The strength of field-aligned currents coupling the magnetosphere to the ionosphere was obtained by the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) using the network of Iridium® spacecraft. The distribution of current was integrated giving total current in and out of the ionosphere on the dayside and nightside of the Earth in both hemispheres. The onset of auroral zone negative bays and midlatitude positive bays corresponds to an increase in nightside upward current. The total outward current tends toward saturation with increasing solar wind driver strength. The optimum solar wind coupling function for AL index predicts ~73% of the variance in nightside upward current. The dayside and nightside predictors of upward current rise to a peak at 30–45 min and decay slowly over 2.5 hr. Nightside response is delayed relative to dayside.
- Field-aligned currents exhibit saturation as driver strength increases
- Substorm onsets are associated with an increase in upward nightside current
- Prediction filters for field-aligned current are very similar to those for AL and exhibit saturation
Plain Language Summary
The control of electric currents linking the outer parts of the Earth's magnetic field to the ionosphere is investigated. It is found that these currents are closely linked to the solar wind and that a function of several solar wind parameters can predict a significant fraction of the variations in these currents. In addition, it is shown that these currents are connected to the currents that flow in disturbances of the aurora.
The solar wind drives convection of plasma and magnetic field. Convection effects are transmitted to the ionosphere by field-aligned currents (FACs). These drive ionospheric Pedersen and Hall currents. The Hall currents create magnetic perturbations on the ground, while the FAC and their closure are nearly undetectable. However, spacecraft pass through these azimuthal sheets measuring magnetic perturbations. These currents are known as Region 1 and 2 (R-1 and R-2) currents. The high-latitude R-1 current is toward the ionosphere on the dawnside and away on the duskside. The lower latitude R-2 currents are oppositely directed.
A second FAC system flows during substorms, the substorm current wedge (SCW). This system forms at the onset of the substorm expansion and was first seen in geosynchronous magnetometers (McPherron, 1972; McPherron, Russell, & Aubry, 1973). The SCW can be modeled as a downward sheet of current on the dawnside, azimuthal westward closure through the expanding aurora, and an outward current from the westward surge (Chu et al., 2014; Horning et al., 1974).
We have developed an index of midlatitude effects caused by the SCW (Chu et al., 2014; McPherron & Chu, 2016). The midlatitude positive bay (MPB) index is the square of the horizontal perturbation caused by the SCW in the range 20° < |magnetic latitude| < 50°. A substorm is seen as a pulse rising rapidly to a peak in about 20 min that decays more slowly over the next 40 min. This pulse is closely associated with the development of a negative bay.
Initial observations of the R-1/R-2 current system were only measurement of local sheet current density. With the advent of the Iridium® network described in section 2 it became possible to obtain the spatial distribution of current densities (Anderson et al., 2002; Anderson, Takahashi, & Toth, 2000; Waters et al., 2001). Recently, processing of these data has been improved and the polar grid of current densities can be integrated to obtain the current flowing upward or downward through a given area (Anderson et al., 2014). Several recent reports have used these data to study the relation of FAC to solar wind driving and substorms (Clausen et al., 2012; Clausen, Baker, et al., 2013; Clausen, Milan, et al., 2013; Coxon et al., 2014a, 2014b). Details of the relation of FAC to substorm onset and to the formation of the current wedge were examined by Murphy et al. (2012) and Murphy et al. (2013).
In this report we use a larger data set than previously available spanning 5.5 years and a new parameter, the total upward current on the dayside and nightside of the Earth. Our results generally confirm previous results but extend them showing the dynamic and nonlinear nature of the response.
2 Field-Aligned Currents Calculated by Active Magnetosphere and Planetary Electrodynamics Response Experiment From Iridium® Measurements
The derivation of FACs from the network of Iridium® spacecraft is described in the papers cited above. The information relevant to this report includes the following. Current densities are derived from a 10 min window advanced 2 min at a time. The time assigned to each window is the time at the start of the window. To correspond to the centered averages from other sources, we add 6 min. The radial current densities are averaged separately from dawn to dusk and from 60 to 90° latitude on the dayside and nightside in each hemisphere.
3 Analysis Procedure and Results
In this paper we investigate the response of magnetospheric FAC to the solar wind and substorms. Our inputs include the currents described in section 2; solar wind data propagated to the bow shock at 1 min resolution in an OMNI file at National Aeronautics and Space Administration (NASA) National Space Science Data Center (NSSDC), the SML index from the SuperMag project, and the MPB index. These data were low-pass filtered and resampled at 2 min resolution. The analysis was done in several steps. The first examines the relation of total current to the solar wind driver. The second selected substorm expansion onset times. The third performed a superposed epoch analysis (SEA) based on the onsets. The fourth used linear prediction to determine the solar wind impulse response to solar wind coupling and the AL index.
3.1 Relation of Total Upward Current to Solar Wind Coupling Strength and AL Index
Current to the ionosphere depends on the polar cap potential and ionospheric conductance. Since the polar cap potential saturates (Gao et al., 2012), we expect the same for FAC. We examine this possibility in Figure 1. We have considered five different coupling functions as listed in Table S1. These include epsilon (Perreault & Akasofu, 1978), VBs (Rostoker & Fälthammar, 1967), universal coupling function (ucf) (Newell et al., 2007), the optimum AL coupling function (opn) (McPherron, Hsu, & Chu, 2015), and the phi function (Milan et al., 2012). Figure 1a presents a contour map of log10(nbin) as a function of instantaneous upward nightside (IUN) FAC and opn. Over one million points were used in the plot but most are located at low values of coupling and current. There are few observations of strong coupling. Fits to raw data are dominated by points near zero. To allow larger values to influence the fits, we must reduce the weight of points near zero. We did this by using fits to binned medians. We have defined bins of coupling every 0.5 mV/m with width 1.0 mV/m and determined the median IUN in each bin. Because of the rapid falloff of the number of points, we have used a simple technique described by O'Brien and McPherron (2000) to make accurate estimates of the median at the bin center. This also allows us to extend the estimates to slightly higher values of coupling. These estimates are shown by the white line with circles. We then fit the median curve with a linear fit (red line) and with a saturation function (yellow curve). The saturation function has the form Iup = β1 ⋅ β2 ⋅ C/(C + β2). In this equation C (mV/m) is the coupling function, β2 (mV/m) is the saturation value, and β1 scales the ratio to obtain units of current (MA). Visually, the saturation curve follows the median curve better than the linear fit and the prediction efficiencies confirm this.
The response of FAC to the solar wind is delayed so we expect that a running average of the coupling function might better organize the data than its instantaneous value. We therefore define the strength of a coupling function at a given time as the average over the preceding 110 min. This value was determined empirically to provide the best fit of a saturation curve. Figure 1b shows a plot of IUN versus strength of opn. The contour map is better organized than instantaneous values. The prediction efficiency is higher for the saturation curve than for the linear fit.
We have repeated this analysis for all five coupling functions on both the dayside and nightside. The parameters and quality of the fits are summarized in Table S1. In almost every case the fits to median coupling strength are slightly better than the fits to instantaneous coupling medians. The saturation fits are always better than linear fits. The epsilon function has the poorest relation to FAC, followed by VBs and phi, with ucf and opn nearly equal. The saturation parameters determined from coupling strength for ucf and opn are 6.9 and 6.3 mV/m. The results for all coupling function suggest that the FACs tend to saturate as the strength of the driver increases. However, our values are higher than found for the polar cap potential (3–5 mV/m).
3.2 Substorm Onset Lists
Investigation of the relation of upward FACs to substorms requires a list of substorm onsets. Available lists are discussed in Newell and Gjerloev (2011), Chu et al. (2014), Forsyth et al. (2015), and McPherron and Chu (2016). We recently applied the technique of onset determination described in McPherron and Chu (2016) to both the MPB and SML (SuperMag AL) index series to obtain two new lists. We also visually selected onsets for the year 2010. These lists rarely agree with each other to better than 30%, and every list misses onsets. The five different lists contain the following number of onsets in 2010: Chu MPB (828), SuperMag SML (881), McP SML (2971), McP MPB (3298), and Visual SML and MPB (1514). The SEA described below uses our new SuperMag SML list for all 6 years (10,363 events). Despite differences between lists we find all produce similar results. An example of the relation between the solar wind, substorms, and FACs is presented in Figure 2. The four panels present opn, the dayside and nightside FACs, the MPB index, and the SuperMag SML index. On this day coupling in Figure 2a was weak never exceeding 2 mV/m. The strength of upward FAC in Figure 2b was 2 MA or less with the nightside current stronger than dayside with a daily median ratio of 1.5. Frequent sharp increases in the nightside current in Figure 2b are a consequence of substorm onset as demonstrated by the bottom two panels. Figure 2c contains the MPB index. The signature of substorm expansion is a positive pulse such as the one at 12:48 UT. Our algorithm for detection of MPB onsets found 11 onsets. Each onset is denoted by a blue dotted line and annotation at the top of the panel. An earlier and more conservative algorithm selected only five onsets as shown by the vertical red triangles along the bottom of the panel. Figure 2d presents the SML index. Our algorithm identified 12 negative bay onsets shown by red dotted lines. Only three negative bay onsets were identified by the SuperMag project as indicated by downward pointing blue arrows.
There are significant differences between the four lists portrayed in these panels. Only two events in the older lists shown by triangles are closely associated (09:23 and 12:49 UT). The association of the newer lists is somewhat better with five close associations. However, there are obvious onsets in MPB that were missed (e.g., 04:50 UT) as is the case in SML (14:34 UT). Note also that associated onsets in SML and MPB can often differ by as much as 8 min (see ~06:00). Weak events such as those after 16:00 UT are poorly identified and often not mutually associated. We have found that the SuperMag onset list contains negative bays with peak strength of −400 nT while our list peaks at −200 nT.
For this day we have visually identified onsets. These times are denoted by 12 dashed black lines. Almost all are associated with a sharp increase in nightside FAC, for example, 12:47:39 UT. However, there are three cases of apparent substorm onset where FACs are constant or decreasing (14:34, 15:26, and 20:37 UT). Because of the variability of the association between the changes in FAC and the indices, we turn to SEA to find the average response. For this analysis we use our new list of SML onsets (10,363 events).
3.3 Superposed Epoch Analysis
Results of a SEA of various indices are presented in Figure 3. The reference time corresponds to the onset of 10,363 negative bays in the SML index during the years 2010 to May 2016. This list contains many more events than the list available from the SuperMag project. Figure 3a shows that the median solar wind coupling is a maximum at bay onset. Figure 3b displays the Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) FAC on the dayside (dashed blue), the nightside (red diamonds), and their total (black). The three phases of a substorm are obvious in the traces with about 1 hr of growth phase, 20 min of expansion, and 2.5 hr of recovery. During the growth phase the FAC increases gradually both day and night, but the dayside current is larger. At expansion onset the nightside FAC increases sharply becoming 1.7 times as large as the dayside current. Figure 3c presents the change in square root of the MPB index. On average this reaches a peak of 2.5 nT in ~28 min. The MPB signal decays much more rapidly than the FAC disappearing with 1.5 hr. Figure 3d plots the median change in the SML index.
3.4 Calculation of Solar Wind and AL Prediction Filters for Upward Current
In this equation opn and Iup are measured quantities while co and bj are model parameters determined as described in McPherron et al. (2015). The results are presented in Figure 4. In Figure 4a the abscissa is filter lag sampled every 2 min. The ordinate is the response of FAC to a pulse of unit magnitude in coupling. The two traces are solutions determined by singular value decomposition using 60 eigenvalues. The red curve shows the response of dayside current and the blue curve nightside current. These filters were calculated from all data records in 2010–2016. Prior to the inversion both input and output time series were deflagged using spline interpolation of gaps up to 10 min in duration. Longer gaps were not interpolated but records containing these gaps were removed. The input time series was shifted by 20 min to account for propagation delays through the sheath and along field lines to the ionosphere and for the offset in AMPERE time tags. Annotation on the plot shows that 458,604 records were used in the inversion. The prediction efficiency (square of the linear correlation between data and model prediction) is much higher than might be expected 67% on dayside and 73% on nightside, when seasonal, solar cycle, and nonlinear effects are ignored. The area underneath each filter is the expected value of the current driven by a steady input of unit amplitude that lasts longer than the impulse response (see equation 5 in McPherron et al., 2013).
The shape of the prediction filters is very similar to those found for the AL index (McPherron et al., 2015). The dayside filter rises rapidly from zero lag to a peak at ~40 min and then decays slowly for the next 2.5 hr. The nightside response is similar but it is delayed relative to the dayside peaking at ~60 min. The total lengths of the response functions are 3 hr. Table S2 shows the prediction efficiency of each of the coupling functions. Epsilon is very poor, VBs is better, and the remaining three are nearly equivalent.
We have also investigated how filter area changes as the data used to calculate the filter are based on progressively stronger coupling. This area corresponds to the asymptotic response of the FAC to a unit step in the coupling function. As shown in Figure S1 the area progressively decreases as more disturbed data are used in the calculation. This implies that the system is nonlinear with the output a successively smaller multiple of the input coupling function as driver strength increases. In the limit of saturation the output is constant regardless of the strength of the input.
Figure 4b presents the response of FAC to AL. These filters are not causal having output before zero lag because both are driven by the solar wind. The filters with AL as input are narrow pulses centered at zero lag. These transform AL to FAC with no time offset and a somewhat smoother waveform. Both filters are about ±30 min wide at their base. The filter for IUN on the nightside is slightly offset toward future lags (negative) suggesting that it is FAC creating AL. The nightside filter has a larger area than the dayside filter, which means nightside currents are stronger than dayside.
Several authors have examined the relation between the solar wind and substorms, and AMPERE FAC. Murphy et al. (2012) concluded that there is a reduction in FAC near the location of onset about 6 min prior to onset. Murphy et al. (2013) showed that the spatial distribution of current is highly structured in latitude. A technique to derive the location and strength of the R-1 and R-2 current densities was developed by Clausen et al. (2012), who demonstrated that the R-1 oval expands during the substorm growth phase and contracts during the expansion phase. This work was extended in a statistical study by Clausen, Baker, et al. (2013), who used SEA to study the relation of the R-1 and R-2 currents to substorm onset. Based on 772 onsets determined with Time History of Events and Macroscale Interactions during Substorms all-sky cameras, they showed that luminosity increases for about 10 min after onset while the AL index decreases for 20 min. Also, the diameter of the R-1 oval increases during the growth phase and for about 20 min after and then decreases. Dayside R-1 is larger in the growth phase while nightside R-1 is dominant in the expansion phase. Clausen, Milan, et al. (2013) repeated this analysis for three subsets chosen according to the size of the R-1 oval at onset concluding that the intensity of a substorm depends on the amount of open flux at expansion onset.
The preceding work was extended by Coxon et al. (2014a), who demonstrated that the strength of R-1 and R-2 currents increases as both the dayside reconnection rate (the phi coupling function) and the AL index increase. They found correlations of ~0.64 for current versus phi and close to −0.8 for the AL index. In both cases the correlations with R-1 current were higher than with R-2 current. Coxon et al. (2014b) performed a larger SEA using 2,900 SuperMag onsets. The results were similar to those described above but the larger list allowed subsets of onsets to be selected according to the SuperMag latitude of onset. As onset latitude decreases, the location of the R-1 and R-2 ovals decreases and their separation increases. Changes in current and oval size after onset also become larger.
Our results confirm and extend these studies. Our SEA and prediction filters show that dayside FAC respond earlier than nightside and are initially larger. At substorm onset the nightside current increases sharply and dominates. Simultaneously, there is a peak in solar wind coupling, the onset of a MPB, and the onset of a negative bay. The analysis clearly shows three substorm phases and their time constants similar to the results of Weimer (1994). The high prediction efficiency (73%) obtained between solar wind coupling and the nightside current indicates that the FACs are primarily driven by the solar wind. We find that the AL index, a good but a-causal predictor of FAC, indicates that they are both controlled by solar wind coupling.
In one respect our results differ from previous work. A recent study by Weimer et al. (2017) concludes that there is no evidence that FACs saturate with increasing interplanetary electric field. We find otherwise, although, that our saturation values are higher (~6 mV/m) than those found for the polar cap potential (3–5 mV/m). We have used median values rather than averages and applied a special technique to extend our estimates to higher values of the driver. Furthermore, we compare the FAC to an average over earlier values of the coupling function (coupling strength) rather than directly to the coupling values. Additionally, we correlated five different drivers with the FAC. Finally, we compared linear fits to saturation fits (both two parameter models) and found that the saturation fits are always better. Furthermore, our prediction filters show that the filter area decreases as we limit the filter derivation to progressively higher coupling strength indicating weaker coupling or saturation. We agree with Weimer et al. (2017) that if saturation occurs, it is at a much higher value than for the polar cap potential and that a definitive answer to the question of whether FAC saturates in response to the solar wind will require additional data at higher driver strengths.
Research by R. L. M. was self-supported. Xiangning Chu was supported by a NASA Fellowship NESSF grant NNX14AO02H. The AMPERE project was supported by the National Science Foundation under grant ATM-0739864 to The Johns Hopkins University Applied Physics Laboratory. Additional support was provided by NSF grant ATM-1003513. Solar wind data used to calculate the coupling function and the standard AL index data were downloaded from the NASA NSSDC. The SuperMag SML index data were downloaded from http://supermag.jhuapl.edu/indices/. The SuperMag SML onset list is available at http://supermag.jhuapl.edu/substorms/. AMPERE data are available via http://ampere.jhuapl.edu. The MPB index and a list of substorm onsets derived from it were created by Chu as part of his dissertation research. The MPB index time series and list of onsets can be requested at [email protected] or can be found as supporting information in McPherron and Chu (2016). Supplementary information supporting the conclusions of this paper are attached to this publication.
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