  (abridged) Huge amplitude X-ray outbursts in a few galaxies were reported in
the last few years. As one of the exciting possibilities to explain these
observations, tidal disruption of a star by a supermassive black hole has been
proposed. In the present paper, we perform a detailed discussion of this and
other possible scenarios for the X-ray outburst in NGC 5905, and a comparison
of NGC 5905 and IC 3599 in outburst as well as in quiescence. To this end we
present (i) a thorough analysis of all ROSAT observations of NGC 5905, (ii)
optical photometry of NGC 5905 quasi-simultaneous to the X-ray outburst, (iii)
the first post-outburst optical spectra of NGC 5905 and high-resolution
post-outburst spectra of IC 3599, and (iv) photoionization models for the
high-excitation emission lines that were discovered in the optical outburst
spectrum of IC 3599. The investigated outburst models include, besides the
tidal disruption event, a supernova in dense medium, an accretion-disk
instability, an event of extreme gravitational lensing, and the X-ray afterglow
of a GRB. The optical spectra of both galaxies in quiescence are carefully
examined for signs of permanent low-level Seyfert-activity. Whereas IC 3599
shows several signs of activity, none is revealed for NGC 5905. At present, and
among the X-ray bursts, this makes NGC 5905 the only safe candidate for a tidal
disruption event in an otherwise non-active galaxy. We briefly comment on a
search for further highly variable objects on the basis of ROSAT observations.
Several with factors 10-20 are found.
