Investigations of stellar encounters in cluster environments have demonstrated their potential influence on the mass and angular momentum of protoplanetary discs around young stars. In this study it is investigated in how far the initial surface density in the disc surrounding a young star influences the outcome of an encounter. Based on a power-law ansatz for the surface density, $Sigma(r) propto r^{-p}$, a parameter study of star-disc encounters with different initial disc-mass distributions has been performed using N-body simulations. It is demonstrated that the shape of the disc-mass distribution has a significant impact on the quantity of the disc-mass and angular momentum losses in star-disc encounters. Most sensitive are the results where the outer parts of the disc are perturbed by high-mass stars. By contrast, disc-penetrating encounters lead more or less independently of the disc-mass distribution always to large losses. However, maximum losses are generally obtained for initially flat distributed disc material. Based on the parameter study a fit formula is derived, describing the relative mass and angular momentum loss dependent on the initial disc-mass distribution index p. Generally encounters lead to a steepening of the density profile of the disc. The resulting profiles can have a r^{-2}-dependence or even steeper independent of the initial distribution of the disc material. From observations the initial density distribution in discs remains unconstrained, so the here demonstrated strong dependence on the initial density distribution might require a revision of the effect of encounters in young stellar clusters. The steep surface density distributions induced by some encounters might be the prerequisite to form planetary systems similar to our own solar system.
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