻¹, shown as red) during 2009 may be attributed to the presence of a flat HCS lying close to the ecliptic plane, as discussed in the next section. What is strongly suggested by Figure 3 is that long-term changes in the underlying photospheric field strength have a greater influence on the charge-state ratio than on the wind speed.

In Figure 4, we have plotted 6-CR running averages of O⁷⁺/O⁶⁺, B₀, v_E, and the sunspot number R_I over the interval 1998–2011. The solar cycle variation of O⁷⁺/O⁶⁺ shows striking similarities to that of B₀, with the correlation coefficient cc being as high as 0.84; both quantities are also well correlated with R_I (cc = 0.80 and 0.93, respectively). In contrast, the long-term modulation of the wind speed is poorly correlated with the other parameters. The pronounced dip in the O⁷⁺/O⁶⁺ ratio seen in 2003 coincides both with a peak in v_E due to the presence of large, long-lived high-speed streams in the ecliptic, and with a simultaneous weakening of the footpoint fields. It is interesting to note that the increase in the average wind speed during 2010–2011 is accompanied by an increase, rather than a decrease, in O⁷⁺/O⁶⁺; again, this can be explained by the dependence of the charge-state ratio on B₀, which increases steeply during the rising phase of the cycle.

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The poor anticorrelation (cc = −0.08) seen between wind speed and O⁷⁺/O⁶⁺ in Figure 4 is a result of averaging these parameters over timescales greater than or on the order of a CR. On daily or weekly timescales, variations in v_E and O⁷⁺/O⁶⁺ are highly anticorrelated with each other. In contrast to the wind speed, the footpoint field strength undergoes its greatest variation over the solar cycle itself, not within individual CRs. By smoothing out the fluctuations associated with v_E, which dominate on short timescales, long-term averaging acts to increase the correlation between O⁷⁺/O⁶⁺ and B₀, but to decrease that between O⁷⁺/O⁶⁺ and v_E.

Although the large-scale photospheric field was unusually weak at the end of cycle 23, a steep maximum-to-minimum fall in B₀ also occurred during cycles 21 and 22. Figure 5 shows the variation of B₀ over the period 1976–2015 (CR 1642–2172), as derived from WSO magnetograph measurements. Also plotted are the monthly mean sunspot number and the radial IMF strength B_E (all curves represent 6-CR running means). The footpoint field strengths decrease by an order of magnitude over the declining phase of every cycle, falling to values below 5 G at sunspot minimum. This suggests that the systematic change in the O⁷⁺/O⁶⁺ ratio observed in cycle 23 is likely to have been a feature of all modern-era cycles. In contrast to B₀, the IMF strength undergoes only a modest (factor of ∼2) variation over each cycle. Given that the freezing-in of the oxygen charge states occurs in the lower corona, it is the local photospheric field that is of greater relevance in determining the O⁷⁺/O⁶⁺ ratio.

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Based on the criterion of Zhao et al. (2009), almost all of the slow wind originated from coronal holes during 2007–2009, whereas the bulk of it came from streamers during 1998–2004. However, this prediction appears to be inconsistent with the fact that the streamer belt was situated far closer to the ecliptic plane during the minimum period than near sunspot maximum, when the HCS was oriented at large angles to the ecliptic.

The left column of Figure 6 displays, for CR 2080 (2009 February 10–March 9), the latitude–longitude distribution of the MWO photospheric field and of streamer structures observed at $r\simeq 10$ R_⊙ with the COR2 coronagraph on STEREO A. The two white-light maps were constructed from east- (middle left panel) and west-limb (bottom left panel) data; the horizontal dashed line marks the latitude of the ecliptic. The top right panel shows the boundaries/separatrices between different open-field domains at the source surface, as inferred by applying a PFSS extrapolation to the MWO measurements; white pixels mark the source-surface neutral line (which divides open flux of opposite polarity), while gray pixels indicate pseudostreamer locations (dividing open-field regions of the same polarity). The middle and bottom right panels show the east- and west-limb brightness patterns that would be produced by Thomson scattering from plasma sheets that extend radially outward from the source-surface separatrices (see Wang et al. 2007).

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Over a range of longitudes around ϕ ∼ 90°, the streamer belt and the source-surface neutral line/HCS are seen to be very flat and to lie only a few degrees from the ecliptic plane. On the other hand, the observed streamers are shifted northward from the ecliptic by ∼20° at ϕ ∼ 180°–270°, and southward by ∼10° at ϕ ≳ 300°. The simulations in the right column of Figure 6 somewhat underestimate the actual northward excursion of the streamer belt, probably because the MWO measurements have overestimated the relative strength of the north polar field.

Figure 7 shows, as a function of Carrington longitude, the variation of the solar wind speed and O⁷⁺/O⁶⁺ ratio during CR 2080; time runs from right to left and a four-day shift has been applied to account roughly for the Sun–Earth propagation time. Also plotted is the (arbitrarily normalized) IMF azimuth angle, defined such that relatively high (low) values indicate ${B}_{r}\lt 0$ (${B}_{r}\gt 0$). At longitudes ϕ ∼ 45°–135°, where the HCS/streamer belt lies very close to the ecliptic, v_E is typically of the order of 370 km s⁻¹ and O⁷⁺/O⁶⁺ of order 0.1. At ϕ ∼ 180°–270°, where the HCS undergoes its northward excursion, the wind speeds are typically of the order of 450 km s⁻¹ and the corresponding charge-state ratios of order 0.05. At ϕ ≃ 180°; however, v_E rises steeply to ∼675 km s⁻¹ and O⁷⁺/O⁶⁺ falls to only ∼0.01.

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Again from Figure 7, we see that the O⁷⁺/O⁶⁺ ratio reaches a maximum value of ∼0.2 at ϕ ∼ 290°, which coincides with a sector boundary where the HCS/streamer belt intersects the ecliptic plane at a moderately steep angle (see Figure 6). As the sector boundary is approached from either side, the O⁷⁺/O⁶⁺ ratio undergoes a gradual increase, mirroring the progressive decrease of the wind speed from its peak values far from the boundary; there is no sharply defined transition that might distinguish streamer from coronal hole wind.

Again for CR 2080, the latitude–longitude maps in Figure 8 display the distribution of Fe xv 28.4 nm emission observed with the Extreme-Ultraviolet Imager (EUVI) on STEREO B, the PFSS-derived footpoint areas of open field lines, and the source-surface field. The open-field footpoint areas are color-coded to indicate the corresponding expansion factors, with brighter colors denoting smaller f_ss. Colored diamonds (also plotted on the map of the source-surface field) indicate the values of f_ss associated with Earth-directed flux tubes, with white lines connecting their ecliptic positions to their photospheric footpoints.

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According to the footpoint area map in Figure 8, almost all of the solar wind recorded in the longitude range ∼40°–300° originates from the corrugated edges of the polar holes. Outward-pointing IMF dominates in Figure 7 because most of the Earth-directed open flux is rooted in the positive-polarity south polar hole. The wind speeds at ϕ ∼ 45°–135° are lower than those at ϕ ∼ 180°–270° because the flux tubes associated with the lower speeds are located even closer to the polar hole boundary and the source-surface neutral line, and thus have larger expansion factors. The brief episode of very fast wind at ϕ ∼ 180° appears to be associated with an equatorward protrusion of the south polar hole, while the moderately fast stream centered at ϕ ∼ 340° comes from a small, negative-polarity equatorial hole.

An examination of other CRs in 2009 yields analogous results. During this period, the HCS/streamer belt often lay within a few degrees of the ecliptic plane. At such times, the wind speed decreases below 400 km s⁻¹ and reaches "floor" values as low as ∼300 km s⁻¹,³ while the O⁷⁺/O⁶⁺ ratios fluctuate around values of the order of 0.1. Both inside and outside the streamer belt, v_E and O⁷⁺/O⁶⁺ vary in opposite directions, with no evidence for a sudden change in the fundamental properties of the wind as Earth enters the streamer belt.

From the preceding sections, it should be evident that the O⁷⁺/O⁶⁺ ratio alone cannot be used to discriminate between coronal hole and streamer or non-coronal hole wind. This was made especially clear during the 2007–2009 activity minimum, when the median value of O⁷⁺/O⁶⁺ underwent a precipitous decrease, despite the fact that ACE spent far more time inside the streamer belt then than during the high-activity years of cycle 23.

Our main results may be summarized as follows.

• 1.  
  In addition to being inversely correlated with the wind speed v_E, the O⁷⁺/O⁶⁺ ratio is an increasing function of the footpoint field strength B₀. The decrease in the median value of O⁷⁺/O⁶⁺ from 0.15 in 1998–2004 to 0.06 in 2007–2009 reflects the decrease in the median B₀ from 21 G to less than 3 G.
• 2.  
  Because v_E is essentially uncorrelated with B₀ (Figure 2(c)), the O⁷⁺/O⁶⁺–v_E curve shifts downward as a whole as the median value of B₀ decreases (Figure 1(a)).
• 3.  
  Variations in O⁷⁺/O⁶⁺ on timescales less than a CR are strongly anticorrelated with fluctuations in v_E, but its long-term variation instead tracks the solar cycle evolution of B₀ while being only weakly anticorrelated with v_E (Figure 4).
• 4.  
  If v_E is replaced by the expansion factor f_ss (with which it is inversely correlated), the O⁷⁺/O⁶⁺ ratio may be regarded as an increasing function of two independent magnetic parameters, f_ss and B₀ (Figures 1(b) and (c)).
• 5.  
  The highest charge-state ratios are thus associated with source regions having very strong footpoint fields that diverge rapidly with height. These footpoint areas do not necessarily lie inside streamers, but may be located just inside the coronal holes that form at the peripheries of active regions.

A physical explanation for the dependence of O⁷⁺/O⁶⁺ on the parameters f_ss and B₀ was suggested earlier by Wang & Sheeley (2003) and Wang et al. (2009) (see also Cranmer et al. 2007). The basic assumption is that the heating rate along a coronal flux tube depends on the local field strength. If the flux tube diverges rapidly with height, the heating will be concentrated near the coronal base; the temperature maximum thus occurs at relatively low heights, which is also where the oxygen charge states decouple from each other or freeze in. As the footpoint field strength and total energy-flux density (${F}_{{\rm{w}}0}\propto {B}_{0}$) increase, so will the peak temperature T_max and the O⁷⁺/O⁶⁺ ratio. The strong low-coronal heating drives a large downward heat flux, which in turn increases the mass-flux density at the coronal base and reduces the energy available per escaping proton. Large values of f_ss and B₀ thus produce slow solar wind with high O⁷⁺/O⁶⁺ ratios.

We remark that this scenario differs from that of Schwadron et al. (2011), who postulate a "scaling law" in which the energy injected per particle is taken to be the same in both fast and slow wind. Their model assumes that the field strengths and expansion factors are approximately uniform and time-independent in open-field regions. As is apparent from Figures 1–5, however, B₀ and f_ss may vary by orders of magnitude, and the footpoint fields are systematically much stronger near solar maximum than at solar minimum.

It should be emphasized that, by using low-resolution maps of the photospheric field, we have effectively averaged over the supergranular network. On scales less than a supergranular cell diameter (∼30 Mm), the actual values of B₀ and f_ss may undergo significant variations around the spatial averages employed here. This may contribute to the short-term variability of slow wind, for which the energy deposition is concentrated at heights where the field remains relatively nonuniform (in contrast to the case of fast wind, where the heating extends to greater heights). Such low-coronal fine structure may also help to explain the lack of correlation between wind speed and compositional properties on timescales less than an hour (Kepko et al. 2016); dynamical interactions during the Sun–Earth transit will reduce supergranular-scale fluctuations in speed, but not in composition.

Our procedure for deriving the footpoint areas of the solar wind is based on the assumption of a steady-state, current-free coronal field, and does not allow for the possibility of transient processes involving the release of material from streamer loops. However, even if the source regions of the slow wind were located just outside the PFSS-inferred open-field regions, the values of B₀ would be similar to those obtained here, since the photospheric field strength (unlike the coronal magnetic topology) generally undergoes little change across the boundary of a hole.

As already noted, the O⁷⁺/O⁶⁺ ratio tends to show a progressive increase as the wind speed decreases from moderate (∼450–500 km s⁻¹) to low values. This behavior is clearly seen in the high-speed streams located at longitudes of ∼140°–190° and ∼300°–360° in Figure 7. If it is accepted that the trailing portions of these streams, where v_E continues to decrease monotonically, originate from the same coronal holes that are the source of their leading portions, then it would appear that holes can produce wind as slow as ∼300–400 km s⁻¹, with O⁷⁺/O⁶⁺ ratios comparable to those observed inside the streamer belt.

White-light coronagraph observations indicate that the streamer emission beyond r ∼ 2–3 R_⊙ is confined to narrow plasma sheets, which in turn consist of fine ray-like features. In addition, inhomogeneities with densities exceeding that of the plasma sheet by typically less than ∼10% are continually emitted from the cusps of helmet streamers, and accelerate outward along the HCS, reaching speeds of ∼300–400 km s⁻¹ at r ∼ 30 R_⊙. COR2A/B observations suggest that these blobs are flux ropes (Sheeley et al. 2009), presumably formed as expanding streamer loops reconnect with each other and pinch off. In contrast to helmet streamers, pseudostreamers do not produce blob-like ejecta. Thus far, there have been few unambiguous detections of streamer blobs in situ (see Rouillard et al. 2010); and small transient structures do not constitute the main part of the slow solar wind (Kilpua et al. 2009).

On average, slow wind (${v}_{{\rm{E}}}\lesssim 450$ km s⁻¹) occupies a band having an angular extent of ∼15° on each side of the HCS near sunspot minimum, and spreads over an even wider band (≳30°) at sunspot maximum (see, e.g., Zhao & Hundhausen 1981; Wang et al. 1997; Zhao et al. 2009). At in situ pseudostreamer crossings where fast wind runs into slow wind but the polarity does not reverse, superposed epoch analysis by Crooker et al. (2014) shows low wind speeds and high charge-state ratios occurring for up to several days before the arrival of the stream interface; the same holds for HCS-associated stream interfaces where the polarity reverses. In contrast, white-light streamer structures in the outer corona, when viewed edge-on near the sky plane, generally have widths of a few degrees or less (see Figure 1 in Wang et al. 1998). The narrowness of these plasma sheets, which is also manifested in the sharpness of the polarity transitions at IMF sector boundaries, is difficult to reconcile with a streamer loop origin for the bulk of the slow wind.

These arguments support the idea that most of the slow solar wind comes from just inside the boundaries of coronal holes, with the observed variations in v_E and O⁷⁺/O⁶⁺ being attributable to variations in the footpoint field strength and the flux-tube expansion factor. The actual streamer component of the slow wind is confined to within a few degrees of the HCS, and includes the blobs and other transients that pinch off from the helmet streamer cusps, as well as the heliospheric plasma sheet itself; a small contribution may also be provided by the plasma sheet extensions of pseudostreamers. Perhaps because of the effect of turbulent mixing, the coronal hole and streamer components of the slow wind are not easily distinguishable at 1 au, although a clearer separation may become possible using observations from the upcoming Solar Probe Plus and Solar Orbiter missions.

I thank Y.-K. Ko and D. G. Socker for helpful discussions. This work was supported by the Chief of Naval Research.