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This Article Appeared in a Journal Published by Elsevier. the Attached (This is a sample cover image for this issue. The actual cover is not yet available at this time.) This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Author's personal copy Icarus 218 (2012) 348–355 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus Late-stage impacts and the orbital and thermal evolution of Tethys ⇑ Ke Zhang , Francis Nimmo Earth and Planetary Sciences Department, University of California, Santa Cruz, CA 95064, USA article info abstract Article history: An inferred ancient episode of heating and deformation on Tethys has been attributed to its passage Received 9 September 2010 through a 3:2 resonance with Dione (Chen, E.M.A., Nimmo, F. [2008]. Geophys. Res. Lett. 35, 19203). Revised 14 December 2011 The satellites encounter, and are trapped into, the e-Dione resonance before reaching the e-Tethys reso- Accepted 14 December 2011 nance, limiting the degree to which Tethys is tidally heated. However, for an initial Dione eccentricity Available online 24 December 2011 >0.016, Tethys’ eccentricity becomes large enough to generate the inferred heat flow via tidal dissipation. While capture into the e-Dione resonance is easy, breaking the resonance (to allow Tethys to evolve to its Keywords: current state) is very difficult. The resonance is stable even for large initial Dione eccentricities, and is not Resonances, Orbital broken by perturbations from nearby resonances (e.g. the Rhea–Dione 5:3 resonance). Our preferred Satellites, Dynamics Tides, solid body explanation is that the Tethyan impactor which formed the younger Odysseus impact basin also broke Saturn, satellites the 3:2 resonance. Simultaneously satisfying the observed basin size and the requirement to break the resonance requires a large (250 km diameter) and slow (0.5 km/s) impactor, possibly a saturnian satellite in a nearby crossing orbit with Tethys. Late-stage final impacts of this kind are a common feature of satellite formation models (Canup, R.M., Ward, W.R. [2006]. Nature 441, 834–839). Ó 2011 Elsevier Inc. All rights reserved. 1. Introduction The absolute age of Ithaca Chasma is uncertain – depending on the impact flux model used, the age of its interior could be any- Tidal heating is responsible for much of the geological activity thing from a 0.4 to 4 Gyr (Giese et al., 2007). More importantly, in the outer Solar System, both ongoing (e.g. Enceladus; Porco however, the interior of Ithaca Chasma is older than the giant im- et al., 2006) and ancient (e.g. Ganymede; Showman et al., 1997). pact basin Odysseus (Giese et al., 2007). The fact that Odysseus Because satellites’ orbits evolve under the influence of dissipation formed after the heating episode associated with Ithaca Chasma in the primary, they can become trapped into mean-motion reso- is an important part of the argument we will develop below. nances which may excite their eccentricities and increase tidal Chen and Nimmo (2008) suggested that this deformation epi- heating (see, e.g., Peale et al., 1980). Depending on the stability sode was a result of Tethys having had a higher eccentricity in of each resonance, a satellite may have passed through several the past due to a 3:2 paleo-resonance with Dione (Ithaca Chasma such resonances before attaining its present-day configuration is sufficiently young that any primordial eccentricity of Tethys (see, e.g., Dermott et al., 1988; Meyer and Wisdom, 2008a; Zhang would likely have decayed well before it formed). They further ar- and Hamilton, 2008). These paleo-resonances thus provide one gued that the inferred heat flow was higher than the equilibrium possible explanation for ancient episodes of deformation. tidal heating associated with this resonance, and suggested that The saturnian satellite Tethys is currently in an inclination-type non-equilibrium or periodic heating might have occurred (Ojakan- resonance with Mimas, and has an orbital eccentricity indistin- gas and Stevenson, 1986). They did not, however, explore the likely guishable from zero. However, Tethys does show signs of ancient orbital evolution of Tethys in any detail. deformation. In particular, the Ithaca Chasma canyon system ex- Dermott et al. (1988) pioneered the study of ancient orbital res- tends across 3/4 of Tethys’ surface, having a width of several tens onances in satellite system. In this paper we follow similar analyt- of km, a depth of about 3 km, and an extension factor of about ical and numerical approaches to investigate the orbital evolution 10% (Giese et al., 2007). Although the cause of this focused defor- of Tethys as it encounters the 3:2 mean motion resonance with mation is uncertain, Giese et al. (2007) used rift-flank flexural pro- Dione. We find that Tethys’ eccentricity is transiently excited to files to infer a global heat flow of 60–100 GW during or after high enough values to account for the heat flow inferred by (Giese canyon formation. et al., 2007). The resonance is sufficiently strong that likely pertur- bations (e.g. from Rhea) are insufficient to break it and allow Tethys and Dione to evolve to their current resonances with Mimas ⇑ Corresponding author. Fax: +1 818 393 4445. and Enceladus, respectively. However, the subsequent Odysseus- E-mail address: [email protected] (K. Zhang). forming impact is capable of breaking the resonance, as we show 0019-1035/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2011.12.013 Author's personal copy K. Zhang, F. Nimmo / Icarus 218 (2012) 348–355 349 semi-analytically. This result illustrates the fact that large impacts on the collision geometry and energy loss. Second, the low collision can not only have direct effects on their target bodies, but may also velocities that we find are consistent with the simple impact sce- alter their long-term orbital and thermal evolution. nario (see Section 4). This impact geometry leads to a maximum change in orbital semi-major axis for given projectile mass and im- pact velocity. A head-on impact has the same effect, but it can not 2. Methods break the resonance trapping (see Section 3.4) In our simulations, the system consists of Saturn, Tethys, and 2.1. Orbital evolution Dione. For the two satellites, the gravitational effects of the Sun and other planets are weak and can be safely ignored. The physical The orbit of a synchronous satellite must be eccentric in order parameters and initial orbital configurations of the two satellites for tidal heating to occur (e.g. Yoder and Peale, 1981). On the other are listed in Table 1. The initial semi-major axes of the two satel- hand, tidal dissipation in the satellite acts to damp orbital eccen- lites are derived from their current values and are consistent with tricity. For Tethys, assuming reasonable values for k /Q (k is the 2 2 tidal migration due to planetary tides. Each simulation runs second order tidal Love number, and Q is tidal dissipation factor; through the 3:2 resonance, and an impact on Tethys then follows both are internal properties of a body and the ratio of the two at a user-defined time. We accelerate tidal evolution artificially determines how efficiently tides dissipate energy), the eccentricity (by increasing k2/Q of all bodies) to achieve practical computing damping timescale is on the order of 10 Myr (Murray and Dermott, time. The same technique was employed by Zhang and Nimmo 1999). Hence, any primordial eccentricity the satellite’s orbit might (2009) and many other authors (e.g., Showman et al., 1997; Meyer have inherited from formation would have damped away in the and Wisdom, 2008b). We typically use an acceleration factor of first few tens of Myr of the system’s history. However, a subse- 10,000, but we also run a few slower integrations with an acceler- quent mean-motion resonance passage during satellite tidal ation factor of 1000 in comparison to make sure that the major migration could have excited the satellite’s orbital eccentricity. evolution features are not affected by the artificial speed-up. One If Saturn spins faster than a particular satellite orbits, as for other assumption in our numerical setup is that the satellite orbits Tethys and Dione, the planetary tidal bulge raised by the satellite are co-planar and in the equatorial plane of Saturn. This is justified is carried ahead of the planet–satellite line and exerts a positive tor- by their small orbital inclinations and the fact that inclinations que on the satellite. Consequently, the satellite is accelerated and its play little role in tidal dissipation (Burns, 1977). orbit migrates outwards, i.e., orbital semi-major axis (a) increases and mean motion (n) decreases. The orbital migration history of 2.3. Crater scaling the saturnian satellites has been discussed in a few previous papers (see, e.g., Greenberg, 1984; Callegari and Yokoyama, 2008; Meyer In order to estimate the size and impact velocity of the incom- and Wisdom, 2008b; Zhang and Nimmo, 2009). Due to their differ- ing object which formed Odysseus, and thus its effect on Tethys’ ent sizes and distances from Saturn, satellites migrate at different orbit, it is important to know how the size of an impact crater rates and may encounter mean-motion resonances.
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