University of Kansas
Cassini Studies
DRAFT
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University of KansasCassini Studies |
DRAFT
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The model was run until steady-state conditions were reached. Figures 4, 5 and 6 display the plasma velocity in a number of ways. The flow vectors in Figure 4 show that the plasma flow is diverted around Titan without the presence of a bow shock. This is not surprising given that the external flow is subsonic and submagnetosonic. Two regions can be discerned in Figure 4: an outer region (r > 2 RT) of rapid magnetospheric flow and an inner region (r < 2 RT) in which the flow is quite slow. The magnetic field strength is enhanced in the slow flow region (Figure 7a), which thus acts as an obstacle to the external magnetospheric flow. Figure 7b shows color contours of plasma speed outside the slow flow region.
In the outer fast-flow region the speeds are greater in the flank region than along the ram axis (Figures 4, 6, and 7b). Qualitatively, the flow resembles classic potential fluid flow around a cylindrical obstacle with a radius of 2 RT, as will be discussed later. The flow appears to be significantly (10% or so) affected by Titan only for radial distances less than ~ 10 RT (Figure 6).
In the inner slow-flow region the plasma flow speeds drop to well under 1 km/s, and in the ionosphere itself (r ~ 1.5 RT or altitude z ~ 1500 km) the plasma flow is directed radially downward at all azimuth angles (Figure 5). The flow near the main ionospheric peak is essentially one-dimensional, which supports the applicability of 1-D models such as Keller et al. [1994] and Ip [1990] for the inner region. However, horizontal flow speeds in the topside ionosphere (r ~ 2000 km) start to be substantial (more than a km/s or so), suggesting that one-dimensional models are no longer appropriate.
Figures 7a, 8, and 9 display the calculated magnetic field strength in the vicinity of Titan. The dashed lines in Figures 8 and 9 are the Keller et al. [1994] one-dimensional MHD results. Recall that the magnetic field lines in our 2D model are aligned with the cylinder axis and are able to be convected with the flow around the obstacle. The field strength remains almost unaltered at the upstream value of B ~ 5 nT throughout the outer region. The magnetic field only builds up into a magnetic barrier for radial distance less than about 2 RT. The field strength reaches a maximum of about 18 nT in the ram direction for r ~ 4300 km (i.e., r ~ 1.7 RT). The field strength falls off at lower altitudes reaching a value of about 12 nT at the bottom of the ionosphere. The magnetic field is frozen into the plasma flow almost everywhere except in the lower ionosphere where magnetic diffusion allows magnetic flux to move through the plasma (Keller et al. [1994], or for Venus see Cravens et al. [1984] or Luhmann and Cravens [1991]). The effective magnetic diffusion coefficient somewhat exceeds the "actual" collisional diffusion coefficient, and consequently, the bottom of the magnetic barrier is not as sharp as it was in the 1D MHD model. The boundary condition we used was partial B/partial r = 0 which allows magnetic flux to slip through the lower boundary. We expect that there should be leakage of magnetic flux through the ionosphere and into the lower atmosphere. The field strength is somewhat larger in the ram direction than at other azimuthal angles.
The thermal pressure variation with radial distance is displayed in Figures 10, 11, and 12 along with other diagnostics such as magnetic pressure, dynamic pressure (approximately ru2), and total pressure. Total thermal pressure (total ion pressure and electron pressure) is shown here, although the model calculates the individual pressures for each ion species. The electron pressure is determined from pe = nekBTe where Te is the adopted electron temperature and the electron density is equal, via quasi-neutrality, to the sum of the calculated ion densities. Thermal pressure is the dominant dynamical factor in the magnetosphere surrounding Titan. The pressure remains roughly constant in the fast flow region but decreases sharply in the inner region. In the magnetic barrier, the increase of magnetic pressure largely compensates for the decrease of the thermal pressure. In the lower ionosphere the thermal pressure is again enhanced due to the high electron density near the ionospheric peak with the total pressure (thermal plus magnetic) remaining constant down to about r = 3600 km (or z = 1100 km) in the lower ionosphere. Below this altitude ion-neutral drag is the dominant factor in the momentum balance.
Density profiles for the three generic ion species are displayed in Figure 13 for the ram direction and for the inner (i.e., ionospheric) region. The ion densities in the outermost region (not shown in this figure) are essentially magnetospheric as specified by the boundary conditions. There are no heavy ions in the inflowing magnetospheric plasma which consists of H+ (light) and N+ (medium) ions. Heavy species are added to the flow only near Titan. In the ionosphere, the heavy species is dominant with a peak density of about 4000 cm-3 at an altitude of 1100 km. Agreement with one dimensional ionospheric models [Keller et al., 1992, 1994, 1997; Ip, 1990] is reasonable. These models have heavier ion species being dominant near the peak and have peak electron densities ~ 6000 cm-3 on the dayside. Our model and the photochemical model agree reasonably well below about 4000 km for the light and medium ion species, but the agreement is not good at larger radial distances. The density distributions in the vicinity of the ionospheric peak are clearly photochemically controlled and not affected by the dynamics. For the heavy species (and the overall plasma density), our MHD model significantly departs from the photochemical model only for radial distances greater than about 4500 km, suggesting that beyond this distance dynamical/transport effects become important.
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Tizby Hunt-Ward tizby@ku.edu |