8 Discussion and conclusions

Symbiotic binaries are a heterogeneous class of objects. Therefore, the determination of system parameters turns out to be hampered often by some peculiar property of the individual object. This makes a statistical analysis of basic system parameters for symbiotic systems difficult. For example, there are entire subgroups, like the d-type symbiotics, for which we do not even know the orbital period of a single system.

The spectral type of the red giant is certainly a parameter, which is most readily available. But even the determination of this parameter requires a careful assessment of the specialties of symbiotic spectra. So it is in most cases not possible to use the traditional classification criteria in the blue (photographic) spectral region, because there, the emission from the ionized nebula and/or from the hot component often dominates the spectrum. Even the use of the red spectral region may give erroneous results (see Sect. 3) if the veiling by the nebular emission is not taken properly into account.

We based our determination of spectral types on near-IR spectra of molecular bands. In this spectral region the above mentioned problems can often be avoided, because the red giant spectrum is much more prominent and the nebular emission is in most cases negligible. Nonetheless, the diversity of symbiotic systems requires still a special treatment for some objects. For instance, we had to use blue spectra for giants with earlier spectral types having no molecular bands in the near IR. Still, a few of the observed systems escaped classification because the red giant is heavily obscured by dust and no spectral features are visible in the 4000-9000 Å region.

We determined the spectral type of the cool giant in about 100 symbiotic systems. Together with literature data we collected classifications in about 170 systems. This is unique in the sense that no other parameter is known for almost the complete sample of symbiotic systems, including all subgroups.

Our study further supports and elucidates the finding that the red giants in symbiotic systems are strongly biased towards late spectral types. While the frequency of M subtypes in the solar neighbourhood is decreasing from M0 to M8, the distribution of the symbiotic systems peaks at M5. Similarly, the relative frequency of mira variables is 6 times larger in symbiotic systems. For M-giants late spectral types are associated with large stellar radii, with extended atmospheres, and with heavy mass loss. The predominance of very late M-giants in symbiotic systems indicates that these properties are key ingredients for triggering symbiotic activity.

A major result of this study is the strong correlation between the spectral type of the cool giant and the orbital period. The distribution of objects in the spectral type - orbital period diagram indicates that there exists for a given spectral type a lower limit for the orbital period, which is about 250 d for spectral type M1, 560 d for M4, and 1260 d for M7. Only one system, the recurrent novae T CrB, lies clearly below this limit, suggesting that its very individual properties may be related to this exceptional feature.

Very interesting conclusions emerge when the spectral types and the orbital periods are converted into photospheric radii and critical Roche lobe radii, respectively. We find that the limiting line from the spectral type - orbital period diagram is practically identical with the relation $\ell_1=2~\cdot~R$,where $\ell_1$ is the distance from the center of the cool giant to the Lagrangian point L₁, and R is the red giant's radius. This strongly suggests that at least most symbiotic systems are well detached. A large fraction of the systems cluster close to the $\ell_1=2~\cdot~R$ limit, suggesting that this configuration is ideal for producing strong and long-lived symbiotic activity on the companion.

The present catalogue of spectral types for the cool giants in symbiotic systems may provide an important input for further statistical studies. Spectroscopic parallaxes based on the spectral types could provide a better assessment of the space frequency and the galactic distribution of symbiotic systems. In particular a comparison with related objects, like barium star type binaries or planetary nebulae with double star nuclei could clarify the evolutionary status and the interaction processes of symbiotic systems.

Acknowledgements

It is a pleasure to thank Regina E. Schulte-Ladbeck for allowing us to use her spectral data. We thank our colleagues Thomas Dumm, Orsola De Marco, Joachim Krautter, Harry Nussbaumer, Hans Schild, and Werner Schmutz for many useful comments. HMS acknowledges financial support by the Deutsche Forschungsgemeinschaft (KR 1053/6-1).