On the progenitors of AM CVn stars as LISA sources: the evolved donor
  star channel
  The space gravitational wave (GW) detector Laser Interferometer Space Antenna
(LISA) that was planed to launch in the early 2030s is to detect the
low-frequency GW signals in the Galaxy. AM CVn stars were generally thought to
be important low-frequency GW sources. Employing the MESA code, in this work we
calculate the evolution of a great number of binary systems consisting of a
white dwarf (WD) and a main sequence (MS) star, and diagnose whether their
descendants-AM CVn stars can be visible by the LISA. The simulated results show
that the progenitors of these LISA sources within a distance of 1 kpc are WD-MS
binaries with a donor star of $1.0-1.4~M_\odot$ (for initial WD mass of
$0.5~M_\odot$) or $1.0-2.0~M_\odot$ (for initial WD mass of $0.7~M_\odot$), and
an initial orbital period slightly smaller than the bifurcation period. Our
simulations also indicate ten verification AM CVn sources can be reproduced by
the standard magnetic braking model, and are potential LISA sources. Based on
the birthrate of AM CVns simulated by the population synthesis, the birthrate
of AM CVn-LISA sources evolving from the evolved donor star channel within a
distance of 1 kpc can be estimated to be $(0.6-1.4)\times10^{-6}~\rm yr^{-1}$,
and the predicted number of AM CVn-LISA sources is about $340-810$. Therefore,
the evolved donor star channel play an important role in forming AM CVn-LISA
sources in the Galaxy.
