\label{sect:omega0} From a mathematical point of view, the starting point of the integration in the plane of the disk can be chosen freely anywhere between \(\omega=0\) and \(\omega=R_0(z=0)\). Figure \ref{fig:omega_0} compares different starting points under otherwise equal conditions. For small initial radii the ram pressure of the stellar wind pushes the shock surface out in a small \(\Delta z\). This leads to small pre-shock speeds in this region because the direction of the flow and the shock surface are almost parallel. This region also represents a large fraction of the total mass loss of the stellar wind, because it covers a large solid angle. Consequently, models with small values of \(\omega_0\) heat less material to high temperatures.
Physically, the position of the shock front is restricted by the position of the disk - the shock between the stellar wind and the disk material (in the disk itself or the disk wind) must occur within the inner hole of the disk. Figure \ref{fig:omega_0} shows that the two solutions for \(\omega_0=0.01\) AU and \(0.1\) AU are almost indistinguishable and the exact value for this parameter is not important as long as \(\omega < 0.5\) AU. We use \(\omega_0 = 0.01\) AU as the fiducial starting point for the integration.