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Astron. Astrophys. 329, 559-570 (1998)

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6. Conclusions

We have investigated outbursts in dwarf nova accretion disks in the framework of the disk instability model. The long-term evolution of an accretion disk was calculated with the high resolution required to resolve transition fronts adequately.

By solving the Navier-Stokes equations for the radial flow velocity and the azimuthal velocity we were able to take into account deviations of the azimuthal velocity from the Keplerian velocity. Though even inside a heating wave, the deviation from the Keplerian value is only a few percent, the gradient [FORMULA] can deviate byup to [FORMULA] 20% from the Keplerian value influencing the distribution of heating and diffusion of angular momentum within the front. It turns out however, that this has only a small effects on the overall outburst behavior of the accretion disk.

A discussion of the energy equation reveales the following results: lateral heat diffusion is only important in the region of a heating wave. It leads to a considerable broadening of the wave. For this, only the radial energy flux carried by viscous processes is responsible, the radial energy flux carried by radiative processes can be neglected. While the pressure term [FORMULA] may be neglected the advective term [FORMULA] should not. The contribution of the frictional stresses [FORMULA] and [FORMULA] to the viscous heating is small compared to the contribution of [FORMULA]. Nevertheless, when compressibility is included these terms should not be neglected because they are responsible for the damping of sound waves.

A comparison with calculations by Mineshige (1987) and Cannizzo (1993) has shown general agreement with our results. Especially, our solutions show the multi-modal outburst behavior which was also obtained by Cannizzo. The underlying property for this is that long outbursts are those in which the entire disk is transformed to the hot state, while in short ones the outward moving heating wave is reflected as a cooling wave before reaching the outer disk rim. In our calculations all outbursts start near the inner disk edge. From observations of SS Cygni we know (see Mauche 1996), that at least long outbursts can start also near the outer disk edge. Within the usual two-alpha description for the viscosity such outside-in outbursts can not be obtained. For getting outside-in outbursts a viscosity prescription is needed which produces a sufficiently steep radial gradient of the viscosity. This, for example, can be achieved by taking [FORMULA] proportional to [FORMULA] with [FORMULA], where [FORMULA] is the tidal radius which is about [FORMULA] of the binary separation (see Ichikawa & Osaki, 1992). Also an ([FORMULA])-dependent [FORMULA] can lead to outside-in outbursts (Meyer & Meyer-Hofmeister 1984). Alternatively, hole formation e.g. by disk evaporation during quiescence (Liu et al. 1997) may shift the point of triggering of the outburst outward.

Comparison of the present calculations with those by Ludwig et al. (1994) show that front velocities were obtained which are in good agreement with those obtained here. However, the localized front approximation in its simple form does not yield a complex (e.g. a bimodal) outburst behavior, since the detailed internal structure of transition waves decides on their formation and fading with consequences for the long-term behavior of the disk.

Finally, our calculations have shown that within the thermal limit-cycle model of dwarf nova outbursts the observed sequencing in SU UMa systems can be explained in a natural way. Also the (at least occasionally) observed increase of the recurrence time during the sequence of short normal outbursts between two superoutbursts is succesfully obtained in our calculations.

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© European Southern Observatory (ESO) 1998

Online publication: December 8, 1997