German Title: Über einen neuen Zugang zum Problem von Moden in Mestelscheiben

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Abstract

In this work I examine the modes admitted by the Mestel disk, a disk with a globally flat rotation curve. In contrast to previous analyses of this problem by Zang (1976) and Read (1997), I approximate the orbits to obtain almost closed expressions for the kernel of the integral equation governing the behaviour of the modes. I investigate the modes admitted by both the self-consistent and a cut-out Mestel disk, the difference being that in the latter case a part of the matter in the disk is immobilized. This breaks the self-similarity and produces a pronouncedly different picture. While the expressions for the kernel in the self-consistent disk are quite managable (though still beyond the reach of analytic techniques), the kernels for cut-out disks tends to rather complicated indeed. In general, my approximation reproduces the results of the previous works remarkably well. Due to the sheer size of the terms, examining the solution behaviour in the approximation does not save computing time compared to Zang's method at least for the cut-out disks. The more handy expressions in the self-consistent disk, on the other hand, allow an intuitive understanding of most of the properties of neutral (nonrotating, nongrowing) modes there. Also, non-axisymmetric modes of finite growth rate and pattern speed in the self-consistent disk become almost treatable. I can prove that there are no such modes above the velocity dispersions at which the neutral modes appear, and that any modes that exist below these thresholds cannot possess a bounded Mellin transform. Unfortunately, I still cannot prove the existence of such modes.