Gravitational Waves from Double White Dwarfs as probes of the Milky Way
  Future gravitational wave detectors, such as the Laser Interferometer Space
Antenna (LISA), will be able to resolve a significant number of the ultra
compact stellar-mass binaries in our own Galaxy and its neighborhood. These
will be mostly double white dwarf (DWD) binaries, and their underlying
population characteristics can be directly correlated to the different
properties of the Galaxy. In particular, with LISA we will be able to resolve
$\sim\mathcal{O}(10^4)$ binaries, while the rest will generate a confusion
foreground signal. Both categories can be used to address a number of
astrophysical questions. Analogously to how the total electromagnetic radiation
emitted by a galaxy can be related to the underlying total stellar mass, in
this work we propose a framework to infer the same quantity by investigating
the spectral shape and amplitude of the confusion foreground signal. For a
fixed DWD evolution model, we retrieve percentage-level relative errors on the
total stellar mass, which improves for increasing values of the mass. At the
same time, we find that variations in the Miky Way shape, at a fixed mass and
at scale heights smaller than 500~pc, are not distinguishable based on the
shape of stochastic signal alone. Finally, we utilize the catalogue of
resolvable sources to probe the characteristics of the underlying population of
DWD binaries. We show that the DWD frequency, coalescence time and chirp mass
(up to $<0.7\,$M$_\odot$) distributions can be reconstructed from LISA data
with no bias.
