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

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2. Model for dust ejection

Cometary dust is released from the nucleus surface by ice sublimation with negligible initial velocity. Then dust is dragged out by the expanding gas in the coma, and at about ten nuclear radii the grain reaches its terminal velocity (Crifo 1991). For the largest particles, the deceleration due to nucleus gravity must be taken into account (Wallis 1982). Detailed dust-gas interaction models (Gombosi 1986, Crifo 1987) allow to obtain the time and size dependent dust ejection velocity, but they require precise data on the nucleus size, on the gas loss rate, and on the dust size distribution. These quantities are affected by large uncertainties, and are unavailable for the comets we consider. Moreover, no in-situ experiment has test such models. Ground-based observations require multi-parametric models to extract information on the dust velocity, and provide results which can be compared with the outputs of dust-gas drag theory.

All models describing dust comae and tails must take into account the time and size dependence of the dust ejection velocity as free parameters. In the majority of these models, the dust velocity is an input parameter, and the sensitivity of the model results on it was never tested. It follows that the successfull fits of these models with observations never provided any information on the reliability of the adopted dust ejection velocity. To our knowledge, two models only consider the dust velocity as an output parameter, thus providing a significant test of dust-gas drag theory: dust tail models (Finson & Probstein 1968, Kimura & Liu 1977, Richter & Keller 1987, Fulle 1987, Fulle 1989) and neck-line models (Fulle & Sedmak 1988, Cremonese & Fulle 1989). Tail models provide the time dependence of the dust velocity, whereas its size dependence must be treated as an input parameter. Then it is necessary to test the sensitivity of the model output on this input parameter. Neck-line models provide directly the size dependence of the dust velocity and the velocity value at a fixed time.

For the large sizes typical of meteoroids, dust-gas drag theory provides a dust velocity size dependence which can well be approximated by a power law with index [FORMULA] of the dust diameter s. All models (Crifo 1991) provide [FORMULA] for [FORMULA] m. However, the results of neck-line models provide [FORMULA]. Exhotic phenomena as dust fragmentation or gas evaporation seem to be possible explanations of [FORMULA], but detailed and realistic models of so complex dust behaviours are not available (Crifo 1991). A prudential conclusion is that all dust coma and tail models should test the sensitivity of their results on all power indices [FORMULA], but this approach was followed in the applications of the inverse Monte-Carlo dust tail model only (Fulle 1989). Since the aim of this paper is to verify the sensitivity of meteoroid orbital evolution on its ejection velocity, we are forced to take into account the results provided by the quoted inverse tail model.

The kernel of the inverse tail model is an automatic least square fit of the observed tail images with the model tail images. The free parametric function which allows to minimize the residual of such least square fit is the product of the dust loss rate times the time-dependent size distribution, which are the automatic linear outputs of the model. However, the tail model images too (which are built-up by means of a Monte-Carlo procedure considering keplerian dust dynamics) depend on other free parameters, in particular on the dust ejection velocity. Changes of this non-linear free parameter allow to optimize the data fit and the stability of the linear output. Therefore, inverse Monte-Carlo tail models provide self-consistent estimates of all physical quantities describing a cometary dust environment which do not depend on dust-gas drag models. The performed tests showed a low sensitivity of the model outputs on the power index u and on the dust ejection anisotropy. Computational details of the inverse model can be found in Fulle et al. (1992).

Inverse tail models can provide information on the dust velocity in limited time and size ranges, because the input images have limited size and spatial resolution. We will test the sensitivity of meteoroid orbit evolution on the dust size and ejection anisotropy at a fixed ejection time. Due to the inverse tail model limitations, we will analyse such sensitivity on a dust diameter change of a factor 10 only: from about 10 µm to 100 µm for P/SW1, and from about 20 µm to 200 µm for P/GS. The analysis of the sensitivity of meteoroid orbit evolution on the dust production during long times will be possible for P/SW1 only, because the ground-based observation of P/GS allowed to extract its dust environment during two weeks only around perihelion. For P/SW1, the published results (Fulle 1992) cover about one year before perihelion. We have integrated them with unpublished results obtained from the analysis of P/SW1 steady dust coma images taken in 1993 (Jockers, private communication), in order to extend the time interval to about three years after perihelion. The dust ejection velocity provided by inverse tail model is related to the comet nucleus. Trivial vectorial geometry was applied to compute the starting orbit of each sample dust particle, i.e. the input of orbit evolution codes.

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© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998