Large scale structure prior knowledge in the dark siren method

TL;DR

The paper tackles the redshift inference problem for gravitational-wave dark sirens under galaxy catalog incompleteness by introducing variance completion, a large-scale-structure–aware galaxy-filling method. It casts the out-of-catalogue contribution as a ratio function $R(z,\hat n)$ that multiplies the homogeneous completion and embeds this into the gwcosmo LOS prior, enabling straightforward usage with existing pipelines. The authors implement this on the GLADE+ catalog, validate it with GW190814, and apply it to LVK O3 data, finding results broadly consistent with homogeneous completion while highlighting potential gains for well-localized events. They discuss limitations—such as voxel resolution and power-spectrum modeling—and outline future benefits as galaxy surveys improve, making variance completion a practical tool for tightening $H_0$ measurements from dark sirens. Overall, the method enhances the dark siren framework by integrating large scale structure information, with clear applicability to upcoming GW and galaxy surveys.

Abstract

Gravitational wave dark sirens are a powerful tool for cosmology and inference of compact object population hyperparameters. They allow for a measurement of the luminosity distance to the source, but not their redshift. Galaxy catalogues in the source localization volume can be used to infer the redshift of the source in a statistical manner. Catalogues are, however, limited by their incompleteness, which can be significant at redshifts corresponding to current GW events. In this work, we detail how to implement in practice variance completion, a novel galaxy completion method which uses knowledge of the large scale structure to optimize the potential of dark sirens analyses. We compress the prediction for the missing number of galaxies into a ratio between the predictions of variance completion and the standard homogeneous completion method. This ratio format can be easily incorporated into existing line of sight computations used in dark sirens software; we demonstrate this procedure using the GLADE+ galaxy catalogue and the gwcosmo software package. We discuss the robustness of the method, and apply it to well-localized event GW190814 as a proof of concept. Finally, we apply the method to data from the third observing run of LIGO-Virgo-KAGRA, finding that it yields results that are consistent with homogeneous completion. We also discuss the prospects for an improvement if the GW localization volume shrinks.

Figures (12)

• Figure 1: We sketch the contribution of 1 galaxy to a voxel. A galaxy can contribute a fraction of itself to several voxels. This is typically the case for photometric redshift bins, while spectroscopic redshift contribute in general to only 1 voxel.
• Figure 2: Here, we show the magnitude threshold map $m_{\rm th}(\boldsymbol{\hat{n}})$ in the K-band for the GLADE+ galaxy catalogue for $n_{\rm side} = 32$, from which we can compute the completeness fraction in each voxel. Pixels for which $m_{\rm th}(\boldsymbol{\hat{n}})<13$ are plotted with the same color as $m_{\rm th}(\boldsymbol{\hat{n}}) = 13$. The minimum magnitude threshold determined is $10.378$, while pixels left blank have $m_{\rm th} = -\infty$. The higher the magnitude threshold, the better we estimate a pixel to have been observed.
• Figure 3: Here, we show a map of the 12 classes of pixels with similar estimated completeness fractions $\hat{f}_\mathcal{S}$. This map is found by ranking pixels according to their magnitude threshold, which is presented in Fig. \ref{['fig:mth_map']}.
• Figure 4: We plot 3 lines of sight at different levels of postprocessing. In black, we show the outcome of variance completion, after filling the gaps and removing values which are below the threshold of $\bar{n}_{\rm m}/10$. This explains why the average over the region $\mathcal{S}$ (thick black) differs from $1$. In blue, we show the same curves after Savitzky-Golay filtering. In red, we show the same curves after renormalizing them such that the average of $R(z)$ over the 1024 lines of sight of this region average to 1 at each redshift $z$. The thick curves show the average over the region $\mathcal{S}$ at each stage of postprocessing.
• Figure 5: We plot 200 ratio functions $R(z,\boldsymbol{\hat{n}})$ for 200 lines of sight in a same region $\mathcal{S}$. Some lines of sights have less galaxies over the relevant redshift range, implying that variance completion sets them to a value $R<1$. However, they are expected to be as complete as other lines of sight, based on their magnitude threshold, which is probably dominated by galaxies seen at lower or (higher) redshift. The peaks at $R(z)\sim 2$ denote that these lines of sight are likely to host an over-dense region such as a cluster or a filament at this redshift. This class of lines of sight has a maximum redshift $z_{\rm max}(\boldsymbol{\hat{n}})=0.105$, where the completeness in the B-band drops below $10\%$.