Striking a Chord with Spectral Sirens: multiple features in the compact binary population correlate with $H_0$

TL;DR

This work investigates spectral-siren cosmology by exploiting features in the source-frame mass distribution of compact-binary coalescences observed by LVK during O3. It builds a hierarchical population model with flexible mass distributions (PDB, PDB$\times$P, DoubleDip, MultiPDB) and performs joint inference of $H_0$ and the mass-population hyper-parameters under flat $\Lambda$CDM, transforming to detector-frame quantities to incorporate cosmology. The analysis identifies robust features near $9\,M_\odot$ and $32\,M_\odot$, plus a high-mass roll-off around $46\,M_\odot$, and shows the $\sim 32\,M_\odot$ peak correlates most strongly with $H_0$; it also introduces model-independent summary statistics that capture the mass distribution’s shape and reveal that multiple features contribute independently to constraining $H_0$. These results suggest spectral-siren measurements can robustly constrain the Hubble constant, even in the presence of evolving stellar-physics, by leveraging multiple independent features in the mass spectrum.

Abstract

Spectral siren measurements of the Hubble constant ($H_0$) rely on correlations between observed detector-frame masses and luminosity distances. Features in the source-frame mass distribution can induce these correlations. It is crucial, then, to understand (i) which features in the source-frame mass distribution are robust against model (re)parametrization, (ii) which features carry the most information about $H_0$, and (iii) whether distinct features independently correlate with cosmological parameters. We study these questions using real gravitational-wave observations from the LIGO-Virgo-KAGRA Collaborations' third observing run. Although constraints on $H_0$ are weak, we find that current data reveals several prominent features in the mass distribution, including peaks in the binary black hole source-frame mass distribution near $\sim$ 9 $\rm{M}_{\odot}$ and $\sim$ 32$\rm{M}_{\odot}$ and a roll-off at masses above $\sim$ 46$\rm{M}_{\odot}$. For the first time using real data, we show that all of these features carry cosmological information and that the peak near $\sim$ 32$\rm{M}_{\odot}$ consistently correlates with $H_0$ most strongly. Introducing model-independent summary statistics, we show that these statistics independently correlate with $H_0$, exactly what is required to limit systematics within future spectral siren measurements from the (expected) astrophysical evolution of the mass distribution.

Figures (7)

• Figure 1: (left) Schematic representation of $p_{1D}(m|\Lambda)$ (Eq. \ref{['eq:1d-mass']}) and associated hyper-parameters. The model (green solid) is based on a broken power law (black dotted) with roll-offs at both high- ($m_\mathrm{max}$) and low-masses ($m_\mathrm{min}$). Additional Butterworth notch filters (purple) and Gaussian peaks (orange) are included as multiplicative factors. See Appendix \ref{['sec:pop_models']} for details. (right) The associated joint distribution $p(m_{1s}, m_{2s}|\Lambda)$ (Eq. \ref{['eq:joint mass']}). Note that features in $p_{1D}$ appear in both $m_{1s}$ and $m_{2s}$farah2023kindcomparingbigsmall.
• Figure 2: (left) Posterior medians and 90% symmetric credible regions for $p_{1D}(m_s|\Lambda)$ as a function of mass conditioned on the O3 catalog for (top to bottom) PDB (Sec. \ref{['sec:pdb']}), PDB$\times$P (Sec. \ref{['sec:pdbp']}), DoubleDip and MultiPDB (Sec. \ref{['sec:multiple peaks']}). In general, $p_{1D}$ decreases as a function of mass, but models that allow for additional flexibility often find evidence for peaks at $\sim$ 9$\rm M_{\odot}$ and $\sim$ 32$\rm M_{\odot}$. (right) Corresponding posterior distributions (linear scale) for the Hubble parameter ($H_0$) along with 2-$\sigma$ error bars from the finite number of samples used. Median values and 90% symmetric credible regions are shown in each panel. We also show the 1- and 2-$\sigma$ constraints from the Planck and SH0ES collaborations as vertical bars planck2018Riess_2022. Although mostly uninformative, the data primarily disfavors large values of $H_0$. See Table \ref{['tab:prior']} for priors.
• Figure 3: (left) Joint and marginal posterior distributions for $\mu^{\mathrm{peak}}_2$ and $H_0$ conditioned on the presence of wide (green, $\sigma^{\mathrm{peak}}_2 \geq$$8$$\,\rm M_\odot$) and narrow (blue, $\sigma^{\mathrm{peak}}_2 \leq$$8$$\,\rm M_\odot$) peaks with MultiPDB. Contours in the joint distributions show the 50% and 90% highest-probability-density credible regions. Median and 90% symmetric credible regions are shown in the marginal distributions, and the Pearson correlation coefficients ($r$) are shown in the joint distribution. (right) Analogous model-independent summary statistics derived from $p_{1D}$ ($\hat{\mu}^{25:40}_2$ and $\hat{\sigma}^{25:40}_2$) for MultiPDB. We apply different thresholds on $\sigma^{\mathrm{peak}}_2$ and $\hat{\sigma}^{25:40}_2$ based on their one-dimensional posterior medians.
• Figure 4: Joint posterior distributions for $H_0$ and $m_{\mathrm{max}}$, $m_{99}$ obtained with PDB. Contours denote the 50% and 90% highest-probability-density credible regions. Both mass scales trace the location of the roll-off at high masses. Even for models without prominent peaks, cosmological information is still encoded in the mass distribution.
• Figure 5: Joint posteriors between $H_0$ and $\hat{\mu}^{7:11}_1$ (purple), $\hat{\mu}^{25:40}_2$ (green). Contours denote the 50% and 90% highest-probability density credible regions. The estimator functions defined in Eq. \ref{['eq:nonparam_estimators']} are applied to MultiPDB. They correlate similarly for both local overdense regions.