The effects of plasmaspheric plumes on dayside reconnection

Abstract

We summarize the results of a study on the impact of plasmaspheric plumes on dayside reconnection using a three-dimensional magnetospheric simulation code. We find that the mass loading of magnetospheric flux tubes slows local reconnection rates, though not as much as predicted by Borovsky et al. (2013) due to differences in how well the Cassak-Shay theory matches magnetospheric configurations with and without plasmaspheric plumes. Additionally, we find that in some circumstances reconnection activity is enhanced on either side of the plumes, which moderates its impact on the total dayside reconnection rate. These results provide evidence that plasmaspheric plumes have both local- and global-scale effects on dayside reconnection.

Key Points

• Plasmaspheric plumes slow dayside reconnection through global and local effects
• Reconnection may be enhanced on either side of plasmaspheric plumes
• Simulated reconnection rates better match Cassak-Shay predictions when merging plasma populations have similar densities

1 Introduction

Magnetic reconnection plays a key role in magnetospheric dynamics, particularly at the dayside magnetopause where coupling between the solar wind and magnetosphere occurs [e.g., Cowley, 1984; Frey et al., 2003]. Though solar wind conditions and magnetosphere-ionosphere coupling both play a role in regulating dayside reconnection, recent observations of plasmaspheric ions at the dayside magnetopause have raised questions as to what role the plasmasphere plays in governing magnetopause merging [Borovsky and Denton, 2006; Walsh et al., 2014]. Of primary interest has been the effect of plasmaspheric plumes on both the local and total reconnection rates; the local rate given by the component of the electric field parallel to the line along which reconnection occurs and the total rate being the integral of the electric field along the line's extent (see, e.g., Vasyliunas [1984], Sonnerup [1988], and Siscoe et al. [2001] for discussions of reconnection terminology in the context of the magnetopause). Broadly speaking, two hypotheses about how these rates are affected by plasmaspheric ions have emerged in the literature.

The first hypothesis was proposed by Borovsky et al. [2008]. This study examined dayside reconnection under southward interplanetary magnetic field (IMF) conditions using a version of the Block Adaptive Tree Solarwind Roe Upwind Scheme Block-Adaptive-Tree-Solarwind-Roe-Upwind-Solver (BATS-R-US) 3-D magnetospheric simulation code [Powell et al., 1999; T⊙th et al., 2012], modified to artificially enhance plasma resistivity at the magnetopause nose. It was shown that magnetic reconnection in these simulations was largely controlled by local plasma parameters such as the magnetic field strengths and plasma densities in the magnetopause and magnetosheath. Additionally, a reduction in the dayside reconnection rate was observed during a geomagnetic storm when mass convected from the inner magnetosphere to the magnetopause. These findings showed that were a plasmaspheric plume to impinge on the dayside magnetopause, the reconnection rate would be reduced in this region but remain unaffected outside of the plume.

Building upon this work, Borovsky et al. [2013] made a series of predictions based on the Cassak-Shay theory of asymmetric reconnection and a previous theory of dayside reconnection derived from first principles [Cassak and Shay, 2007; Borovsky, 2008, 2013; Borovsky et al., 2013]. First, they predicted that the local reconnection rate E should scale as E ∼ ME₀, where M ≡ (1 + ρ_mB_s/ρ_sB_m)^−1/2. Here, ρ_m,s and B_m,s are the mass densities and magnetic field strengths in the magnetosphere and magnetosheath, respectively, and E₀ is the local reconnection rate for the case where ρ_m=0. Additionally, they developed scaling laws for the length of the dayside X line along which reconnection occurs, showing that for cases where magnetospheric plasma impinges upon the entire length of the X line, its length scales as L ∼ ML₀, where the subscript again denotes the case where ρ_m=0. Therefore, in these situations, the total dayside reconnection potential should roughly scale as ϕ = EL ∼ M²E₀L₀=M²ϕ₀.

The second hypothesis was presented by Lopez et al. [2010]. Using 3-D simulations of the magnetospheric response to southward IMF conditions, the authors concluded that force balance in the magnetosheath plays a key role in determining the region on the magnetopause where reconnection preferentially occurs. Based on this analysis, Lopez et al. [2010] hypothesized that the total reconnection rate would be less sensitive to the effects of plasmaspheric plumes than predicted by Borovsky et al. [2008], speculating that if reconnection was less efficient in a region where a plume impinged on the dayside magnetopause, the magnetosheath flux not reconnected there would simply merge elsewhere on the magnetopause. In light of these studies, we are left with an intriguing question regarding dayside merging: do local conditions alter the total dayside reconnection rate or is it determined by global factors?

Recent results using ionospheric outflow to load the magnetosphere with mass have shown that both these hypotheses have regimes of validity [Zhang et al., 2016]; here we study the problem using a global-scale MHD simulation of the magnetosphere which incorporates the Gallagher plasmasphere model [Gallagher et al., 1988]. The effects of plasmaspheric plumes on local and total dayside reconnection rates are presented, as well as their consistency with these theoretical predictions. Finally, we discuss the factors that may determine how plasmaspheric plumes impact total dayside reconnection behavior.

2 Simulation Descriptions

This study employed the multifluid extension of the Lyon-Fedder-Mobarry global-scale MHD simulation code [Lyon et al., 2004], the MFLFM. In this version of the code, an arbitrary number of ion fluids can be included in the simulation, with coupled sets of equations for density, momentum, and plasma energy evolved for each. More specific information on the inner workings of this code may be found in Brambles et al. [2010], Damiano et al. [2010], Garcia et al. [2010], and Wiltberger et al. [2010]. The frozen-in condition is broken with numerical resistivity, where reconnection can occur when magnetic gradients approach the computational grid's spatial resolution, approximately 500 km near the subsolar point. This numerical resistivity also creates the parallel electric fields which can be used to measure the local and global reconnection rates. The local reconnection rate in this code is comparable to other codes that produce fast reconnection, on the order of one tenth the product of the inflowing magnetic field strength and Alfvén speed [Ouellette et al., 2013].

The plasmasphere was modeled using an early version of the so-called Gallagher plasmasphere model which predicts the spatial distribution of H⁺ in the inner magnetosphere using an empirical relation based on the Kp parameter [Gallagher et al., 1988]. Our study focused on how the plasmasphere affected reconnection for a short period following a southward IMF turning, well below the several hours-days required for plasmaspheric refilling [Su et al., 2001]. Therefore, refilling effects were not included in the plasmasphere model. All simulations were initialized with the plasmaspheric plasma at rest in the inertial frame with a tempertaure of 1 eV. The plasmaspheric component remains cold during the entire simulation. Corotation is introduced and enforced by a corotation potential applied at the inner boundary at 2 R_E. The Earth's gravitational force was also included.

Our simulation suite contained three sets of IMF conditions, B_z=−5,−10,and − 20 nT with B_x and B_y=0 nT in SM coordinates. For each of these runs, three different plasmaspheric configurations were simulated—a baseline run without a plasmasphere, a run using the Gallagher plasmasphere, and one doubling the Gallagher model's densities. All simulations used zero geomagnetic dipole tilt and were initialized with an 8 h period of 5 nT northward IMF to allow the plasmasphere to achieve corotation before the final solar wind conditions were imposed. Throughout the entire simulation, the solar wind speed, mass density, and pressure were fixed at 400 km s⁻¹, 7 amu cm⁻³, and 4 pPa, respectively. The plasmasphere predicted by the Gallagher model for Kp = 1 was inserted at the beginning of the run and then evolved for the rest of the simulation, and the ionosphere was set to have a constant Pedersen conductivity of 10 mho.

For all analysis, time-averaged values of the simulation were employed to determine the mean behavior of the system. We focused on the period of the simulation after the southward turning of the IMF, typically beginning our analysis 2 h after the turning once the magnetotail had settled into a steady magnetospheric convection (SMC) pattern. For the runs with a plasmasphere, the plasmasphere evolves from extending along a wide swath of the magnetopause shortly after the IMF conditions change to a relatively narrow plume several hours later. To capture the period when plasmaspheric plumes were most likely to impact dayside reconnection, we chose to analyze an approximately 40 min average when the plasmaspheric plume was at its widest extent. Since runs without a plasmasphere do not contain a similarly time dynamic feature, simulation data for these runs were averaged from shortly after the magnetosphere had entered an SMC state until the end of the run, typically 3 h.

3 Results and Analysis

3.1 Equatorial Plane Analysis

A comparison of simulation results is shown in Figure 1. Figure 1 (left) illustrates the magnetospheric configuration in the equatorial plane for the runs with and without a plasmasphere included for IMF B_z of −10 nT, and Figure 1 (right) shows the configuration of the merging region in the noon-midnight plane. An interesting feature is the protrusion in the nose of the magnetopause for the run with the plasmasphere, which is somewhat wider than the region where mass impinges on the magnetopause. We can see from the presence of the wave-like structure emanating from the bow shock that the presence of the plasmasphere has an influence that extends well out into the magnetosheath. This wave changes the flow characteristics of the magnetosheath as it goes around to the flanks, changing the shape of the magnetopause in this region.

Figure 1

(left) Equatorial and (right) noon-midnight plane views of the time-averaged magnetosphere for a baseline and plasmasphere run. The equatorial planes are colored by density with dayside reconnection lines indicated in white. The noon-midnight planes are colored by out-of-plane current density, magnetic field lines are drawn in brown, and the center of the current layer is drawn in red. The points where outflow quantities were measured for purposes of a Cassak-Shay analysis are indicated by the red dots.

To study the influence of plumes on properties of reconnection across the magnetopause, we first needed to identify the line along which merging occurred, the separator line. For southward IMF conditions, this line can be identified as the contour in the equatorial plane along which B_z=0. To find this line, we performed a series of radial cuts at constant values of magnetic local time (MLT) and found the points where the minimum |B_z| value occurred. These points formed a set of radial distances versus MLT which we then fit with a smoothing spline to eliminate small-scale variations in the direction of the separator. The local reconnection rate at any given position on this line was then calculated as the component of the electric field parallel to it [e.g., Vasyliunas, 1984]. To determine the dayside reconnection potential, which will be discussed in more detail in section 3.3, the electric field was integrated along this path and the contour was truncated at the two points separated by the largest potential drop, the magnitude of which specifies the total amount of solar wind flux reconnected at the magnetopause [e.g., Vasyliunas, 1984; Ouellette et al., 2010].

In order to determine the values of the inflowing quantities ρ_m,s and B_m,s, we needed to define two contours where these plasma densities and magnetic field strengths would be measured. To do so, we first found the distances from the reconnection site to the magnetosphere and magnetosheath edges of the current layer at the subsolar point, δ_m and δ_s. As in a previous study, these bounds were defined by the point where the component of the current perpendicular to the merging plane vanished, indicating that field lines were no longer bent as part of the merging process [Ouellette et al., 2014]. We then constructed two contours at distances δ_m and δ_s perpendicular to the separator line, measuring the inflow quantities along these curves.

The first row of Figure 2 shows the local reconnection rate versus MLT for the three simulated IMF conditions, the next two rows show the mass and density ratios for the two inflow populations, and the fourth row shows the value of M ≡ (1 + ρ_mB_s/ρ_sB_m)^−1/2 computed from the two inflow contours. Note that the MLT axes are reversed to provide a visual reference consistent with a view of the equatorial plane above the geographic North Pole. The plasmaspheric plumes are easily identified as the peaks in the density ratio and corresponding troughs in M around local noon. The plume densities for runs with the Gallagher model vary from 20 to 60 amu cm⁻³ and have a local time extent of approximately 4–6 h, consistent with satellite measurements of “young” plumes [Borovsky and Denton, 2008]. In contrast to the large change in the ratio ρ_m/ρ_s, the ratio of B_m/B_s remains relatively constant near the subsolar point.

Figure 2

Local reconnection rates (E_||), plasma density ratio, magnetic field strength ratio, M, and E_||/M values for the simulations versus magnetic local time. Different sets of solar wind conditions run from left to right, and the runs are color coded by plasmasphere configuration. The plasmaspheric plumes can be identified as the locations near the subsolar point where the density ratios peak and M < 1.

As expected, M≈1 near the subsolar point for the baseline runs, indicating that ρ_m≪ρ_s there. For the plasmasphere runs, the minimum value of M drops as the IMF strength increases and the magnetopause nose moves farther into the plasmasphere and is reduced further for the runs which doubled the plasmasphere's mass density. As predicted by Borovsky et al. [2013], the local reconnection rates drop where the plume impacts the magnetopause, and the decrease is more pronounced for the runs with a denser plasmasphere. Along the magnetopause flanks, M < 1 for all runs and of comparable magnitude, as are the reconnection rates. The fact that M < 1 in these regions for all simulations is not a plasmaspheric effect; the additional mass in these regions is due to the natural earthward convection of solar wind ions from the magnetotail.

Of note are the enhancements in reconnection activity off noon in some runs with a plasmasphere, an effect most noticeable for the run with B_z=−20 nT. In these cases we observe reconnection rates near 8 and 16 MLT that are approximately 20% larger than the corresponding run without a plasmasphere. This enhanced reconnection activity shows an interesting interplay between local and global effects. Because the plasmaspheric plume quenches reconnection activity near the subsolar point, the flux that would normally reconnect there is diverted to merge along the magnetopause flanks. This is consistent with the ideas of Lopez et al. [2010] that the magnetosphere can adjust reconnection activity to maintain a constant level of solar wind-magnetosphere coupling. From this study alone, we are not certain when this effect occurs as a function of solar wind or plasmasphere parameters nor whether it is a common or rare phenomenon. Further research will be required to determine the importance of these factors, but the situation does serve to illustrate the complex nature of the global reconnection system.

To assess how well the prediction that E ∼ M, we computed the quantity E_scaled≡E/M, plotted in the last row of Figure 2. If this relation holds then for each set of solar wind conditions simulated, the three curves should overlap. For all three runs, the scaled reconnection rates at the subsolar point for the runs with a plasmasphere exceed those in the baseline runs, most notably in the run with IMF B_z=−20 nT. This indicates that the reduction in the reconnection rate due to magnetospheric mass loading is somewhat less than the factor of M predicted by Borovsky et al. [2013]. It is also interesting to note that the scaled reconnection rates exceed the baseline values in the regions of reconnection enhancement away from local noon. This may be a sign that the effects of the magnetosphere compensating for reduced reconnection at the subsolar point are affecting local reconnection in these regions as well, another sign of the complex and interconnected nature of solar wind-magnetosphere coupling.

3.2 Cassak-Shay Analysis at the Subsolar Point

To determine why the reduction in the local reconnection rates was not as large as expected, we carried out an analysis of the local reconnection properties at the subsolar point similar to that contained in Ouellette et al. [2014]. Because the predictions of Borovsky et al. [2013] leveraged results of the Cassak-Shay theory [Cassak and Shay, 2007], we analyzed how well the theory predicted the local reconnection rates. A diagram of the noon-midnight plane where the analysis was performed is shown in Figure 1 (right). The center of the current layer was determined by fitting a smoothing spline through the points of maximum magnetic curvature along a series of radial cuts made at constant magnetic latitudes. This contour was truncated at the locations northward and southward of the reconnection site where either the outflow speed peaked or the current fell to 1/e≈0.37 of its maximum value, whichever occurred closer to the subsolar point. The layer half-width δ was determined in the same manner as described previously—half the width of the region with positive J_y along the Sun-Earth line. To maintain consistency with the equatorial plane analysis, the inflow quantities were measured along the Sun-Earth line, instead of at a distance 3L/4 above and below the subsolar point as in Cassak and Shay [2007]. As a result, our values for quantities predicted by the Cassak-Shay theory are likely overestimates since the magnetic field strength and outflow density are somewhat larger along the Sun-Earth line than at higher and lower magnetic latitudes. The benefit of this approach, however, is that it is consistent with the analysis in section 3.1 and allows us to identify the sources of error in predicted scaling of the reconnection rate with M at the subsolar point.

Figure 3 shows a comparison between several quantities predicted by the Cassak-Shay theory and their measured values. Values from runs performed with a plasmasphere are denoted by the red crosses; values from runs without a plasmasphere are denoted by the blue dots. The blue and red lines are linear best fits constrained to pass through the origin for each case, and the slopes of these lines are indicated in the upper left corner of each plot. As seen in the plots, the Cassak-Shay formula's predicted reconnection rate, outflow speed, and outflow density are all much closer to their measured values for the runs with a plasmasphere than for the baseline runs. In the plasmasphere runs, the theory tends to overestimate the reconnection rate and outflow speed and underestimate the outflow density. The comparatively better performance of the Cassak-Shay theory in runs with a plasmasphere likely owes to the more symmetric nature values of ρ of the inflowing plasma populations in these simulations. In the baseline runs, a tenuous magnetospheric plasma with a strong magnetic field merges with a dense magnetosheath plasma with a weaker magnetic field. In the baseline runs, the magnetosheath is typically 1000 times denser than the magnetosphere. In contrast, the ratio ρ_m/ρ_s ranges from unity to approximately 7 in runs with a plasmasphere. As discussed in Ouellette et al. [2014], the Cassak-Shay theory assumes that the mass density in newly merged flux tubes has time to equilibrate before reaching the edge of the current layer, a behavior not observed in our simulations. However, it seems reasonable that the density in the merged flux tubes would come closer to its equilibrium value in situations where the two merging plasmas were similarly dense.

Figure 3

Comparison of Cassak-Shay (C-S) predicted and measured values for the nine simulations. The baseline runs are indicated by the blue dots and runs with a plasmasphere by the red crosses. Best fit lines constrained to pass through the origin are drawn and their slopes indicated in the legend.

3.3 Dayside Reconnection Potential

Lastly, we turn our attention to the total dayside reconnection rate. Figure 4 summarizes this parameter for all nine simulations. The potentials, which are calculated by integrating the local reconnection rates along the entire merging line, are plotted versus the average value of M along the same contour. We fit two curves through the reconnection potential for the baseline run—one assuming the potential scales as M and one assuming it scales as M². A reduction of M² would be consistent with the results of Borovsky et al. [2013] in the case of uniform mass distribution along the X line; the M scaling is presented for comparison purposes. We see that the total dayside rates are reduced as M decreases, but the average reduction does not appear to follow a specific scaling. It is not surprising that these results do not match the M² scaling since the mass loading is not uniform along the length of the dayside X line in our simulations. Rather, the mass loading impinges upon one half to one third of the X line, depending on the particular run. Therefore, it seems reasonable that the reduction in the total dayside potential would be somewhat less given that its effect is restricted to a particular portion of the X line rather than its entire extent.

Figure 4

Total dayside reconnection rate for all nine simulations. Two fits are shown, one assuming that the potential scales as the average value of M for the dayside merging line, and one assuming that the potential scales with M².

4 Conclusions and Discussion

Based on our simulations, we find that the local and total dayside reconnection rates are reduced when a plasmaspheric drainage plume impinges on the dayside magnetopause, consistent with the predictions of Borovsky et al. [2013]. However, the magnitude of the reduction in the local and total reconnection rates is less than predicted, owing to a differences in how well the Cassak-Shay theory predicts the merging rates for cases with and without plumes. The theory is in agreement with our simulations when a plasmasphere is present but overpredicts the merging rate in the absence of plumes, suggesting that the theory performs better when the two merging plasma populations are similarly dense. Additionally, we have observed enhanced reconnection activity on either side of the plume in some simulations, suggesting that the magnetosphere-plasmasphere interaction may work to maintain the same level of solar wind-magnetosphere coupling as in cases without plasmaspheric mass loading. In this way we see evidence supporting both the local and global control hypotheses advocated by Borovsky et al. [2013] and Lopez et al. [2010], respectively.

These results raise interesting questions about the precise manner that plasmaspheric plumes affect dayside reconnection. Since most of the merging is centered on the subsolar point, it is reasonable to posit that mass loading in this region would be the most effective at reducing the dayside reconnection potential. However, if the plume is sufficiently narrow, the local reconnection rate may be enhanced off noon as flux that would normally merge at the magnetopause nose reconnects in these locations. This suggests that there are (at least) three aspects of plasmaspheric plumes that impact dayside reconnection: density, location, and extent; and these three factors combine to determine the fraction by which magnetopause merging is reduced. For example, it is reasonable to posit that a wide, tenuous plume centered on the subsolar point may be just as effective at quenching dayside merging as a dense cloak which impinges on the magnetopause flanks or a narrow dense plume at magnetopause nose. Recent results have shown that the transition from local to global control of dayside reconnection depend on precisely these factors [Zhang et al., 2016]. Quantifying this complex relationship is an interesting avenue for further investigation.

Acknowledgments

This work was supported by NASA grant NNX10AQ60G S05. The authors would like to acknowledge high-performance computing support from Yellowstone (ark:/85065/d7wd3xhc) provided by NCAR's Computational and Information Systems Laboratory, sponsored by the National Science Foundation. The data files and analysis scripts used in this study may be obtained by contacting the corresponding author at [email protected].