Irregular singularity of the magnetorotational instability in a keplerian disk

The center of a Keplerian disk is an irregular singularity for the eigenfunctions of magnetorotational instabilities. The system is studied using the small-radius approximation, which by no means implies that the analysis is valid only in the vicinity of the center of the astrophysical disks. In fact, the singularity has an effect on the entire disk and yields continuous eigenvalues (growth rates in the unstable regime and real frequencies in the stable regime) with rather intriguing implications for the non-Hermitian nature of the rotating plasmas. Through the Laplace transform, as well as numerical simulations, interesting long-term behavior of the instability has been found.