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

TL;DR

This paper develops an analytical method to quantify how the acceleration of a tertiary object can bias the measurement of mass and distance of double white dwarf binaries in gravitational-wave observations, especially with LISA.

Contribution

The paper introduces a new analytical approach to assess mass and distance biases caused by tertiary-induced acceleration in DWDs for GW measurements.

Findings

Approximately 9% of DWDs have biased mass measurements due to tertiary acceleration.

Biases can cause misclassification of DWDs as other compact binary types.

Mass bias affects inferred distance, impacting the perceived distribution of DWDs.

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 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. Based on our analytical method, we conduct mock observation of DWDs by the Laser Interferometer Space Antenna (LISA). We find that in about $9\%$ of the cases the measured chirp mass is biased due to the presence of a tertiary by $(5-30)\%$. Even more extreme cases 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 measurement of distance, resulting in a seemingly over-density of DWDs within a heliocentric distance of $1$ kpc as well as beyond $100$ kpc. Our result highlights the necessity of modeling the astrophysical environments of GW sources to retrieve their correct physical parameters.