Astron. Astrophys. 324, 357-365 (1997)

3. Definitions and geometric analysis

Here, we use the term ejecta to denote the material ejected by the explosion after fragment entry. We assume this material is ejected in a variety of ballistic trajectories. We have generated synthetic trajectories for ballistic material, for different sets of parameters (initial velocity, altitude of explosion from the 100-mbar level, impact longitude from Midnight Meridian and terminator longitude from Midnight Meridian). The altitude of these trajectories is plotted versus time in Fig. 4, along with the minimum height that the impact ejecta should have reached to be observable in sunlight. The parameters used are those for H and L (Chodas and Yeomans, predictions as of July 16) with a zero altitude set to the 100-mbar level and assuming trajectories. Hereafter in the text, we will cite only the vertical component of the velocity.

Fig. 4a and b. a Height above the 100-mbar level as a function of time after impact L for ejecta with several vertical velocities, as indicated in the labels. The continuous lines represent the minimum height above which the ejecta are visible in sunlight. The upper continuous line corresponds to 6 km/s and the lower corresponds to 12 km/s. As can be seen, the 6-km/s ejecta do not intercept the curve of height for the sunlit level corresponding to 6 km/s. That means that the 6-Km/s ejecta cannot be visible in reflected sunlight. Also plotted in continuous lines at the bottom of the graph is the minimum height that the ejecta should have to be visible in emission, as a function of time, for the 12-km/s and 6-km/s ejecta. b  The same as a  but for H impact. The boxes in a and b represent particularly interesting regions discussed in the text

The terminator level was also assumed to be at 100 mbar. The jovian radius at and 100 mbar was obtained by correcting for oblateness the 100-mbar equatorial radius. The gravity acceleration was corrected for oblateness in the following way: 23.22+2.85sin² (latitude) (where 23.22 m/s² is the equatorial gravity acceleration, in Jupiter, Anderson, 1976). The gravitational acceleration has also been corrected for altitude in each step. Coriolis correction has not been applied (this does not have an important effect on the vertical component). Refraction effects would have a minor influence on the very lower parts of the trajectories and have been ignored (see Hammel et al., 1995). Note that the horizontal velocity of the plumes plays an important role in lowering the level where the plumes reach sunlight (see Figs. 4a, 4b).

The moment of first detection of the plumes provides information on the maximum plume vertical velocity or, at least, on the fastest ejecta which carry a sufficient amount of material to be visible in sunlight. From the work by Schleicher et al. (1994), the first indication of the plume is 220 20 seconds after the L impact, the begining of the flux increase in their lightcurve. Fitzsimmons et al. (1996) report their first detection about 210 s after impact. The 220 20-sec time is consistent with plume velocity of 9 1 km/s, as can be seen in Fig. 4a (intersection of vertical trajectory with the curve of sun illumination level for its corresponding velocity). This is best seen in Fig. 5, which shows an enlarged version of Fig. 4a along with the curve for 3.5-km/s ejecta. The first detection of H from the WHT data is somewhat later (300 s) which would suggest slightly slower ejecta. On the other hand, the telescope was not observing earlier, so this value represents a lower limit. For L, we believe most of the material is ejected at velocities between 9 and 12 km/s, since, for that velocity range, the material returns to the original level between 780 and 1000 seconds after impact, which is the time of rise and decline of the second maximum in the lightcurve of Schleicher et al. We believe this maximum is due to thermal emission. The maximum itself occurs when the 11 km/s-material returns to the original altitude ( 900 sec after impact). Then, for the L impact, we conclude that the largest amount of material optically thick in the visible is ejected at 11 km/s, but there is also material thrown at other velocities, with a maximum of 12 km/s. We can make comparisons with the G impact results, as both G and L are in the same class in the categorization scheme of Hammel et al., releasing similar amounts of energy and leaving similar scars, etc. This maximum velocity of 12 km/s is in agreement with the velocity derived by Hammel et al. (1995) for the highest velocity ejecta in G plume by measuring its highest altitude, a completely different approach to that followed here, which is based on timings. For the H impact, the time of the second maximum from Fig. 1 is much more uncertain, but seems to be shorter than what we would expect for 11 km/s ejecta. This would require slower ejecta, which would be consistent with the observations of a smaller energy release in H impact compared to L and a smaller crescent-shaped scar.

Fig. 5. Enlargement of Fig. 4a for short times after impact. Also in this graph has been included the height as a function of time for 3.5-km/s ejecta, which are the slowest ejecta which can reach the limb height and be detectable in emission

The first maximum is reached when most of the ejected material is above the sunlit limit and with its maximum vertical spreading. For L, taking a section in Fig. 4a we observe that the maximum spreading (while all the 7.5-12 km/s material is still in sunlight) corresponds to time 500 s. This value is in perfect agreement with the time of maximum shown in the lightcurve of Schleicher et al. (1994) and with the time of first maximum brightness by Fitzsimmons et al. (1996). After that moment, some material starts to cross below the illumination limit, whereas no other material is capable of reaching the sunlight level (in Fig. 4a, the 6 km/s curve does not intercept the 6 km/s sunlit level). Then, the visible flux starts to decrease. For H, we see the first maximum 430 s after impact (Fig. 1) which would require slower ejecta, but the time sampling is not good enough to conclude that. We suggest that the minimum in the lightcurves occurs when a considerable part of the material (that ejected at velocities between 7.5-9 km/s) crosses the level illuminated by sunlight on its descent, after which the amount of reflected light observed decreases. The minima in the lightcurves for H and L occur at 720 100 sec and 720 20 sec after impact, respectively, according to Fig. 1c. This is in agreement with predictions in Figs. 4a, 4b, for the dissapearance of 9 km/s ejecta.

The following maximum in the CCD lightcurve arises mainly from thermal emission by the particulates or gas, as well as from reflected sunlight from the rest of the plume. The thermal emission starts to decrease as the material cools down and the small fraction of ejecta which was thrown highest (velocity 12 km/s) reaches the original level (where there is no longer reflected sunlight contributing to the thermal emission). Following Figs. 4a, 4b, the 12-km/s velocity material reaches the initial level 1000 seconds after the explosion.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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