A numerical-relativity surrogate model for hyperbolic encounters of black holes: challenges in parameter estimation

TL;DR

This paper introduces a surrogate model for hyperbolic black hole encounters that is highly accurate but highlights the challenges in parameter estimation due to degeneracies, requiring very loud signals for precise inference.

Contribution

We developed a new surrogate numerical-relativity model for hyperbolic black hole encounters, covering specific impact parameters and spins, with high fidelity to simulations.

Findings

Model achieves mismatches below 10^{-3} with numerical relativity.

Parameter estimation is hindered by degeneracies, even at high SNRs.

Certain parameter combinations may still be detectable with current detectors.

Abstract

We present a surrogate numerical-relativity model for close hyperbolic black-hole encounters with equal masses and spins aligned with the orbital momentum. Our model, generated in terms of the Newman-Penrose scalar $\psi_4$, spans impact parameters $b/M\in [11, 15]$ and spin components $\chi_{i} \in [-0.5,0.5]$, modeling the $(\ell,m)=(2,0)$, $(2, \pm 2)$, $(3,\pm 2)$ and $(4,\pm 4)$ emission multipoles. The model is faithful to numerical relativity simulations, yielding mismatches lower than $10^{-3}$. We test the ability of our model to recover the parameters of numerically simulated signals. We find that, despite the high accuracy of the model, parameter inference struggles to correctly capture the parameters of the source even for SNRs as large as 50 due to the strong degeneracies present in the parameter space. This indicates that correctly identifying these systems will require of extremely large signal loudness, only typical of third generation detectors. Nevertheless, we also find that, if one attempts to infer certain combinations of such degenerated parameters, there might be a chance to prove the existence of this type of events, even with the current ground-based detectors, as long as these combinations make sense astrophysically and cosmologically.