ABSTRACT
We present observational evidence of core electron heating in solar wind reconnection exhausts. We show two example events, one which shows clear heating of the core electrons within the exhaust, and one which demonstrates no heating. The event with heating occurred during a period of high inflow Alfvén speed (VAL), while the event with no heating had a low VAL. This agrees with the results of a recent study of magnetopause exhausts, and suggests that similar core electron heating can occur in both symmetric (solar wind) and asymmetric (magnetopause) exhausts.
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1. INTRODUCTION
Magnetic reconnection is a universal plasma process that converts energy stored in the magnetic field to plasma energy, both kinetic (in the form of plasma jets) and thermal (heating of the plasma). Plasma jetting is well understood theoretically and has been widely confirmed by in situ observations in space plasmas (e.g., Sonnerup et al. 1981; Gosling et al. 2007b).
In recent years, several studies have focused on the problem of electron acceleration and heating. Simulations and observations have shown that suprathermal electron populations can be effectively accelerated by the process of reconnection (e.g., Hoshino et al. 2001; Øieroset et al. 2002). Scudder et al. (2012) showed observations of electron heating within the electron diffusion region (EDR) at the Earth's magnetopause, accompanied by signatures of demagnetization of the electrons. The region exhibiting these signatures is spatially limited to the area close to the EDR (Scudder & Daughton 2008). The focus of this letter is on the plasma entering the exhaust region along the boundaries of the exhaust, at distances sufficiently far from the EDR that the electrons do not pass through the EDR or its vicinity. In the solar wind, a few reported reconnection exhausts have shown no core electron heating (Gosling et al. 2005b, 2007a). In contrast, observations in reconnection exhausts in the Earth's magnetopause (Gosling et al. 1986; Phan et al. 2013) and magnetosheath (Phan et al. 2011) have shown clear evidence for electron heating. This suggests that the degree and characteristics of core electron heating depend strongly on plasma parameter regimes and/or the boundary conditions of a reconnecting current sheet.
Recent observations (Phan et al. 2013) of core electron heating in reconnection exhausts at the Earth's magnetopause indicate that the heating is related to the inflowing Alfvén speed for asymmetric reconnection (VAL, asym), as defined by Cassak & Shay (2007):
In Equation (1), ρ represents the ion mass density and BL represents the component of the magnetic field in the outflow (L) direction, in minimum variance LMN coordinates. The subscripts 1 and 2 denote measurements from opposite sides of the reconnection exhaust region.
Quantitatively, the core electron heating found by Phan et al. (2013) in exhausts at Earth's magnetopause is given by
where mi is the proton mass. Equation (2) can be interpreted as a statement that a small fraction (∼1.7%) of the inflow magnetic energy per proton–electron pair is converted to thermal (core) electron heating. In the solar wind at 1 AU, the Alfvén speed is typically low (∼50 km s−1) and field shear angles are typically small compared to that at the magnetopause. For typical solar wind conditions Equation (2) yields predicted core electron temperature increases of less than 1 eV. This may help to explain why core electron heating has not previously been observed in solar wind reconnection exhausts.
In this Letter, we present a study of two solar wind reconnection exhausts, one where core electron heating was present and one where it was not. In the first event VAL, asym was 135.7 km s−1 whereas in the second event VAL, asym was 56.6 km s−1. We compare the observed core electron heating in these two events to what would be predicted by Equation (2). The agreement between observed and predicted core electron heating suggests that Equation (2) may not be limited solely to the magnetopause, but may have applicability to reconnection exhausts in general.
2. ELECTRON FITTING
2.1. Fitting Solar Wind Electrons
The solar wind electron velocity distribution function (eVDF) includes both thermal (core) and suprathermal (halo and strahl) components. Accurate measurements of the core electron temperature are difficult: since the suprathermal populations contribute substantially to the total thermal energy density (Feldman et al. 1975), the accuracy of simple temperature moments is limited. Fits that separate the distinct core, halo and strahl populations are required for accurate core measurements.
The core electron temperature in the solar wind typically ranges from about 7 to about 17 eV (Feldman et al. 1977), considerably smaller than the core electron temperatures encountered in the magnetosheath. At the low end of this temperature range, electron measurements can be significantly affected by spacecraft potential and by the finite energy threshold of electron detectors (Salem et al. 2001).
We have developed a fitting procedure which isolates and separately fits the thermal (core) and suprathermal (halo/strahl) solar wind electron populations, and which corrects for spacecraft potential using an accurate absolute density reference obtained from the thermal noise spectrum provided by the Wind/WAVES Thermal Noise Receiver (TNR; Bougeret et al. 1995). Our method, outlined briefly below, is described in full in Pulupa et al. (2014). The electron velocity distribution function (eVDF) is measured in the spacecraft frame, using data from the low- and high-energy electrostatic analyzers on the Wind spacecraft (EESA-L and EESA-H), which are part of the three-dimensional plasma (3DP) instrument suite (Lin et al. 1995). The accumulation time for measurement of the full eVDF is 3 s, corresponding to one spacecraft spin period. Due to telemetry limitations, full eVDFs are typically transmitted to the ground only once every 90 s.
The electron energies are corrected using an initial estimate of the spacecraft floating potential obtained from a simple current balance model (Salem et al. 2001). The resulting eVDF is transformed to a field-aligned solar wind frame, using magnetic field data from the Wind Magnetic Field Investigation (MFI) magnetometer (Lepping et al. 1995). Using a model eVDF featuring a bi-Maxwellian core and a bi-kappa halo (Maksimovic et al. 2005), fits are performed to perpendicular and parallel cuts through the eVDF. From these fits, the density, temperature, velocity, and heat flux are obtained for the core, halo, and strahl populations, as well as for the eVDF as a whole.
As a final step, the accuracy of the potential estimate is confirmed by comparing the fit density to the density obtained from the thermal noise spectrum. Because the thermal noise is not sensitive to spacecraft potential, it offers an accurate reference value for the total electron density. If the densities do not agree, the spacecraft potential estimate is iteratively adjusted, repeating the entire fitting procedure until the fitted eVDF density matches the thermal noise density. Once this procedure is complete, a final fit is performed to the correctly adjusted eVDF and the final moment values are obtained.
Because the core electron temperature in the solar wind is similar to typical spacecraft floating potential values, the core electron moments are particularly sensitive to potential effects. The ability to determine the spacecraft potential using independent reference values from TNR, coupled with our robust analysis and fitting procedure, improves the accuracy of the core moments and enables reliable detection of small changes in core electron temperature.
2.2. Fitting in Reconnection Exhausts
The algorithm described above was optimized for automated operation over years of data, enabling detailed statistical analysis of tens or hundreds of thousands of eVDFs (Bale et al. 2013; Pulupa et al. 2014). The basic principles of the algorithm remain valid even within reconnection exhausts. However, our approach must be re-optimized for studies of individual reconnection events, which often occur during periods of non-quiet time solar wind such as coronal mass ejections (CMEs).
As shown by Scudder & Daughton (2008), electrons in the vicinity of the EDR can exhibit agyrotropy, which would invalidate the gyrotropic assumption inherent in our fitting algorithm. Variation of the magnetic field direction during the accumulation time for each eVDF can also introduce aliasing errors during times when the magnetic field is changing rapidly. Therefore, for each eVDF, we both compute the agyrotropy A∅ using the pressure tensor (Scudder & Daughton 2008, Appendix A) and calculate the variation in magnetic field direction using the highest cadence (11 Hz) magnetic field data. For each eVDF included in this study, the measured agyrotropy was small (A∅ < 0.1) and the variation in the direction of B was less than the 5
6 angular resolution of the electrostatic detectors. This implies that, for the exhausts in this study, the gyrotropic assumption is valid and effects of aliasing due to variation in B are negligible.
Within reconnection exhausts and during events such as CMEs, additional populations of electrons may be present in the solar wind. For example, during CMEs, bi-directional streams of suprathermal electrons are often seen, rather than the uni-directional strahl typical of the quiet time solar wind (Gosling et al. 1987). Electron distributions within reconnection exhausts can also exhibit complex structure in the suprathermal electrons (Lavraud et al. 2009).
These additional electron populations can confound the automated algorithm, which is based upon detection and isolation of a uni-directional strahl. Without the ability to clearly isolate the thermal from the suprathermal electrons, the suprathermal electrons will affect the fit of the core, making an accurate estimate of the core temperature impossible. For this reason, in the present study we must inspect each eVDF individually, and manually adjust the core fitting parameters if necessary to ensure that we are not including suprathermal electrons in the core fit.
In addition to these complications in the electron data, the thermal noise data can also be affected during reconnection exhausts. Electrostatic plasma wave activity has been observed during reconnection exhausts in the solar wind (Huttunen et al. 2007). During periods of intense electrostatic wave activity, the thermal noise spectrum, which we use as a basis for the electron fitting algorithm, can be affected. Based on the maximum amplitudes of wave activity reported by Huttunen et al. (2007), we anticipate that it is still possible to accurately determine the plasma frequency from the thermal noise spectrum, and therefore determine the total electron density. However, since this measurement of electron density is an essential component of the fitting procedure, we must manually verify the correctness of the plasma line determination for each electron measurement.
Thus, in contrast to the automated algorithm for the solar wind, our procedure for studying electrons near reconnection exhausts requires manual verification for each measurement. Detailed examples are discussed in the following section.
3. OBSERVATIONS
We present data for two Wind reconnection exhausts, one showing core electron heating and one showing no core electron heating. The event with heating was observed on 1997 November 23, and the one without was observed on 2005 January 11. Overview plots of these events, which were previously studied by Gosling et al. (2005a) and Phan et al. (2009), are shown in Figures 1 and 2, respectively. The reconnection exhaust is recognized in the data by the presence of roughly Alfvénic accelerated outflows in the L direction, within the region where the field reverses direction. The changes in VL and BL are correlated on one edge and anti-correlated on the other edge of each exhaust, consistent with Alfvén waves propagating in opposite directions along B away from a reconnection site (Gosling et al. 2005a). Both events exhibit large shear angles across the exhaust, with measured shear angles of 155° for the 1997 November 23 exhaust and 162° for the 2005 January 11 exhaust (Phan et al. 2009).
Figure 1. Solar wind reconnection exhaust observed on 1997 November 23. Panel (a) shows the thermal noise spectrum from the Wind/WAVES TNR, with the electron densities derived from the plasma line shown as white diamonds. Panel (b) shows the magnetic field observed at Wind in LMN minimum variance coordinates. Panel (c) shows the proton LMN velocity, while panel (d) shows the proton density. The core electron perpendicular temperature is shown in panel (e), the core parallel temperature in panel (f), and the ratio of parallel to perpendicular core temperature in panel (g). Temperatures derived from automated fitting techniques are shown as black dots; temperatures derived from hand optimization of the fitting technique are indicated by red asterisks. Dashed vertical lines denote the boundaries of the exhaust.
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Figure 2. Solar wind reconnection exhaust observed on 2005 January 11. The format of this figure is identical to that of Figure 1. Hand optimization for the electron fits was not needed for this event, so only the automated fits are shown in panels (e)–(g).
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Standard image High-resolution image3.1. 1997 November 23: Evidence for Core Electron Heating
For the reconnection exhaust observed by Wind on 1997 November 23, both the automated and manually optimized fitting methods reveal increases in both the perpendicular and parallel core electron temperatures within the exhaust region. The core temperature is systematically lower for the fits obtained by hand than for the automated fits. This is likely due to the fact that the exhaust occurred within a CME in which bi-directional streams of suprathermal electrons were present: a portion of those bi-directional suprathermal electrons tend to be included in the automated core fit, artificially increasing the core temperature.
The heating is particularly evident in the parallel direction (Figure 1(f)), with the core temperature increasing from 12–15 eV (as measured with the manual fitting technique) in the region before the exhaust, to 20–25 eV within the exhaust, and returning to about 10–13 eV in the region following the exhaust. There is less, but still noticeable, heating in the perpendicular direction (Figure 1(e)), where the core temperature increases from 13–14 eV prior to the exhaust, to 15–17 eV within the exhaust, before dropping back down to about 11–13 eV following the exhaust. The ratio of parallel to perpendicular core temperature (Figure 1(g)) increases from approximately 1.0 (i.e., nearly isotropic) outside the exhaust to approximately 1.5 within, illustrating preferential heating in the parallel direction.
Several examples of manual fits to the eVDFs are shown in Figure 3. The heating can be seen in Figure 3 as a broadening of the distribution function fits within the reconnection exhaust. These fits are shown in the center column of the figure. The heating is particularly evident in the parallel direction. Taking the definition of total (core) electron temperature,
and using the variation between individual measurements to characterize the uncertainty of the measurement, we find that the electron heating ΔTe is equal to 4.6 ± 1.3 eV.
Figure 3. Perpendicular and parallel cuts through fitted eVDFs, at times before, during, and after the 1997 November 23 reconnection exhaust shown in Figure 1. Data points from EESA-L and EESA-H are shown with diamonds and asterisks, respectively. The one count levels for each instrument are also shown with dashed curves lying below the data points. The perpendicular cuts are shown in the top row, with the core electron perpendicular fit indicated with a red line. The parallel cuts are shown below, and the parallel core fit is indicated with a green line. Evidence of heating can be seen in the broadening of the core fit within the exhaust, in both perpendicular and parallel directions. Core heating is particularly evident in the parallel direction.
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Standard image High-resolution imageWe can compare our observations of core electron heating within this solar wind exhaust with the results of the Phan et al. (2013) study of magnetopause exhausts using Equation (2). In order to be as consistent as possible with Phan et al. (2013), we use the fully asymmetric form of the Alfvén speed as defined in Equation (1), despite the fact that this solar wind reconnection event is nearly symmetric. For this event, VAL, asym is 142.3 ± 5.5 km s−1, yielding a predicted ΔTe, pred of 3.6 ± 0.3 eV. Thus the observed core electron heating in this solar wind event is slightly higher than predicted, although the difference is within the limit of experimental uncertainty.
3.2. 2005 January 11: No Core Electron Heating
The exhaust observed on 2005 January 11 is shown in Figure 2. This event shows no evidence of electron heating, with the core temperature remaining at about 9–10 eV in both the perpendicular and parallel directions both inside the reconnection exhaust and on either side. Figure 4 shows, in a format similar to Figure 3, cuts through the fitted electron distribution function for the 2005 January 11 event. The red and green fit curves show no broadening within the exhaust, consistent with previous solar wind observations (Gosling et al. 2005b, 2007a). Overall we find that for this event ΔTe = −0.1 ± 0.7 eV. The measured VAL, asym for this event is 56.6 ± 3.1 km s−1 and the amount of core electron heating predicted by Equation (2) is 0.6 ± 0.1 eV. As with the 1997 November 23 event, these measurements agree with the prediction from magnetopause observations within experimental uncertainties.
Figure 4. Perpendicular and parallel cuts through fitted eVDFs, at times before, during, and after the 2005 January 11 reconnection exhaust shown in Figure 2. The format of this figure is identical to that of Figure 3. In both the perpendicular and parallel directions, no core electron heating is evident.
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4. SUMMARY
Previous, limited studies revealed no evidence for core electron heating within reconnection exhausts in the solar wind. Based on studies of reconnection exhausts at Earth's magnetopause, Phan et al. (2013) suggested that this lack of evidence for heating in solar wind exhausts was related to the fact that Alfvén speeds in the solar wind are generally, although not universally, modest compared to those in the vicinity of the Earth's magnetopause. The present study of two solar wind exhausts reveals that when the Alfvén speed, and particularly VAL, asym, is higher than usual, and the shear angle is large as in the 1997 November 23 event, core electron heating consistent with that observed in reconnection exhausts at the dayside magnetopause can be detected. But when VAL, asym is relatively modest, as in the 2005 January 11 exhaust, core electron heating is either absent or too small to be detected.
The results of this initial study are, within experimental uncertainty, consistent with the Equation (2) that was obtained in the Phan et al. (2013) study. Magnetopause reconnection is highly asymmetric—the density, magnetic field, and Alfvén speed vary significantly between the magnetosheath and magnetosphere. In contrast, reconnection exhausts in the solar wind tend to be more symmetric, with similar parameters on each side of the exhaust. This preliminary study suggests that symmetric and asymmetric reconnection may behave similarly with respect to the heating of the core electrons.
A study featuring only two reconnection exhausts is suggestive, but not definitive. Statistical analysis of a larger number of solar wind reconnection exhausts will, in the future, provide a more definitive test of Equation (2) for the solar wind. Such an analysis can provide the theory and simulation communities with a rigorous set of constraints against which proposed core electron heating mechanisms can be tested.
This work was supported by NASA grants NNX14AC09G, NNX10AC03G, NNX10AF26G, NNX08AO83G, and NNX08AO84G and SHINE grant 0962726.