Research Byte - By Liana Rauf
Published in the RSAA Lunations
Vol1 Issue60 1–31 March 2025
The detection of the binary neutron star (BNS) merger GW170817 set in motion an age of multi-messenger gravitational wave astronomy. Following a multi-band campaign with ground and space-based telescopes, a kilonova electromagnetic counterpart was identified. The counterpart, now known as AT 2017gfo, was confidently associated with the host galaxy NGC4993. The host’s cosmological redshift, combined with the direct measurement of the luminosity distance from the BNS, provided a measurement of the expansion of the Universe, known as the Hubble constant (H0). This approach, referred to as the bright standard siren technique, provided a promising avenue for independent and systematic free measurement of H0. With the exception of GW170817, there have been an overwhelmingly large number of GW events without EM counterparts - 85 confirmed GW events from binary black hole (BBH) mergers. Instead, a wide range of statistical analyses have been performed for cosmological inference. Galaxy catalogues have been utilised to obtain the redshift information of the GW source. Combined with the sky localisation volume and luminosity distance, a list of possible host galaxies can be identified in the catalogue. Due to the lack of EM counterparts, this method is often referred to as the dark siren technique, originally presented by Bernard Schutz in 1986.
There are two main challenges with this method. Firstly, galaxy catalogues are magnitude limited and become more incomplete with redshift. The dark siren technique relies on the completeness of galaxy catalogues being well modelled. For an incomplete galaxy catalogue, assumptions need to be made for the prior on the background galaxy distribution. For accurate predictions of cosmology, deeper
and more expansive surveys are required to target host galaxies of GW events. Secondly, the catalogue footprint may only cover a small fraction of the large localisation volumes for most dark sirens. These poor localisations will contain thousands of potential hosts, which would significantly reduce the contribution from the correct host galaxy. This would decrease the ability to constrain cosmological parameters. Other complications can also arise due to systematic errors and modelling assumptions, which can bias the H0 inference:
- Uncertainties in the luminosity distance due to instrument calibration when converting the GW signal to data.
- The measured redshift error can vary depending on whether the redshifts of galaxies are obtained photometrically
or spectroscopically. - Assumptions are needed for the prior knowledge on the distribution of dark sirens as a function of redshift.
This highlights the need for novel approaches to constrain H0. Utilising outputs from simulations and mock catalogues may hold the key to robust testing of the impact of systematics in the dark siren technique and shed light on what aspects of the technique need improving.
In the paper, Exploring binary black hole mergers and host galaxies with Shark and COMPAS, we study the correlation between the intrinsic host galaxy properties and the BBH merger rate (number of GW events from BBH mergers per year) by populating host galaxies from Shark with binary systems from COMPAS. We find that the merger rate is strongly correlated with the stellar mass. This result can be implemented in the dark siren technique as an astrophysically motivated and informative prior on the host galaxies more likely to host GW events. We further
investigate the impact of the photometry on the completeness of the BBH merger rate in future galaxy surveys (see Figure 1). This information is ideal for designing galaxy surveys specific to GW follow-up. We also found that the merger rate would vary orders of magnitude depending on the our population modelling assumptions. In the paper, A trifecta of modelling tools: a Bayesian binary black hole model selection combining population synthesis and galaxy formation models, we extend our analysis to compare the population parameters of our COMPAS models against current GW observation source parameters, and determine the models that best describe the formation of the BBH sources we are currently observing. This not only enables us to constrain the uncertainty in the modelling of BBHs, but also allows for more accurate predictions for the BBH merger distribution, which can
be implemented in the dark siren technique.
I aim to use these outputs as prior knowledge for modelling the distribution of GW events and galaxies in the dark siren technique, and determine what is the best weighting scheme to constrain H0 and other cosmological parameters. The next generation of ground- and space-based detectors, combined with deeper galaxy surveys, will reduce current systematics and enable accurate and precise measurements of cosmological parameters. For now, we must leverage the power of simulations to improve the current modelling implemented in the dark siren technique.
Liana Rauf
Figure 1: Volumetric rate (merger rate per unit volume) of GWs emitted
from galaxies observed by different surveys, as a function of distance. The
lines show the average volumetric rate, while the shaded regions are the range
from bootstrapping the galaxy sample. The right plots show the effective
completeness, which is the fraction of GW host galaxy mergers observed by
each survey, relative to the total number of expected mergers in the Shark
simulation volume. Credit: Exploring binary black hole mergers and host
galaxies with Shark and COMPAS
