Uncovering stealth bias in LISA observations of double white dwarf binaries due to tidal coupling

Double white dwarfs are important gravitational wave sources for LISA, as they are some of the most numerous compact systems in our Universe. Here, we consider finite-sized effects due to tidal interactions, as they are expected to have a measurable impact on these systems. Previous studies suggested that tidal effects would allow the individual masses to be measured, but there was a subtle error in those analyses. Using a fully Bayesian analysis, we find that while tidal effects do not allow us to constrain the individual masses, they do yield informative lower bounds on the total mass of the system. Including tidal effects is crucial to the accuracy of our estimation of the chirp and total mass. Neglecting tidal effects leads to significant biases toward higher chirp masses, and we see that the lower bound of the total masses is biased toward a higher value as well. For many systems observed by LISA, tidal effects can lead to a ``stealth'' bias, since only the first derivative of the frequency can be measured. To separate tidal effects from the usual point-particle decay we need to be able to measure the change in the second derivative of the frequency cause by the tides. This can only be done for high frequency systems observed with high signal-to-noise ratio. The bias, if not accounted for, can have significant astrophysical implications; for example, it could lead to an incorrect estimation of the population of potential Type Ia supernovae progenitors.