LISA double white dwarf binaries as Galactic accelerometers

TL;DR

This paper investigates using LISA-detected double white dwarfs as Galactic accelerometers to probe the Milky Way’s gravitational potential. It develops a three-component Galactic model and creates a synthetic DWD catalog to study how apparent GW frequency drifts encode line-of-sight and perspective accelerations, employing a Fisher-matrix framework to evaluate measurability. The analysis finds strong degeneracies between acceleration and intrinsic chirp in GW data alone, making GW-only accelerometry unlikely, but shows that incorporating EM measurements of DWD parameters and identifying many EM counterparts can enable a robust determination of the Galactic potential normalization $\mathcal{N}$. The work highlights a feasible multimessenger pathway for mapping Galactic mass distribution with LISA DWDs, while also outlining key systematics and the need for realistic modeling of non-GW effects.

Abstract

Galactic double white dwarf (DWD) binaries are among the guaranteed sources for the Laser Interferometer Space Antenna (LISA), an upcoming space-based gravitational wave (GW) detector. Most DWDs in the LISA band are far from merging and emit quasimonochromatic GWs. As these sources are distributed throughout the Milky Way, they experience different accelerations in the Galactic gravitational potential, and therefore each DWD exhibits an apparent GW frequency chirp due to differential acceleration between the source and LISA. We examine how Galactic acceleration influences parameter estimation for these sources; and investigate how LISA observations could provide insight into the distribution of matter in the Galaxy.

Figures (7)

• Figure 1: Model maps of Galactic acceleration. Left: Galactic line-of-sight acceleration contribution $\Delta{\boldsymbol{a}}\cdot\hat{n}$. Center: Shklovskii (perspective) contribution using only $v_\mathrm{circ.}$. Right: Sum of the two contributions. The contours of these quantities are shown as functions of $x$ and $y$, the Galactocentric coordinates on the Galactic plane, aligned such that the location of the Sun (labeled by $\odot$) is along the $x$ axis. Insets in each panel show acceleration maps centered on the Sun, with enhanced contrast.
• Figure 2: Synthetic population of Galactic DWDs observable in the 10 yr LISA mission. Left: Aitoff projection of the population in the Galactic longitude and latitude map. Right: The population shown in the amplitude spectral density (ASD) vs. frequency plane, together with the LISA noise curve (in gray), which includes the DWD confusion noise. DWD sources are simulated following Ref. Thiele:2021yyb (the total number of sources is 16264); verification binaries (labeled with red stars) are from Ref. 2018MNRAS.480..302K. For both panels, DWD symbol color indicates LISA SNR for the associated GW.
• Figure 3: Yellow dots show the synthetic DWD binary population considered in this work in the frequency vs. chirp mass plane. Other types of compact binaries listed in the legend are verification binaries (VB), binary neutron stars (BNS), black hole--neutron star binaries (BH--NS), and binary black holes (BBH). The red lines are contours of constant dephasing $\delta\psi_k=2\pi$. The plot suggests that there should be a sizeable portion of the DWD population with measurable $\dot{f}_0$ (i.e., to the right of the $k=1$ line), while $\ddot{f}_0$ is only measurable for a few binaries (roughly, those to the right of the $k=2$ line).
• Figure 4: (a) Beginning of DWD GW observation by LISA. (b) Time $t_s$ passes according to a clock at the source. We assume that the displacement of the source is much less than the source distance $D$ at any point during the LISA observation.
• Figure 5: Measurement uncertainties for a synthetic population of Galactic DWDs (model FZ from Ref. Thiele:2021yyb) using GWs alone. Left: The second time derivative of the GW frequency $\ddot{f}_0$ is either included (red) or excluded (blue) from the set of parameters in the Fisher matrix calculation. Here, numbers quoted at the top of plots refer to the "red" case. Right: The parameters include either the observed first and second time derivatives of the GW frequency (red, same points as in the left panel), or the source GW frequency $\dot{f}_{\rm s0}$ and the global parameter $\mathcal{N}$ (purple), which is related to the Galactic gravitational potential as in Eq. (\ref{['eq:overall_mass_normalization']}). Here, numbers quoted at the top of the plots refer to the "purple" case.