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Astron. Astrophys. 319, 995-1006 (1997)

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1. Introduction

Periodic comet Schwassmann-Wachmann 1 (hereafter referred to as P/SW1) is known for its irregular lightcurve. Compared to other comets, its orbit has only a very small eccentricity (present state [FORMULA]). Its mean heliocentric distance is about 6 AU. Although most other comets observed at this distance appear as faint objects P/SW1 has a persistent coma throughout its orbit and a strong unpredictable variability of its brightness is reported (Whipple 1980). In recent data analyses Cabot et al. (1996) and Cabot (1996) found a correlation between the mean brightness and the heliocentric distance. It was only during the last few years that carbon monoxide (CO) could be identified by means of radio spectroscopic observations as an important driver of the activity of P/SW1. Indeed, this molecule has already been suspected as free water ice sublimation is too weak at 6 AU to account for the observed brightness. The derived CO production rate is [FORMULA] - [FORMULA] (Senay & Jewitt 1994; Crovisier et al. 1995) which seems to be more or less stable since more recent observations come up with similar values. During an outburst, however, increases of a factor 4 have recently been observed (Bockelée-Morvan, private communication). The CO production rate is sufficient to generate the observed coma.

In this study we investigate the activity of P/SW1 by means of numerical modelling. We present a thermodynamic model of cometary nuclei. Its development is motivated in part by the need of a working model for the future Rosetta mission. The model concept is akin to earlier works (e.g. Espinasse et al. 1989, 1991; Tancredi et al. 1994). The main achievement of this model is a high spatial and temporal resolution as well as a physically more fundamental description of the gas diffusion within the nucleus. In fact, comet nucleus models published so far have typically used the fast rotator approximation of a sphere. Transport equations for heat and gas are numerically integrated exclusively for the radial direction with a time step of a few days. Unlike the fast rotator approximation, physico-chemical reactions taking place in comets are non-linear with respect to temperature and can be very different at the poles and the equator as well as between day and night. The transport equations in our model are integrated for the radial and meridional directions. A 3D solution is obtained by relating the boundary conditions to the comet's hour angle. For simplification several of the previous models assume that only Knudsen gas diffusion takes place inside the nucleus (e.g. Benkhoff 1995; Tancredi et al. 1994). Some works seek a more complete description by using parametrised diffusion coefficients of a free molecular and a viscous regime (e.g. Fanale & Salvail 1984; Prialnik et al. 1990). Other works studied also the transition of a gas from a molecular to a viscous regime (e.g. Steiner 1991; Bouziani 1995). In this work we adapted the Chapman-Enskog method (Chapman & Cowling 1960) which has not been used so far for cometary modelling. This method provides transport coefficients of pure or mixed gases for all possible diffusion regimes from the solution of the linearised Boltzmann equation.

We consider that with these new achievements the model provides production rates which can be directly tested against those measured by astronomical observations.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998