Data-Driven Trends and Subpopulations in the Gravitational Wave Binary Black Hole Merger Population with UMAP

Abstract

The rapidly expanding Gravitational-Wave Transient Catalog (GWTC) necessitates the development of model-independent techniques to uncover trends and subpopulations within the binary black hole (BBH) population. We present the first usage of the Uniform Manifold Approximation and Projection (UMAP) algorithm, a novel dimensionality-reduction technique, for the purpose of analyzing BBH mergers in GWTC-3. We show that UMAP, paired with a clustering algorithm, effectively partitions the population into four well-segregated subgroups principally via their primary and secondary mass components along with an outlier event, GW$190521\_030229$. UMAP clearly identifies objects in the ${\sim}10~M_\odot$ buildup in the BBH mass spectrum as their own group with aligned spins and mass ratios of ${\sim}0.2{-}0.7$ while objects in or above the ${\sim}35~M_\odot$ overdensity are all in the same, largest group and display typically lower effective spins as well as larger mass ratios (${\sim}0.5{-}0.9$) on average. With the aid of hierarchical population inference, we interpret these as subpopulations from different formation pathways, consistent with previous findings. We also find a transitional group of a handful of objects with masses in between the aforementioned buildups and broad support for anti-aligned spins. We examine the low-mass UMAP subgroup, which exhibits anti-correlation between the mass ratio and effective spin, and show that it drives such anti-correlation for the entire GWTC-3 sample. Overall, we demonstrate that UMAP is an interpretable, non-parametric framework that can not only be used for visualization but also for probing the astrophysics of the BBH population.

Figures (13)

• Figure 1: Two-dimensional output space of our fiducial UMAP analysis of GWTC-3 binary black holes. The axes, labeled UMAP$\mathrm{_1}$ and UMAP$\mathrm{_2}$, carry no intrinsic meaning such that relative spacing between points is arbitrary. The fives groups are delineated via a combination of the HDBSCAN clustering algorithm and visual group boundary determination. The median $m_1$ posterior sample for events GW$190521\_030229$ ('+'), GW$190412\_053044$ ('X'), and GW$150914\_095045$ ('$\bigtriangleup$') are also indicated. Lastly, we demarcate the median $m_1$ posterior sample of events that contribute to the ${\sim}70~M_{\odot}$ peak with gray diamonds.
• Figure 2: Two-dimensional output space of our fiducial UMAP analysis for GWTC-3 binary black holes, color-coded by the sample's $m_1$ (top left), $m_2$ (top center), $M_\mathrm{chirp}$ (top right), $\chi_{\rm eff}$ (bottom left), $z$ (bottom center), and $q$ (bottom right) value. One can discern increasing and decreasing evolution in these parameters within individual groups.
• Figure 3: UMAP output space where each panel displays results from a different set of GW parameter inputs into the UMAP algorithm: $M_{\mathrm{chirp}}$ and $\chi_{\rm eff}$ (left), $M_{\mathrm{chirp}}$ and $q$ (center), $M_{\mathrm{chirp}}$ and $z$ (right). For comparison to Figure \ref{['fig:main']}, we color each sample by its group designation in our fiducial output space. Most of the fiducial differentiation between samples still appears when only $M_{\mathrm{chirp}}$ and $\chi_{\rm eff}$ are used as inputs.
• Figure 4: The left (right) panel shows the output space for the Simulation I (II) event samples with each sample colored by its group designation. The black squares represent the true injected parameter values for each event classified in the output space by the embedding produced from the samples. Black squares with yellow fill color indicate injections with $m_1 > 40 M_{\odot}$. The yellow polygons in each panel roughly enclose a region that only contains samples from $m_1 > 40 M_{\odot}$. Both simulations follow a PowerLaw+Peak black hole mass population model, but the main difference between the two is that Simulation II assumes an intrinsic correlation between mass ratio and effective spin. Appendix \ref{['appendix:figures']}, Figure \ref{['fig:sims_35Msol']} displays the clustering of samples near the ${\sim}35~M_\odot$ in the UMAP simulations space.
• Figure 5: The left (right) panels show the output space for the Simulation I (II) injections with each event colored by its mass ratio (top panels) or effective spin (bottom panels). The gray points represent the UMAP output space of all of the posterior samples of the injected events. Simulation II assumes an intrinsic anti-correlation between mass ratio and effective spin, which is also visually clear in the output space when comparing the top and bottom right panels.