Signatures of Enceladus in Saturn s E ring

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1 Click Here for Full Article GEOPHYSICAL RESEARCH LETTERS, VOL. 34,, doi: /2006gl029120, 2007 Signatures of Enceladus in Saturn s E ring Antal Juhász, 1 Mihály Horányi, 2,3 and Gregor E. Morfill 2 Received 18 December 2006; revised 7 March 2007; accepted 23 March 2007; published 5 May [1] Dust production from Enceladus has long been suggested as the main source of dust in Saturn s E ring. This was supported by the observation that the ring s optical depth peaks close to the orbit of this moon. However, both HST and Keck observations indicated that the peak of the optical depth distribution in fact lies outside the orbit of Enceladus, with a displacement of approximately 10 4 km. Though this outward shift has been suspected to be a result of electromagnetic forces, it could not be reproduced in earlier studies. Here we show that it is intimately related to the initial inclinations of the grains produced in the recently discovered plumes. For grains with radii r g >0.5mm, the small initial inclination greatly reduces their re-collision probability, allowing for sufficiently long lifetimes for plasma drag to transport them outwards. Our numerical results can also be used in the simultaneous interpretation of the measurements by the Cassini CDA, RPWS instruments and imaging. Citation: Juhász, A., M. Horányi, and G. E. Morfill (2007), Signatures of Enceladus in Saturn s E ring, Geophys. Res. Lett., 34,, doi: /2006gl Introduction [2] Saturn s E ring provides an excellent opportunity to study single particle dynamics in a planetary ring as, due to its low optical depth t [Showalter et al., 1991], collisions or collective effects are negligible in this region. From ground based, HST and Voyager observations [Showalter et al., 1991], the ring appears to occupy the region approximately between 3 < r <8R S (the radius of Saturn, R S = 60,330 km) and encompasses the five major satellites: Mimas (r M = 3.08 R S ), Enceladus (r E = 3.95 R S ), Tethys (r Te = 4.89 R S ), Dione (r D = 6.26 R S ), and Rhea (r R = 8.75 R S ). Recent in situ observations by Cassini Cosmic Dust Analyzer (CDA) show that the E ring material continuously extends much further from Saturn, engulfing even the orbit of Titan (r Ti = 20.3 R S )[Srama et al., 2006; Kempf et al., 2006; S. Kempf et al., The E ring in the vicinity of Enceladus: Spatial distribution and properties of the ring particles, submitted to Icarus, 2007, hereinafter referred to as Kempf et al., submitted manuscript, 2007]. This large extension was also indicated by the RPWS instruments on the Voyagers [Gurnett et al., 1983]. [3] Enceladus has been long suspected to be the main source of dust particles comprising the E ring, as the ring s 1 Department of Space Physics, KFKI Research Institute for Particle and Nuclear Physics, Budapest, Hungary. 2 Max-Planck-Institute for Extraterrestrial Physics, Garching, Germany. 3 Permanently at Laboratory for Atmospheric and Space Physics and Department of Physics, University of Colorado, Boulder, Colorado, USA. Copyright 2007 by the American Geophysical Union /07/2006GL optical depth distribution sharply peaks close to its orbit. Dust production due to bombardment by interplanetary dust particles [Showalter et al., 1991], bombardment by the E ring particles themselves [Hamilton and Burns, 1994], or active geysers on Enceladus [Haff et al., 1983] were suggested as possible mechanisms. Observations of the E-ring during the 1995 ring plane crossings - perhaps due to their better signal-to-noise ratios and/or spatial resolutions - indicated that the peak of the optical depth distribution lies outside the orbit of Enceladus [Showalter, 1996; de Pater et al., 2004]. An outward displacement of about 10 4 km ( 0.15 R S ) remained difficult to understand, based on studies of the lifetime and orbital dynamics of the dust grains released from Enceladus with the previously assumed small relative velocities once they escape the gravitational dominance of this moon. [4] One of the most interesting findings of the Cassini mission to date was the discovery of geophysical activity in the south-polar region of Enceladus during the close flyby on July 14, 2005 (special issue on Enceladus in Science, 311, March, 2006). [5] The high-rate detector (HRD) subsystem of CDA observed a dense cloud of grains that appeared asymmetric relative to the closest approach position, indicating a locally enhanced dust production in the south polar region of Enceladus [Spahn et al., 2006a]. A comprehensive study of the CDA data by Spahn et al. [2006b] suggested that at least 85% of the grains (above the HRD detection threshold) are generated near Enceladus south pole. These grains are either entrained in the outflow of the plumes, or grow in situ in the expanding and cooling gas. They attain velocities larger than the escape velocity from the surface of Enceladus (v esc = 210 m/s), or gain energy from the gas flow, so that they have a nonzero residual velocity on the order of m/s after leaving the gravity field of the satellite [Porco et al., 2006]. Interestingly, the ejecta particles generated via bombardment by interplanetary dust grains are also expected to have a characteristic residual velocity of about 110 m/s [Krivov, 1994]. Here we show that this initial decoupling velocity of the dust grains from Enceladus is ultimately responsible for the formation of the outward shift of the peak optical depth in the E ring. This is due to the greatly prolonged lifetimes of grains with radii r g >0.5mm against re-collision with Enceladus, combined with their outward transport due to plasma drag. Simultaneously, the initial velocity distribution of the escaping dust particles also explains the bright regions approximately km above and below the ring-plane near Enceladus, recently observed by Cassini (C. C. Porco, Saturn s faint rings share some of their secrets, 2006, available at view.php?id=2096, hereinafter referred to as Porco, 2006). This double-peaked vertical structure was also noticed by the Radio and Plasma Wave Science (RPWS) instrument, 1of5

2 JUHÁSZ ET AL.: SATURN S E RING but the amplitudes of these enhancements remained on the order of the statistical noise [Kurth et al., 2006]. 2. Dynamics of Dust Particles From Enceladus [6] Our approach here is identical to our earlier dynamical models [Juhász and Horányi, 2002, 2004] applied now to investigate the effects of the initial decoupling velocity of dust from Enceladus. We follow the trajectories of the particles by simultaneously integrating their equation of motion (accounting for gravity, electromagnetic forces, radiation pressure and plasma drag), their charging (accounting for the collection of electrons and ions, and the emission of secondary and photoelectrons), as well as their mass loss due to sputtering. We use the Voyager model of the magnetospheric fields and plasma environment [Connerney, 1993; Richardson, 1995; Richardson et al., 1998] that was qualitatively confirmed by Cassini measurements as well [Persoon et al., 2005; Sittler et al., 2005, 2006]. This approach was successful in reproducing the average properties of the ring as seen by remote optical observations [Juhász and Horányi, 2002], as well as to predict its seasonal variations [Juhász and Horányi, 2004]. In these earlier studies the initial velocity of the grains produced only by interplanetary dust impacts were neglected. However, grains escaping from the plumes on Enceladus seem to have an initial decoupling speed on the order of m/s, directed anti-parallel to the orbital angular momentum vector of the moon [Porco et al., 2006]. Grains produced by impacts are also expected to have a similar decoupling velocity [Krivov, 1994]. [7] The collision probability, p m (t)dt, of an orbiting dust particle with a nearby moon, m, in the time interval of dt, can be calculated given the orbital elements of the grain and the moon, assuming randomly oriented orbits [Öpik, 1976]. For example, this probability rapidly drops as soon as the amplitude of the initial vertical oscillation due to orbital inclination exceeds the radius of Enceladus ( 250 km). [8] These are typically very small probabilities and can be treated as independent in the case of multiple moons as possible targets. Hence, the total collision probability is (S m p m (t))dt, and the probability that a particle has collided by time t becomes: R Pt ðþ¼1 exp t ð P 0 m pmðþ t Þdt ð1þ [9] It is convenient to define the collisional lifetime of a particle, t c, by setting R 0 tc (S m p m (t))dt = 1, i.e., P(t c )=1 1/e By numerically integrating the trajectories of grains starting from Enceladus, their expected lifetime against collision with any of the moons can be calculated using equation (1). [10] A particle will be lost from the E ring if any of these conditions are met: (1) its age is t > t c ; (2) the grain hits Saturn or the main rings; (3) the grain sputters away and its radius drops below 10 nm; or (4) the grain leaves the magnetosphere of Saturn (r >20R S ). [11] In general, the lifetime of grains with radii 1 mm remains independent on v z, as it is set by mass loss due to sputtering. However, the lifetime of larger grains is set by collisions with the moons, and it becomes significantly modified by nonzero v z. Figure 1 shows the final lifetime estimates for the escaping particles as function of their size. The lifetimes reflect the orbital history, as well as the mass loss of these grains. For comparison, Figure 1 also shows that the lifetime estimates do not drastically differ by including or neglecting plasma drag. [12] An interesting feature of Figure 1 is the deep minimum at particle sizes around 1.4 mm where the lifetime is only a few years, even for v z 6¼ 0. This is the size range where the precession rate caused by the oblateness of Saturn nearly cancels the regression rate caused by the Lorentz force, so that these charged grains can attain high eccentricities due to solar radiation pressure and quickly become lost in collision with the A ring [Horányi et al., 1992]. The secondary ejecta particles generated in these collisions have been suggested to be a possible source of the stream particles, that are small positively charged grains accelerated to high speeds escaping the magnetosphere of Saturn [Kempf et al., 2005; Srama et al., 2006]. 3. Dust Distribution Near Enceladus [13] In order to model the dust distribution of the E ring near Enceladus we need the initial size and velocity distributions of grains. For now, we only consider grains from the active plumes in the south-polar regions of Enceladus, as they are likely to dominate the dust population around this moon [Spahn et al., 2006b]. Given the initial conditions, we follow a large number of individual grain trajectories by simultaneously integrating the equations of motion, charging, and mass loss due to sputtering. These trajectories are sampled to give estimates for the spatial and size distributions of the grains in order to calculate the optical depth and brightness as functions of wavelength and phase angle [Juhász and Horányi, 2002], and to predict impact rates for in situ dust measurements [Juhász and Horányi, 2004]. In these simulations, the results are combined from the trajectories of ice particles, with a density r =1gcm 3, initial radii from 0.1 to 3 mm, bin size of 0.1 mm, and with index of refraction of lossy ice m = i in the Mie code calculations of the brightness of the ring. [14] Based on recent images, the plume particles seem to escape with a significant velocity of m/s, relative to Enceladus (Porco, 2006). The final escape speed is likely to be a function of the size of the particles entrained in the gas flow. Though the underlying energy source could be very different from the case of a dusty-gas flow in the coma of a comet, it is likely that the physics of exchanging momentum and energy between the expanding gas and the dust particles remains similar [Gombosi et al., 1986]. At some distance from the source, the gas-dust collisions became negligible, and the dust grains are no longer accelerated by the flow. This decoupling radius is approximately the size of Enceladus (radius = 256 km), well within the region where the moon s gravity dominates over Saturn s (Hill radius = 860 km). For now, we assume a constant residual velocity that is independent of particle size, and examine the sensitivity of the results by repeating our calculations for v z = 50 and 100 m/s. Similarly, there are large uncertainties in the initial size distribution of the particles as well. Here we assume that they follow an initial power law size distribution n(a)da a g da, where a is the radius and the index is expected to be g 3.5 [Juhász and 2of5

3 JUHÁSZ ET AL.: SATURN S E RING Figure 1. The lifetime of grains from Enceladus as function of their initial radius, assuming an initial decoupling velocity v z =0, 50, and 100 m/s including (continuous lines) or neglecting (dashed lines) plasma drag. Horányi, 2002, 2004]. Our results are sensitive to the assumed initial velocity and size distributions. A sizedependent initial velocity distribution would likely result in smoother spatial distributions. Also, an initial size distributions with a larger (smaller) g would shift the calculated radial brightness peak closer to (further away from) Enceladus. A more exhaustive study of these assumptions will be discussed in subsequent publications. [15] Figure 2 shows the calculated brightness distribution near Enceladus using the same wavelength (l = 2.26 mm) and zero phase angle as the Keck observations [de Pater et al., 2004], assuming an outflow velocity of v z =0, 50 and 100 m/s. While the earlier assumed v z = 0 results in a brightness distribution that remains centered on Enceladus, the other cases give similar results to the Keck observations: a peak brightness that is shifted outward by approximately 10 4 km. For outflow speeds in the range of 100 < v z < 50 m/s, the collision probability does not change significantly, hence the radial profiles remain similar. Figure 2 also shows that independently of the initial outflow speed, without plasma drag, the brightness distribution would remain centered and symmetric with respect to the orbit of Enceladus [Horányi et al., 1992; Dikarev, 1999]. [16] Though the outward shift in the brightness at l = 2.26 mm is well reproduced, this does not indicate that the density distribution of all particles exhibit this behavior. The brightness in the Keck observations is dominated by the contributions of particles with radii r g >1mm (Figure 3), hence this shift is mainly due to the combination of radiation pressure and plasma drag effects. [17] For example, Figure 3 shows the column densities and the contribution to the brightness as function of particle size, for the same parameters as in Figure 2. The location of the peaks of these distribution is a nonlinear function of the size of the grains due to the complex dynamics of these charged particles moving under the influence of electromagnetic forces, radiation pressure, neutral and plasma drags, and gravity. The maximum density of the smallest grains (0.1 < r g < 0.5 mm) peaks at r 5 R S. In the intermediate size range (0.5 < r g <1mm) the distribution peaks at the orbit of Enceladus, while the density of the larger grains (1 < r g <3mm) is shifted to r 4.1 R S. However, when these are weighted with their light scattering efficiencies their combined contribution at the wavelength of l = 2.26 mm, matches reasonably well the Keck observations. [18] While the initial dust velocities of v z = 50 or 100 resulted in a very similar radial dependence of the vertically integrated dust column densities, the predicted vertical distributions will be quite different. Figure 3 also shows the vertical dust density distribution for these two cases. As expected the larger outflow speed results in a more vertically extended distribution. Currently (2007), the density distribution of the smallest particles (0.1 < r g <0.5mm) peaks above the ring-plane at z 1000 and 1500 km for v z = 50 and 100 m/s, respectively. This displacement is expected to shift below the ring-plane in about 15 years, in half the orbital period of Saturn [Juhász and Horányi, 2004]. Near Enceladus, the particles in the size range of 0.5 < r g < 1 mm show an approximately symmetric distribution with a characteristic full-width-at-half-max (FWHM) of about 2000 and 4000 km, for v z = 50 and 100 km/s, respectively. The few micron radius grains (1 < r g <3mm) show a sharp double peaked distribution with peaks close to 1000 and 2000 km above and below the ringplane for v z = 50 and 100 km/s, respectively. Figure 4 shows the edge-on brightness distributions calculated for v z = 50 m/s (l = 0.74 mm, and phase angle 174 ) that matches well the recent SSI images reporting on a doublebanded structure of the E-ring (Porco, 2006). Clearly, the dust size distribution is a sensitive function of location, and the assumption of a single power law or a mono-disperse size distribution [Showalter et al., 1991] could not describe this ring. [19] Perhaps it is not surprising to note, that based on these calculations, it is expected that the comparisons between in situ dust measurements by CDA and RPWS, as well as the remote sensing optical observations remain difficult, as each of these is likely to be dominated by a Figure 2. The observed and the calculated normal I/F distributions near Enceladus. All calculations were done for the parameters of the Keck observations, wavelength l = 2.26 mm and zero phase angle [de Pater et al., 2004], and assumed dust decoupling velocities of v z =0, 50, and 100 m/s. Independently of the value of v z, the calculated I/F remains centered and symmetric over the orbit of Enceladus if plasma drag is ignored. 3of5

4 JUHA SZ ET AL.: SATURN S E RING Figure 3. (top) The radial distribution of (left) the column density, and (right) the contribution to brightness as function of grain size, for the same parameters as in Figure 2 for the case of vz = 50 m/s. (bottom) Also, the vertical dust density distribution at r = 4 RS, as function of the grain size for (left) vz = 50 m/s, and (right) vz = 100 m/s. somewhat different fraction of the dust population. The observed radial profile of the impact rates by RPWS remained highest at the orbit of Enceladus [Kurth et al., 2006], while the rates observed by CDA showed a steady increase with distance just outside Enceladus orbit [Kempf et al., 2006; Kempf et al., submitted manuscript, 2007]. The observed vertical profile near Enceladus by RPWS indicates a double peaked structure approximately km above and below the ring-plane [Kurth et al., 2006]. A similar structure was seen in the brightness distribution by imaging (Porco, 2006). The observations by the High Rate Detector (HRD) of CDA indicate a symmetric dust distribution peaking in the ring-plane with a characteristic fullwidth-at-half-max FWHM 4000 km [Kempf et al., 2006; Kempf et al., submitted manuscript, 2007]. With the exception of the RPWS radial profile, these observations are all consistent with the different size thresholds that are believed to characterize the instruments. Based on our simulations presented here, both the radial and the vertical profiles reported by CDA/HRD seem consistent with their size threshold of slightly below 1 mm (Kempf et al., submitted manuscript, 2007). Compared to our simulation results, the RPWS measured vertical profile is consistent with their estimated size threshold of 2.4 mm, but it should have seen the peak in the radial profile outside the orbit of Enceladus [Kurth et al., 2006]. [20] It is also interesting to note that, due to their longer lifetimes, grains from Enceladus alone could be responsible for the entire E ring. By examining the relative velocity distribution near Enceladus we conclude that dust production due to bombardment of Enceladus by the E ring particles themselves becomes negligible as the average impact speed due to plasma drag - remains much below earlier estimates of vimpact 5 km/s [Hamilton and Burns, 1994; Spahn et al., 2006b]. Here we found vrel 0.5 km/s, nearly independent of grain size, and hence the ejecta flux, F v3.5 rel [Spahn et al., 2006b], is reduced by a factor of about The last candidate mechanism, ejecta production via the ongoing bombardment by interplanetary dust particles reaching the Figure 4. The edge-on brightness distribution of the E ring (for wavelength l = 0.74 mm, and phase angle of 174 ) is very similar to recent SSI images of the double-banded brightness distribution near Enceladus (Porco, 2006). (The color represents relative brightness in units of %). 4 of 5

5 JUHÁSZ ET AL.: SATURN S E RING surface with speeds on the order of 15 km/s, is expected to make a small (<15%) contribution to the dust population near Enceladus. 4. Summary and Conclusions [21] The simple model presented here shows the importance of the initial velocities of the dust grains escaping from Enceladus. Based on images, the estimated velocities are on the order of 50 < v z < 100 m/s (Porco, 2006) and result in a spatial and size distribution of dust particles that could, in principle, explain the observations from the Keck and Cassini images, and the in situ observations by the CDA and RPWS instruments. We have identified the role of the initial decoupling velocity of the small grains from Enceladus to significantly prolong their lifetime, and the importance of plasma drag in shifting the peak of the radial brightness distribution of the E ring. [22] As the observations from Cassini accumulate further simulations, similar to the ones presented here, could be used to better characterize the initial size and velocity distributions of the grains entering the E ring. However, some of the difficulties in analyzing the in situ dust measurements could also be due to our incomplete understanding about the detection of small ice particles in space. For example, RPWS was not designed to detect dust, but it works very well as a proxy dust instrument. The signals from the dust impact generated plasmas can be well recognized, but it remains difficult to identify the size of the grains, and the effective cross section of the spacecraft as a dust detector, further both of these are likely to change with impact speed and dust composition [Wang et al., 2006; Kurth et al., 2006]. Similarly, CDA was never calibrated for ice grain impacts [Srama et al., 2004]. Remote images also present their own difficulties to derive the size and spatial density distributions of dust grains. For example, using Mie calculations for the optical depth or brightness is valid only if one assumes spherical particles with a given index of refraction. [23] The model presented here offers an approach to simultaneously optimize the match between the calculations and the various observations. As more data will be available, the assumptions about the initial size and velocity distributions will be made more realistic, allowing us to learn about the dust production from Enceladus. These simulations will also be useful to better understand the detection of small ice particles by the RPWS and CDA instruments. [24] Acknowledgments. Comments by A. Krivov greatly improved this paper. The authors acknowledge support from the Cassini project. 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