Degeneracy between mass and peculiar acceleration for the double white dwarfs in the LISA band

Understand

Mass and distance are fundamental quantities to measure in gravitational-wave (GW) astronomy.

• However, recent studies suggest that the measurement may be biased due to the acceleration of GW source.
• Here we develop an analytical method to quantify such a bias induced by a tertiary on a double white dwarf (DWD), since DWDs are the most common GW sources in the milli-Hertz band.
• We show that in a large parameter space the mass is degenerate with the peculiar acceleration, so that from the waveform we can only retrieve a mass of ${\cal M}(1+\Gamma)^{3/5}$, where ${\cal M}$ is the real chirp mass of the DWD and $\Gamma$ is a dimensionless factor proportional to the peculiar acceleration.