University of Kansas
Cassini Studies
(DRAFT)
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University of KansasCassini Studies |
(DRAFT)
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Figure 1 shows the magnitude of the magnetic field calculated for case I, for which the upstream plasma parameters are close to those observed by Voyager 1. The field is very close to being symmetric (as it should be) within both the xy-plane and the xz-plane but not between the two planes. The field strength remains constant at about 5 nT in the outer region upstream of Titan. Within a radial distance of about 2 RT, the field builds up into a magnetic barrier. The field strength peaks at a value of about 17 nT on the ram side of Titan and at a radial distance of about r = 1.7 RT (see Cravens et al., 1997). This barrier extends around Titan as the magnetic field lines become draped and gradually slip around the obstacle. The field is confined to a narrow region in the near wake of Titan extending back about 3 RT. The upper magnetic tail lobe is clearly visible. Further downstream, the field flares out and Alfven wings develop as suggested by Ness et al. [1982]. The wake is asymmetric, being much narrower in the xy-plane (i.e., perpendicular to the upstream field) than in the xz plane (i.e., parallel to the upstream field).
Figure 2 shows magnetic field vectors overlaid by density contours for the xz-plane. This figure shows the draping of the magnetic field lines around Titan. The field upstream of Titan is unperturbed until a radial distance of about 2 RT. The field then starts to drape and form a tail but is confined to within about 1.7 RT above and below Titan. The field is then stretched back until about 3 RT where it forms the Alfven wings. Figure 3 shows the projection of the magnetic field vectors in the xy-plane. A clear draping pattern is seen around Titan with a peak xy-field strength of about 15 nT present within the wake. A narrow plasma tail with enhanced density is also evident in Figures 2 and 3. The density enhancement is narrow, with the maximum density occurring in the center of the wake.
The calculated plasma velocity for the Voyager upstream plasma parameters is shown in Figures 4, 5, 6, and 7a. Figure 4 shows the plasma flow vectors in the xy-plane (the same plane as the 2-D model of Cravens et al. [1997]). The flow is clearly diverted around Titan. There is a slow flow region that extends out to about 1.5 RT in the ram direction, about 4000 km along the flanks and which extends down into a narrow tail region. This slow flow region is associated with an enhanced magnetic field (see Figure 7b in Cravens et al. [1997]). The enhanced magnetic field acts as a barrier to the magnetospheric plasma flow. Figure 5 shows the plasma flow vectors in the xz-plane. The slow flow region in this plane is similar to what it is in the ram and flank directions. The wake, however, is not symmetric, differing in the xy-plane and in the xz-plane. The slow flow wake region seen in Figure 5 extends back in a narrow band about 2-3 RT long and then flares out into a set of wings. These wings are associated with the Alfven wings in Figure 1.
Figure 6 shows the speed along the x and y axes. Along the x-axis there is a gradual decrease in the speed of the plasma flow (i.e., as Titan is approached in the ram direction), followed by a slow increase in the wake. Along the flanks (y-axis) there is initially an increase in the speed as Titan is approached and then a sharp decrease at a radius of 6000 km. Figure 7a shows color contours of the flow speed in both the xy and xz planes. The slow flow regions evident in this figure show excellent agreement with the high magnetic field regions in Figure 1.
Figures 7b and 7c show flow speed contours for the supermagnetosonic cases. In both cases II and III the slow flow regions in the wakes show no sign of flaring out. Both cases show a wider wake region (near Titan) than in the Voyager case (case I, Figure 7a). Figure 7b shows a weak shock where the speed of the flow drops from 120 km s-1 to about 90 km s-1. There is a speed-up in the flow speed downstream from the shock to about 140 km s-1 in the xy-plane. In the strong shock case (Figure 7c), the shock is more swept back. The plasma flow speed drops at the shock from 120 km s-1 down to about 80 km s-1.
Figure 8 shows the number density and pressure along the x-axis. Starting upstream the number density (solid line) gradually increases until a distance of 2 RT where the ion production starts. At this point the number density rapidly increases to 50 cm-3 within our obstacle. The density is maintained at this value within "Titan." In the wake the number density decreases to about 9 cm-3. At Voyager's closest approach to Titan (6969 km downstream), the calculated number density is about 20 cm-3, which is 100 times greater than the plasma number density in the upstream flow. The thermal pressure (dashed line) increases to 1.3 x 10-9 dynes/cm2 at 1.6 RT then decreases to 8.8 x 10-10 dynes/cm2 at 1 RT. This thermal pressure decrease occurs where the magnetic barrier begins (see Figure 1). In the wake, the thermal pressure falls to 4.1 x 10-10 dynes/cm2 at 2.7 RT and then increases.
Figure 9a shows the modeled number density and the magnitude of the magnetic field along the trajectory of Voyager 1. But note that our model does not include the flow aberration evident in the Voyager data, and in this case the trajectory passes more through the top lobe than the lower lobe. The number density remains constant at 0.2 cm-3 until y = -5500 km, and then increases to about 29 cm-3 at y = 700 km. At 1200 km the number density decreases, returning to 0.2 cm-3 at y = 5700 km. The shape of the number density curve is not symmetric. The magnitude of the magnetic field increases from 5 nT to 6.5 nT at y = -3700 km, then drops to 4.5 nT at y = -2200 km. The magnitude then climbs to 15.2 nT at y = -800 km. A second dip occurs at y = 1900 km with the magnitude dropping to 1.5 nT. The field strength then climbs to 8 nT at y = 3800 km, and then gradually returns to 5 nT.
Figure 9b shows the modeled number density and the magnitude of the magnetic field for the Voyager case (case I), along a line parallel to the z-axis at a distance of 7,000 km (2.7 RT) downstream from Titan. The density is higher between the two magnetic lobes than in the lobes (i.e., there is a plasma sheet). The number density also shows two peaks at (z = + 1400 km), but also looking at Figure 4 and taking into account the 500 km spatial resolution one should be wary of over-interpretation. The magnitudes of the peaks are different, 40 cm-3 at z = -1400 km and 30 cm-3 at z = 1400 km. The number density remains constant at distances of more than 5000 km. The magnitude of the magnetic field shows two peaks or lobes at z = -2200 km and z = 1500 km, with magnitudes of 16.9 nT and 17.5 nT. At distances greater 4500 km the magnetic field remains between 5.5 - 6.5 nT.
Figure 10a shows the modeled number density and the magnitude of the magnetic field approximately along the trajectory of Voyager 1 for Mf = 2.5 (case III). The number density is asymmetric, peaking at 49 cm-3 where y = 250 km. The number density curve is slightly higher for y < 0 than for y > 0. The magnetic field strength is between 4-5 nT for distances greater then 6000 km. Within distances of 6000 km the magnitude of the magnetic field varies from 0.2-3 nT. For this case the upstream magnetic field strength was 2.6 nT; the 4-5 nT values for distances between 6000-10000 km are a result of being in the magnetosheath of Titan (see Figure 10b).
Figure 10b shows the modeled number density and the magnitude of the magnetic field for the Mf = 2.5 (case III), along a line parallel to the z-axis at a distance of 7,000 km (2.7 RT) downstream from Titan. The peak number density is 49 cm-3 at z = -200 km. The number density remains constant at distances of more than 8000 km. There is a dip in number density between the peaks with a value of 21.5 cm-3 at z = 100 km. The magnitude of the magnetic field shows an increase for distances between 16000-17000 km to between 3.5-4 nT. This is where the shock occurs. There is a small dip in the magnetic field strength down to 1.5 nT at z = -200 km.
Figure 11a shows the projection of the measured magnetic field vectors in the xy-plane along the Voyager trajectory from Ness et al. [1982]. A draping pattern is clearly present. The width of the wake is about 3 RT. For comparison, the projected model magnetic field vectors for the Voyager case (case I) are shown in Figure 11b. There is a reasonably good agreement between the general characteristics of the field observed by Voyager and the model results. The modeled field vectors along Voyager's path point in the same general direction as those observed by Voyager. The width of the perturbed field in the model is 3.5 RT; however, a strong draping pattern is evident in a region only 2 RT across. The strong shock case (case III) is shown in Figure 11c. There is a large reduction in the projected magnetic field magnitude within about 2 RT. The draping pattern is spread out farther than in the submagnetosonic Voyager case, with a width of about 6 RT.
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Tizby Hunt-Ward tizby@ku.edu |