We investigate the stability of stationary integral solutions of an ideal irrotational fluid in a general static and spherically symmetric background, by studying the profile of the perturbation of the mass accretion rate. We consider low angular momentum axisymmetric accretion flows for three different accretion disk models and consider time dependent and radial linear perturbation of the mass accretion rate. First we show that the propagation of such perturbation can be determined by an effective 2 × 2 matrix, which has qualitatively similar acoustic causal properties as one obtains via the perturbation of the velocity potential. Next, using this matrix we analytically address the stability issues, for both standing and travelling wave configurations generated by the perturbation. Finally, based on this general formalism we briefly discuss the explicit example of the Schwarzschild spacetime and compare our results of stability with the existing literature, which instead address this problem via the perturbation of the velocity potential.

Using the disc instability model for dwarf novae and soft X-ray transients, we investigate the stability of accretion discs in long-period binary systems. We simulate outbursts due to this thermal-viscous instability for two symbiotic systems, RS Ophiuchi and Z Andromedae. The outburst properties deduced from our simulations suggest that, although the recurrent nova events observed in RS Oph are due to a thermonuclear runaway at the white dwarf surface, these runaways are triggered by accretion disc instabilities. In quiescence, the disc builds up its mass and it is only during the disc-instability outburst that mass is accreted on to the white dwarf at rates comparable to or larger than the mass-transfer rate. For a mass-transfer rate in the range 10 −8 to 10 −7 M yr −1 , the accretion rate and the mass accreted are sufficient to lead to a thermonuclear runaway during one of a series of a few dwarf nova outbursts, barely visible in the optical, but easily detectable in X-rays. In the case of Z And, persistent irradiation of the disc by the very hot white-dwarf surface strongly modifies the dwarf-nova outburst properties, making them significant only for very high mass-transfer rates, of the order of 10 −6 M yr −1 , much higher than the expected secular mean in this system. It is thus likely that the so-called 'combination nova' outburst observed in years 2000 to 2002 was triggered not by a dwarf-nova instability but by a mass-transfer enhancement from the giant companion, leading to an increase in nuclear burning at the accreting white-dwarf surface.