Computer Science – Sound
Scientific paper
Dec 2004
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2004agufm.p53a1447p&link_type=abstract
American Geophysical Union, Fall Meeting 2004, abstract #P53A-1447
Computer Science
Sound
5410 Composition, 5430 Interiors (8147), 5440 Magnetic Fields And Magnetism, 5455 Origin And Evolution, 6280 Saturnian Satellites
Scientific paper
I report a predicted bulk chemical composition and internal structure for Titan based on the idea that this body is a captured satellite of Saturn which originally condensed within the gas ring shed by the proto-Solar cloud (PSC) at Saturn's initial helio-centric distance ˜ 8.1 AU . The case for capture rests on the large disparity (by a factor of ˜ 58) between the masses of Titan and Rhea. Rhea's mass (2.3 × 1024 g) is consistent with the mass mcond = 9.3 × 1024 of rock, H2O, and NH3 ices expected for a native moon of Saturn, had Rhea condensed from a gas ring shed by the proto-Saturnian cloud (Prentice, \textit{JPL Pub.} 80-80 1980; \textit{Proc. Astron. Soc. Australia} 4 164 1981; \textit{Earth, Moon Planets} 30 209 1984). Here I assume an efficiency of 25% in the process of satellite accretion and adopt the proto-solar elemental abundances of Lodders (\textit{Astrophys.J} 591 1220 2003). Titan's mass exceeds mcond by a factor of ˜ 14, so speaking against a native origin (http://www.aas.org/publications/baas/v36n2/aas204/887.htm). Previously it has been supposed that the process of shedding discrete gas rings by the parent gas cloud comes about solely through the action of large turbulent stresses arising from powerful convective motions (Prentice, \textit{Moon & Planets} 19 341 1978, \textit{Earth, Moon & Planets} 87 11 2001, http://www.lpi.usra.edu/meetings/mercury01/pdf/8061.pdf). This has necessitated convective speeds vt up to ˜ 5 times the local adiabatic sound speed vs, which is unacceptable. An exact numerical simulation of supersonic turbulent convection in a model atmosphere which represents the outer layers of the PSC shows, however, that the upper layers are strongly super-adiabatic (Prentice & Dyt, \textit{MNRAS} 341 644 2003). This results in a natural density inversion at the top boundary . Gas ring shedding can now be achieved for speeds vt ≤ 3vs, which is OK. A new model for PSC has thus been constructed to include the influence of very strong super-adiabaticity. The controlling paramters are chosen so that the mean density of the condensate at the orbit of Mercury matches the inferred uncompressed value ρ unc = 5.3 g/cm3 and that the fraction of water vapour in the gas ring at Jupiter's orbit which condenses is φ {H{2 O}} = 0.665. This later accounts for the densities of Ganymede and Callisto, following condensation from the gas rings shed by proto-Jovian cloud (Prentice 2001). At Saturn's initial orbit, where the gas ring temperature is Tn= 94 K and the mean orbit pressure pn= 4.7 × 10-7 bar, the bulk chemical constituents of the condensate are anhydrous rock (mass fraction 0.494), water ice (0.474) and graphite (0.032). The mean density is 1.52 g/cm3. Structural models for a present-day Titan based on this composition yield mean densities of 2.10 g/cm3 (homogeneous case) and 1.93 g/cm3 (differentiated 2-zone case). For the latter, C/MR2 = 0.32. Titan is thus most likely fully differentiated between its rock, graphite and water ice constituents. It is predicted that Titan has no internal ocean or induced magnetic field but it may possess a small magnetic dipole moment of magnitude ˜ 2× 1011 T m3. This was acquired through thermoremanence at ˜ 1.5 × 109 yr after satellite formation. Capture of Titan was achieved by gas drag within the proto-Saturnian envelope whose initial size was ˜ 60 RSat. Titan's surface should thus look much like that of Triton. I thank John D. Anderson [NASA/JPL] for much support, and Nicole Rappaport and Bob Jacobson for helpful discussions.
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