8 Conclusions

We have analyzed the light curve of MT Ser, the binary central star of the planetary nebula Abell 41, within the framework of two quite different models. An unambiguous decision between the two models appears impossible in view of the current knowledge about the system.

Model 1 consists of a hot sub-dwarf and a cool companion leading to brightness variations dominated by the combined effect of reflection of the light of the hot component off the illuminated surface of the cooler star and of ellipsoidal variations of one or both components. It suffers from an unsatisfactory match between the observed and the best fit WD model light curve. Moreover, the orbital inclination would be much lower than suggested by the morphology of the planetary nebula. Points in favour of Model 1 are the agreement of the predicted system luminosity with that of the central star of the planetary nebula and of the predicted distance with the one derived from nebular physics. These quantities, however, may not be very reliable as pointed out in the literature.

Model 2 explains the observed light curve as being due to the combined effect of partial eclipses and ellipsoidal variations in a system consisting of two hot sub-dwarfs with almost equal temperatures. The points in favour of Model 1 (predicted system luminosity and distance) are just those points where Model 2 has difficulties: Both, luminosity and distance are too high (at least if extreme model parameters are avoided). As if to make up for this deficiency the best fit WD light curve for Model 2 is in excellent agreement with the observations. The O-C curve is indistinguishable from a random distribution of data points. Moreover, the orbital inclination is almost hauntingly close to that derived from the structure of the nebula surrounding MT Ser.

Thus, both models have pros and cons. A final decision may have to be postponed until a radial velocity curve is available which will permit to definitely exclude either the longer or the shorter of the possible values of the orbital period. Such observations are complicated by the strong Balmer emission lines of the planetary nebula superposed upon the stellar absorptions, making the use of the fainter helium lines indispensable for radial velocity measurements. Moreover, in the case of Model 2, blending of the lines of both stellar components will be an additional serious complication.

If the model of two hot sub-dwarfs similar in size and almost in contact with each other in a $5^{\rm h}26^{\rm m}$ orbit is realized MT Ser loses its status as the pre-cataclysmic binary with the shortest orbital period. In fact, it should not be regarded as a pre-cataclysmic binary at all since it will not evolve into a cataclysmic variable; at least not into a classical one. Instead, both components will turn into white dwarfs. Their current separation is such that angular momentum loss due to gravitational radiation (assuming that the currently elevated level of angular momentum loss indicated by the high value of $\dot{P}$ is due to ongoing mass loss of the planetary nebula phase and will not persist for a long time) makes their orbit decay on time scales of $0.6 \times 10^9$ years or $16 \times 10^9$ years in the high and low mass limits, respectively. The system may then turn into a double degenerate cataclysmic variable of the AM CVn type.

Acknowledgements

This work was partially supported by grants of the Conselho Nacional de Pesquisa (CNPq; grant No. 301029), the Fundação Amparo a Pesquisa de Minas Gerais (FAPEMIG; grant No. 205096).