Elaborate theoretical studies on the formation and evolution of symbiotic systems have been made recently, e.g. by Yungelson et al. (1995), Han et al. (1995) and Iben & Tutukov (1996). These investigations provide a very comprehensive picture of our present understanding of these systems and they reproduce successfully many observed properties. However, they also show that much work still needs to be done in order to fully understand the interaction processes and the complex evolutionary phenomena in symbiotic systems.
We will not repeat the findings of the mentioned works but only address a few topics where our statistical analysis of the spectral types for the red giants in symbiotic systems may help clarifying the current understanding.
It is generally accepted that most symbiotic binaries are detached systems consisting of a red giant and a white dwarf. Accretion at a rate of 10-9 to 10-7 /yr is probably due to capture from a wind emitted by the giant. The activity of the hot component is explained as nuclear burning of the accreted hydrogen-rich matter (e.g. Tutukov & Yungelson 1976).
However, for very few systems a physically distinct model is often advocated: a binary system consisting of a Roche-lobe filling red giant and a low-mass main-sequence accretor (see e.g. Kenyon & Webbink 1984; Kenyon 1992). With new observations this class has been shrinking and currently there are only very few systems left, like AX Per and CI Cyg, where comprehensive observational studies support, or at least do not exclude, this possiblity (e.g. Mikoajewska & Kenyon 1996b). We believe that a "normal'', detached system with the white dwarf companion cannot be ruled out for AX Per nor CI Cyg. Because both systems are eclipsing the interpretation of the observational data is complicated due to the possible presence of obscuring matter in the orbital plane. In our period-spectral type and -diagrams both, AX Per and CI Cyg, are located near the limiting line, in the midst of the other symbiotic systems. In particular, their location indicates that they are detached systems. Also, AX Per and CI Cyg do not show periodic (double wave per orbital period) photometric variations of in the V-band as expected for a tidally distorted, Roche-lobe filling red giant.
These findings argue against the main sequence accretor model requiring very high mass transfer rates () in order to yield the high luminosity of the ionizing radiation source. Such high transfer rates are only expected for Roche-lobe overflow in a semi-detached system. Thus, we propose that AX Per and CI Cyg could be detached systems with white dwarf companions because they seem to obey the general limit as well.
The controversy on the interpretation of the AX Per and CI Cyg systems also opens the more general question, whether a red giant with a main sequence accretor can indeed produce enough ionizing radiation for producing the higher excitation emission lines, which are characteristic for symbiotic binaries.
According to the previous sections the distribution of spectral types is strongly biased towards late spectral types. Further, we found the spectral types or the radii of the red giants to be correlated with the orbital periods, indicating that there exists a similar strong bias in the period distribution. In fact, the distribution of periods for symbiotic systems peaks around 2 years. No system is known with P<200 days, and only 2 systems in Table 7 have a period above 4 years.
The short period cut-off for symbiotic systems is comparable to the period cut-off found for barium-star type binaries, indicating a close relationship. The barium-star type systems are composed of a red giant with an abundance anomaly (s-process elements enhanced) and a white dwarf (e.g. McClure & Woodsworth 1990; Jorissen & Mayor 1992). The abundance peculiarity is explained by mass transfer from the companion which has undergone AGB-star evolution and is now a white dwarf. For shorter period double star systems such a phase of heavy mass transfer from a cool giant is probably dynamically unstable and will end up in a short period system ( days) similar to catalcysmic binaries (e.g. Paczynski 1976; Meyer & Meyer-Hofmeister 1979; Iben & Tutukov 1984). Thus, the presence of a white dwarf naturally explains the paucity of short orbital periods (P<1 year) for symbiotic and barium-star type binaries. In fact, there are several symbiotic systems known with a barium-star like abundance anomaly (e.g. Smith et al. 1996, 1997). If red giants with main sequence accretors are viable symbiotic binary models then it is not clear why there are no systems with shorter periods around 50-200 days.
Only few symbiotic systems with orbital period beyond 1500 days are known (see Table 4). This is in contrast to the barium-stars which show a period distribution extending well to 3000 days or even beyond (Jorissen 1997). Selection effects for such a comparison are certainly important, particularly when considering that no periods are known for symbiotic miras. Nontheless, the available period distribution for the subsample of s-type symbiotic systems should be quite representative, and this shows a clear deficiency for long period systems when compared to barium stars. Possibly, the mass transfer and, in consequence, symbiotic activity is reduced for very large orbital separations corresponding to periods P>1500 days, even for the quite rare case where the cool star reaches the large radius of a very late M giant of spectral type M6 or M7. Thus the strong peak in the spectral type distribution around for the red giants in symbiotic systems reflects the orbital period distribution with its maximum around 500 to 700 days.
Symbiotic activity for much longer period systems is again possible if the cool giant has a substantially enhanced mass loss. Such strongly enhanced mass loss rates are observed for luminous AGB stars like the mira-variables with dust shells. The corresponding class are the d-type symbiotic systems. Unfortunately, nothing firm is known about their period distribution. The expectation for the orbital periods are very long ( years).
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