To: Joe Veverka From: Don Yeomans Subject: CONTOUR Dust Fluence Models Date: April 20, 2000 The following analysis is provided in an effort to estimate the dust particle fluence experienced by the CONTOUR spacecraft during its flybys of comets 2P/Encke, (hereafter Encke), 73P/Schwassmann-Wachmann 3 (SW3), and 6P/d'Arrest (d'Arrest). Because there are little data on these comets and because the model only provides rough estimates, the dust fluence numbers presented here are very rough estimates only and they could easily be error by an order of magnitude or more. The computations were done using an EXCEL spreadsheet prepared by Ray Newburn at JPL. Similar models were run a few years ago but since then the model itself has been refined and a few input parameters have been improved. The theory used is one developed by Haser (1) and the following general assumptions and input sources were used: The gas flow from the comet is isotropic (no jets) The gas flow velocity from the comets is 500 m/s (input quantity) The dust particle size distribution is one determined for comet Halley by O'Donnell et al. (1991) using data from the Giotto spacecraft. Solar irradiance values have been taken from Neckel and Labs (1984) The dust phase function is taken from the work of Neil Divine and Ed Ney provided in the form of a curve by Ray Newburn (private communication). The flyby distance has been taken as 100 km. For other distances, the fluence values scale linearly. Input parameters peculiar to individual comet targets: Encke SW3 (Case 1) d'Arrest Flyby Date 11/12/03 06/18/06 08/16/08 Days from perihelion (P) P-47 P+12 P+1 Helioc. distance at flyby (AU) 1.07 0.95 1.35 Geocen. distance at flyby (AU) 0.27 0.33 0.36 Phase angle at flyby (deg.) 12 100 68 Relative velocity (km/s) 28.2 14.0 11.8 Comet radius (km) 2.4 1.0 2.3 Comet nucleus albedo 0.049 0.04 0.04 Fraction of surface active 0.002 0.04 0.05 Water production rate (mol./s) 5.9E27 7.8E27 2.0E27 Comet Encke: The water production rate information was taken from A'Hearn et al (1995) and the continuum flux data from Osip et al. (1992). Comet SW3: Comet SW3 broke into pieces in late 1995. The pre-breakup water production rate information as well as the continuum flux data was taken from Fink and Hicks (1996). This pre-breakup case was termed "Case 1." Upon recovering the comet in Jan. 2000, Anita Cochran noted that the comet was 2 magnitudes brighter than expected. Case 2 assumes the activity of the comet has increased by a factor of (2.5)**2 = 6.25 over the pre-breakup activity (Case 1). Case 3 is a worst case upper limit whereby the comet somehow maintains the activity shown just after the 1995 breakup. The 1995 post-breakup water production rate data was taken from Crovisier et al. (1996). For Cases 2 and 3, the model was run with the water production rates increased to 4.84E28 and 2.22E29 molecules/s respectively while the dust cross sectional area was increased to 2.0E08 and 9.33E08 m**2 respectively. No other changes were made. Comet d'Arrest: The water production rate information was taken from A'Hearn et al (1995) and the continuum flux data from Osip et al. (1992). The water production rate noted in A'Hearn et al. and the dust cross sectional area derived from the data in Osip et al. were decreased by a factor of four since the comet is now intrinsically fainter by 1.5 magnitudes because its perihelion distance increased from 1.29 AU to 1.35 AU between its 1989 and 1995 apparitions. References: A'Hearn, M. et al. (1995). Icarus, v. 118, pp. 223 - 270. Crovisier, J. et al. (1996). Astron. & Astrophys., v. 310, L17. Fink, U. and Hicks, M.D. (1996). Ap.J., v. 459, pp. 729 - 743. Haser, L. (1957). Bull. Acad. Roy. Sci. Belgique, v. 43, pp. 740 - 750 Neckel, H. and Labs, D. (1984). Solar Physics, v. 90, pp. 205-258. O'Donnell, J.A.M., Lamy, P.L., and Pankiewicz, G.S. (1991). Comets in the post-Halley era (R. Newburn, J. Rahe, M. Neugebauer, eds.), v. 2, pp. 1043 - 1073. Osip, D. J. (1992). Icarus, v. 98, pp. 115 - 124. Table 1. Comet Encke Dust Fluence Dust Particle Size range (m) Dust Fluence Particles/m2 1.00E-07 2.00E-07 3.44E+06 2.00E-07 4.00E-07 1.96E+06 4.00E-07 7.00E-07 9.50E+05 7.00E-07 1.00E-06 4.16E+05 1.00E-06 2.00E-06 3.39E+05 2.00E-06 4.00E-06 4.28E+04 4.00E-06 7.00E-06 4.94E+03 7.00E-06 1.00E-05 7.42E+02 1.00E-05 2.00E-05 3.37E+02 2.00E-05 4.00E-05 4.19E+01 4.00E-05 7.00E-05 5.09E+00 7.00E-05 1.00E-04 1.81E+00 1.00E-04 2.00E-04 2.71E+00 2.00E-04 4.00E-04 1.90E+00 4.00E-04 7.00E-04 6.19E-01 7.00E-04 1.00E-03 1.11E-01 1.00E-03 2.00E-03 5.94E-02 2.00E-03 4.00E-03 9.46E-03 4.00E-03 7.00E-03 1.39E-03 7.00E-03 1.00E-02 2.49E-04 1.00E-02 2.00E-02 1.33E-04 2.00E-02 4.00E-02 2.12E-05 4.00E-02 7.00E-02 3.10E-06 7.00E-02 1.00E-01 5.57E-07 1.00E-01 2.00E-01 2.98E-07 Table 2a. Comet SW3 Dust Fluence (Case 1) Dust Particle Size range (m) Dust Fluence Particles/m2 1.00E-07 2.00E-07 9.71E+07 2.00E-07 4.00E-07 5.54E+07 4.00E-07 7.00E-07 2.68E+07 7.00E-07 1.00E-06 1.17E+07 1.00E-06 2.00E-06 9.55E+06 2.00E-06 4.00E-06 1.21E+06 4.00E-06 7.00E-06 1.40E+05 7.00E-06 1.00E-05 2.09E+04 1.00E-05 2.00E-05 9.51E+03 2.00E-05 4.00E-05 1.18E+03 4.00E-05 7.00E-05 1.44E+02 7.00E-05 1.00E-04 5.10E+01 1.00E-04 2.00E-04 7.63E+01 2.00E-04 4.00E-04 5.37E+01 4.00E-04 7.00E-04 1.75E+01 7.00E-04 1.00E-03 3.14E+00 1.00E-03 2.00E-03 1.68E+00 2.00E-03 4.00E-03 2.67E-01 4.00E-03 7.00E-03 3.91E-02 7.00E-03 1.00E-02 7.02E-03 1.00E-02 2.00E-02 3.75E-03 2.00E-02 4.00E-02 5.98E-04 4.00E-02 7.00E-02 8.76E-05 7.00E-02 1.00E-01 1.57E-05 1.00E-01 2.00E-01 8.40E-06 Table 2b. Comet SW3 Dust Fluence (Case 2) Dust Particle Size range (m) Dust Fluence Particles/m2 1.00E-07 2.00E-07 6.04E+08 2.00E-07 4.00E-07 3.44E+08 4.00E-07 7.00E-07 1.67E+08 7.00E-07 1.00E-06 7.29E+07 1.00E-06 2.00E-06 5.94E+07 2.00E-06 4.00E-06 7.51E+06 4.00E-06 7.00E-06 8.67E+05 7.00E-06 1.00E-05 1.30E+05 1.00E-05 2.00E-05 5.92E+04 2.00E-05 4.00E-05 7.34E+03 4.00E-05 7.00E-05 8.93E+02 7.00E-05 1.00E-04 3.17E+02 1.00E-04 2.00E-04 4.75E+02 2.00E-04 4.00E-04 3.34E+02 4.00E-04 7.00E-04 1.09E+02 7.00E-04 1.00E-03 1.95E+01 1.00E-03 2.00E-03 1.04E+01 2.00E-03 4.00E-03 1.66E+00 4.00E-03 7.00E-03 2.43E-01 7.00E-03 1.00E-02 4.37E-02 1.00E-02 2.00E-02 2.33E-02 2.00E-02 4.00E-02 3.72E-03 4.00E-02 7.00E-02 5.44E-04 7.00E-02 1.00E-01 9.77E-05 1.00E-01 2.00E-01 5.22E-05 Table 2c. Comet SW3 Dust Fluence (Case 3) Dust Particle Size range (m) Dust Fluence Particles/m2 1.00E-07 2.00E-07 2.82E+09 2.00E-07 4.00E-07 1.61E+09 4.00E-07 7.00E-07 7.77E+08 7.00E-07 1.00E-06 3.40E+08 1.00E-06 2.00E-06 2.77E+08 2.00E-06 4.00E-06 3.50E+07 4.00E-06 7.00E-06 4.05E+06 7.00E-06 1.00E-05 6.07E+05 1.00E-05 2.00E-05 2.76E+05 2.00E-05 4.00E-05 3.43E+04 4.00E-05 7.00E-05 4.16E+03 7.00E-05 1.00E-04 1.48E+03 1.00E-04 2.00E-04 2.21E+03 2.00E-04 4.00E-04 1.56E+03 4.00E-04 7.00E-04 5.07E+02 7.00E-04 1.00E-03 9.10E+01 1.00E-03 2.00E-03 4.86E+01 2.00E-03 4.00E-03 7.74E+00 4.00E-03 7.00E-03 1.13E+00 7.00E-03 1.00E-02 2.04E-01 1.00E-02 2.00E-02 1.09E-01 2.00E-02 4.00E-02 1.73E-02 4.00E-02 7.00E-02 2.54E-03 7.00E-02 1.00E-01 4.56E-04 1.00E-01 2.00E-01 2.44E-04 Table 3. Comet d'Arrest Dust Fluence Dust Particle Size range (m) Dust Fluence Particles/m2 1.00E-07 2.00E-07 4.19E+06 2.00E-07 4.00E-07 2.39E+06 4.00E-07 7.00E-07 1.16E+06 7.00E-07 1.00E-06 5.06E+05 1.00E-06 2.00E-06 4.12E+05 2.00E-06 4.00E-06 5.22E+04 4.00E-06 7.00E-06 6.02E+03 7.00E-06 1.00E-05 9.03E+02 1.00E-05 2.00E-05 4.11E+02 2.00E-05 4.00E-05 5.10E+01 4.00E-05 7.00E-05 6.20E+00 7.00E-05 1.00E-04 2.20E+00 1.00E-04 2.00E-04 3.30E+00 2.00E-04 4.00E-04 2.32E+00 4.00E-04 7.00E-04 7.54E-01 7.00E-04 1.00E-03 1.35E-01 1.00E-03 2.00E-03 7.23E-02 2.00E-03 4.00E-03 1.15E-02 4.00E-03 7.00E-03 1.69E-03 7.00E-03 1.00E-02 3.03E-04 1.00E-02 2.00E-02 1.62E-04 2.00E-02 4.00E-02 2.58E-05 4.00E-02 7.00E-02 3.78E-06 7.00E-02 1.00E-01 6.79E-07 1.00E-01 2.00E-01 3.63E-07