Resolving white dwarf binaries within globular clusters with LISA

TL;DR

The paper investigates whether LISA can identify white-dwarf binaries residing in Milky Way globular clusters as belonging to their host clusters by leveraging sky localization and distance measurements to separate GC binaries from Milky Way disc binaries. It builds a Milky Way disc WD population with SeBa, applies a loose S/N > 5 resolvability cut via GWToolbox, and forecasts LISA errors, then evaluates overlaps with 20 massive GCs by placing test binaries at GC locations. The results reveal a three-class separability: five GCs allow GC binaries to be distinguished by sky location alone, five more require combining sky location with distance, and ten remain indistinguishable due to heavy overlaps near the Galactic centre; the outcome strongly depends on GC sky position, with 47 Tucanae emerging as the most promising candidate. These findings guide expectations for identifying GC-hosted WD binaries with LISA and highlight avenues for future work, including incorporating eccentric GC DWDs as additional discriminants.

Abstract

Context: Globular clusters (GCs) around the Milky Way (MW) are expected to host white dwarf (WD) binaries emitting gravitational waves that could be detectable by LISA. Aims: Our aim is to investigate whether LISA can resolve WD binaries in GCs well enough in terms of sky location and distance that they can be distinguished from binaries in the MW disc. Methods: We used a sample of 20 of the most massive GCs around the MW and simulated LISA's sky location and distance measurement errors for WD binaries in these GCs using the software package GWToolbox. We did this in the context of a model of the LISA-detectable binaries in the MW from the population synthesis code SeBa. Results: We find that for five of the GCs in our sample, binaries in the GC could be easily distinguished from MW disc binaries using the sky location alone; for another five, binaries in the GCs could be distinguished using a combination of LISA's sky location and distance measurements; and for the final ten, binaries in the GCs could not be distinguished from overlapping MW disc binaries. The results depend strongly on the sky locations of the GCs, with GCs far away from the Galactic plane being easy to resolve, while GCs close to the Galactic centre overlap with many MW disc binaries. The most promising GC for finding a WD binary that could be resolved to that GC, based on sky location and GC mass, is 47 Tucanae.

Figures (6)

• Figure 1: Illustrations of the relationship between the properties of a binary and its LISA measurement uncertainties, for three different test sources in two different GCs. The first panel shows how a binary's S/N varies with its frequency. The second shows how sky location error varies with S/N, and the third how relative distance error varies with S/N.
• Figure 2: Sky locations of the 20 GCs in our sample. The GCs are coloured based on the number of overlapping DWDs from the MW disc. The blue line marks the Galactic plane.
• Figure 3: 10 grid plots for GCs with <500 overlapping sources. The red dot marks the location of the GC, and the red ellipses are the 1$\sigma$ error ellipses for test binaries in the GC with S/N=10,20,40. The black ellipses are 1$\sigma$ for MW disc binaries, and the grey ellipses are 2$\sigma$. The 2$\sigma$ ellipses are omitted for M14 (panel 7) to reduce clutter. The background colours indicate the expected number of MW disc binaries in each cell based on their sky location uncertainty distributions.
• Figure 4: 10 grid plots for GCs with >500 overlapping sources. Details are as for Fig. \ref{['plot_10deg_low']}, except the error ellipses of MW disc binaries are omitted to reduce clutter.
• Figure 5: Comparison of distance error distributions between test binaries within a GC and the overlapping MW disc DWDs, for each of the 20 GCs in our sample. The blue lines are the weighted sums of the distance distributions of the overlapping MW DWDs for each GC. The other coloured lines add to this distribution a test binary at the distance of the GC with a certain S/N. The dashed black lines mark the distance of each GC.