SOLAR WIND MAGNETIC FLUCTUATIONS AND ELECTRON NON-THERMAL TEMPERATURE ANISOTROPY: SURVEY OF WIND-SWE-VEIS OBSERVATIONS

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1 2016. The American Astronomical Society. All rights reserved. doi: / /833/1/49 SOLAR WIND MAGNETIC FLUCTUATIONS AND ELECTRON NON-THERMAL TEMPERATURE ANISOTROPY: SURVEY OF WIND-SWE-VEIS OBSERVATIONS M. L. Adrian 1,4, A. F. Viñas 1,P.S.Moya 1,2,3, and D. E. Wendel 1 1 NASA/Goddard Space Flight Center, Greenbelt, MD 20770, USA; Mark.L.Adrian@nasa.gov 2 Department of Physics, Catholic University of America, Washington DC 20064, USA 3 Departmento de Fısica, Facultad de Ciencias, Universidad de Chile, Santiago, Chile Received 2015 July 13; revised 2016 March 27; accepted 2016 July 17; published 2016 December 6 ABSTRACT The solar wind electron velocity distribution function (evdf) exhibits a variety of non-thermal features that deviate from thermal equilibrium. These deviations from equilibrium provide a local source for electromagnetic fluctuation emissions, including the commonly observed electron whistler-cyclotron and firehose instabilities. We present a systematic analysis of Wind-SWE-VEIS observations of solar wind electron plasma and associated Wind- MFI observed magnetic fluctuations. For the first time using the full solar wind electron distribution and its moments, without separation of the various electron components, we show clear evidence that the temperature anisotropy threshold of the parallel electron cyclotron anisotropic instability bounds solar wind electrons during slow solar wind periods. We also demonstrate that during periods of slow solar wind, collisions while infrequent are the dominant mechanism by which solar wind electrons are constrained, leading to isotropization. During fast solar wind periods, magnetic fluctuations and solar wind anisotropies are enhanced above the parallel whistler anisotropic threshold boundary and collisional effects are significantly reduced. Preliminary calculations further show that the oblique electron whistler mirror anisotropic instability bounds both the slow and fast solar wind. Regardless of speed, the solar wind electron thermal anisotropy appears globally bounded by the parallel electron firehose instability for anisotropies Te^ Te < 1. Our results indicate that collisions, while infrequent, play a necessary role in regulating the solar wind evdfs. In striking contrast to solar wind ions, solar wind electron plasma, when considered globally as a single evdf, is only marginally stable with respect to parallel propagating instabilities. Key words: instabilities kinematics and dynamics methods: data analysis plasmas solar wind turbulence 1. INTRODUCTION The flow of the super-alfvénic solar wind into the heliosphere is regulated by adiabatic expansion, plasma instabilities, binary particle Coulomb collisions, and the large-scale ambipolar electric field (Feldman et al. 1975; Scudder & Olbert 1979a, 1979b; Pilipp et al. 1987a, 1987b, 1987c; Marsch 1991; Salem et al. 2003). As the solar wind expands, both the plasma density and magnetic field strength ( B ) decrease monotonically with increasing radial distance. Furthermore, as the solar wind plasma expands into the heliosphere, the electron velocity distribution (evdf) exhibits a variety of non-thermal features (e.g., different electron populations, for example, for the core, halo, and strahl electron components with different temperatures, thermal anisotropy, suprathermal tails, and beam-like features) that deviate from thermal equilibrium. These non-thermal features are present even when the global evdf is treated as a single velocity distribution function (VDF) without decomposing it into its core, halo, and strahl populations. Conventional wisdom holds that collisions are rare in the heliospheric solar wind plasma and cannot constrain these deviations from thermal equilibrium; the collective behavior of this plasma system can only be mediated by fluctuations via wave particle interaction. This mechanism involves long-range correlation between plasma particles and plasma instabilities as the principal process of relaxation, whenever the plasma deviates from thermal equilibrium (Marsch 1991, 2006). These departures from thermal equilibrium 4 Corresponding Author: M.L. Adrian, Geospace Physics Laboratory, Mail Code 673, Heliophysics Science Division, Sciences and Exploration Directorate, NASA/Goddard Space Flight Center, 8800 Greenbelt Road, Greenbelt, MD , USA. appear not only for electrons, but also for other species like protons and heavy ions as well. To date, our understanding of what processes regulate the solar wind electron properties are not fully understood. Recently, Viñas et al. (2015) studying plasma relaxation, performed a comparative analysis of electron whistler-cyclotron and firehose fluctuations based upon anisotropic plasma modeled with Maxwellian and Tsallis kappa-like particle distributions in order to explain the correspondence relationship of the magnetic fluctuations as a function of the electron temperature and thermal anisotropy in the solar wind and magnetosphere plasmas. Their analysis is based on the correlation theory of the fluctuation dissipation theorem and the dispersion relation of transverse electromagnetic fluctuations, with wave vectors parallel to the uniform background magnetic field in both a finite temperature anisotropic thermal bi-maxwellian and non-thermal Tsallis kappa-like magnetized single electron proton plasma. Their results show that the electromagnetic fluctuations are enhanced and bounded along the instability thresholds of the electron whistler-cyclotron and firehose instabilities. Moreover, they show that there is an enhancement of the fluctuations level in the case of nonthermal Tsallis kappa-like distributions due to excess suprathermal particles. A long-time survey of solar wind proton temperature anisotropies observed by the two Faraday Cup (FC) instruments of the Solar Wind Experiment (SWE, Ogilvie et al. 1995) on the Wind satellite (Kasper et al. 2002) have shown direct correspondence to the measured magnetic fluctuation wave power (Bale et al. 2009) obtained by the 1

2 Magnetic Field Investigation (MFI) (Lepping et al. 1995). These studies show that solar wind proton temperature anisotropy Tp, > Tp, ^ is constrained by proton parallel beta b p = 8pnkT p B p B0 2 consistent with stability limitations imposed by both the proton firehose ( T^ p T p < 1) and mirror or Alfvén cyclotron instabilities ( T^ p T p > 1) ; where the parameters T p and T ^p are the proton parallel and perpendicular temperatures relative to the background magnetic field. From a purely theoretical perspective, Seough & Yoon (2012) and Seough et al. (2013) use quasi-linear fluctuation dissipation theory to demonstrate that the saturated states of the proton beta-anisotropy are bounded by the mirror and oblique firehose instabilities, producing signatures superficially similar to those observed in the data. However, to date, similar measured systematic results have yet to be performed for electrons in the solar wind. The only previous attempt to study the electron non-thermal effects is limited to a single report (S tverák et al. 2008) derived from a Maxwellian model-dependent approach that presents a statistical study of the electron thermal anisotropy. In their paper, S tverák et al. (2008) separate and model the electrons into core-halo components that does not consider magnetic fluctuations and is limited to a statistical study on the number of occurrences of the electron anisotropies with respect to the parallel electron beta ( b e ). These authors speculate that their data which include evdfs from Helios I, Cluster II (Samba), and Ulysses are most probably constrained by the oblique instability threshold, despite the fact that the threshold boundaries shown with their data are calculated for parallel propagation. Salem et al. (2003) carried out an observational study of the electron temperature anisotropy and heat flux with respect to the effects of Coulomb collisions via the collisional age (A e ) using the Wind-3DP electron observations. Although they do not calculate magnetic fluctuations or instability thresholds, they characterize the electron temperature, thermal anisotropy, and heat flux as a function of slow and fast solar wind, and the collisional age defined as the ratio between the expansion time and the collisional time (i.e., A e = t exp t cc ). Here, we like Bale et al. (2009) carry out a systematic analysis of electrons using the instrumentation aboard the Wind spacecraft to probe the possible correspondence of measured magnetic wave power fluctuations to anisotropy-driven electron instabilities. For the first time, our analysis considers only the global anisotropy of the electrons without any separation into its constituent components and employing Wind-SWE- Vector Electron and Ion Spectrometer (VEIS) solar wind electron measurements acquired for the same time interval considered by Salem et al. (2003) investigate the dependency of the global electron population parallel beta ( b e ) and temperature anisotropy ( G= e Te ^ Te ) as a function of physical parameters such as the number of occurrences, magnetic fluctuations, magnetic compressibility, and collisional age for periods of slow and fast solar wind. We do not consider here the large-scale effects on the electron VDFs of the ambipolar electric field since our analysis is local and spatially limited to 1 au. Our intent is to characterize the effect of wave particle interactions versus the degree of collisionality in regulating the global electron temperature anisotropy during slow and fast solar wind periods, where these processes play a role in the dynamics of the solar wind electron distribution and manifest Figure Wind orbital segments, color-coded as a function of the initial time of the orbital segment, identified as a result of the selection criteria 2 2 XGSE 0 where R = ( X + Y ) 1 2 GSE GSE GSE 50 - RE under the assumption that observations in this regime are of pristine solar wind. For reference, the figure contains model magnetosheath and magnetopause boundaries resulting from a solar wind pressure of 2.1 np and an interplanetary magnetic field z- component (IMF Bz) of 0 nt typical of a standard SSCWeb orbital analysis requests. The focus of this work is the collection of SWE observations of solar wind electrons and associated MFI data acquired during the first orbital segment shown in dark purple that encompasses data from 1995 January 01 (Day 001) as indicated by the filled dark purple spot with open saltire ( ) through 1995 July 31 (Day 212) as indicated by the filled dark purple diamond containing a saltire ( ). themselves throughout the Wind-SWE-VEIS solar wind measurements. 2. SOLAR WIND INSTRUMENTATION AND OBSERVATIONS Here we conduct an in-depth analysis similar to that performed for protons (Kasper et al. 2002; Bale et al. 2009), but focused solely upon Wind-SWE-VEIS (Ogilvie et al. 1995) observed solar wind electron plasma moments. As a first cut to this analysis, the Wind orbit between the years 1995 through the end of 2001 the period of SWE-VEIS operation have been examined to identify intervals of encountering pristine electron solar wind. Recognizing the fact that Wind maintains a low inclination with respect the solar ecliptic plane, our analysis seeks to avoid contamination from the electron foreshock by employing the caveat that the desired observations occur when the spacecraft is located at X 0 and 2 GSE GSE GSE RGSE = ( X + Y ) 50 - RE. As shown in Figure 1, this examination reveals the existence of 54 orbital periods matching these criteria. For reference, the figure contains model magnetosheath and magnetopause boundaries resulting from a solar wind pressure of 2.1 np and an interplanetary magnetic field z-component (IMF B Z ) of 0 nt typical of a standard SSCWeb orbital analysis request. Here, we present an analysis of the first of these orbital periods the deep purple trace of Figure 1 spanning from 1995 January 01 at 00:12:00-UT through 1995 July 31 at 01:48:00-UT, providing independent SWE-VEIS measurements of solar wind electron plasma; comparable to the volume of proton data analyzed by Bale et al. (2009). The three-dimensional VDF measurements used in our study have been obtained from the 3 s time resolution data of Wind- SWE-VEIS and the electron moment calculations have been 2

3 determined via the quadrature method over the whole electron VDFs (details of the instrument characteristics are given by Ogilvie et al. 1995). The SWE-VEIS instrument consists of six programmable analyzers that form three pairs of mutually orthogonal sensors. The analyzers measure electrons in the energy range from 7 ev to 25 kev in 16 logarithmically spaced energy steps with an energy resolution of about 6%. For solar wind electron studies the effective energy range has been constrained from 10 ev to 3 kev. Each sensor full energy sweep takes 0.5 s, which is also the highest time resolution at which the moments are determined. For statistical purposes the moments have been averaged out to the full satellite spin period of 3 s. The moment calculations have been corrected for the spacecraft potential (which usually ranges between 3 to 15 V depending upon solar wind conditions) using either the proton and alpha measurements from the Wind-SWE-FC experiment or the electron density estimates of the plasma frequency line from the Wind-WAVES experiment (Bougeret et al. 1995; Maksimovic et al. 1998). The higher-order moments (e.g., temperature and thermal anisotropy) have been calculated by properly shifting the VDFs into the solar wind frame using the proton bulk velocity interpolated to the electron times. Since we seek to implement a model-independent approach, based solely upon the use of moments derived from the entire observed electron VDFs, it is impractical to evaluate each of the 1.4 million SWE-VEIS solar wind electron plasma distributions employed in this study (distribution-by-distribution) for evidence of contamination from Earth s electron foreshock as manifested in the form of counter-streaming/ reflected electron beams. Therefore, we opt instead to perform an analysis of the cone angle of the interplanetary magnetic field (IMF) associated with each individual VEIS observation and then use this cone angle as a (circumstantial) proxy for the probability of any individual VEIS observation having direct connection to the electron foreshock. The cone angle of the IMF is here defined as q = cos -1 ( B B ), ( 1) B yielding a measure of the angle of the IMF with respect to the Earth Sun line. According to this definition, those VEIS observations possessing cone angles of 0 (parallel-) or 180 (antiparallel-propagation) possess the highest probability of potential contamination from the electron foreshock. Figure 2 presents such an analysis for the 1.4 million SWE- VEIS observations employed herein, binned in 10 increments. It is apparent from these data that less than 3% of the observations possess cone angles within 10 of being parallel/ antiparallel and less than 9% of the observations possess angles within 20 of parallel-/antiparallel-propagation. Hence, in excess of 90% of the data presented herein should represent observations of pristine electron solar wind plasma, free of contamination from Earth s electron foreshock. We conclude, therefore, that the results and conclusions derived from the SWE-VEIS data presented below should exhibit little or no influence from the presence of electron foreshock plasmas. Figure 3 presents the occurrence of the SWE-VEIS derived electron temperature anisotropy ( G= e Te ^ Te ) as a function of parallel electron beta ( b e ) separated as a function of slow/ fast solar wind with the delineating solar wind speed of X Figure 2. Distribution of the interplanetary magnetic field (IMF) cone angles for the SWE-VEIS data from the first Wind orbital segment utilized in this study. The cone angle (q B ) here is defined as the angle between the IMF (B) and B X. Since Wind is at low inclination angles with respect to the geocentric solar ecliptic (GSE) equatorial plane during this orbital segment, our conjecture is that only those data intervals where q B ~ 0 or 180 have the greatest probability of direct connection to Earth s electron foreshock, and thus, possible contamination from counter-streaming electron beams reflected back from that structure. These data indicate that less than 3% of the observations possess cone angles within 10 of being parallel/antiparallel and less than 9% of the observations possess angles within 20 of parallel-/antiparallelpropagation. Hence, in excess of 90% of the data presented herein should represent observations of pristine electron solar wind plasma, free of contamination from Earth s electron foreshock. V SW = 500 km s 1. The data are binned equally in log 10 -space such that D log ( b ) = Dlog ( G ) = ( 2) e The range of electron temperature anisotropy ( G e ) as a function of parallel electron beta ( b e ) is selected to match that of the theoretical work presented by Viñas et al. (2015) for comparison purposes. Note that binning/incremenatation is consistent with the resolution of VEIS (δe/e = 6%) in velocity space (δv/v ), particularly for values of be -Ge space equal to and greater than an equivalent value in log-space. The location of maximum occurrence for each distribution is indicated by an open-cross ( ) which corresponds to a pixel centered at ( be, G e) = ( 2.69, 0.93) for slow solar wind and carries information from 1420 observations, and a pixel of ( be, G e) = ( 1.02, 0.81) for fast solar wind and 583 observations. The solar wind electron data are presented against instability growth threshold contours of g = 10-1 Wce, 10-3 Wce and 10-4 Wce (where W ce is the electron cyclotron frequency) for the electron cyclotron-whistler instability (black lines), obliquely propagating electron whistler-mirror mode instability for g = 40 for g = 10-3 Wce (dark gray dashed line), and 10-4 Wce for the electron firehose instability (light gray dashed lines) assuming bi-maxwellian (M) and Tsallis kappa-like (k) particle distributions (Viñas et al. 2015). It must also be noted that, unlike the results presented by S tverák et al. e 3

4 Figure 3. This set of observations present a statistical overview of the Wind-SWE-VEIS observations of the solar wind electron distribution occurrence frequency organized as a function of parallel electron beta ( b e ) and electron temperature anisotropy ( Te^ Te ) for slow solar wind speed (V SW < 500 km s 1 ) on the left and fast solar wind (V SW = 500 km s 1 ) on the right. The data are plotted against theoretical thresholds for parallel propagating electron whistler-cyclotron instability (black lines for g = 10-1 W, g = 10-3 ce Wce and 10-4 Wce), obliquely propagating electron whistler-mirror mode instability for θ = 40 (dark gray dashed line for g = 10-3 Wce), and the parallel electron firehose instability (light gray dashed lines for 10-4 Wce) that have been derived by Viñas et al. (2015) assuming both bi- Maxwellian (M) and Tsallis kappa-like (k) electron distributions. The location of the maximum occurrence pixel of each distribution has been indicated using an open cross ( ). (2008), the results presented here are a model-independent approach and based solely on quadrature moments over the full electron velocity distribution, making no attempt to separate contributions from the solar wind electron core, halo, and strahl evdfs. Figure 3 shows similar results to S tverák et al. (2008). In comparing the threshold boundary 10-3 Wce in our plots, for the domain of the whistler-cyclotron instability ( G>1 e ), with that of S tverák et al. (2008) of 10-3 Wce it is clear that the slow wind data set is constrained by the instability threshold when considering the global electron anisotropy properties of the distribution without breaking it into components. Statistically, the peak of the number of occurrences lies just below the instability threshold displayed for 10-3 Wce in the slow solar wind while during fast solar wind periods the number of occurrences decreases and there are brief periods in the data that shift above this threshold boundary. This implies that during slow solar wind periods there seems to be a tendency for reducing the whistler anisotropic instability by constraining the anisotropy data below the threshold boundary, whereas during fast solar wind periods there are intervals where the tendency is to increase the anisotropy just above the instability threshold. This result, as we shall see, reinforces the currently held general belief that during slow solar wind periods, Coulomb collisions play a role in mediating the thermal anisotropy of the electrons. However, during fast solar wind periods, the Coulomb effects are reduced and wave particle kinetic instabilities mediate the electron plasma. The instability threshold boundary of 10-3 Wce provides a reasonable timescale of about 3.6 s for an average mean magnetic field of 10 nt, which is comparable to timescales of many electron kinetic processes in the solar wind. As such, we argue that the electron velocity distribution is stable or quasi-stable for the duration of the sampling period of the Wind-VEIS instrument. Before continuing our present analysis of the SWE-VEIS solar wind electron plasma data, we make one final note concerning Figure 3. Apparent within the data, regardless of solar wind speed, is the presence of a distinctive minimum apparently centered at G e = 1. While beyond the scope of our present effort, this feature could owe its presence to two possibilities: (1) instrumental or systematic errors in derivation of the electron plasma moments; or (2) a physical mechanism/ reason for a lack of solar wind electron isotropy. To date, reviews of the design and operation of the SWE-VEIS instrument, as well as the procedures employed to derive the electron plasma moments from the VEIS observations, have failed to reveal any instrumental or systematic error to explain a lack of observations in the vicinity of G e = 1. Hence, we speculate this feature is the result of processes the presence of the strahl, for example that limit the ability of the solar wind electrons to reach an isotropic equilibrium. But again, contemplation of the presence of this minimum feature is beyond the scope of this work and, having no bearing upon the analysis or conclusions that follow, will be left for future analysis. We next consider the potential correlation of the full solar wind electron distribution with magnetic field fluctuations. For each SWE-VEIS data point in the survey of Figure 3, a second window of high-resolution (up to 22 vectors s 1 ) MFI data, centered on the SWE-VEIS time stamp and averaged over the timescale of the electron measurements of the full distribution function, undergoes statistical analysis to determine a mean field value ( B 0 ) and a standard deviation ( db ). Figure 4 presents the distribution of the average normalized magnetic fluctuation amplitude á db B 0 ñ as a function of the pixelated be Ge parameter space for both slow and fast solar wind using an analysis similar to that presented by Bale et al. (2009). The results show that the average fluctuation amplitude increases, seemingly independent of temperature anisotropy, with increasing electron b e for the slow solar wind periods, reaching maximum amplitude for b e > 1. This trend is also observed during periods of fast solar wind but with maximum fluctuation amplitudes that extend to lower b e ( 0.5) and at both lower/higher electron thermal anisotropies. There is also evidence that there is a gradient in average fluctuation 4

5 Figure 4. Distribution of average magnetic fluctuation amplitudes á db B 0 ñfor slow/fast solar wind associated with the Wind-SWE-VEIS observations of solar wind electron plasma distributions where the location of the maximum occurrence pixel of each distribution from Figure 3 has been indicated using an open cross ( ). amplitude producing an enhancement along the instability threshold boundaries/edges for both solar wind speed conditions, suggesting that the instability thresholds bound the fluctuation amplitude. Moreover, the magnetic fluctuations are clearly enhanced at, and just above, the instability threshold of the whistler anisotropy instability during fast solar wind periods. Similar to Figure 3, the average normalized magnetic fluctuation amplitudes in Figure 4 are also constrained by the parallel electron whistler-cyclotron anisotropy instability threshold boundary depicted by the g = 10-3 Wce boundary associated with instability growth for G e > 1. Given that the data in Figure 4 presents the average normalized magnetic fluctuation amplitude in be -Ge parameter space, we briefly explore the actual distribution of normalized magnetic fluctuation amplitudes to which each pixel of be -Ge parameter space is exposed for a few representative pixels, as shown in Figure 5. Figure 5(a) reproduces the slow solar wind conditions of Figure 4 while Figure 5(b) shows the distribution of normalized magnetic fluctuation amplitudes for the peak occurrence pixel ( be, G e ) = ( 2.69, 0.93). The distribution of normalized amplitudes appears as a skewed-gaussian distribution possessing a mode at a normalized amplitude of and possessing a width of The conditions of the fast solar wind are presented once again in Figure 5(c) while the distribution of normalized fluctuation amplitudes for the peak occurrence pixel at ( be, G e) = ( 1.02, 0.81) are shown in Figure 5(d). Again, this distribution is a skewed-gaussian, with a mode at an amplitude of and width of Finally, we consider the conditions to which the pixel at the heart of the fluctuation hot spot in the fast solar wind data, centered at ( be, G e ) = ( 0.72, 0.66), is exposed. Figure 5(e) shows the location of that pixel, while Figure 5(f) presents the albeit limited distribution of normalized fluctuation amplitudes. Here, the distribution again resembles that of a skewed-gaussian distribution with a mode at an amplitude of and width of In these sample pixels, the distributions all appear to be skewed-gaussian in nature and narrowly confined/collimated in amplitude space hence the limited, approximately order of magnitude range of average normalized magnetic fluctuation amplitude governing the color bar presented in Figures 4 and 5. Collectively, these data indicate an increasing normalized fluctuation amplitude centroid and increasing spectral width in association with increasing solar wind speed even more so in the case of the fast solar wind magnetic fluctuation hot spot. These results lead to the natural questions: 1. Why are these magnetic fluctuation distributions skewed from a normal-gaussian? 2. Are there any physical conditions for this asymmetry or is there any systematic error in the data that yields such skewness? These are questions, although they are important, that are beyond the objectives of this paper. Figure 6 presents the magnitude of unnormalized magnetic fluctuations db averaged into bins of be -Ge parameter space for slow/fast solar wind. Regardless of solar wind speed, there is evidence of enhancements in magnetic fluctuation amplitude along the electron whistler-cyclotron and firehose instability thresholds, with the greatest enhancements observed during intervals of fast solar wind. Additionally, regardless of speed, it is clear from these data that an enhancement in magnetic, indicating that instabilities play a role in the isotropization of the solar wind electrons. The role of instabilities appears substantially more pronounced in the fast solar wind where the enhancement in magnetic fluctuation amplitude is greater than that for slow solar wind and disperses across a broader range of anisotropies fluctuation amplitude exists for plasmas near G = 1 e with decreasing b e for values below b = 1 Figure 7 presents the distribution of computed average parallel magnetic compressibility C B = db db db^ = e. db db ( 3) in the electron be -Ge parameter space for both slow and fast solar wind. The results clearly show that the magnetic compressibility is bounded along the instability threshold of the parallel whistler anisotropy instability at all b e values during slow solar wind periods. However, during high solar wind periods, there is evidence of an enhancement in compressibility above g = 10-3 Wce, a growth rate threshold 5

6 Figure 5. Overview of the normalized magnetic fluctuation amplitudes to which a sample population of be Ge pixels is exposed. Panel (a) reproduces the distribution of average magnetic fluctuation amplitudes for slow solar wind presented in Figure 4 while (b) shows the distribution normalized magnetic fluctuation amplitudes experienced by the peak occurrence pixel ( be, G e) = ( 2.69, 0.93) indicated by an open cross ( ). The distribution of normalized amplitudes appears as a skewed- Gaussian distribution that possesses a mode located at with a width of The fast solar average fluctuation amplitude distribution is presented once again in (c) while (d) presents the distribution of normalized fluctuation amplitudes for the peak occurrence pixel at ( be, G e ) = ( 1.02, 0.81). Again, this distribution is a skewed-gaussian, with a mode at an amplitude of and width of Finally, the pixel at the heart of the fast solar wind fluctuation hot spot centered at ( be, G e) = ( 0.72, 0.66) is presented in panel (e) while (f) presents the albeit limited distribution of normalized fluctuation amplitudes for this pixel. Again, the distribution loosely resembles that of a skewed-gaussian distribution whose mode is at an amplitude of and width of These sample pixels all display amplitude distributions that appear to be skewed-gaussian in nature and narrowly confined/collimated in amplitude space hence the limited, approximately order-of-magnitude range of average normalized magnetic fluctuation amplitude governing the color bar presented. boundary for the parallel electron whistler-cyclotron instability, which then decreases with increasing electron anisotropy ( G>1 e ). Next we consider the effect of Coulomb collisions depicted by the collisional age ( A E = t exp t cc ) (Salem et al. 2003) where t exp is the rate of radial solar wind expansion and t cc is the rate of electron collisions which defines the most probable number of collisions experienced by solar wind electrons during the radial expansion of the solar wind. The collisional age ( A E ) is estimated by integrating the number of collisions suffered by a thermal electron during the time of expansion of the solar wind over the scale of the density gradient, i.e., from R = 0.5 au to R = 1.0 au assuming the solar wind flow velocity U sw is constant and that density N e and temperature 6

7 Figure 6. Distribution of magnitude of unnormalized magnetic fluctuations db averaged into bins of be Ge parameter space for slow/fast solar wind associated with the Wind-SWE-VEIS observations of solar wind electron plasma distributions. The location of the maximum occurrence pixel of each distribution from Figure 3 has been indicated using an open cross ( ). T e vary with distance as R- 2 and R- 1 2, respectively (Salem et al. 2003). Here, we employ the algorithms of Salem et al. (2003) and calculate the electron collision frequency (n e ^ ) (Equation (5), Salem et al. 2003) and collisional age (A E ) (Equation (6), Salem et al. 2003) using these authors intermediate value for solar wind expansion (α = 0.45) and SWE-VEIS-derived bulk electron parameters (Ne, Te, Ve, etc.). Figure 8 presents the average collisional age áa E ñ of the SWE-VEIS observed electrons for slow and fast solar wind as a function of the electron be Ge parameter space. The results clearly show that slow solar wind is more strongly collisionally dominated than fast solar wind. In particular, the enhancement of the collisional age near the isotropy boundary (G e = 1) for slow solar wind, when compared to the magnitude of unnormalized magnetic fluctuation amplitudes of Figure 6, suggests that collisions dominate the isotropization of the electrons as they propagate to 1 au. In contrast, the data for fast solar wind is, overall, weakly collisional. Furthermore, a comparison between collisional age and unnormalized magnetic fluctuation amplitudes near the isotropy boundary ( G=1 e ) for fast solar wind indicates that these mechanisms are equally important to the isotropization of the electrons as they propagate to 1 au. It is also worth noting that the collisional age is also bounded along the whistler-cyclotron instability threshold during slow solar wind, whereas a moderate enhancement above this threshold is observed for fast solar wind conditions. Expanding upon these last points in detail, it is clear from the SWE-VEIS data presented herein that both instabilities and Coulomb collisions play a role in the isotropization of the solar wind electrons. This is particularly evident by the response of magnetic fluctuation amplitude and collisional age proximate to anisotropies of G e = 1. However, these data indicate a substantial difference as to the role of each mechanism in isotropization of the solar wind electrons. Notice from Figure 6 that the magnetic fluctuation amplitudes associated with G e = 1 increase by a factor of 3 5 with respect to those observed in association with anisotropic electron plasmas. In stark contrast, Figure 8 shows that the collisional age of these same electron plasmas increases by an order of magnitude or more. This difference in associated parameter response indicates that Coulomb collisions, while infrequent, are the dominant mechanism leading to the isotropization of solar wind electrons as they propagate to 1 au. All data Figures 3 4 and 6 8 clearly show that the solar wind electrons are constrained below the instability threshold of the electron firehose instability ( G<1 e ) for both slow and fast solar wind conditions. This suggests the tendency for stability with respect to whistler firehose modes. Finally, we consider the possible correlation between magnetic fluctuations and collisional age of the solar wind electron plasma. Figure 9 presents the distribution of normalized magnetic fluctuation amplitude ( db B 0 ) as a function of collisional age (A E ) where the data have been binned according to the relation D log ( db B ) = D log ( A ) = 0.02 ( 4) 0 for both slow and fast solar wind. The differences between slow and fast solar wind are striking. These results clearly show that the magnetic fluctuations associated with the slow solar wind typically peak at across a broad range of collisional age. For fast solar wind, however, the magnetic fluctuations are centered closer to a normalized amplitude of and are enhanced (i.e., the peak is elongated along the amplitude of magnetic fluctuation db B 0 ) and more confined to lower collisional ages in comparison to that of slow solar wind; simply due to the fact that the fast solar wind is collisionally younger than the slow solar wind. This result again reinforces the general belief that Coulomb collisions play a role in the evolution of magnetic fluctuations by mediating the thermal anisotropy of the electrons. Simply put, as Coulomb collisions isotropize the electrons, the ability of the plasma to generate anisotropic instabilities is reduced. Furthermore, this result shows that the solar wind electron collisional age is larger than that of solar wind protons (Bale et al. 2009) by an order of magnitude, particularly in the slow solar wind. 3. DISCUSSION AND CONCLUSIONS We have presented an observational study of the relaxation of solar wind electrons by two mechanisms e.g., wave particle interaction and Coulomb collisions during period of E 7

8 Figure 7. Distribution of magnetic compressibility á db db ñ for slow/fast solar wind associated with the Wind-SWE-VEIS observations of solar wind electron plasma distributions where the location of the maximum occurrence pixel of each distribution from Figure 3 has been indicated using an open cross ( ). slow and fast solar wind at 1 au using global properties of evdf. The results presented are a model-independent approach and solely based on quadrature moments over the global electron velocity distribution, without any attempt of separation into its components. Preliminary analysis of Wind-SWE-VEIS solar wind electron plasma and MFI magnetic field data presents a similar, but more comprehensive, picture of the solar wind electron plasma compared to a recent analysis carried out by S tverák et al. (2008) on which the velocity distribution of electrons was separated into its core and halo components via a model-dependent approach. The results of our analysis quite clearly show that solar wind electrons for anisotropies G e < 1 are highly stable and appear to be constrained well below the parallel electron firehose stability threshold of g = 10-4 Wce. This result is consistent with the results obtained by S tverák et al. (2008). When considering the anisotropy domain where G e > 1, however, the solar wind electron distribution is constrained by the parallel anisotropic electron whistler-cyclotron instability for slow solar wind conditions. However, when considering the instability threshold boundary of g = 10-3 Wce used by S tverák et al. (2008) during fast solar wind conditions, our results clearly indicate that the fluctuations are moderately enhanced above this boundary. This implies that the electrons are marginally stable, but there is some free energy available during these periods to drive the whistler anisotropic instability. The fast solar wind data presented in Figures 3 4 and 6 8 indicate that there exists an increased propensity for the parallel electron whistler-cyclotron instability to become unstable above the threshold of g = 10-3 Wce. This implies that during slow solar wind periods there is a regulating mechanism that keeps the instability limited and marginally bounded. We believe this conjecture to be consistent with the hypothesis that, while Coulomb collisions are infrequent during periods of slow solar wind, collisions as opposed to the generation of instabilities are the dominant mechanism by which solar wind electrons are constrained, leading to thermalization, as shown in Figure 8 for collisional age and also Figure 9 for magnetic fluctuations. Thus, our results are consistent with those obtained by S tverák et al. (2008), although these authors did not show any estimate of the collisional age. It is fair to say that some of the differences between S tverák et al. (2008) and the results shown here, can be due to S tverák et al.ʼs separation of the electron velocity distributions (via a model-dependent fitting approach to determine components) into core and halo populations. Another possible explanation could be the fact that the observed magnetic fluctuations are not necessarily parallel propagating and there is actually a large contribution of obliquely propagating whistler mirror waves contained within the data. This last point is also consistent with the fact that there is a large magnetic compressibility due to the enhancement of a parallel fluctuating component as shown in Figure 7. Moreover, the analysis of oblique electron modes, represented by the instability of g = 10-3 Wce at a propagation angle of q = 40, suggests that these thermal anisotropy instabilities are fully constrained, even for fast solar wind, by the oblique electron mirror mode instability threshold as shown in Figures 3 4 and 6 8. The results presented in Figures 8 and 9 clearly show that slow solar wind is more strongly collisionally dominated than fast solar wind. In other words, the slow wind is collisionally older than the fast wind with a tendency to isotropize, as suggested by the enhancement of the collisional age near the in Figure 8 and the extension of the magnetic fluctuations at higher collisional age values in Figure 8, recalling the comparison of the magnetic fluctuation versus collisional age for slow and fast solar wind periods shown in Figure 9. Although collisional effects seem to be important during slow wind intervals, the difference between the average level of magnetic fluctuations (Figure 6) associated with fast and slow wind is relatively small, even though during fast wind the fluctuations level tends to be larger than during slow wind intervals (Figure 9). In addition, from Figure 3 we isotropy boundary G = 1 e observe that for G > 1 e, and the fact that solar wind electrons seem to be in a stable state with respect to the firehose instability threshold. In summary, solar wind electrons seem to be in a state in which wave particle interactions and Coulomb collisions coexist and each the data appear to be well constrained by the parallel whistler instability threshold obtained considering strictly collisionless plasmas. Thus, wave particle interactions seem to play an important role even during slow wind events. However, collisional effects may explain the differences between fast and slow wind for anisotropies G < 1 e 8

9 Figure 8. Distribution of average collisional age áa E ñ for slow/fast solar wind associated with the Wind-SWE-VEIS observations of solar wind electron plasma distributions where the location of the maximum occurrence pixel of each distribution from Figure 3 has been indicated using an open cross ( ). Figure 9. Distribution of normalized magnetic fluctuation amplitudes ( db B 0 ) as a function collisional age ( A E ) for slow (left) and fast (right) solar wind. Note that the distribution of normalized fluctuation amplitudes for slow solar wind remains relatively flat with respect to collisional age with a centroid located at The distribution for fast solar wind is quite distinct with its collisional age limited to values below 60 and possessing a broadened/elongated distribution of amplitudes centered at a collisional age of A ~ 6 E. can be the dominant effect in regulating the evdf, dependent upon local conditions that are yet to be fully identified and understood. The results presented in Figure 9 clearly demonstrate the confinement of enhanced magnetic fluctuation for lower collisional age values during periods of fast solar wind. To this discussion, we add the question: why do the magnetic fluctuations remain enhanced during slow solar wind periods when collisional effects are stronger? Our observations appear contradictory to the generally held convention that collisions should quench the enhancement of magnetic fluctuations. Thus, a puzzle exists. We cannot, however, dismiss the role that local wave particle interaction processes may play in sustaining the magnetic fluctuations, even in slow solar wind periods. Nor can we rule out that fluctuations can be injected at large scales near the Sun and then cascade down to smaller scales and transported by the super-alfvénic solar wind flow (Vainio et al. 2003; Shergelashvili & Fichtner 2012). Future studies could focus on the level of fluctuations at or near the cyclotron frequency as opposed to the total power, which could be dominated at times by turbulence. An overall result of our analysis clearly indicates that the electron and magnetic fluctuation observations are well bounded against the parallel electron whistler firehose instability threshold in both the slow and fast solar wind. Therefore, we conclude that the fluctuation dissipation theory could well explain our results for slow solar wind conditions for a parallel propagation dispersion analysis of transverse fluctuations as shown by Viñas et al. (2015) for bi-maxwellian, magnetized electron proton plasma. We have also included in Figures 2 7 the threshold boundary of the firehose instability of g = 10-4 Wce obtained form the non-thermal kappa-like distribution at parallel propagation for comparison purposes. It is clear that, although the threshold boundary shifts closer to the observations for this mode, the electrons seem to be firehose stable in spite of the presence of a suprathermal distribution for all solar wind conditions. Similar results (not shown) are obtained for the whistler anisotropic instability. 9

10 And finally, we cannot overlook the simple fact that our analysis of magnetic fluctuations associated with the Wind- SWE-VEIS observations may be restricted by the MFI sampling resolution of 22 vectors s 1 which results in a Nyquist frequency of 11 Hz. Under these observational constraints, MFI may simply fail to sample the high-frequency magnetic fluctuations that are actually associated with the dynamics resulting in the solar wind electron distributions manifested by the Wind-SWE-VEIS data. In fact, the data presented in Figures 4 8 may be more representative of the fluctuations found within the intermediate frequency range lying between proton and electron dynamic scales. Summarizing our results in their entirety, the data above indicate that the solar wind electrons are extremely stable with respect to the parallel electron firehose instability in the lowanisotropy regime, and marginally stable in the high-anisotropy regime with respect to the parallel electron whistler-cyclotron instability. Yet, despite the apparent marginal ability to supply free energy to the parallel electron whistler-cyclotron instability in the high-temperature anisotropy regime, the associated magnetic fluctuation power is much lower than that of the solar wind protons due to the increased collisional age of the electron distribution. In short, the data indicate that the solar wind electrons undergo considerable relaxation during their transit from the Sun to 1 au. Yet, despite this relaxation, the solar wind electron distribution does not display an isotropic state. The conclusions above must be considered with some level of caution, however. While the volume of data considered above is comparable to that presented by Bale et al. (2009) for solar wind protons, the data herein only encompass 5% of a solar cycle in contrast to that of Bale et al. (2009). At this point, it is possible that solar cycle phase effects cannot be ruled out, and there is evidence in the SWE-VEIS data of this first orbital element that suggests but not presented herein that there may be some organization of the data as a function of Carrington rotation. Future studies are underway to incorporate additional viable, independent SWE-VEIS electron plasma observations from the remaining 53 identified Wind orbital segments into the results presented herein. In addition, efforts are underway to separate the solar wind electron plasma into its basic constituents core, halo, and strahl and then repeat the above analysis for each component separately, replicating the efforts of S tverák et al. (2008) more closely and systematically. While it is tempting to establish analogies between the results presented here for electrons and those of protons reported by Bale et al. (2009), we must remember that the thermal properties of electrons are very different from those of ions; including their characteristic times and spatial scales for wave particle interactions. Furthermore, the collisional processes that control the electrons and protons occur on very different scales, as clearly demonstrated by the results herein. The authors gratefully acknowledge Dr. Adam Szabo at NASA/Goddard Space Flight Center and the Coordinated Data Analysis Web (CDAWeb for providing access to the Wind-SWE-VEIS solar wind electron moments data, as well as the high-resolution Wind-MFI data, that formed the foundation to the work presented above. Additionally, the authors would like to acknowledge Dr. Lynn Wilson, III for his numerous insightful discussions and comments. P.S.M. is grateful for the support of CONICyT Chile through FONDECyT grant No and Conicyt PIA project ACT1405. REFERENCES Bale, S. D., Kasper, J. C., Howes, G. G., et al. 2009, PhRvL, 103, Bougeret, J.-L., Kaiser, M. L., Kellogg, P. J., et al. 1995, SSRv, 71, 231 Feldman, W. C., Asbridge, J. R., Bame, S. J., Montgomery, M. D., & Gary, S. P. 1975, JGR, 80, 4181 Kasper, J. C., Lazarus, A. J., & Gary, S. P. 2002, GeoRL, 29, 1839 Lepping, R. P., Acŭna, M. H., Burlage, L. F., et al. 1995, SSRv, 71, 207 Maksimovic, M., Bougeret, J.-L., Perche, C., et al. 1998, GeoRL, 8, 1265 Marsch, E. 1991, in Physics of the Inner Heliosphere II, Vol. 21 ed. R. Schwenn & E. Marsch (Berlin: Springer) Marsch, E. 2006, LRSP, 3, 1 Ogilvie, K. W., Chornay, D. J., Fritzenreiter, R. J., et al. 1995, SSRv, 71, 55 Pilipp, W. G., Miggenrieder, H., Montgomery, M. D., et al. 1987a, JGR, 92, 1093 Pilipp, W. G., Muehlhaeuser, K.-H., Miggenrieder, H., Montgomery, M. D., & Rosenbauer, H. 1987b, JGR, 92, 1075 Pilipp, W. G., Muehlhaeuser, K.-H., Miggenrieder, H., Rosenbauer, H., & Schwenn, R. 1987c, JGR, 92, 1103 Salem, C., Hubert, D., Lacombe, C., et al. 2003, ApJ, 585, 1147 Scudder, J. D., & Olbert, S. 1979a, JGR, 84, 2755 Scudder, J. D., & Olbert, S. 1979b, JGR, 84, 6603 Seough, J., & Yoon, P. H. 2012, JGR, 117, A08101 Seough, J., Yoon, P. H., Kim, K.-H., & Lee, D.-H. 2013, PhRvL, 110, Shergelashvili, B., & Fichtner, B. 2012, ApJ, 752, 142 S tverák, Š, Trávícĕk, P., Maksimovic, M., et al. 2008, JGR, 113, A03103 Vainio, R., Laitinen, T., & Fichtner, H. 2003, A&A, 407, 713 Viñas, A. F., Moya, P. S., Navarro, R. E., et al. 2015, JGR, 120,

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