JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A07210, doi:10.1029/2011JA016598, 2011
Energetic electron spectra in Saturn’s plasma sheet J. F. Carbary,1 C. Paranicas,1 D. G. Mitchell,1 S. M. Krimigis,1 and N. Krupp2 Received 25 February 2011; revised 25 March 2011; accepted 19 April 2011; published 12 July 2011.
[1] The differential spectra of energetic electrons (27–400 keV) in Saturn’s plasma sheet can be characterized by power law or kappa distributions. Using all available fluxes from 2005 to 2010, fits to these distributions reveal a striking and consistent pattern of radial dependence in Saturn’s plasma sheet (∣z∣ < 1 RS = 60,268 km). The electron spectral indices show harder spectra at large radial distances (20–30 RS), softer spectra at middle radial distances (10–20 RS), and very steep spectra inside the orbit of Rhea (∼8.5 RS). The dayside spectra are somewhat harder than the nightside spectra outside the orbit of Titan (∼20 RS), although there is no local time dependence inside ∼10 RS. This spectral behavior exhibited essentially no dependence on pitch angle and remained remarkably constant throughout the Cassini mission. Inward of about 10 RS, the presence of the electron radiation belts and losses of lower‐energy electrons to the gas and grain environment give rise to the very hard spectra in the inner magnetosphere, while the hard spectra in the outer magnetosphere may derive from auroral acceleration at high latitudes. The gradual softening of the spectra from 20 to 10 RS is explained by inward radial diffusion. Citation: Carbary, J. F., C. Paranicas, D. G. Mitchell, S. M. Krimigis, and N. Krupp (2011), Energetic electron spectra in Saturn’s plasma sheet, J. Geophys. Res., 116, A07210, doi:10.1029/2011JA016598.
1. Introduction [2] The most intense fluxes of energetic electrons at Saturn are found in the region of the strong dipole (r < 10 RS). Here, the magnetic field of the planet guides the motion of these particles. Because perturbations to that field tend to be small in comparison with the steady state field, particle trapping timescales can be very long. At greater distances from Saturn, the dipole weakens and various current systems play a role in determining the net magnetic field. This paper examines the spectral behavior of the energetic electrons from the radiation belt to the outer magnetosphere to understand energization processes. [3] In planetary magnetospheres, the differential spectrum of energetic electrons (defined here as E > 10 keV) is often characterized by a power law distribution in energy: jðEÞ / E
ð1Þ
where j is the differential flux (electrons · cm−2 · s−1 · keV−1), E is energy in keV, and g is the spectral index. Alternately, the kappa distribution offers a more subtle and accurate description of the differential spectrum: jðEÞ / ð1 þ E=E0 Þ
ð2Þ
where E0 is a characteristic energy and is the kappa index. In the limit that E E0, the kappa distribution becomes the 1 Johns Hopkins University Applied Physics Laboratory, Laurel, Maryland, USA. 2 Max‐Planck‐Institut für Sonnensystemforschung, Katlenburg‐Lindau, Germany.
Copyright 2011 by the American Geophysical Union. 0148‐0227/11/2011JA016598
power law distribution; in the opposite limit, E0 may be thought of as analogous to the thermal energy of a Maxwellian distribution. The g and indices generally have negative values; values near −1 represent “hard” spectra, while values of −4 or less are considered “soft” spectra. [4] These spectral forms appear often in the terrestrial plasma sheet [e.g., Bame et al., 1967; Montgomery, 1968; Christon et al., 1988] and in the magnetospheres of the outer planets [e.g., Krimigis et al., 1983; Mauk et al., 1987; Krimigis et al., 1990]. Recent analysis of Saturn electrons from 0.6 eV to 15 MeV employed a double‐ distribution to fit the entire spectrum; equations (1) and (2) consider only the higher‐ energy part [Schippers et al., 2008; Arridge et al., 2009]. [5] Changes in the g or indices can be associated with the electron energy gain or loss. For example, when they increase, there are more particles at higher energy; this is termed a “hardening” of the spectra. Conversely, when the indices decrease, the spectra “soften.” For relativistic electrons, the spectrum generally softens (becomes steeper) for inward transport in a dipole field when the relativistic adiabatic invariants of motion are conserved. Therefore, the indices represent a convenient parameterization of electron spectra that implies electron energization or de‐energization. [6] A few previous studies have considered the behavior of the spectral index in Saturn’s magnetosphere. Periodicities in charged particles at Saturn were originally discovered in the electron spectral index g observed during the Voyager encounters [Carbary and Krimigis, 1982]. The ratio of electron fluxes at two energies (110–365 keV/220– 385 keV), which is a crude spectral index, indicated that the electron spectra generally became harder for L < 10 [Krimigis et al., 1983; Carbary et al., 2009]. This behavior implies that inward radial diffusion should be occurring to
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Figure 1. Comparison of the various statistical measures of electron fluxes binned within 1 RS of the equatorial plane in the radian range 14–16 RS. Crosses represent all differential fluxes of 27.1– 49.5 keV electrons measured during 2007 at 16 different pitch angles. Characteristic fluxes at each pitch angle can be determined from the mean and standard deviation (red), the median and quartiles above and below the median (green), or by the mean of the logarithms of the fluxes (blue). energize electrons in this energy range. However, examination of a single equatorial pass of Cassini in 2006 suggested that the spectral slope of energetic electrons had very little radial dependence [Schippers et al., 2008]. [7] The present study considers energetic electron spectra (27–400 keV) by using spectral indices derived from fitting the differential spectra to equations (1) and (2). Electron data from 6 years of observation (2005–2010) are used to derive a complete statistical survey of such electrons in Saturn’s plasma sheet. Here, the plasma sheet is defined purely by geometry: ∣z∣ < 1 RS. Because the plasma sheet warps away from the equator in the outer magnetosphere [Arridge et al., 2008], the analysis is confined to cylindrical radial distances less than 30 RS, which is close to the “hinge” point in the warping model. The spectral indices are examined in radial distance, pitch angle, mission epoch, and local time using observations from 2005 through 2010.
2. Instrumentation and Data Set [8] The energetic electron data are from the Low Energy Magnetospheric Measurement System (LEMMS) on the Cassini spacecraft. LEMMS is a subsystem of the Magnetospheric IMaging Instrument (MIMI), which has been fully
described by Krimigis et al. [2004]. LEMMS measures electrons in two energy ranges: the “C” detectors observe electrons in eight log‐spaced channels between 18 keV and 475 keV, while the “E” detectors observed electrons in five log‐spaced channels from 110 keV to over 4 MeV. Operating in a lower energy regime, the C channels offer better statistics than the E channels, albeit at the cost of higher backgrounds. In some cases, C backgrounds are sufficiently high as to render the data unusable. Furthermore, the turntable upon which LEMMS is mounted ceased operation in early 2005, which prevents continuous sampling of the complete pitch angle distribution. Roussos et al. [2007] give a complete discussion of the limitations of the LEMMS electron detectors. Electron data examined here were either fully background corrected or, that failing, were removed from the data set. [9] To facilitate processing and improve statistics, the electron fluxes were averaged from their original 5.375 s resolution to 6 min (0.1 h). Furthermore, the fluxes were averaged into 16 pitch angle bins of 180°/16 = 11.25° each. The pitch angles were determined from the observed magnetic field from the Cassini magnetometer [Dougherty et al., 2004]. Only the C1 through C6 electron channels (27.1–496 keV) were employed. The C0 channel was not used because it
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Figure 2. (top) The median values are used to characterize the fluxes in range and pitch angle bins. (bottom) These values are collapsed in pitch angle by computing the means and medians in each radial bin. Tick marks indicate the orbits of Saturn’s large moons. most frequently experienced debilitating background; channels above C6 were excluded because fluxes at their energies are negligible the outer magnetosphere (r > 15 RS). [10] Each 6 min sample was tagged with time and spacecraft position in the Saturn‐Z‐Sun (SZS) coordinates x completes the (^z axis along spin axis, ^ y = ^z × ^ vsun, and ^ right‐hand system, with ^ vsun being a vector from Saturn to the Sun). The samples were constrained to lie within ±1 RS of the equator (z = 0); other samples were not used. Data outside of a model magnetopause distance were also excluded [Arridge et al., 2006]; this filtering applied a high solar wind ram pressure (0.020 nPa), which ensures all data lie within the magnetopause. The 6 min averages of the
C1–C6 electrons were then binned in cylindrical radial distance and pitch angle, with radial bins of 2 RS.
3. Binning in Radial Distance [11] Before computing spectra indices, the statistical behavior of the electrons was formulated by binning in radial distance and pitch angle over a time period of 6 years. Two types of binning were considered for finding the characteristic fluxes within a bin. First, simple averaging offered the usual summary, with standard deviations measuring the range of values in the bin. However, fluxes vary considerably in Saturn’s outer magnetosphere so that averages and
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Figure 3. Fitting the differential spectra of electrons 27–400 keV. The symbols represent the median fluxes centered on the radial bin at 17 RS (16–18 RS) and pitch angle bin 95.6° (90°–101°). The vertical extension of each point indicates the upper and lower quartiles, while the horizontal extent measures the width of the energy channel. The blue line shows a power law fit; the red line shows a distribution fit. standard deviations capture not the characteristic flux but are skewed by outliers in the distribution. Even at the same location, extreme variations of an order of magnitude or more in the electron fluxes arise from plasma injections in the inner and middle magnetosphere [e.g., Paranicas et al., 2007, 2010] and from periodic plasma sheet oscillations and plasmoid releases in the outer magnetosphere [e.g., Carbary et al., 2007; Hill et al., 2008]. [12] A second type of binning employs the median, with the quartile values measuring the spread in the distribution. The latter method proved more useful in characterizing the fluxes and their variation over a long time interval. Figure 1 exhibits fluxes from the C1 channel accumulated for 1 year and shows how the mean fluxes and their standard devia-
tions (red) compare with the median fluxes and their quartiles (green) for all pitch angles in one radial bin. Clearly, using medians and quartiles minimizes the effect of outliers in the fluxes and provides a good characterization of statistical spreading. The scatter in the data represents the high level of activity coming outside the region dominated by the strong dipole field. [13] Figure 2 illustrates the appearance of the medians in a map of pitch angle range using data accumulated from 2005 through 2010 (top) and radial dependence of fluxes when collapsed (both by averages and medians) in pitch angle (bottom). The fluxes clearly peak near the orbit of Rhea and decrease with radial distance away from Rhea. This morphology has previously been noted by, e.g., Carbary
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Figure 4. Characterizing the radial dependence of the spectral index for 2005–2010. (top) The spectral index is indicated for median values of the electron data in each radial and pitch angle bin. (bottom) The radial dependence collapsed in pitch angle is indicated. The uncertainties in Figure 4 (bottom) derive from the standard deviations of the pitch angle averages. et al. [2009] and Paranicas et al. [2010], who interpreted this pattern in terms of energization of particles as they are injected into the inner dipole field. At some distance near ∼10 RS, the injections become less frequent and energy loss processes (such as passing through the neutral torus) become significant. Also significant, the pitch angle distributions tend to be field aligned outside ∼10 RS and more isotropic or pancake inside, which has also been documented [Schippers et al., 2008; Carbary et al., 2011]. The field‐aligned distributions were interpreted as consistent with a low‐altitude polar source for the energetic electrons
[Carbary et al., 2011]. Figure 2 (bottom) indicates that when the fluxes are collapsed in pitch angle, either by averages or by medians, the resulting radial profiles are similar (do not confuse this averaging in pitch angle with the bin averaging).
4. Spectral Fitting [14] After binning in radial distance and pitch angle, the median fluxes are fitted to a power law or kappa distribution. Figure 3 shows examples of these fits. The fluxes are
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Figure 5. Characterizing the radial dependence of the index for 2005–2010. The format is the same as in Figure 4, and the spectral behavior is the same as that for the spectral index. obtained from the middle magnetosphere (17 RS) at a middle pitch angle (96°); the data are also confined to the plasma sheet (∣z∣ < 1 RS). Figure 3 displays the median fluxes. The vertical bars denote lower and upper quartiles from the medians, and the horizontal bars indicate width of the channel in energy. The spectrum is representative. Both the power law fit and the kappa fit are reasonable approximations to the measured spectrum, with the kappa describing the observed “bend.” If the spectrum is extended to lower energies, a two‐ kappa distribution may be necessary to portray the spectrum [Schippers et al., 2008], but for this spectral range one will
suffice. In either instance, variation in g or will indicate a spectral hardening or softening. (For the kappa fits, E0 = 50 keV is the characteristic energy of equation (2).) Because the main goal of this work is to characterize the spectral steepening, either the g or index will suffice. Initially, both g and maps will be provided, but as the discussion proceeds, only the spectral index g will be promulgated.
5. Spectral Mapping [15] As used here, a spectral “map” refers to the behavior of gamma or kappa in pitch angle and range. Figure 4 shows
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Figure 6. Comparison of the spectral behavior of electrons in terms of the spectral index and index, when collapsed in pitch angle. These are the same curves as appear in Figure 4 (bottom) and Figure 5 (bottom). Uncertainties are standard deviations of the averages in pitch angle (not quartiles). such a spectral map in a format similar to Figure 2 for fluxes. The median fluxes were fitted to power law distributions in radial bins of 2 RS and pitch angle bins of 11.25° within 1 RS of the equator. All usable data from the beginning of 2005 to the end of 2010 is included; over 1.8 × 106 flux samples went into the construction of this map. Figure 4 (top) indicates the resulting map of spectral hardness in pitch angle versus radial distance, while Figure 4 (bottom) shows the spectral index collapsed in pitch angle. [16] Figure 4 illustrates the dramatic changes in the electron spectra with radial distance. In the inner magnetosphere, the spectra are very hard and the spectral index takes on values close to −1. This extreme hardness denotes the radiation belts inside r ∼5 RS. The spectra rapidly soften with increasing radial distance, achieving a minimum of −3 between 10 and 15 RS. Notably, this minimum appears outside the orbit of Rhea and outside the outer edge of the E ring. Beyond 15 RS, the spectra become progressively harder with increasing radial distance, achieving an index of −2 at 30 RS, the outer edge of this survey. Despite the variations in the outer, nondipolar region, the index behaves monotonically here. This behavior suggests that coherent mechanisms probably control the spectral slope in this region. The spectral index shows little variation in pitch angle; the most extreme variations in g appear in radial distance.
[17] Figure 5 shows the same spectral map in terms of the kappa index, which shows essentially the same behavior as the spectral index from the power law fits. The spectra vary from very hard in the inner magnetosphere, achieve a softness minimum in the middle magnetosphere, and progress to mildly hard in the outer magnetosphere. The kappa indices are not organized in pitch angle. [18] Figure 6 summarizes the radial dependences of the electron spectra, comparing the variation in the spectral index with that of the kappa index. The vertical lines indicate standard deviations from averages along the pitch angle dimension. The consistency between the two representations gives confidence that either g or index can faithfully measure the hardness or softness of the electron spectra. For the rest of this paper, only the spectral index will be considered.
6. Epochal Behavior [19] The spectral maps discussed above subsume data from the beginning of 2005 to the end of 2010. The problem of outliers in the binning has already been mentioned. The outliers in the binning process represent fluxes and indices much different from normal, median values. Do these outliers represent a systematic trend in the data or are they statistical aberrations arising from the long duration of the
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Figure 7. Comparison of spectral behavior of electrons by epoch. The solid curve shows the spectral index for the first 3 years of the study (2005–2007), while the dashed curve shows the spectral index for the last 3 years of the study (2008–2010). analysis? For example, do the spectra differ between the early mission and later in the mission. To test for a systematic trend, radial profiles of the spectral indices were computed for two time periods: 2005–2007 and 2008–2010. Cassini did sample different regions of Saturn’s magnetosphere during these two periods, and Saturn did change seasons from near southern solstice to vernal equinox. Thus, some differences might be expected on the basis of sampling alone. [20] Figure 7 compares the radial profiles of the early (2005–2007) and more recent (2008–2010) phases of the mission. The profiles were computed exactly as before, by collapsing the indices in pitch angle. The radial profiles of the two time periods are very similar; differences generally lie within the standard deviations of the averaging in pitch angle, and the spectral profiles have the same general radial behavior seen previously. However, small persistent differences can be noted: the later epoch has somewhat softer spectra outside the orbit of Titan, while that epoch has somewhat harder spectra in the minimum region between 9 and 18 RS. The differences between the early and late epochs might be caused by seasonal effects, since Saturn moved from solstice conditions to equinox conditions from 2004 to 2009. Continued observation of Saturn’s electrons with Cassini will reveal if this interpretation is correct. Alternately, these differences might be ascribed to local time
changes in the spectrum as the Cassini orbit evolved. Local time effects are discussed in section 7.
7. Local Time Behavior [21] Figure 8 compares the spectral indices for four different local time sectors. The radial profiles of the spectral indices were computed as before by collapsing two‐ dimensional spectral map along the pitch angle dimension. In this case, the spectra were segregated by local time sector. Each sector occupies 90° (6 h) centered on noon, midnight, dawn, and dusk; all data from 2005 to 2010 are included. [22] The radial profiles for all local time sectors display the same general structure as before, where hard spectra in the inner and outer magnetosphere flank soft spectra in the middle magnetosphere. More variation in the spectra occurs outside the orbit of Rhea. The hardest spectra occur on the dayside beyond the orbit of Titan, although the proximity of the magnetopause limits the sampling here. The hardness of the dayside spectra may be due to magnetospheric compression by the solar wind, as suggested by Krimigis et al. [2007]. Notably, the softest spectra appear in the midnight sector where one might expect plasma sheet heating would energize electrons and lead to hard spectra. In the middle magnetosphere, where the sampling is similar, the hardest spectra are in the dusk sector and the softest exist in the
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Figure 8. Comparison of spectral behavior of electrons by local time. The uncertainties are shown only for noon but are comparable for the other local time sectors. midnight and noon sectors. No local time dependence can be discerned in the inner magnetosphere inside ∼10 RS.
8. Discussion [23] As all the radial profiles indicate, the electron spectra become softer from 30 RS inward to about 15 RS, and then become dramatically harder within 10 RS as the radiation belts are entered. The inward softening from the outer magnetosphere to the middle magnetosphere is qualitatively consistent with inward transport that conserves the adiabatic invariants of motion. The gradual change at the largest distances is due to modest changes in the field strength at those distances. Hardening in the inner magnetosphere may be associated with conservation of the invariants as the electrons move inward and the field becomes stronger and more dipolar. Inside ∼10 RS, the spectra become very hard, as noted in Voyager observations [Krimigis et al., 1983]. In addition to inward diffusion, this behavior derives from two effects: contributions from the spatially confined radiation belts and loss of energy from lower energy electrons to the neutral gas‐grain medium of the E ring. Both of these effects tend to remove lower energy electrons and, relatively, increase the higher energy electrons [Paranicas et al., 2010]. [24] The spectral behavior evidences little dependence on pitch angle. Electron pitch angle distributions beyond ∼10 RS are bidirectional but become “pancake” with a peak
near 90° in the inner magnetosphere [e.g., Saur et al., 2006; Schippers et al., 2008; Carbary et al., 2011]. This migration of pitch angles suggests inward radial transport. The vast majority of particles at these energies could be accelerated in the auroral region by field‐aligned potentials similar to those postulated for Earth’s auroral regions [Klumpar et al., 1988; Marklund et al., 2001]. Inward migration of these particles could drive the spectral shape in the field‐aligned region. Auroral acceleration has been implied for the formation of ion conics and field‐aligned electron beams at Saturn [Mitchell et al., 2009]. The spectral change between 10 and 20 RS may signal such acceleration. [25] Consider the following process for electron acceleration. Electrons are accelerated in the auroral region at radial distances outside ∼15 RS. This acceleration gives rise to field aligned distributions. These particles are transported inward toward the planet. During this transport, their equatorial pitch angles increase and the spectral index decreases as observed. Such a process conserves the first two adiabatic invariants and agrees with previous analyses [Carbary et al., 2011]. Data presented here are consistent with spectral changes consistent with invariant conservation for the region between 15 and 30 RS. Undoubtedly, electron energy loss and scattering within the neutral cloud also contribute to the spectral behavior inside ∼15 RS. [26] As an aside, note that the 27–400 keV electrons discussed here are not the primary source of ionization for
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the H, O, and H2O products that comprise Saturn’s neutral torus. The cross section for electron ionization of neutral H peaks below 100 eV, while those for electron ionization of O and most water products peak near 100 eV [Kim et al., 2010]. The energetic electrons may lose energy through scattering and secondary collisions to achieve low enough energies to interact with the neutrals. This process occurs in Saturn’s ionosphere to cause auroral emissions and heating. Ionization of the neutral torus also results from photon impacts in the far and extreme ultraviolet and from charge exchange processes. A complete discussion of these ionization sources is beyond the scope of this investigation; a thorough examination of these sources may be found in work by Smith et al. [2010, and references therein].
9. Conclusions [27] When fitted to a power law with spectral index g or a kappa distribution characterized by a index, energetic electrons (27–496 keV) in Saturn’s plasma sheet display spectral behavior with distinct patterns in radial distance. Both spectral indices decrease with radial distance from the outer magnetosphere to ∼15 RS, at which point indices achieve a minimum. Inside the orbit of Rhea, the spectral indices rapidly harden with decreasing radial distance. There appears to be little dependence of the spectra on pitch angles, and a coherent organization of the spectra in r obviously exists. This organization has persisted with little variation throughout the Cassini mission (2005–2010). Outside the orbit of Titan, the spectra are somewhat harder on the dayside than the nightside, while no local time dependence exists inside radial distances of ∼10 RS. The radial profiles are interpreted as a consequence of inward radial motion of electrons accelerated at high latitudes above Saturn’s aurora. Inside ∼10 RS, the neutral torus removes lower energy electrons and promotes a hardening of the spectrum. [28] Acknowledgments. This research was supported in part by the NASA Office of Space Science under Task Order 003 of contract NAS5‐97271 between NASA Goddard Space Flight Center and the Johns Hopkins University and in part by NASA grant NNX08AQ77G from the Cassini Data Analysis Program. [29] Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.
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[email protected]) N. Krupp, Max‐Planck‐Institut für Sonnensystemforschung, Max‐ Planck‐Str. 2, Katlenburg‐Lindau D‐37191, Germany.
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