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.
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