5. Parametrisation of surface erosion
So far our model description contains only the mass loss due to sublimation and subsequent effusion. Nevertheless emission of solid particles from the surface takes place which can be evaluated by broadband photometry. These grains are dragged out of the ice-dust matrix by the escaping gas. If CO is the most important driver of the activity of P/SW1 there should exist a correlation function relating the dust emission rate to the CO gas production rate .
A microphysical description of this process is complex and difficult to quantify as the origin of the cohesion forces (physical or chemical) is unknown. Therefore, we have chosen to parametrise . It seems that has the property of an amplification function as the measured CO production rate is more or less constant but the brightness varies several orders of magnitudes. This non-linearity could also be an artefact due to grain fragmentation as the collision rate per unit volume increases with the square of grain density.
At the current state of the model development we prefer to retain a linear relationship between and . We consider a constant normalised grain size distribution. Such a case is favoured with particles having a fractal dimension of since the density of a fractal decreases in this case with size according to the relation
This fractal dimension is yielded from accretion models of the primordial solar nebula (Meakin & Donn 1988). Finally the parametrisation of the mass loss rate becomes
The modelled CO production rate is
where A is the size of a surface element of the discretised sphere.
By analysing isophotes of the dust tail of P/SW1, Fulle (1992) suggested a dust production rate of . The production rate could even be larger as the used IRAS images contain only information on grains of sizes between 5 and 2 cm. Fulle concluded that the persistent coma would result of steady activity rather than of overlaps of outburst shells. One can expect that icy-dust grains are emitted from the surface. If we assume a dust to ice mass ratio of about 1 the water ice erosion rate would be . The modelled sublimation rate through free surface sublimation at 6 AU is . However, the icy grains can completely sublimate and contribute to the production rate. As water is not observed so far in P/SW1 the production rate has to be in agreement with the detection limit of (Bockelée-Morvan, private communication).
The CO production rate is given by radio spectroscopic observations. The measured CO gas production rate is about 1200 to (Senay & Jewitt 1994; Crovisier et al. 1995). The parameter , relating the dust and CO gas production rate, is therefore chosen equal to 0.5 .
Although the erosion is not strictly uniform we suppose that the approximation of the spherical shape of the model nucleus holds for the simulation over a few revolutions.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998