We have explored the ideas that parametric resonance affects nearly geodesic motion around a black hole or a neutron star, and that it may be relevant to the high frequency (twin) quasi-periodic oscillations occurring in some low-mass X-ray binaries. We have assumed the particles or fluid elements of an accretion disc to be subject to an isotropic perturbation of a hypothetical but rather general form. We find that the parametric resonance is indeed excited close to the radius where epicyclic frequencies of radial and meridional oscillations are in a 2 : 3 ratio. The location and frequencies of the highest amplitude excitation vary with the strength of the perturbation. These results agree with actual frequency ratios of twin kHz QPOs that have been reported in some black hole candidates, and they may be consistent also with correlation of the twin peaks in Sco X-1.

Thin viscous Keplerian accretion disks are considered asymptotically stable, even though they can show significant dynamic activity on short timescales. In this paper the dynamics of nonaxisymmetric hydrodynamical disturbances of disks are investigated analytically building upon the steady state three-dimensional structure and evolution of axisymmetric perturbations explored in previous work. Assuming a polytropic equation of state solutions are found by means of an asymptotic expansion in the small parameter measuring the ratio of the disk thickness to characteristic radius. In-depth analysis shows that every perturbation that disturbs the radial velocity induces significant transient growth in the (acoustic) energy of the evolving disturbance. This effect is most evident in the density and vertical velocity. The transient growth observed is tied to the nonseparable nature of the solutions where, in particular, pattern evolution is controlled by a similarity variable composed of the radial coordinate and time. This leads to growing winding perturbations that display successive radial peaks and troughs. We argue that these transient non-axisymmetric structures may precipitate secondary instabilities which, consequently, may be a critical element for a new alternative picture of turbulence arousal in non-magnetized astrophysical disks.

The origin of quasi periodic modulations of flux in the kilohertz range (kHz QPOs), observed in lowmass X-ray binaries, is usually assumed to be physically distinct from that of the "normal branch oscillations" (NBOs) in the Z-sources. We show that a low-frequency modulation of the kHz QPOs is a natural consequence of the non-linear relativistic resonance suggested previously to explain the properties of the high-frequency twin peaks. The theoretical results discussed here are reminiscent of the 6 Hz variations of frequency and amplitude of the kHz QPOs reported by Yu, van der Klis and Jonker (2001).

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To overcome difficulties in understanding the origin of the submillisecond optical pulses from SN 1987A we apply a model similar to that of Kundt and Krotscheck for pulsed synchrotron emission from the Crab. The interaction of the expected ul-trarel_tivistic e :e pulsar wind with the pulsar dipole electromagnetic wave reflected from the walls of a "pulsar cavity" Within the SN 1987A nebula can generate pulsed optical emission with efficiency at most Om_x ,_ 10 -3. The maximum luminosity of the source is reproduced and other observational constraints can be satisfied for an average wind energy flow _-, lOaeerg/(s;steraclian) and for electron Lorentz factor "r "-_105. This model applied to the Crab yields pulsations of much lower luminosity and frequency.