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Astron. Astrophys. 327, 620-635 (1997)

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5. Conclusion

Previous works in the field of mass transfer in close binaries usually centered on conservative mass transfer, even when observation directs us to consider mass loss from the system, as is the case with white dwarf neutron star binaries. If these systems form from mass transfer in red giant neutron star systems, then one must find a way to start with a secondary star sufficiently massive to evolve off the main sequence in a Hubble time, ([FORMULA]), in a binary with a [FORMULA] neutron star and reduce the secondary's mass by [FORMULA], while keeping the neutron star below [FORMULA]. To do this, some 3/4 of the mass from the secondary must be ejected from the system. Results here indicate that it is possible to remove this much mass in winds, while maintaining stable mass transfer on the nuclear timescale.

For the most part, nonconservative mass transfer, in which mass is lost in fast winds, mimics the conservative case. For the typical initial mass ratios ([FORMULA]), [FORMULA] ranges from about -0.7 to -0.2. The rate of mass transfer is given by Eq. (73), and is lowest at the start of mass transfer, when [FORMULA] is low. The total time is therefore set almost entirely by [FORMULA] and [FORMULA], and so differs by maybe a factor of 3, over all possible wind models.

It is worth repeating that changes in [FORMULA] arising from nonconservative evolution do not alter the relationship between white dwarf mass and binary period by more than a couple of percent. This is true, by the following arguement. The final red giant and core masses differ only at the few percent level. Approximately, then, the red giant mass sets the red giant radius and therefore the Roche radius. In the (low q) approximation used by Paczyski (1971 ), orbital period is a function of [FORMULA] and [FORMULA], only. P vs. [FORMULA] is a function of the final state, alone. Using Eggleton's formula instead of Paczyski's introduces only a very weak dependence on the mass of the other (neutron) star. In the end, the theoretical motivation for the existence of a P - [FORMULA] relation is significantly more solid than, say, our knowledge of the red giant R - [FORMULA] relation, on which the exact P - [FORMULA] curve depends.

The exact mode of mass transfer will effect [FORMULA], as is evident from Eq. (29). This could be important, in statistical studies of white dwarf neutron star binaries, and trying to predict the distribution of P from the initial mass function, and distribution of initial orbital periods. This is dependent, of course, on the development of a quantitative understanding of the common envelope phase.

Finally, and probably the most useful thing, is that if one assumes only accretion and wind-like mass transfer, then most binaries in which mass is transferred from the less massive star are stable on both dynamical and thermal timescales. If the mass donor has a radiative envelope (not treated here), it will shrink in response to mass loss, and lose mass in a stable way. If the donor has a convective envelope, a modestly sized core will stabilize it sufficiently to prevent mass loss on the dynamical timescale. Only if one has a very low mass (or no) core, will the mass transfer be unstable on the dynamical timescale, and then, only for [FORMULA]. High values of [FORMULA], and low core mass in a convective star may lead to instability on the thermal timescale, if the mass ratio, q is sufficiently low (see Fig. 5).

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© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998