The E ring in the vicinity of Enceladus

Abstract

Saturn's diffuse E ring is the largest ring of the Solar System and extends from about $3.1R_{\mathrm{S}}$ (Saturn radius $R_{\mathrm{S}}=60,330\text{km}$) to at least $8R_{\mathrm{S}}$ 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 $3.95R_{\mathrm{S}}$ agrees well with a Gaussian with a full-width–half-maximum (FWHM) of $\sim 4200\text{km}$. We show that the FWHM at $3.95R_{\mathrm{S}}$ 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 $16\times {10}^{\mathrm{-2}}{\text{m}}^{\mathrm{-3}}$ and $21\times {10}^{\mathrm{-2}}{\text{m}}^{\mathrm{-3}}$ for grains larger 0.9 μm, and $2.1\times {10}^{\mathrm{-2}}{\text{m}}^{\mathrm{-3}}$ and $7.6\times {10}^{\mathrm{-2}}{\text{m}}^{\mathrm{-3}}$ for grains larger than 1.6 μm. Our data imply that the densest point is displaced outwards by at least $0.05R_{\mathrm{S}}$ with respect of the Enceladus orbit. This finding provides direct evidence for plume particles dragged outwards by the ambient plasma. The differential size distribution $n(s_d)\mathrm{d}{s}_d\sim s_d^{-q_s}\mathrm{d}{s}_d$ for grains $>0.9\text{μm}$ 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 $>0.8\text{μm}$ at Mimas orbit is also well described by Gaussian with a FWHM of $\sim 5400\text{km}$ and displaced southwards by $\sim 1200\text{km}$ 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.

Introduction

Ever since the discovery of Saturn's vast diffuse E ring by Feibelman (1967) its study has been mainly based on images obtained from both ground-based and space-bound astronomical observations (Baum et al., 1981, de Pater et al., 1996, de Pater et al., 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 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 ($r_{\mathrm{M}}=3.07R_{\mathrm{S}}$), Enceladus ($r_{\mathrm{E}}=3.95R_{\mathrm{S}}$), Tethys ($r_{\mathrm{T}}=4.88R_{\mathrm{S}}$), Dione ($r_{\mathrm{D}}=6.25R_{\mathrm{S}}$), and Rhea ($r_{\mathrm{R}}=8.73R_{\mathrm{S}}$). 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 $\tau \sim 1.6\times {10}^{\mathrm{-5}}$ 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 $2.2\text{μm}$ (de Pater et al., 2004) implying a narrow grain size range centred between 0.3 and $3\text{μm}$ (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 $9000\text{km}$ between Mimas' and Enceladus' orbit, with a minimum of $8000\text{km}$ at $r_{\mathrm{E}}$. The same FWHM had been found by Nicholson et al. (1996) from HST data at visible wavelength. Surprisingly, in Cassini images the FWHM at $r_{\mathrm{E}}$ is only $5000\text{km}$ (Porco et al., 2006). Outside $r_{\mathrm{E}}$, the FWHM rises to $13,000\text{km}$ at Tethys' orbit and increases up to $15,000\text{km}$ before the ring blends with the background. Baum et al., 1981, Baum et al., 1984 reported an even larger FWHM of $40,000\text{km}$ at about $8R_{\mathrm{S}}$. 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 $n_{\perp }$ increases radially between its inner rim at about $3R_{\mathrm{S}}$ and Enceladus orbital radius $r_{\mathrm{E}}\sim 3.94R_{\mathrm{S}}$ as $n_{\perp }(r)\sim r^{15}$, and falls off outside $r_{\mathrm{E}}$ as $n_{\perp }(r)\sim r^{\mathrm{-7}}$. 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

$$\sigma (r)=\sigma (3R_{\mathrm{S}}){\left(\frac{\sigma (8R_{\mathrm{S}})}{\sigma (3R_{\mathrm{S}})}\right)}^{(r-3R_{\mathrm{S}})/5R_{\mathrm{S}}},$$

with $\sigma (3R_{\mathrm{S}})\sim 2500\text{km}$ and $\sigma (8R_{\mathrm{S}})\sim 15,900\text{km}$.

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, Juhász and Horányi, 2004 performed extensive numerical simulations of the long-term 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 et al. (1991) brightness profile they predicted that the satellites Mimas, Enceladus, Tethys, and Dione as dust sources contributing in the ratio $\{<0.01:1.0:0.3\pm 0.1:<0.01\}$. Furthermore, they determined the index of the power-law size distribution to be $3.1\pm 0.4$.

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 $5\times {10}^{12}{\text{s}}^{\mathrm{-1}}$, 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 $>2\text{μm}$ 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, Grün et al., 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 $\gtrsim 1\text{μm}$. 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.