The effects of finite entropy become noticeably important for . Isentropic WD with (i) have larger radii than objects and (ii) the – relations for them are steeper than for (i.e. in the range of interest they are still negative but have a lower absolute value). By virtue of Equations (63, 64) this means that for a given orbital period they have higher . This effect is illustrated in the left panel of Figure 18. (The period–mass relation is not single-valued, since the – relation has two branches: a branch where the object is thermally supported and a branch where degenerate electrons provide the dominant pressure support.) The right panel of Figure 18 compares a model of the population of AM CVn-stars computed under assumptions that the donor white dwarfs have and a model which takes into account cooling of the prospective donors between formation and RLOF. The change in the rate of evolution (shown in the left panel) shifts systems with “realistic” cooling to longer orbital periods as compared to the population.
Finite entropy of the donors also influences the gravitational waves signals from AM CVn-stars. Again, by virtue of the requirement of , the systems with donors and hot donors will have a different for the same combination of component masses, i.e. different radii at the contact and different relation between chirp mass and . This alters the GW amplitude, Equation (17.
For instance, if a donor is fully degenerate, it overflows its Roche lobe at and then evolves to longer . If “realistic” cooling is considered, there are donors that make contact at up to 25 min. Hotter donors at fixed are more massive, increasing and increasing . Thus, the contribution of the individual systems to the integrated GW flux from the total ensemble increases, but their higher rate of evolution decreases the density of population of the sources detectable at low , since they are lost in the background confusion noise of Galactic WDs. But altogether, the ensemble of sources detectable by LISA with diminishes by about 10% only. Note that finite entropy of donors does not significantly affect the properties of the 10,000 systems that are expected to be observed both in electromagnetic spectrum and gravitational waves.
There are some more subtle effects related to finite entropy for which we refer the reader to the original paper.
© Max Planck Society and the author(s)