The Milky Way's bar structural properties from gravitational waves

TL;DR

This study demonstrates that LISA's resolved double white dwarf population can map the Milky Way's central bar with high fidelity, while spiral structure remains more elusive in gravitational-wave maps. By combining a SeBa-based DWD population with the GALAKOS Milky Way–like simulation and analyzing mock LISA detections via Fourier decomposition of the DWD density, the authors recover a bar axis ratio of approximately $R_-/R_+ \approx 0.27$ and a viewing angle near $30^{\circ}$, with bar length inferred from the phase. The bar appears clearly in GW data and the results are competitive with electromagnetic tracers, illustrating GW tomography as an independent extinction-free probe of Galactic structure and a path toward GW–EM synergy. The work also discusses limitations (e.g., simplified 2D bar, homogeneous DWD population) and outlines improvements, such as high-frequency DWD selections and multi-detector networks, to enhance the accuracy of bar and bulge mapping.

Abstract

The Laser Interferometer Space Antenna (LISA) will enable Galactic gravitational wave (GW) astronomy by individually resolving $ > 10^4$ signals from double white dwarf (DWD) binaries throughout the Milky Way. In this work we assess for the first time the potential of LISA data to map the Galactic stellar bar and spiral arms, since GWs are unaffected by stellar crowding and dust extinction unlike optical observations of the bulge region. To achieve this goal we combine a realistic population of Galactic DWDs with a high-resolution N-Body simulation a galaxy in good agreement with the Milky Way. We then model GW signals from our synthetic DWD population and reconstruct the structure of the simulated Galaxy from mock LISA observations. Our results show that while the low signal contrast between the background disc and the spiral arms hampers our ability to characterise the spiral structure, the stellar bar will instead clearly appear in the GW map of the bulge. The bar length and bar width derived from these synthetic observations are underestimated, respectively within $1σ$ and at a level greater than $2σ$, but the resulting axis ratio agrees to well within $1σ$, while the viewing angle is recovered to within one degree. These are competitive constraints compared to those from electromagnetic tracers, and they are obtained with a completely independent method. We therefore foresee that the synergistic use of GWs and electromagnetic tracers will be a powerful strategy to map the bar and the bulge of the Milky Way.

Figures (11)

• Figure 1: The star formation history giving rise to the DWD population used in this work boi99. The present day value is 1.87 M$_\odot$ yr$^{-1}$.
• Figure 2: Projected mass density maps of the Galaxy model, in the $X-Y$ plane, $Z-Y$ plane, $X-Z$ plane, and $R-Z$ plane, where $R^2 = X^2 + Y^2$ and $(X, Y, Z)$ is the triad of Cartesian coordinates centred on the Galactic centre. Included are the bulge and disc components. The black triangle marks the Sun's position. Our line of sight makes an angle of $\sim 30$ degrees with respect to the bar's long axis.
• Figure 3: Projected number density maps of DWDs individually detected with LISA in $4\,$yr of mission projected on the Galactic plane ( top panel) and the same map corrected for the distance bias using Eq. \ref{['eq:bias']} ( bottom panel). The black triangle indicates the location of the LISA detector at $X=8.1$ kpc, and $Y=0$.
• Figure 4: A sketch of a uniform bar with half-length $R_{\rm b}$ and full width $H$. From geometrical considerations we can see that $\phi_{\rm c}\left(R\right) = \arcsin\left(\frac{H}{2R}\right)$
• Figure 5: Three examples of density distributions (left panels) with (in the right panels) the respective plots of the normalised $m=2$ Fourier mode magnitude (solid lines) and its complex phase (dotted lines) as a function of $R$. Top panels: A uniform density bar under two different rotations. The magnitude vanishes for radii smaller than half the bar width, and then quickly converges to 1. The phase is constant for all radii, and is shifted by twice the angle to the $x$-axis. Middle panels: A toy barred spiral with infinitesimally thin bar and logarithmic spirals. In this case the magnitude is constant for all radii and equal to 1, while the phase is constant for radii smaller than the bar length and drops beyond. The jumps in the phase are due to phase-wrapping to the interval $\left(-\pi,\pi\right]$. Bottom panels: A 2D Gaussian bar density model. The grey solid line denotes the profile of a bar with half the semi-minor scale length of the model shown. The magnitude is 0 only at the origin and converges to 1. The speed of this convergence depends on the bar semi-minor scale length. The phase is constant at 0 (except at the origin where it is undefined) like the uniform bar.