  In this work, we investigate the impact of tidal torques and mass transfer on
the population of double white dwarfs (DWDs) that will be observed with LISA.
Starting from a distribution of DWDs at formation predicted by numerical
simulations, we use a semi-analytical model to evolve DWDs under different
hypotheses for the efficiency of tidal coupling and the birth spins of white
dwarfs. We then estimate the stochastic foreground and the population of
resolvable binaries for LISA in each scenario. Our predicted DWD binary
distribution can differ substantially from the distribution expected if only
gravitational waves (GWs) are considered. If white dwarfs spin slowly, then we
predict an excess of systems around a few mHz, due to binaries that outspiral
after the onset of mass transfer. This excess of systems leads to differences
in the confusion noise, which are most pronounced for strong tidal coupling. In
that case, we find a significantly higher number of resolvable binaries than in
the GW-only scenario. If instead white dwarfs spin rapidly and tidal coupling
is weak, then we find no excess around a few mHz, and the confusion noise due
to DWDs is very small. In that scenario, we also predict a subpopulation of
outspiralling binaries below 0.1 mHz. Using the Fisher matrix approximation, we
estimate the uncertainty on the GW-frequency derivative of resolvable systems.
We estimate that, even for non-accreting systems, the mismodelling error due to
neglect of effects other than GWs is larger than the statistical uncertainty,
and thus this neglect would lead to biased estimates for mass and distance. Our
results highlight the need for flexible tools in LISA data analysis. Because
our semi-analytical model hinges upon a simplistic approach to determining the
stability of mass accretion it will be important to deepen our comprehension of
stability in mass-transferring DWD binaries.
