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Astron. Astrophys. 324, 770-777 (1997)

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3. Numerical integration of dust orbits

The trajectories of the dust particles emitted by the comet are integrated in the context of a nine-body problem (Sun, seven planets - except Mercury and Pluto - and the particle) with two additional drag terms due to the solar radiation and solar wind forces. These non-gravitaional terms in the dust-grain equation of motion, presented in detail in Marzari and Vanzani (1994a, 1994b), include the transverse contribution of the wind pressure arising from the deviation of the wind flow from the radial direction as in Mukai and Yamamoto (1982). The orbits of grains were integrated by RA15 (Everhart, 1985). The choice for this integration method was motivated by the large number of close approaches with Jupiter which require high-precision modelling of fast changes of the planet gravity attraction on the grain. This is undertaken in RA15 by using a variable stepsize.

To express conveniently the non-gravitational terms, we have to assume an appropriate composition for the material of cometary grains. From the data taken by Vega missions on individual grain composition, it turns out that 30% were CHON, 35% were a mixture of CHON and silicates (Mg, Si and Fe) and 35% contained no appreciable content of low atomic number elements except oxygen (Brownlee & Kissel, 1990). A quite strong effect observed by Giotto approaching the nucleus was a decrease in the relative abundance of the C-H-O composition particles with increasing distance from the nucleus. It has been suggested that this could be the result of sublimation of an intermediate volatility compound such as formaldehyde or formaldehyde polymer. We assume a fluffy structure for the grains with a reference value of bulk density [FORMULA] = 1 g cm-3. Sublimation of the water-ice fraction should occur just after the ejection from the cometary nucleus. Further mass loss during the subsequent dynamical evolution is not taken into account. For this material the radiation pressure coefficient averaged over the solar spectrum, [FORMULA], is estimated to be about 1. This follows assuming that the dust particles are spherical adopting then the Mie theory. Even if different values of [FORMULA] and [FORMULA] could be selected, the same value of [FORMULA] can be obtained simply changing the dust particle size.

For the non-gravitational terms we used standard expressions, as in Jackson and Zook (1992), with the ratio of solar wind drag to Poynting-Robertson drag assumed to be 0.3, as by Jackson and Zook. We performed also additional simulations including, as in Marzari and Vanzani (1994a, 1994b), the non-radial component of the wind pressure introduced by Mukai and Yamamoto (1982) to account for a non-radial flow of the solar wind, as resulting on a theoretical basis. However, as pointed out by Gustafson (1994), observational results on this non-radial flux appear to be controversial and a radial flow remains a good approximation when averages are made over a solar rotation (Mariani and Neubauer 1990). The initial positions of the planets at the epoch of dust ejection are derived from the ephemerides JPL DE200.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998