## 2. MHD models and scaling lawsThe plasma flow in a comet can be described by the equations of
ideal magnetohydrodynamics (MHD) with source terms (see e.g. Schmidt
& Wegmann 1982; Wegmann 1995). One can combine the gas production
rate which determines the size of the region where the solar wind interacts with the comet. We adopt a coordinate system
centered at the nucleus with When the spatial coordinate is
measured in units of , and time
The main consequence of this is a In this paper we are mainly interested in the brightness which is directly proportional to the column density of cometary ions. We recall (Wegmann 1995) that the density and the column density of cometary ions scale like with functions and which are independent of the solar wind and of the cometary parameters. It has been demonstrated by Wegmann et al. (1999) that along a line through the nucleus perpendicular to the sun-comet line, with the nondimensional coordinate . This means that at a fixed point on this line the density as well as the brightness vary like the inverse of the dynamic pressure of the solar wind when all other parameters are kept fixed. We have calculated models with parameters listed in Table 1.
The parameters labeled 'slow1' and 'fast1' are for slow and fast solar
wind data taken from Gosling et al. (1978), Fig. 2, eight hours
before and after the interface of a corotating interaction region
(CIR). The data 'big1' are for a big Halley type comet with solar wind
data taken from Gosling et al. (1978), Fig. 1, two days before a
CIR. The data 'slow2' and 'fast2' are for the oblique shock model (S4)
calculated by Wegmann (1995). We calculate all models with
photo-ionisation only, with a constant rate
s
The small models and
s We use the same numerical method as in our previous paper (Wegmann 1995). The code is based on a second order Godunov method using an approximate Riemann solver for the MHD equations. Spurious magnetic monopoles generated by numerical errors are removed in each time step (Schmidt-Voigt 1989). The code is able to capture shocks. The flow is calculated on a non equidistant grid with finest resolution of 8000 km near the nucleus for the small models. Advanced codes (e.g. Gombosi et al.1994) for the solar wind - comet interaction use also second order Godunov methods with an approximate Riemann solver. Adaptive grid refinement improves the accuracy of stationary models. These codes have not yet been used for time-dependent calculations. © European Southern Observatory (ESO) 2000 Online publication: June 8, 2000 |