Degeneracy between mass and peculiar acceleration for the double white dwarfs in the LISA band. Issue 3 (6th February 2021) - Xuan, Zeyuan; Peng, Peng; Chen, Xian
ABSTRACT: 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 star 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 ${\cal M}(1+Γ)^{3/5}$, where ${\cal M}$ is the real chirp mass of the DWD and Γ is a dimensionless factor proportional to the peculiar acceleration. Based on our analytical method, we conduct mock observation of DWDs by the Laser Interferometer Space Antenna. We find that in about $9{{\ \rm per\ cent}}$ of the cases the measured chirp mass is biased by $(5-30){{\ \rm per\ cent}}$ due to the presence of a tertiary. Even more extreme biases are found in about a dozen DWDs and they may be misclassified as double neutron stars, binary black holes, DWDs undergoing mass transfer, or even binaries containing lower-mass-gap objects and primordial black holes. The bias in mass also affects the measured distance, resulting in a seemingly overdensity of DWDs within a heliocentric distance of 1 kpc as well as beyond 100 kpc. Our result highlights the necessity of modelling the astrophysical environments of GW sources to retrieve their correct physical parameters.