[Paper Review] Constraining the Milky Way potential with Double White Dwarfs

Valeriya Korol, Elena M. Rossi+1 more|arXiv (Cornell University)|Oct 9, 2018

Gamma-ray bursts and supernovae2 references4 citations

TL;DR

This paper demonstrates that gravitational wave detections of double white dwarfs (DWDs) by the LISA mission will enable precise, unbiased constraints on the Milky Way's baryonic structure—specifically the scale radii of the disc and bulge—with percent-level accuracy. By combining LISA's all-sky DWD detections with optical data from missions like Gaia and LSST, the study shows that multi-messenger observations can yield competitive mass estimates for the disc and bulge, while halo mass constraints remain limited without tighter dark matter halo priors.

ABSTRACT

The upcoming LISA mission is the only experiment that will allow us to study the Milky Way's structure using gravitational wave signals from Galactic double white dwarfs (DWDs). The total number of expected detections exceeds $10^5$. Furthermore, up to a hundred DWDs can be simultaneously detected in both gravitational and optical radiation (e.g. with Gaia and LSST as eclipsing), making DWDs ideal sources for performing a multi-messenger tomography of the Galaxy. We show that LISA will detect DWDs everywhere, mapping also the opposite side of the Galaxy. This complete coverage will: (1) provide precise and unbiased constraints on the scale radii of the Milky Way's bulge and disc, and (2) allow us to compute the rotation curve and derive competitive estimates for the bulge and disc masses, when combining gravitational wave and optical observations.

Motivation & Objective

• To investigate the potential of double white dwarfs (DWDs) as gravitational wave tracers for mapping the Milky Way’s baryonic structure.
• To assess how LISA’s all-sky DWD detections, combined with optical data, can improve constraints on the Galaxy’s disc and bulge parameters.
• To evaluate the precision of scale radii and mass estimates for the disc, bulge, and dark matter halo using joint gravitational wave and optical observations.
• To identify limitations in constraining the dark matter halo due to lack of optical data beyond R ≈ 11 kpc.

Proposed method

• A synthetic Milky Way model is generated using the SeBa population synthesis code with realistic initial conditions, including Kroupa initial mass function, log-flat orbital distribution, and common envelope evolution via the γαα prescription.
• The model includes a stellar disc with scale radius Rd = 2.5 kpc and scale height Zd = 0.3 kpc, a spherically symmetric bulge with Mb = 2.6×10¹⁰ M⊙ and radius rb = 0.5 kpc, and a Navarro-Frenk-White dark matter halo with ρh = 0.5×10⁷ M⊙/kpc³ and rs = 20 kpc.
• LISA’s sensitivity to mHz gravitational waves is simulated using the Mock LISA Data Challenge pipeline, modeling DWD signals via nine parameters including amplitude, frequency, sky position, inclination, and polarization.
• Optical counterparts are simulated using Gaia-like proper motion and distance measurements, with 10⁵ Monte Carlo realizations per DWD to estimate observed rotation speeds and uncertainties.
• The rotation curve is reconstructed from LISA and optical data using an MCMC fitting procedure, with free parameters M_d, M_b, ρ_h, and r_h, and flat, uninformative priors over physical ranges.
• Constraints on the dark matter halo are tested by comparing posterior distributions to fiducial values, revealing limited sensitivity due to lack of optical data beyond R ≈ 11 kpc.

Experimental results

Research questions

• RQ1 Can LISA’s all-sky DWD detections provide unbiased and precise constraints on the scale radii of the Milky Way’s disc and bulge?
• RQ2 To what extent can joint gravitational wave and optical observations improve mass estimates for the disc and bulge components?
• RQ3 Why are dark matter halo parameters poorly constrained in this multi-messenger approach?
• RQ4 How does the inclusion of DWDs as tracers overcome limitations of traditional electromagnetic observations, such as dust extinction and distance bias?

Key findings

• LISA is expected to detect over 10⁵ resolvable double white dwarfs, enabling complete sky coverage including the Galactic far side, overcoming dust extinction and luminosity bias in electromagnetic surveys.
• The scale radius of the disc (Rd) is reconstructed as 2.54 ± 0.08 kpc, and the bulge radius (rb) as 0.51 ± 0.01 kpc, in excellent agreement with the fiducial model, demonstrating percent-level precision.
• The disc mass is constrained to M_d = 5.30⁺¹.²⁹₋₁.⁷¹ × 10¹⁰ M⊙, and the bulge mass to M_b = 2.49⁺⁰.⁴⁴₋⁰.⁴² × 10¹⁰ M⊙, showing competitive precision compared to electromagnetic tracers.
• The dark matter halo parameters (ρh and rh) are poorly constrained due to lack of optical data beyond R ≈ 11 kpc, where the halo dominates the potential.
• The posterior distribution for the halo parameters shows a broad uncertainty, with ρh = 0.67⁺⁰.⁷⁷₋⁰.³⁸ × 10⁷ M⊙/kpc³ and rh = 15.19⁺⁷.⁵⁰₋⁴.⁰² kpc, indicating that tighter halo priors are needed for improved baryonic mass measurements.
• The study confirms that DWDs are ideal multi-messenger tracers for galactic structure, enabling tomographic mapping of the Milky Way’s baryonic components with minimal systematic bias.