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Session 42 - Solar Systems.
Display session, Tuesday, January 16
North Banquet Hall, Convention Center
Radar delay-doppler images are non-intuitive to interpret, but can be used to constrain a shape model of an asteroid (Hudson and Ostro, Science, 263:940 (1994). This modelling is complicated, and requires many observations; therefore, we investigate what can be learned about the shapes of asteroids from delay-doppler images. In this work, we examine synthetic images of an arbitrarily cratered model of Gaspra, in an attempt to measure the size-frequency distribution of craters from delay-doppler images and determine how well craters can be seen. These images are generated using a model developed by Black and Campbell (DPS 1993), who examined the overall shapes of synthetic d-d images of the Martian satellites and asteroid 951 Gaspra.
We generated an exponential size/frequency distribution using four average crater sizes: 30 m, 100m, 300m, 1000m. The function fit random frequencies chosen within reasonable ranges for the largest and smallest craters. Angular positions were also generated randomly. We then deposited parabolic craters with cubic rims onto Gaspra according to the distribution, and fed the resulting coordinate file into the model discussed above. We assumed that the asteroid's maximum radius is 1.5 km and its rotation period is 5 hrs.
First, we conducted a blind crater count on images made under the following distribution and compared the counts to the actual number visible within the limits of the delay-Doppler projection:
\begintabularlrccc SNR:&&10^4&3*10^4&10^5&3*10^5 srlat:&&0&30&60 srlon:&&0&10&90 \endtabular Averaging over the percentages counted for all subradar positions, we obtain:
\begintabularlrccc SNR:&&10^4&3*10^4&10^5&3*10^5 percent counted:&&15&36&41&52 \endtabular
Knowledge of the fraction of craters we are able to observe allows us to calculate the actual number of craters on the asteroid to within experimental errors. We find that a maximum number are counted at 30^ subradar latitude due to optimization of the Doppler dispersion, and that observing two close phases results in higher counts because small features can be registered as craters.
Finally, we looked at the size/frequency/position distribution and determined what SNR and resolution is needed to see the smallest craters. At an SNR of 3*10^4 and resolution of 0.1Hz x 32m, between 3% and 14% 30 m craters were consistently visible as a dim pixel followed by a bright one. At such low SNR and resolution, a small crater's visibility is highly dependent on the orientation of the local surface with respect to the beam.
Arecibo can achieve resolutions approximately twice that used for this simulation. According to a list compiled by Greg Black, three targets in the next ten years will be observable with the upgraded Arecibo telescope at SNRs greater than 20000.
