Regression on Regression: Mapping Data-Driven Binary Black Hole Merger Rate Fits to Progenitor Histories
Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；University of Toronto（多伦多大学）；David A. Dunlap Department of Astronomy and Astrophysics, University of Toronto（多伦多大学戴维·邓普天文学与天体物理学系）
Emma Blanchet, Aryanna Schiebelbein-Zwack, Maya Fishbach
The binary black hole (BBH) merger rate is governed by the progenitor formation rate and the distribution of delay-times between formation and merger, but these functions remain poorly constrained. We introduce a framework that maps the parameters of physics-driven models directly onto existing data-driven fits of the BBH merger rate. This ``regression on regression'' approach enables physical interpretation of flexible population models without the computational burden of reanalyzing the underlying gravitational-wave event data. Applying this method to the \textsc{B-Spline} merger-rate posteriors from the Fourth Gravitational-Wave Transient Catalog, we fit the minimum delay time ($τ_{\text{min}}$), delay-time power-law index ($α$), and progenitor formation parameters controlling the normalization ($\mathcal{A}$), early-time growth ($γ$), and late-time decay ($δ$). Increasing the number of anchoring redshift points from two to four reduces the median sum-squared error (SSE) by a factor of $\approx 4.5$. However, residuals reveal that the physical model does not pass through all four anchors, exposing model misspecification and demonstrating a key strength of the framework: unlike standard inference methods, which preferentially weight compatible curves and mask underlying tensions, our approach exposes BBH posteriors irreconcilable with the model. Despite uncertainties at $z\gtrsim1$, the shape of the progenitor formation rate at low-$z$ is robust and evolves more steeply than the global star formation rate (SFR), supporting a preference for low metallicity environments. Specifically, the log-space slope of the progenitor rate is $\approx 5.3$ times steeper than the SFR between $z=0.1$ and $z=1.0$. Ultimately, a more complex phenomenological model is required to match the \textsc{B-Spline} merger rates.
Double Neutron Star Delay Times Across Cosmic Metallicities: The Role of Helium Star Progenitors
University of Florida（佛罗里达大学）；Institute for Fundamental Theory（基础理论研究所）；Université de Genève（日内瓦大学）；Gravitational Wave Science Center (GWSC)（引力波科学中心）；Northwestern University（西北大学）；Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA)（天体物理学跨学科探索与研究中心）
