Distance Estimation and Sky Localization of Eccentric Double White Dwarf Binaries from Gravitational Wave Observations inside Globular Clusters

TL;DR

This study examines whether gravitational waves from eccentric double white dwarf binaries (DWDs) in globular clusters can yield precise distance measurements and sky localizations with space-based detectors like LISA. It combines MOCCA-based globular-cluster population modeling with GW signal simulations, SNR calculations across multiple harmonics, and Fisher-information matrix–based parameter estimation for both eccentric and circular binaries. The key finding is that eccentricity dramatically improves distance and sky localization precision: relative distance errors can reach as low as $\sim$10$^{-5}$–10$^{-3}$ for $e$ near 1, while sky-localization relative to the host cluster area can reach $10^{-7}$–$10^{-5}$; circular binaries remain poorly localized. The results suggest that a few such highly eccentric DWDs could yield independent, high-precision distance anchors inside MW globular clusters and potentially in the Magellanic Clouds, offering a valuable cross-check for the cosmic distance ladder, though the analysis remains optimistic and should be refined with full Bayesian methods and broader population studies.

Abstract

The cosmic distance scale is built on multiple different techniques for estimating distances in space that are often connected and dependent on multiple measurements and assumptions. Double white dwarf binaries (DWDs) are common objects and are expected to produce gravitational wave (GW) signals that can be observed with space-based detectors such as LISA. By analyzing these signals we should be able to estimate the distance and sky location of the source. Previous studies have done this for circular binaries which, while they are abundant, have, in general, weaker signals than eccentric binaries and it is not possible to differentiate whether a circular binary is in the field or in a dense environment such as a globular cluster (GC). In this paper we used eccentric binaries from MOCCA GC simulations, simulated the GW signal from each binary at locations related to GCs in the Milky Way and estimated the precision on the distance and the sky location of the source. We find that distances can be estimated with higher precision than current day methods even with low eccentricity binaries and higher eccentricity further increases this precision. Although the probability of finding a tight and eccentric DWD is far lower than a circular one, we can expect to find at least a few in the dense environments of the Milky Way, such as GCs. These estimations would be independent measurements with high precision to objects inside dense environments, such as GCs inside the Milky Way and the Magellanic Clouds.

Figures (5)

• Figure 1: Skymap of the GCs location and distance to the GCs that we used for the eccentric binaries (first panel) and the circular binaries (second panel). The plot is made in galactic coordinates and the color map shows the distance to the cluster. The marker size is also related to the distance where a larger marker shows a closer cluster to the Sun.
• Figure 2: Scatter plot of SNRs and distances for 4 different DWDs observed by LISA over 4 years and located in different GCs. Blue, orange, green, and red colors represent the circular binary ($e = 0$), low $e$ binary ($e = 0.18$), high $e$ binary ($e = 0.82$), and very high $e$ binary ($e = 0.97$), respectively.
• Figure 3: Scatter plots of relative errors for different variables for the 4 different binaries at each cluster location. The first panel shows the relative errors on the localization estimate plotted against that on the distance estimate. The second panel shows the relative errors on the chirp mass estimate plotted against that on the frequency estimate. The third panel shows the relative errors on the eccentricity estimate plotted against the initial eccentricity of the binary. Blue is the circular binary, orange the low $e$ binary, green the high $e$ binary and red the very high $e$ binary. The marker size shows the distance to the cluster where a larger marker means a smaller distance to the cluster.
• Figure 4: Skymaps of our 4 binaries placed inside different clusters. In the left column the color bar shows the distance relative error and in the right column the color bar shows the sky location relative error. Each row shows 1 binary and a larger marker indicates a smaller distance to the cluster. The sky maps are in galactic coordinates.
• Figure 5: Same scatter plots as in figure \ref{['fig:scatterAcc']} but with the 5 binaries placed in OCs added as purple circles and two binaries in LMC (stars) and SMC (squares) respectively.