The E ring in the vicinity of Enceladus

The E ring in the vicinity of Enceladus

Icarus 193 (2008) 420–437 The E ring in the vicinity of Enceladus I. Spatial distribution and properties of the ring p...

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Icarus 193 (2008) 420–437

The E ring in the vicinity of Enceladus I. Spatial distribution and properties of the ring particles S. Kempf a,b,∗ , U. Beckmann a , G. Moragas-Klostermeyer a , F. Postberg a , R. Srama a , T. Economou c , J. Schmidt d , F. Spahn d , E. Grün a,e a MPI für Kernphysik, Saupfercheckweg 1, D-69117 Heidelberg, Germany b IGEP, Universität Braunschweig, Mendelssohnstr. 3, D-38106 Braunschweig, Germany c Laboratory for Astrophysics and Space Research, University of Chicago, Chicago, IL 60637, USA d Institut für Physik, Universität Potsdam, Am Neuen Palais 10, D-14469 Potsdam, Germany e Hawaii Institute of Geophysics and Planetology, University of Hawaii, Honolulu, HI 96822, USA

Received 13 January 2007; revised 22 June 2007 Available online 12 September 2007

Abstract Saturn’s diffuse E ring is the largest ring of the Solar System and extends from about 3.1 RS (Saturn radius RS = 60,330 km) to at least 8 RS encompassing the icy moons Mimas, Enceladus, Tethys, Dione, and Rhea. After Cassini’s insertion into her saturnian orbit in July 2004, the spacecraft performed a number of equatorial as well as steep traversals through the E ring inside the orbit of the icy moon Dione. Here, we report about dust impact data we obtained during 2 shallow and 6 steep crossings of the orbit of the dominant ring source—the ice moon Enceladus. Based on impact data of grains exceeding 0.9 µm we conclude that Enceladus feeds a torus populated by grains of at least this size along its orbit. The vertical ring structure at 3.95 RS agrees well with a Gaussian with a full-width–half-maximum (FWHM) of ∼4200 km. We show that the FWHM at 3.95 RS is due to three-body interactions of dust grains ejected by Enceladus’ recently discovered ice volcanoes with the moon during their first orbit. We find that particles with initial speeds between 225 and 235 m s−1 relative to the moon’s surface dominate the vertical distribution of dust. Particles with initial velocities exceeding the moon’s escape speed of 207 m s−1 but slower than 225 m s−1 re-collide with Enceladus and do not contribute to the ring particle population. We find the peak number density to range between 16 × 10−2 m−3 and 21 × 10−2 m−3 for grains larger 0.9 µm, and 2.1 × 10−2 m−3 and 7.6 × 10−2 m−3 for grains larger than 1.6 µm. Our data imply that the densest point is displaced outwards by at least 0.05 RS with respect of the Enceladus orbit. This finding provides direct evidence for plume particles −q dragged outwards by the ambient plasma. The differential size distribution n(sd ) dsd ∼ sd s dsd for grains >0.9 µm is described best by a power law with slopes between 4 and 5. We also obtained dust data during ring plane crossings in the vicinity of the orbits of Mimas and Tethys. The vertical distribution of grains >0.8 µm at Mimas orbit is also well described by Gaussian with a FWHM of ∼5400 km and displaced southwards by ∼1200 km with respect to the geometrical equator. The vertical distribution of ring particles in the vicinity of Tethys, however, does not match a Gaussian. We use the FWHM values obtained from the vertical crossings to establish a 2-dimensional model for the ring particle distribution which matches our observations during vertical and equatorial traversals through the E ring. © 2007 Elsevier Inc. All rights reserved. Keywords: Saturn, rings; Saturn, satellites; Volcanism; Impact processes

1. Introduction Ever since the discovery of Saturn’s vast diffuse E ring by Feibelman (1967) its study has been mainly based on images * Corresponding author. Fax: +49 06221 516324.

E-mail address: [email protected] (S. Kempf). 0019-1035/$ – see front matter © 2007 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2007.06.027

obtained from both ground-based and space-bound astronomical observations (Baum et al., 1981; de Pater et al., 1996, 2004; Bauer et al., 1997; Nicholson et al., 1996). Such a program has had remarkable success, to the extent that a consistent global description of the ring could be achieved by Showalter et al. (1991). Nevertheless, it has in the process become clear that remote sensing observation techniques provide information

Distribution of E ring particles in the vicinity of Enceladus

mainly about ring features due to dust grains which dominate the ring’s optical cross-section, but do not necessarily constitute the most abundant or dynamically most important particle species. Imaging does not provide information about dynamical properties such as the distribution of the orbital elements. Moreover, since an image is a two-dimensional projection of a three-dimensional structure, remote observation techniques are sensitive to more or less global features. It requires additional assumptions about the ring structure, either of empirical or of theoretical nature, to extract parameters such as the radial ring profile from the data. Fortunately, spacecraft explorations of the saturnian system allow a complementary view of the E ring by measuring the dust impacts during passages through the ring. This was demonstrated first by the planetary radio-astronomy (PRA) instrument during Voyager 1 traversal through the E ring in 1980 (Aubier et al., 1983; Meyer-Vernet et al., 1996) which identified the dust impacts on the spacecraft by their characteristic electromagnetic signature. However, since the PRA instrument was not designed to detect dust, the inferred dust properties are rather uncertain. Cassini’s Cosmic Dust Analyser (CDA) is the first dedicated dust detector for investigating the local ring properties including grain size distribution, particle composition, and number densities. The Radio and Plasma Wave Science Investigation (RPWS) is capable to characterise the size distribution and the spatial distribution of dust grains larger than a few microns (Gurnett et al., 2004). A comprehensive picture of Saturn’s enigmatic E ring can only be obtained from both global and the local observation techniques, whose results need to be glued together by a detailed theoretical model for the ring dynamics. The E ring is the largest planetary ring in the Solar System, encompassing the icy satellites Mimas (rM = 3.07 RS ), Enceladus (rE = 3.95 RS ), Tethys (rT = 4.88 RS ), Dione (rD = 6.25 RS ), and Rhea (rR = 8.73 RS ). The icy moon Enceladus was proposed early as the dominant source of ring particles (Baum et al., 1981) since the edge-on brightness profile peaks near the moon’s mean orbital distance. For the same reason, Tethys was identified as a secondary E ring particle source by de Pater et al. (2004). A brightness peak at Dione could not be associated unambiguously with this moon. Photometrical models propose that for micron-sized grains the peak optical depth is τ ∼ 1.6 × 10−5 corresponding to about 180 grains per square centimetre (Showalter et al., 1991). Perhaps the most striking finding is the unusual blue colour of the E ring (Larson et al., 1981). The ratio of reflected intensity I and the incident solar flux πF at Saturn was found to scale as log(wavelength) between 0.3 and 2.2 µm (de Pater et al., 2004) implying a narrow grain size range centred between 0.3 and 3 µm (Nicholson et al., 1996). A power law size distribution seemed to be not compatible with the pre-Cassini E ring data (Showalter et al., 1991). Interestingly, recently de Pater et al. (2006) announced the discovery of a blue ring around Uranus which also has its brightest point at the orbit of an embedded moon. The vertical ring structure is remarkable as well. De Pater et al. (2004) concluded from Earth-bound observations at


infrared wavelength done during the Earth’s ring plane crossing in 1995, that the rings full-width–half-maximum (FWHM) due to grain sizes dominating the optical cross-section is about 9000 km between Mimas’ and Enceladus’ orbit, with a minimum of 8000 km at rE . The same FWHM had been found by Nicholson et al. (1996) from HST data at visible wavelength. Surprisingly, in Cassini images the FWHM at rE is only 5000 km (Porco et al., 2006). Outside rE , the FWHM rises to 13,000 km at Tethys’ orbit and increases up to 15,000 km before the ring blends with the background. Baum et al. (1981, 1984) reported an even larger FWHM of 40,000 km at about 8 RS . Nevertheless, explaining the significant ring thickness which has to be attributed to ring particles moving in inclined orbits, turned out to be a major challenge for models of the ring particle dynamics. Showalter et al. (1991) derived an empirical model for the ring structure which is very useful for comparing remote sensing with in situ data. They modelled an axisymmetric ring whose column dust density n⊥ increases radially between its inner rim at about 3 RS and Enceladus orbital radius rE ∼ 3.94 RS as n⊥ (r) ∼ r 15 , and falls off outside rE as n⊥ (r) ∼ r −7 . Based on Baum and Kreidl (1988), the ring’s vertical profile is approximated by a Gaussian whose width σ linearly depends on the radial distance to Saturn r as   σ (8 RS ) (r−3 RS )/5 RS , σ (r) = σ (3 RS ) (1) σ (3 RS ) with σ (3 RS ) ∼ 2500 km and σ (8 RS ) ∼ 15,900 km. The unique properties of the E ring stimulated many theoretical studies. Horányi et al. (1992) introduced a model, where charged ring particles are subject to perturbations by the planet’s oblate gravity field, electromagnetic forces, and solar radiation pressure. They found that the first two perturbing forces cause the particle’s orbits to precess in opposite directions. For approximately 1 µm particles the two processes nearly cancel causing the orbit’s pericentre of those grains to stay locked with respect to the position of the Sun, which in turn leads to a swift growth of the orbit’s eccentricities due to the solar radiation pressure. This model explains at least qualitatively the narrow size distribution even if particles of a broad size distribution are injected into the ring. It also reproduces the optical depth profile outside Enceladus’ orbit, but fails to explain the optical depth profile inside Enceladus’ orbit as well as the vertical ring structure. Another drawback of this model is that it requires particles moving in highly eccentric orbits (which are rapidly eliminated by collisions with the main rings) to match the radial extent of the visible ring. By adding the plasma drag effect to the particle dynamics Dikarev and Krivov (1998) and Dikarev (1999) showed the particles’ semi-major axis can grow. This allows the grains moving in less eccentric orbits to cover the full radial range of the ring which in turn increases the dust lifetime. Juhász and Horányi (2002, 2004) performed extensive numerical simulations of the longterm evolution of E ring particles. In addition to the disturbing forces considered in previous studies they also included the erosion of the ring particles owing to sputtering. Using a Monte-Carlo approach to fit their simulations to the Showalter


S. Kempf et al. / Icarus 193 (2008) 420–437

et al. (1991) brightness profile they predicted that the satellites Mimas, Enceladus, Tethys, and Dione as dust sources contributing in the ratio {<0.01:1.0:0.3 ± 0.1:<0.01}. Furthermore, they determined the index of the power-law size distribution to be 3.1 ± 0.4. Another focus of extensive research has been the dust production at the ring’s main source Enceladus. Producing fresh dust particles by impacts of fast projectiles onto the moon’s surface (the so-called impactor-ejecta process; see also Krivov et al., 2003) has been considered as the most effective process. Hamilton and Burns (1994) proposed that the E ring particles themselves constitute the main projectile source for replenishing the ring. However, energetic arguments seem to favour the projectile flux being dominated by particles of interplanetary and interstellar origin. Angular distributions of ejecta generated by various populations of interplanetary dust particles (IDPs) were studied by Colwell (1993). Based on this Spahn et al. (1999) numerically studied the spatial ejecta distribution in the vicinity of Enceladus. Their predictions were used to optimise the in situ measurements of the Cassini dust detector CDA during the close flybys of Enceladus in 2005. Recently, Spahn et al. (2006a) reassessed the contributions of E ring particles and IDPs to the projectile flux onto the ring moons and concluded that E ring impactors play a crucial rôle for the dust production within the inner E ring, while IDP impacts dominate the dust production in the outer E ring. Recent measurements by various instruments on the Cassini spacecraft exploring the saturnian system since 2004 have revolutionised our view on the E ring and its sources. During a close Cassini flyby at Enceladus the dust detector discovered a collimated dust jet emerging from Enceladus’ south pole region (Spahn et al., 2006b)—a site characterised by elongated cracks (Porco et al., 2006) significantly warmer than their surroundings (Spencer et al., 2006). The dust jet was accompanied by a neutral (water) gas cloud detected by the Cassini magnetometer (Dougherty et al., 2006) and the ultraviolet imaging spectrometer (Hansen et al., 2006), and its density and composition measured by the ion and mass spectrometer (Waite et al., 2006). Spahn et al. (2006b) inferred from comparison of numerical simulations to the CDA data that the south pole source emits particles larger than 2 µm at a rate of 5 × 1012 s−1 , while the impactor-ejecta mechanism (Krivov et al., 2003; Spahn et al., 2006a) provides at most 10−12 of those particles per second. Thus, the replenishing of the ring with fresh dust is at least for grains >2 µm dominated by particles originating from the plumes at the south-pole. Knowledge of the ambient plasma is essential for modelling the charging of E ring grains (see Horányi, 1996). All theoretical studies of the E ring dynamics mentioned so far were based on the plasma model by Richardson (1995) established with Voyager data. Early measurements by the Cassini plasma instruments (Sittler et al., 2005) deviated significantly in some places from the predictions of the Richardson model. Dust equilibrium potentials derived from dust charge measurements by CDA (Kempf et al., 2006) as well as measurements of the spacecraft potential by the RPWS Langmuir Probe (LP) (Wahlund et al., 2005) were not consistent with the Richardson

model, but could be reproduced by using LP data (Wahlund et al., 2005) for modelling the cold plasma electrons and by using CAPS data (Sittler et al., 2005) for the properties of oxygen and water group ions. Horányi (1996) suggested that Saturn’s rings may be a source of high-velocity streams of nano-meter sized dust. Similar streams originating from the Jupiter were identified by the dust detectors on board of several spacecraft (Grün et al., 1993, 1996; Postberg et al., 2006). In early 2004 when Cassini was approaching Saturn the CDA detected faint impact bursts by high-velocity particles. Dynamical analysis revealed that the streams, which have been registered far from Saturn, are dust streams coming from the outskirts from Saturn’s A ring, while streams detected close to the magnetosphere originates from inside the E ring (Kempf et al., 2005a). Interestingly it was found that the stream particles are mostly silicates while the dominant material of Saturn’s rings as well as of most of its moons is pure water ice (Kempf et al., 2005b). Kurth et al. (2006) discussed the implications of the RPWS measurements during almost equatorial as well as during inclined E ring traversals for the radial and vertical ring profile. Srama et al. (2006) summarised the first year of the in situ investigations of Saturn’s dust environment within Titan’s orbit by the Cassini dust detector CDA. This paper focused on impact rates but did not present the distributions of impact speed and dust mass which are of particular interest for dynamists. Cassini’s onboard radio and plasma science investigation RPWS is capable of detecting impacts by bigger grains and provides measurements complementary to the CDA high rate detector HRD. This is the first of a series of two papers reporting investigations of the E ring in the vicinity of Enceladus with the Cassini in situ dust detector CDA. We present our findings about the radial and vertical structure of the ring, the amount of dust produced in geysers on Enceladus, the dust size distribution, and the dynamical properties of the ring particles. The second paper (Postberg et al., in this issue) is dedicated to investigations of the composition of the ring particles. The outline of this paper is as follows. In the first section we discuss the details of the Cassini dust detector relevant for this paper. In Section 3 we describe the instrument operation and the mission design. Our findings about the spatial structure of the E ring are presented in Section 4, where we discuss both the radial and the vertical distribution of ring particles 1 µm. Furthermore, we compare our observations with numerical simulations of the ring particle evolution. The signatures of the Enceladus gas-dust plumes in the CDA data are considered in Section 5. In Section 6 we present our findings about the size distribution and dynamical properties of the ring particles. Finally, we conclude this paper with a short summary in Section 7. Unless otherwise stated we use the international system of units. All times are spacecraft event Universal time, UT; dates are given in year and day of year. We work in a Saturn centred inertial reference frame where the z-axis is aligned with the planet’s rotation axis. In this paper we will refer to the radius of a dust grain as the size of the particle.

Distribution of E ring particles in the vicinity of Enceladus

2. Sensor description The Cosmic Dust Analyser (Srama et al., 2004) consists of two independent instruments: the High Rate Detector (HRD) and the Dust Analyser (DA). The HRD is designed to monitor high impact rates (up to 104 s−1 ) in dust-rich environments such as during the Saturn ring plane crossings. The particle mass range covered by the HRD ranges from 8 × 10−16 kg to 8 × 10−12 kg for vd ≈ 15 km s−1 . The DA is sensitive to particles within a large mass range (5 × 10−18 –5 × 10−12 kg for vd ≈ 20 km s−1 ) and velocity range (1–100 km s−1 ), and measures the charge carried by the dust grain, mass, impact velocity, and elemental composition of the impactor. This is accomplished by a combination of three detectors: a charge sensing unit (QP detector) in front of the instrument, a classical Impact Ionisation Detector (IID) similar to the Galileo-type dust detector, and a time-of-flight (TOF) mass spectrometer (Chemical Analyser—CA). Here, we only summarise a few instrumental aspects relevant for this paper. The CA detector is described in Postberg et al. (this issue, pp. 438–454). 2.1. CDA dust analyser The CDA impact ionisation detector subsystem (Srama et al., 2004) is similar to the detectors on the Galileo spacecraft (Grün et al., 1992a) and on the Ulysses spacecraft (Grün et al., 1992b). A high velocity impact on the hemispheric target transforms the striking dust particle into a mixture of particle fragments (ejecta) and an impact plasma. After separation in the electrical field, ions and electrons are collected by separate electrodes. Tests have shown that the time required for the collected impact charge to reach its maximum is independent of the impactor mass, and depends upon the impact velocity (Eichhorn, 1978). However, the impact charge is a function of the impactor’s mass as well as of the impact velocity. The IID detector consists of an impact target and an ion grid system mounted in front of a multiplier. To integrate a TOF mass spectrometer into the IID, the spherical impact target was divided into an inner target made of rhodium (Chemical Analyser Target—CAT) and an outer target made of gold (Impact Ionisation Target—IIT). Both targets were attached to charge amplifiers (charge measured at the CAT: QC signal, charge measured at the IIT: QT signal). Furthermore, the positive ion charge is measured at the ion grid (QI signal) and at the multiplier (MP signal). From calibration experiments at the Heidelberg dust accelerator Srama (2006, in preparation) derived that for impacts on the IIT, the impact speed vd and the dust mass md are given by   −1.26 (QI )  vd km s−1 = 9.22 + 1.87 × 105 tr(QT ) [10 ns] − 1.45 × 10−3 tr(QT ) [10 ns], (2)   0.81   (QI ) −3 (QI ) −1 −2.73 md [kg] = 5.71 × 10 q vd km s [C] , (3) −1.35   (QT )  −1 5 (QT ) vd [10 ns] km s = 11.3 + 3.58 × 10 tr − 2.21 × 10−3 tr(QT ) [10 ns], (4)      0.77 −2.69 (QT ) md [kg] = 1.51 × 10−3 q (QT ) [C] vd km s−1 . (5)


Table 1 Impact charge thresholds and corresponding radii of ice particles impacting with 8 km s−1 Counter

Charge threshold (#)

CounGrain radius (vd = 8 km s−1 ) ter (µm)

Charge threshold (#)

Grain radius (vd = 8 km s−1 ) (µm)

m1 m2 m3 m4

2.0 × 106 1.9 × 107 4.1 × 108 5.2 × 109

0.9 1.6 3.5 6.7

1.6 × 106 2.8 × 107 6.2 × 108 5.2 × 109

2.1 4.2 8.6 11.9

M1 M2 M3 M4

The 1-σ error of the dust speed is vd /vd ∼ 1.6 and the error of the dust mass is md /md ∼ 2. In dust accelerator facilities, only dust analogs that can be charged can be used for calibration experiments. Thus, the calibration relations (2)–(5) above are based on experiments with predominantly iron particles. Saturnian ring particles, however, consist of water ice—a material which cannot be studied in hypervelocity impact experiments. Flight measurements of ice particle impacts may be used to fill this gap, provided the mass of the impactors can be obtained by an independent method. Since the DA is capable of measuring the charge Qd carried on big grains by its charge sensing unit QP, the electrostatic potential of the grains is usually known, and the dust mass can be estimated from Qd . Based on measurements of large E ring particles, Kempf et al. (2006) demonstrated that Eq. (3) provides the right masses for ice particles. 2.2. CDA High Rate Detector The High Rate Detector (HRD) is an independent detector of the CDA instrument designed to monitor high impact rates up to 104 s−1 in dust-rich environments where the DA is saturated (Srama et al., 2004). The HRD was designed, built, and tested by the University of Chicago and is mounted piggyback on the front of the CDA main sensor. The HRD detects impacts of at least micron-sized grains by means of two separate polyvinylidene fluoride (PVDF) foil sensors (sensor M: 50 cm2 , 28 µm foil; sensor m: 10 cm2 , 6 µm foil; the back surface of both foils are coated with Chemglas Z-306, 40 µm thick). The PVDF foil consists of a thin film of permanently polarised material. A dust impact on the foil produces rapid local destruction of dipoles, causing a current pulse which can be recorded by the electronics. The released current roughly depends on the grain size and on the impact speed (Simpson and Tuzzolino, 1985). To make use of this dependence, the impact triggers at least one of the 4 counters which are arranged in order of increasing thresholds (Table 1). The detectors were calibrated with 6–65 µm glass particles at the Munich plasma accelerator facility with impact speeds between 2 and 12 km s−1 . The number of electrons at the input of the HRD charge amplifiers produced by a dust impact was found to depend on the grain mass md and the impact speed vd as  3.0 1.3   nm = 3.6 × 1018 md [kg] (6) vd km s−1 for the m-detector and  3.0 1.3   nM = 3.8 × 1017 md [kg] vd km s−1



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for the M-detector. The lower speed limit for detecting an impact is about 1 km s−1 ; the detectable mass range is 5 × 10−19 to 10−13 kg for impact speeds of 40 km s−1 and 10−16 kg to 10−10 kg for impact speed of 5 km s−1 . 3. Observations

ring particle background needs to be determined (Spahn et al., 2006a). Enceladus’ sphere of gravitational influence is characterised by the Hill radius of the moon  1/3 ME 1 Rhill = rE (8) ≈ 948 km, 3 M E + MS

Within the inner E ring, the DA is not able to measure the impact rate with a sufficient spatial resolution, since the number of impacts detectable by the DA is limited to 60 per minute (Srama et al., 2004) and the E ring particles impact more frequently so that the instrument is saturated. As a result CDA investigations of the E ring structure inside about 5 RS are solely based on HRD data. Although the CDA detector has been operated practically continuously throughout the years 2005 and 2006 not all of Cassini’s passages through the inner saturnian system were useful for exploring the dust environment within the inner core of the E ring. This was mostly due to spacecraft orientation incompatibility to CDA measurements. In 2005 we obtained reasonable HRD data during two shallow passages through the ring at the beginning of the year and during six steep ring plane crossings near Enceladus’ orbit. In 2006 we acquired data during steep crossings of the ring plane at 3.16 RS and at 5.01 RS , and during two moderately inclined ring traversals through the ring plane at about 4.75 RS . A summary of the crossing parameters is given in Table 2. In Fig. 1 we show the corresponding spacecraft trajectories at these ring plane crossings. Both shallow ring traversals included a close Enceladus flyby. Unfortunately, both encounters were not useful for investigations of the dust production by impactor ejecta at Enceladus. To do this, the enhancement of the dust number density within the moon’s sphere of gravitational influence with respect to the

where ME = 1.0804776 × 1020 kg and MS = 5.6846218 × 1026 kg are the masses of Enceladus and Saturn, respectively. Both flybys have not been suitable for this purpose: The first flyby on 2005-048 UTC (E3 flyby) was not close enough (closest approach to the moon surface 1264 km). During the second encounter (E4 flyby) on 2005-068 UTC Cassini flew through the Hill sphere (closest approach 499 km) but the spacecraft pointing did not allow for proper ring particle detections. Steep passages through the ring plane are particularly useful for determining the ring’s vertical profile at the distance of the plane piercing RX . The geometry of a steep crossing can be characterised best when plotted in cylindrical co-ordinates (distance to Saturn’s pole axis versus elevation above the ring plane). The crucial parameter here is the piercing angle γX —the larger γX is, the weaker is the radial dependence of the observed impact rate (azimuthal variations during the crossing are second order effects). As can be seen in Fig. 1 the geometries of the crossings 7, 8, 9, 10, 11, and 13 were almost identical. In these cases Cassini pierced the ring plane inside Enceladus’ orbit between 3.90 RS and 3.95 RS with γX ranging between 53◦ and 54◦ . Furthermore, Cassini crossed Enceladus’ orbit below the ring plane. The crossing 11 comprised of the closest flyby at Enceladus so far (E11—closest approach 168 km above the surface). In orbit 31 Cassini pierced the ring plane close to the orbit of the icy moon Mimas at ∼3.16 RS . There were also three cross-

Table 2 Parameters of Cassini’s crossings through Saturn’s ring plane considered in this paper and in Postberg et al. (this issue, pp. 438–454) Orbit #

Crossing parameters tX (UTC)

RX (RS )

γX (◦ )

ζcirc (◦ )


Encounter parameters

3 4 7 8 9 10 11 13

048T00:49 068T10:48 122T23:36 141T03:54 159T08:25 177T13:29 195T19:56 232T09:00

3.50 3.56 3.90 3.90 3.91 3.93 3.95 3.93

– – 53 54 54 53 53 53

7a 80a 36 . . . 38 7...8 90 . . . 0 7...8 22 19 . . . 21

Enceladus (2005) 03:30:29 1264 09:08:01 499 – – – – – – – – 19:55:21 170 – –

26 27 31 32

205T01:15 229T00:21 301T03:09 337T00:37

4.77 4.77 4.97 4.97

37 36 74 74

18 . . . 28 10 . . . 18 12 . . . 15 1

– – – –





21 . . . 23

rCA (km)

Tethys (2006) – – – –

HRD smin

DA qthres

λ (◦ )

m1 (µm)

M1 (µm)


QC (fC)


– – 60 – 36 – 134 120 – 119

0.9 1.0 0.9 0.9 0.9 0.9 0.9 0.9

1.6 1.7 1.7 1.6 1.6 1.6 1.6 1.6

– – 69.7 69.7 385 69.7 385 56.8

– – 65.4 65.4 184 65.4 184 53.4

– – 17.5 17.5 348 17.5 348 13.1

51 162 87 82

1.0 1.1 0.6 0.6

– – – –

– – – –

– – – –

– – – –

– 143


Mimas (2006) –

Given are the ring plane crossing time tX , the distance RX to Saturn at tX , the ring plane crossing angle γX , the angle between the CDA boresight and the impact direction of grains moving in circular orbits ζcirc , the time tCA of Cassini’s closest approach to Enceladus, Cassini’s distance to the Enceladus surface at closest approach rCA , the angle λEnc between Cassini, Saturn, and Enceladus at tX , and the lower size detection thresholds of the two HRD sensors. a Angle given at t . CA

Distribution of E ring particles in the vicinity of Enceladus


Fig. 1. Cassini’s trajectory during the ring plane crossings useful for dust measurements (see also Table 2) plotted in cylindrical co-ordinates. The dotted vertical lines indicate the mean orbital distances of Mimas (M), Enceladus (E), and Tethys (T) to Saturn. CDA was only sensitive to ring particle impacts along trajectory segments marked by thick lines.

ings of the Tethys orbit: two shallow crossings at ∼4.8 RS in orbit 26 and 27 and two steep crossings at ∼5 RS in orbit 31 and 32. On 2005-248T10:42 UTC the HRD M sensor was damaged by an impact of a dust particle probably larger than 100 µm. At this time Cassini was at the outermost tip of Saturn’s G ring. Since then, the M1 counter shows a continuous low level noise drowning out features due to genuine dust impacts. Thus, the analysis of E ring traversals after 2005-248 is based on Msensor data and DA data only. Generally, the instrument orientation was chosen to minimise the angle ζcirc between the instrument boresight and the impact direction of grains moving in circular orbits (the so-

called Kepler RAM direction). However, the CDA sensor was occasionally insensitive (during the steep crossing 9 and during the two shallow passages) to ring particle impacts (see Fig. 1). Note further, that the instrument’s sensitivity also depends on the orbital elements of the ring particles. Due to the pronounced dependence of the DA sensitive area on the impact angle ζ (with respect to the instrument’s boresight) the instrument may be insensitive to large fractions of the ring particle population. This effect is clearly apparent in Fig. 2 where the dependence of the DA sensitive area on the particle’s semimajor axis a and eccentricity e is compared for the crossings in orbit 7 and 8.


S. Kempf et al. / Icarus 193 (2008) 420–437

Fig. 2. DA sensitive area (top row) and relative flux (bottom row) as function of semi-major axis and orbit eccentricity of the impacting particles during ring plane crossings 7 and 8. The flux is given relative to the flux of particles moving in circular Keplerian orbits at 3.94 RS . The contour lines indicate the corresponding orbit inclination.

4. Ring structure 4.1. Vertical ring structure In this section we analyse the vertical structure of the E ring using the HRD data obtained during steep crossings of the ring plane. 4.1.1. Vertical ring structure at Enceladus The right hand plots in Fig. 3 show the impact rates measured by the two HRD sensors during the steep ring plane crossings at approximately 3.95 RS (see Table 2). We calculated the rates from the transmitted impact time sequences with 30 s resolution, which is a good compromise between a large spatial resolution (radial ∼150 km; vertical ∼190 km) and a reasonable signal to noise ratio. To estimate the dust size thresholds of the counters we assumed the impact speed to be given by the speed of particles moving in circular prograde orbits. This is justified by two reasons: first, according to Eqs. (6) and (7) the HRD is insensitive to impacts by fast tiny grains (see also Fig. 12); and second, orbits of bigger particles have small eccentricities since these particles are rather insensitive to disturbing forces (Hamilton, 1993). During all passages the smallest detectable particle size was smin = 0.9 µm for the m-sensor and smin = 2 µm for the M-sensor (assuming spherical water

ice grains of density ρd = 103 kg m−3 ). Both sensors stopped detecting impacts when Cassini’s vertical distance to the ring plane became larger than 0.1 RS . During these periods Cassini moved radially by about 0.16 RS . The rates plotted as functions of elevation above the ring plane can be approximated well 1 with a Gaussian, with a width σ = (8 ln 2)− 2 FWHM, which generally depends on the distance to Saturn’s rotation axis ρ. However, since γX  1 the ring thickness can be assumed to be constant during the crossings. Thus, we fit the measured number densities n(ρ, z) to the product of independent empirical functions for the radial and vertical profile n(ρ, z|ρc , ei , e0 , σ, z0 ) = n0 pρ (ρ|ρc , ei , e0 )pz (z|σ, z0 )


with pz (z|σ, z0 ) = e−(z−z0 ) and pρ (ρ|ρc , ei , e0 ) =

2 /2σ 2

(ρ/ρc )+ei , ρ  ρc , (ρ/ρc )−e0 , ρ > ρc .



Furthermore, n0 is the dust number density at the densest point ρc within the ring plane. One might consider Eqs. (9)–(11) as a local approximation of the Showalter et al. (1991) profile Eq. (1). Here the definitions of the exponents ei and e0 are not

Distribution of E ring particles in the vicinity of Enceladus


Fig. 3. Vertical structure of the E ring in the vicinity of Enceladus’ orbit derived from HRD measurements. (Left) Impact rates versus time. (Right) Ring particle densities versus distance to Saturn’s rotation axis and versus the elevation above the ring plane (blue: m1 sensor; red M1 sensor). Broken and dotted lines mark the times when Cassini crossed the ring plane and Enceladus’ orbit, respectively. Grey areas indicate data gaps.

identical with Showalter et al. (1991), since they expressed the radial profile as a power law for the column density. Even more important, the Showalter et al. (1991) model aims to describe the global ring structure, while we are focusing on the local ring structure in the vicinity of the orbit of the dominant ring source Enceladus. In fact, there is no theoretical evidence that a “glob-

al” power law for the radial number density dependence holds for the denser regions of the E ring. Extensive numerical simulations of the spatial distribution of E ring particles by Juhász and Horányi (2002, 2004) do not support a simple power law dependence of the number density valid from the inner rim to the densest point. Thus it is more appropriate to view Eq. (11)


S. Kempf et al. / Icarus 193 (2008) 420–437

Table 3 Ring parameters derived from ring plane crossing data obtained by the HRD m1 and M1 sensors #

3a 3b 7 8 9 10 11 13 26 27 31 32 28






m1 (10−2 m−3 )

M1 (10−2 m−3 )

m1 (km)

M1 (km)





14.04 11.52 15.02 20.23 – 15.22 – 9.27 – – – – –

9.42 5.33 2.69 6.95 – 3.33 – 2.73 – – –

– – 4313 4322 – 4241 – 4682 4530 6496 5562 7028 5392

– – 4430 4124 – 4532 – 4436 – – – – –

30 54 53 63 – 59 – 36 – – – – 22

71 61 42 62 – 48 – 19 – – – – –

–20 –10 – – – – – – – – – – –

–36 –28 – – – – – – – – – – –

− – 5.0 ± 0.3 5.0 ± 0.5 4.2 ± 0.3 5.4 ± 0.4 4.8 ± 0.7 4.4 ± 0.6 – – – – –

RPWS /r HRD rmax max



– – 97 – – 50 – 73 – – – – –

– – 97 – – 44 – 46 – – – – –

Given are the number density n0 at the densest point ρc within the ring plane, the full-width–half-maximum, the exponents ei and e0 of the radial ring profile, the RPWS /r HRD between the peak impact rates of the RPWS and HRD detectors. The RPWS peak rates slopes qs of the differential size distribution, and the ratios rmax max are from Kurth et al. (2006). a Inbound. b Outbound.

as an approximation of the rather complex dust distribution at Enceladus’ orbit. The multidimensional least-square fits to the data were performed using the Levenberg–Marquardt algorithm (Moré, 1978). In the middle and right panels of Fig. 3 we show the radial and vertical number density profiles derived from the rate measurements. Here, we used the parameters of the best fits to Eq. (9) to transform the measured number densities along Cassini’s trajectory into the number density within the ring-plane, i.e., n(ρ, 0) = n(ρ, z)pz (0)/pz (z), and into the vertical ring density profile at RX , i.e., n(RX , z) = n(ρ, z)pρ (RX )/n0 pρ (ρ)pz (0). In all cases, the χ 2 of the fits turned out to be insensitive on the value of ρc . This is no surprise since the impact rate of steep vertical ring traversals is dominated by the vertical profile. The corresponding radial profiles, however, are strongly affected by ρc . We determined ρc which gives a best fit to the local radial density profile n(ρ, 0) in Eq. (11). Interestingly, for all vertical crossings the fits reproduce n(ρ, 0) reasonably well only if ρc  3.98 RS . This implies that the densest part of the E ring falls outside Enceladus’ orbit at about 3.95 RS . De Pater et al. (2004) also noted an outward shift of the ring’s peak brightness by about 0.25 RS . This effect cannot be attributed to the particles’ non-zero eccentricity (since this would also cause a density enhancement inside rE ) but requires an outward transport of dust particles. In a recent paper, Juhász et al. (2007) study this phenomenon in great detail. Near the Enceladus orbit the ring’s FWHM for grains >0.9 µm is about 4300 km (Table 3). Since the data in orbit 13 are probably affected by a data gap close to the ring plane crossing, we do not use the FWHM values of orbit 13 for further analysis. The average FMHW at 3.98 RS is then found to be 4292 ± 45 km for sd  0.9 µm and 4362 ± 212 km for sd  1.6 µm, which is about half of the FWHM derived from ground-based observations at visible and infrared wavelengths (Nicholson et al., 1996; de Pater et al., 2004), but is about

85% of the FWHM measured in Cassini images (Porco et al., 2006). This implies that grains smaller than 0.9 µm contribute to the ring brightness in the visible wavelength range, since smaller particles are less confined to the ring plane. The radio and plasma wave science (RPWS) investigation on Cassini (Gurnett et al., 2004) also observed dust impacts during most of the ring plane crossings discussed in this paper. Kurth et al. (2006) inferred from the RPWS dust impact data 15 to 20% larger FWHM values. Since the RPWS dust detection threshold is rather uncertain this deviation might be attributed to impacts by smaller fast grains1 which were detected by the DA during the crossings. Our data do not indicate a size dependence of the ring thickness for grain sizes of at least 0.9 µm. This suggests that the vertical distribution of these particles is not affected much by forces disturbing the Keplerian motion of the grains but is mostly due to the initial dust speed component orthogonal to the ring plane. Particles released at the moon’s poles have the largest initial vertical speeds within the ring’s inertial frame and thus have the largest initial orbit inclinations. This suggests that the vertical extent of the ring is mostly due to particles originating from the plumes at Enceladus’ south pole, while particles generated by the impactor-ejecta mechanism predominantly move only in slightly inclined orbits. To verify this idea we performed numerical simulations of the long-term evolution of bigger plume particles. Similar to Juhász and Horányi (2002) we traced the motion of 1.25 µm grains affected by the gravity of Saturn and all E ring moons, by electromagnetic forces due to Saturn’s rotating magnetic field, and by the radiation pres1 The RPWS dust detection threshold is supposed to depend similarly to impact ionisation detectors on vd and md as md vd3.2 (Kurth et al., 2006). Thus implies that fast tiny particles can produce the same signal strength as large slow grains. Thus, the assumption of Kurth et al. (2006), that only grains moving in circular orbits were detected by the RPWS antennas (corresponding to a size detection threshold of ∼4.5 µm) may not be entirely correct.

Distribution of E ring particles in the vicinity of Enceladus

sure due to solar illumination, and followed simultaneously the evolution of the grain charge (consistent with in situ measurements of the grain charge by Kempf et al., 2006). We find that only plume particles with initial speeds vs relative to the moon in excess of 222 m s−1 do not re-collide with Enceladus during their first orbit (Fig. 4). This means that there is an effective es = 222 m s−1 that is larger cape speed for plume particles of vesc than the three body escape speed of particles launched at Enceladus’ south pole  −1  = 207 m s−1 , vesc = 2μE RE−1 − Rhill (12) where RE = 248 km is the Enceladus radius, μE = GME , and G is the gravitational constant. As a consequence ring particles originating from Enceladus’ plumes have a minimum inclination of 0.2◦ and ring particles with smaller inclinations can only be produced by the impactor-ejecta mechanism. Another important consequence of an effective escape speed larger than vesc is that only a small fraction of the particles ejected by the plumes with speeds large enough to escape from the moon’s gravity can actually replenish the ring. A big plume particle mainly acquires its inclination during its first orbit. Because of three-body interactions the particle’s resulting inclination is smaller than its initial inclination

tan(i) =

2 2 Rhill vs2 − vesc + vE2 RE2

1/2 .


Fig. 4. Inclination of plume particles as function of the plume’s ejection speed. Diamonds indicate the particle’s inclination after one orbital period. The solid line marks the initial particle inclination given by Eq. (13). Particles ejected with speed lying within the shaded range are strongly affected by three-body-forces during their first orbit.


According to our simulations i ∼ vs17 for vs  235 m s−1 while the inclinations of faster particles agree well with the asymptote i ∼ vs2 of Eq. (13) (Fig. 4). The strong dependence of i(vs ) for vs  235 m s−1 has an interesting consequence. It is reasonable to assume that the initial speed distribution of the plume parti−β cles can be approximated by a power law n(vd ) ∼ vd (Spahn et al., 2006b) with β  17. If so, then the majority of bigger plume particles have inclinations ranging between 0.2◦ and 0.5◦ corresponding to ejection speeds between 222 and 235 m s−1 . The most abundant inclination of 0.5◦ is due to plume particles ejected with 235 m s−1 . In other words, the vertical distribution of plume particles is rather insensitive to the actual speed distribution of the plume particles. In fact, this idea agrees well with our observations: the width of the vertical profile derived from numerical simulations for vs = 235 m s−1 agrees well with the FWHM derived from our data (Fig. 5). The double-peak appearance of the vertical profiles for fixed start speeds is due to the narrow distribution of the orbit inclinations. The resulting vertical distribution of the dust particles injected by the plumes into the E ring is the convolution of the vertical profiles pz (vs ) with the particle’s ejection speed distribution. As a consequence, the double peak signatures of the individual profiles are smeared out. Only a faint imprint of the most narrow profile due to particles just exceeding the mini = 222 m s−1 mum ejection speed is likely to show up. For vesc the separation between the two maxima is about ∼1700 km (see Fig. 5). Indeed, the E ring appears on Cassini edge-on images along its vertical symmetry plane appears slightly darker than at its upper and lower regions. Based on a preliminary analysis of the images, Burns and Tiscareno (2005) estimated a width of the double stripe feature of about 1000 km. This stimulated us to identify such a feature in our data. All vertical profiles derived from our data fluctuate about the Gaussian with amplitudes of typically one σ interval on spatial scales of 1000 km. The spatial positions of the structures vary from one traversal to the next. Kurth et al. (2006) found, however, some evidence for a double feature of the order of one σ in the RPWS dust data. The feature in the RPWS rate profile measured in orbit 7 (Fig. 7 in their paper) seems to coincide with the peak at z ∼ 0.03 RS in our data (see Fig. 3, top row). However, it is still unclear whether the vertical fluctuations in the CDA data are associated with the double band structure visible in the images and expected due to the dynamics of the ejected plume particles.

Fig. 5. Comparison between the vertical density profile derived from the orbit 8 data (Fig. 3b) and numerical simulations of the long-term evolution of spherical 1.25 µm particles released at Enceladus’ south-pole. The ejection speed is given with respect to the moon’s surface.


S. Kempf et al. / Icarus 193 (2008) 420–437

In contrast to the ring thickness there is some number density variation of the dust from orbit to orbit. We find peak number densities n0 (sd  0.9 µm) between 10−1 m−3 and 2 × 10−1 m−3 which makes at most 40% of the normal optical depth derived by Showalter et al. (1991). The densities inferred from orbits 7, 8 and 10 data vary by only about 20%. Hence, our data provide evidence for density fluctuations on the order of 20%. In Table 3 we compare the HRD peak impact rates with the RPWS peak counting rates for crossings when both instruments performed simultaneous observations. Surprisingly, the RPWS /r HRD ranged between 61 ratio between the peak rates rmax max and 127 for the M-sensor and 55 and 113 for the M-sensor. This RPWS /r HRD is not entirely due to the different senimplies that rmax max sitive areas of the two instruments. A possible explanation is that the RPWS dust detection depends on the spacecraft orientation with respect to the dust impact direction which may affect either the sensitive area or the size detection threshold. 4.1.2. Vertical ring structure at Mimas Dust impact data recorded by the HRD during the steep ring plane crossing in orbit 28 at 3.16 RS allowed us to investigate the particle distribution in the vicinity of Mimas’ orbit. To derive the spatial dust distribution from the HRD M-sensor data we used the same techniques as in Section 4.1.1. The results are shown in Fig. 6. Clearly, the vertical ring profile is well represented by a Gaussian profile. The FWHM at 3.16 RS of 5400 km is about 25% larger than the FWHM at 3.95 RS (see Table 3). De Pater et al. (2004) reported a similar trend for the ring’s vertical extent inside Enceladus’ orbit. The symmetry offset of ∼ −1200 km with respect to the geometric equator comes somewhat as surprise. Numerical simulations of particles 0.8 µm released at Enceladus do not provide evidence for such an effect. One may speculate that the observed particles mostly originate from Mimas itself generated by an impactor-ejecta mechanism. If so, the asymmetry may be attributed to the rather large inclination and eccentricity of Mimas (iMimas ∼ 175iEnc , eMimas ∼ 4eEnc ). The dust impact speed during the crossing was a bit larger than during the Enceladus orbit crossings causing a slightly lower M1 detection threshold of 0.8 µm. Thus, the peak density of 3.0 × 10−3 m−3 at 3.16 RS cannot be compared directly with the number density inferred

from the Enceladus orbit crossing data when the M1 detection threshold was 0.9 µm. Assuming a differential size distribution of ∼ sd−5 (see Section 6) the number density of grains 0.9 µm is approximately 1.9 × 10−3 m−3 which is about two orders of magnitudes lower than at the densest point within the ring plane ρc . 4.1.3. Vertical ring structure at Tethys The data acquired during the four ring plane crossings in the vicinity of the Tethys orbit can be separated into 2 groups: data obtained during rather slow shallow ring plane crossings in orbits 27 and 28, and data obtained during the steep and fast crossings in orbits 31 and 32. As a consequence of the dissimilar impact speeds during the crossings the two groups actually refer to distinct dust populations—the data sets of the first group are due to impacts by micron-sized grains moving in circular orbits, while the data sets belonging to the second group are dominated by much smaller grains moving in probably eccentric orbits (see Table 2). What the data sets of the two groups have in common, however, is that they draw a picture of Tethys’ dust environment that is quite different from what we learned about the environment of Mimas and Enceladus. In particular, the vertical distribution of the dust particles is not represented any longer by a Gaussian (Figs. 7 and 8). All of our attempts to fit a reasonable model for the spatial dust distribution have failed so far. The measurements during crossings belonging to the same group are remarkably consistent. Fig. 7 compares the number densities derived from the two shallow crossings. Due to the rather low impact number during these crossings we determined the rates from impact time sequences with 180 s resolution equivalent to a radial and vertical spatial resolution of 1020 and 690 km, respectively. The lower size detection threshold was 1 µm. During both crossings we observed a broad dust layer with a FWHM ∼5500 km and a second weaker feature above the ring plane approximately at the mean radial distance of Tethys’ orbit. It may be possible that this feature is due to a dust belt populated by particles originating from Tethys (Juhász and Horányi, 2002; Spahn et al., 2006a). Also de Pater et al. (2004) reported a second local maximum in the ring’s brightness at Tethys’ mean orbital distance. However, due to the small

Fig. 6. Spatial distribution of dust particles >0.8 µm at about Mimas’ orbital distance. The time resolution is 120 s corresponding to a radial resolution of 630 km and a vertical resolution of 1000 km. (Left) Impact rates versus time. (Right) Dust number density versus distance to Saturn’s rotation axis and versus the elevation above the ring plane. The broken line marks the time of Cassini’s ring plane crossing.

Distribution of E ring particles in the vicinity of Enceladus


Fig. 7. Spatial distribution of grains 1 µm in the vicinity of Tethys’ orbit inferred from HRD m1 data obtained during the shallow ring plane crossings in orbit 26 and 27. The time resolution is 180 s corresponding to a radial resolution of 1020 km and a vertical resolution of 690 km. (Left) m1 impact rates versus time. (Right) Number density of grains versus distance to Saturn’s rotation axis and versus the elevation above the ring plane. Note that here the shown number densities are not decomposed into n(ρ, 0) and n(RX , z). The ring plane crossing time and the Tethys orbit crossing time are marked by broken and dotted lines, respectively.

Fig. 8. Spatial dust distribution in the vicinity of Tethys’ orbit derived from HRD m1 data recorded during the steep ring plane crossings in orbit 31 and 32. The time resolution is 120 s corresponding to a radial resolution of 420 km and a vertical resolution of 1400 km. The data are presented as in Fig. 7.


S. Kempf et al. / Icarus 193 (2008) 420–437

crossing angle the registered impact rate was not any longer dominated by the vertical dust distribution as was the case for the plane crossings considered before. Thus, our data are not reliable enough to attribute the feature reliably to Tethys, since the feature may as well be associated with the vertical dust distribution. The vertical density profiles inferred from the steep orbit crossings in orbits 31 and 32 are both asymmetric. Due to the large speed of Cassini relative to the dust the detection threshold was 0.6 µm for grains moving in circular orbits. Particles of such size, however, are characterised by eccentric orbits (Horányi et al., 1992; Juhász and Horányi, 2002). This is also indicated by the analysis of the DA data presented in Section 6.2. Probably fast tiny grains moving in highly eccentric orbits contributed significantly to the measured flux. Great care needs to be taken when comparing such results with our findings derived from the slow ring plane crossings. The ring’s FWHM of ∼6300 km at 4.97 RS is slightly larger than at 4.77 RS . 4.2. Radial ring structure In this section we discuss the radial structure of the inner E ring. The global radial distribution of the E ring particles is studied best during long equatorial scans of the ring undisturbed by the spacecraft operations. The observation conditions during Cassini’s traversal of the inner saturnian system in orbit 3 were favourable for this purpose. Fig. 9 shows the radial and vertical distribution of the ring particles for both the inbound and the outbound leg of the trajectory. During long

radial scans the size detection threshold is not constant any longer because the spacecraft speed relative to the ring particles varies significantly with her distance to the planet. This effect must not be ignored—in case of the orbit 3 data the detection threshold of the M1 channel was 0.9 at 3.5 RS and 1.4 µm at 6 RS . By means of plausible assumptions about the particle size distribution it is possible to transform the measured rates into number densities of grains larger than a given size. Our results, presented in Section 6.1, justify the assumption that grains detected by the HRD are approximately distributed as n(sd ) ∼ sd−5 . Then, the appropriate number density correction is found to be n(s1 ) = n(s0 )(s0 /s1 )−4 , where s0 and s1 are the size detection threshold and the corrected size, respectively. We applied this relation to all HRD channels displayed in Fig. 9. We generally chose s1 to be the maximum value of s0 during the period in question. The general dependence of the dust number density on the distance to Saturn’s polar axis suggests describing the spatial dust distribution within the ring by a pair of power laws (see Fig. 9). By doing so, however, one probably oversimplifies the problem. Clearly, the impact rate recorded in orbit 3 depends on both the radial and the spatial distribution of the dust. In contrast to steep vertical ring plane crossings the ring thickness cannot any longer be assumed constant. For this reason we use a modified form of Eqs. (9)–(11) to model our measurements. To describe the dependence of the profile’s thickness σ in Eq. (10) on the distance to Saturn’s pole axis we use a pair of linear laws

σ −σ c i , ρ  ρc , c σ (ρ) = σc + (ρ − ρc ) ρσi0−ρ (14) −σc ρ0 −ρc , ρ > ρc ,

Fig. 9. Spatial distribution of E ring particles 1.3 µm (red) and 2.4 µm inferred from HRD rate measurements inside 6 RS in orbit 3. The upper panel shows the dust number density versus distance to Saturn’s rotation axis (left) and versus the elevation above the ring plane (right) for the inbound segment of the trajectory; the lower panel shows the same for the outbound leg of the trajectory. Light grey areas mark periods when the detector was either insensitive to E ring dust particles or the data were not transmitted to Earth; areas coloured in light grey indicate periods when the instrument operation interfered with the data acquisition.

Distribution of E ring particles in the vicinity of Enceladus

where σi , σc , and σ0 are the width of the vertical profiles at the reference points ρi , ρc , and ρ0 , respectively. This law implies a weak dependence of the ring particle inclinations on ρ. In the previous section we already determined the ring thickness at ∼3.16 RS , at the densest region at ∼3.98 RS , and in the vicinity of Tethys’ orbit at ∼4.75 RS . Thus, the natural choice of the reference points are ρi = 3.16 RS and ρ0 = 4.75 RS . Since we found evidence for a vertical offset of the ring at about the Mimas orbit, we also include a linear dependence of the vertical offset z0 on ρ inside Enceladus’ orbit in our ring model  z0 (ρi ) z0 (ρ) = (ρ − ρc ) ρi −ρc , ρ  ρc , (15) 0, ρ > ρc . Our geometrical model could also easily deal with vertical offsets outside ρc . We decided, however, not to assume vertical shifts outside ρc because there is no evidence for such an effect in the ring data we acquired so far. Our model therefore has 5 fixed parameters derived from the vertical profiles: σi = 2293 km, σc = 1826 km, ρc = 3.98 RS , σ0 = 2336 km, and z0 (ρi ) = −1220 km. The free parameters to be determined are ei , e0 , and n0 . In Fig. 9 we compare the best fits to our ring model with the data obtained during the inbound and outbound part of the orbit 3 trajectory; the corresponding parameters are given in Table 3. Note that Cassini performed a close flyby of Enceladus during the outbound leg of her orbit (see also Section 5). The increased dust density in the vicinity of the moon caused local deviations from the large scale dust distribution. As we will show in the next section there is a clear imprint of the plume particle jet in our data. The obtained fits reasonably match our data. In particular, the fits to the inbound data, which are not affected by the local dust distribution at Enceladus, appears to be remarkably good. Additionally, the density at ρc derived from the inbound and outbound fits are fairly consistent. Discrepancies between the model and our data can be surely



attributed to azimuthal and temporal variations of ring particles. This is supported by numerical simulations by Juhász and Horányi (2002, 2004) which provide clear evidence for strong local density variations. To conclude we will briefly review the ingredients of the model. To match our data we needed to include into the model a positive vertical offset for n(z) inside Enceladus’ orbit. It is sufficient to assume a linear dependence of the ring thickness on ρ inside and outside the ring’s densest point at 3.98 RS . This implies that the inclination of the ring particles >1 µm is preserved despite the action of the disturbing forces. This 2-dimensional geometrical model will be useful in the analysis of the DA impact data. We will use it to make predictions for the HRD measurements during the upcoming ring plane crossings. In turn the new data will be used to test our approach. We plan to further improve the E ring model by incorporating the new data. In particular an improved model for the dependence of the vertical thickness on the distance to the planet will provide us with a better understanding of the longterm evolution of the particles’ inclinations. 5. Fingerprints of Enceladus’ plumes During the close Enceladus encounter on 2005-195 UTC in orbit 11 the HRD discovered a collimated jet of large dust emerging from the moon’s south pole region (Spahn et al., 2006b). However in this paper only the M-sensor impact rates were considered. In Fig. 10a we show the number densities derived from both sensors. During the flyby the m2 threshold coincided with the m1 threshold of 1.6 µm. Thus, the fact that the number densities measured simultaneously by two physically independent sensors agree to within one σ is noteworthy. The peak impact rate of grains  0.9 µm and of grains 1.6 µm occurred about 60 s before the closest approach to the moon surface when Cassini just crossed the Enceladus Hill


Fig. 10. HRD dust measurements during the close flyby at Enceladus in orbit 11. (a) Top panel: Number density of grains larger than the detection threshold versus time. The time resolution is 15 s corresponding to a radial resolution of 75 km and a vertical resolution of 92 km. (a) Bottom panel: Slopes of the differential size distribution versus time. The shaded area marks the period when Cassini traversed Enceladus’ Hill sphere. Vertical dash dot and dotted lines indicate the times of the closest approach and the ring plane crossing, respectively. (b) Comparison between count rates of grains larger 1.6 µm predicted by numerical simulations of the Enceladus dust environment with the HRD M1 data.


S. Kempf et al. / Icarus 193 (2008) 420–437

Fig. 11. HRD dust measurements during the close flyby at Enceladus in orbit 3. The time resolution is 30 s corresponding to a radial resolution of 187 km. The data are presented in the same way as in Fig. 10.

sphere. Spahn et al. (2006b) showed that a temporal offset of the peak rate with respect to the closest approach is an indicator of a localised collimated dust source on the moon. In Fig. 11a we show the dust number densities derived from the HRD taken around the closest approach of the E3 flyby. Due to the larger flyby distance the M1 peak rate is about an order of magnitude smaller than during the E11 flyby. The impact rate has its maximum about three minutes after the closest approach which suggests that the HRD also registered the plume particle jet during the E3 flyby. To verify this idea we compare the E3 data with the count rates predicted by the simulations of the Enceladus dust environment computed along the E3 trajectory. We used the numerical model by Spahn et al. (2006b) which reproduces well the HRD E11 measurements (see Fig. 10b). This model is a self-consistent combination of dust particles provided by the impactor-ejecta process (Spahn et al., 2006a), a localised dust source at the moon’s south-pole, and the E ring particle background. The model predicts the peak rate after the closest approach, in agreement with the data. However, a reasonable match between the data and the model is obtained only if the contribution of the E ring background is about an order of magnitude lower than during the E 11 flyby (Fig. 11b). The reason for this effect is not entirely understood, however the best explanation is that the dust production rate of the plumes is strongly time variable. As discussed in Section 4.1.1 short time variations of the dust production rate do not affect the global structure of the E ring. Consequently, the proposed explanation is consistent with the weak time-dependence of the global ring parameters. 6. Ring particle properties Information about the particle size distribution can be derived from both the HRD and the DA data, while the particle speed distribution can be deduced only from the DA data. First we estimate the size distribution of grains detected by the HRD.

6.1. Properties of large ring particles The HRD registers a particle hitting the PVDF foil if the impact generates a charge signal exceeding the lowest detection threshold given in Table 1. In case of the m-sensor the size detection threshold for water ice grains depends on the impact speed as smin ≈ 4 µm × (vd [km s−1 ])−0.77 . As discussed in Section 4.1.1 the impact speed can be assumed to be given by the collision speed of grains moving in circular orbits. Each of the HRD sensors provides impact rates for three mass intervals. Thus, size distributions derived from HRD measurements performed before the damage of the M-sensor on 2005-248 UTC are based on 6 dust size bins typically ranging between 1 and 10 µm. The differential size distribution inferred from our data is well characterised by a power law of the form n(sd ) dsd ∼ −q sd s dsd . Remarkably, the size slope qs shows some variation from orbit to orbit (see Table 3). During most of the crossings in the vicinity of Enceladus qs ranged from 4.8 to 5.4, equivalent to slopes of the differential mass distribution of 2.3 and 2.5. Size slopes of qs > 4 imply that the mass as well as the geometric cross section of the ring is due to smaller dust grains. It is also noteworthy that the smallest size slope is qs = 4.2 ± 0.3 inferred from the crossing 9 impact data, the crossing is characterised by the largest angular separation λEnc between Enceladus and Cassini of −134◦ (Table 2). Thus, our data provides some evidence for an angular colour variation of the Enceladus dust torus. Generally we obtained smaller size slopes than qs = 6.4 ± 1.0 derived from the RPWS data by Kurth et al. (2006). We also did not yield a large size slope for the orbit 7 data. We note that qs did not change when Cassini flew through the plume particle jet (see bottom panels of Figs. 10a and 11a). Thus, at least for grains 0.9 µm the size distribution of the background E ring particles and of the fresh plume particles is identical. Particles in this size range can be only weakly affected by selective dynamical processes as proposed by Horányi et al. (1992).

Distribution of E ring particles in the vicinity of Enceladus


Fig. 12. Dust impacts on the DA IIT during the ring plane crossings in orbit 7, 8, 10, and 13. In each plot, the top right panel shows the size and impact speed of the individual particles, whilst the bottom right and top left panels display the corresponding differential size and speed distributions. Impacts lying inside the shaded area generated impact charges exceeding at least one of the DA thresholds. The broken line marks the HRD detection threshold.

6.2. Properties of small ring particles To investigate the size and speed distributions of dust particles populating the inner E ring we used the individual dust impacts registered by the DA during the ring plane crossings in orbits 7, 8, 10, and 13. For deriving the distributions we do not need to take DA dead time effects into consideration as it is necessary for deducing DA impact rates (Kempf, 2007). Also incomplete transmissions of the recorded individual dust impacts are of no consequence here. Furthermore, we restricted our analysis to impacts onto the IIT for which the impact speed can be determined much more accurately than for impacts on the CAT. To ensure a high quality of the data sample we manually reanalysed the impact charge signals of the individual dust impacts. We derived the impact speed vd and the grain size sd from the rise time and the charge yield of both, the IIT electron charge signal QT and the ion grid signal QI using Eqs. (2)–(5). However, due to the good agreement between

md and vd derived from QT and QI we only present here the QI dust parameters. Fig. 12 shows the distribution of impact speed and grain size inferred from the DA data. Remarkably, the detector registered in all cases predominantly grains smaller than 0.5 µm whose impact speeds are significantly larger than the impact speed of grains moving in circular Keplerian orbits (vcirc ≈ 8.1 km s−1 ). Clearly, the DA data are due to a different ring particle population than the HRD data. The size distribution displayed in Fig. 12 must not be confused with the size distribution of the ring particles, because the DA data samples suffer from selection processes. This is due to the fact that a DA measurement is triggered by the plasma charge yield q (DA) produced by the impact. q (DA) , however, is a function of the size and the speed of the striking grain [see Eqs. (3) and (5)]. As a consequence, fast tiny particles can produce the same impact charge as slow large dust grains. On the other hand, the impact rate is proportional to the impact speed of the grains. Thus, fast tiny grains can dominate the DA data


S. Kempf et al. / Icarus 193 (2008) 420–437

sample although they may be less abundant than slow large dust particles. In other words, the speed distribution derived from the DA data samples also depends on the size distribution n(sd ) of the ring particles ∞ pvDA (vd ) = vd

  pv (vd |sd )n(sd ) Θ q (DA) (vd , sd ) − qthres dsd ,


(16) and the size distribution of the DA sample also depends on the speed distribution pv (vd |sd ) of the ring particles ∞ nDA (sd ) = n(sd )

  pv (vd |sd ) Θ q (DA) (vd , sd ) − qthres vd dvd .


(17) Both distributions are bound by the number of impacts N de tected by the DA during a time interval t , i.e., nDA (sd ) dsd = N . Assuming a power law size distribution one finds that the size of the largest grain likely to be detected within t depends on the size of the smallest detected grain as smax ≈ N 1/(qs −1) smin . This implies that the DA size range is governed by the most abundant impactor within the data sample. For qs < 0 the most abundant impactors are tiny grains just exceeding the detection threshold, and the DA was not likely to detect larger ring particles. Our attempts to invert Eqs. (17) and (16) numerically have failed so far, mostly due to the poor signal to noise of the DA distributions. We expect, over the time to improve the signal to noise ratio of the DA distribution, allowing us to derive the size distribution of sub-micron ring particles as well. Nevertheless, from the data presented here we can make several conclusions about the properties and the origin of the observed particles. The mean impact speed during the crossings in orbits 8, 10, and 13 is ∼15 km s−1 , while in orbit 7 the mean speed of ∼10 km s−1 is close to vcirc ∼ 8 km s−1 . This is remarkable because the crossing parameters of the four orbits are almost identical (see Table 2). There is only one reasonable explanation for the peculiar orbit 7 speed distribution—the orientation of the DA boresight relative to the dust flux was less favourable for detecting fast grains. This becomes apparent by comparing Fig. 2c with Fig. 2d, where we show the dependence of the flux on the IIT upon the dust’s semi-major axis a and eccentricity e at tX . Clearly, in orbit 8 the flux of grains with small eccentricities is lower than the flux of more eccentric particles. This is in contrast to orbit 7, when the instrument was insensitive to impacts by eccentric grains. This suggests that there is a ring particle population with sizes below 0.5 µm characterised by semi-major axis significantly larger than rE and large eccentricities. 7. Summary We have attempted, in this paper, to describe how the E ring appears to a local observer traversing through its region of interest. To this goal, we analysed dust data acquired by the dust

detector CDA during Cassini’s passages through the inner E ring. Based on our analysis we conclude: 1. The vertical distribution of E ring particles  1 µm interior of about Enceladus’ orbit is well described by a Gaussian. The ring’s FWHM has its minimum of ∼4300 km at Enceladus and is ∼5400 km at Mimas. There is no evidence for a dependence of the FWHM at Enceladus on the particle size for grains 1 µm. 2. Outside the Enceladus orbit the vertical ring structure does not resemble a Gaussian. The FWHM at Tethys is ∼5500 km (for sd  1 µm) and ∼6300 km at 4.97 RS (for sd  0.6 µm). 3. The FWHM values derived from E ring images taken at 2.26 µm (de Pater et al., 2004) are about twice as large as findings for sd  1 µm. This implies that the ring’s brightness is due to sub-micron sized grains. 4. At Mimas the ring is displaced southwards from the equatorial plane by ∼1200 km. Our data provide no evidence of a vertical ring displacement at the Enceladus orbit. 5. The densest point within the ring does not coincide with the Enceladus orbit but is displaced outwards by at least 0.05 RS , which is consistent with the conclusions by de Pater et al. (2004). 6. The radial distribution of the dust is reasonably well described by a pair of power laws centred at the densest point ρc . The vertical thickness increases linearly with distance to ρc . 7. Near Enceladus the differential particle size distribution of grains >0.9 µm has slopes between 4.2 and 5.4. There is evidence for a colour variation of the ring along the Enceladus orbit. The size distribution of freshly injected plume particles concurs with the size distribution of the background E ring particles. 8. There is a population of tiny fast grains, which may be the precursors of saturnian stream particles registered outside the saturnian magnetosphere (Kempf et al., 2005a, 2005b). 9. The vertical thickness of the ring at the Enceladus orbit is closely linked to the dynamics of the plume particle injection. Although particles with initial speeds between 207 and 222 m s−1 are fast enough to overcome the gravitational attraction of the moon, they will get lost due to collisions with the moon during their first orbit. Only plume particles with initial speeds between 222 and 235 m s−1 contribute significantly to the vertical extent of the ring. Acknowledgments This project is supported by the DLR under the Grant 500OH91019. The authors are deeply indebted to the scientists and engineers at JPL who made the reported CDA measurements possible. We thank W. Woiwode and G. Linkert who helped with the data processing. We have benefited from conversations with W. Kurth, A. Juhasz, M. Horányi, M. Hedman, C. Porco, M. Burton, and J. Howard. We warmly thank I. de Pater and L. Esposito for the helpful reviews. Finally S.K. thanks

Distribution of E ring particles in the vicinity of Enceladus

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