Applying the metallicity-dependent binary fraction to double white dwarf
  formation: Implications for LISA
  Short-period double white dwarf (DWD) binaries will be the most prolific
source of gravitational waves (GWs) for the Laser Interferometer Space Antenna
(LISA). Not only will tens of thousands of DWDs be individually resolved, but
DWDs with GW frequencies below ~1 mHz will be the dominant contributor to a
stochastic foreground caused by confusion from overlapping GW signals, limiting
the detectability of individual sources of all kinds. Population modeling of
Galactic DWDs typically assumes a standard binary fraction of 50%. However,
recent observations have shown that the binary fraction of close (P$_{\rm{orb}}
\leq 10^4$ days) solar-type stars exhibits a strong anti-correlation with
metallicity. In this study we perform the first simulation of the Galactic DWD
population observable by LISA which incorporates an empirically-derived
metallicity-dependent binary fraction. We simulate DWDs using the binary
population synthesis suite COSMIC and incorporate a metallicity-dependent star
formation history to create a Galactic population of short-period DWDs. We
compare two models: one which assumes a metallicity-dependent binary fraction,
and one with a binary fraction of 50%. We find that while metallicity impacts
the evolution and intrinsic properties of our simulated DWD progenitor
binaries, the LISA-resolvable populations of the two models remain roughly
indistinguishable. However, the size of the total Galactic DWD population
orbiting in the LISA frequency band is reduced by more than half when
accounting for a metallicity-dependent binary fraction. This effect serves to
lower the confusion foreground, effectively increasing the sensitivity for
detecting all types of low-frequency LISA sources. We repeat our analysis for
three different assumptions for Roche-lobe overflow interactions and find the
population reduction to be robust when a metallicity-dependent binary fraction
is assumed.
