[Paper Review] Discriminating between different scenarios for the formation and evolution of massive black holes with LISA

Alexandre Toubiana, Kaze W. K. Wong+6 more|arXiv (Cornell University)|Jan 1, 2021

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy116 references18 citations

TL;DR

This paper proposes a hierarchical Bayesian inference pipeline to distinguish between competing formation scenarios of massive black holes (MBHs) using LISA gravitational wave observations. By simulating LISA data with mixed populations from light-seed and heavy-seed MBH models, the method accurately infers the mixing fraction between scenarios, demonstrating robustness against instrumental and weak lensing errors, thus enabling LISA to constrain MBH seeding mechanisms.

ABSTRACT

Electromagnetic observations have provided strong evidence for the existence of massive black holes in the center of galaxies, but their origin is still poorly known. Different scenarios for the formation and evolution of massive black holes lead to different predictions for their properties and merger rates. LISA observations of coalescing massive black hole binaries could be used to reverse engineer the problem and shed light on these mechanisms. In this paper, we introduce a pipeline based on hierarchical Bayesian inference to infer the mixing fraction between different theoretical models by comparing them to LISA observations of massive black hole mergers. By testing this pipeline against simulated LISA data, we show that it allows us to accurately infer the properties of the massive black hole population as long as our theoretical models provide a reliable description of the Universe. We also show that measurement errors, including both instrumental noise and weak lensing errors, have little impact on the inference.

Motivation & Objective

• To develop a method for discriminating between competing astrophysical scenarios for massive black hole (MBH) formation using LISA observations.
• To quantify how well LISA can infer the relative contribution of different MBH seeding models (light-seed vs. heavy-seed) in a mixed population.
• To assess the robustness of the inference pipeline against measurement errors from instrumental noise and weak gravitational lensing.
• To demonstrate that LISA can reverse-engineer MBH formation mechanisms by analyzing the population-level properties of coalescing MBHBs.
• To validate the method using realistic LISA data simulations based on updated semianalytic galaxy and MBH evolution models.

Proposed method

• The study employs a hierarchical Bayesian framework to infer the mixing fraction between light-seed (LS) and heavy-seed (HS) MBH formation models as a hyperparameter.
• Simulated LISA data is generated using the semianalytic model of Barausse et al. (2012), incorporating updated treatments of baryonic physics, MBH pair formation, and hardening processes.
• The pipeline uses the phenomenological waveform approximant PhenomHM to model LISA signals, including higher harmonics and spin effects.
• Parameter estimation is performed via the Fisher information matrix in the zero-noise approximation to compute realistic error estimates for intrinsic parameters and luminosity distance.
• Instrumental noise is modeled using the SciRDv1 noise curve, including confusion noise from Galactic binaries and a low-frequency cutoff at 10−5 Hz.
• The robustness of the inference is tested by generating simulated data from different astrophysical models and assessing error impacts from detector noise and weak lensing.

Experimental results

Research questions

• RQ1 Can LISA observations distinguish between light-seed and heavy-seed scenarios for massive black hole formation based on population-level gravitational wave data?
• RQ2 How accurately can the mixing fraction between different MBH formation models be inferred using hierarchical Bayesian inference?
• RQ3 To what extent do instrumental noise and weak lensing errors degrade the ability to discriminate between competing MBH formation scenarios?
• RQ4 Does the inference pipeline remain robust when the true population deviates from the assumed model, particularly in the presence of measurement uncertainties?
• RQ5 Can LISA observations reverse-engineer the underlying astrophysical mechanisms shaping the MBH population, such as seeding mass and hardening efficiency?

Key findings

• The hierarchical Bayesian pipeline successfully infers the mixing fraction between light-seed and heavy-seed MBH formation models with high accuracy when the theoretical models correctly describe the true population.
• The method remains robust against measurement errors from both instrumental noise and weak gravitational lensing, which have minimal impact on the inference of the mixing fraction.
• LISA is capable of distinguishing between different MBH formation scenarios based on the population-level distribution of masses, spins, and redshifts of coalescing binaries.
• The simulation results show that even with realistic LISA data characteristics, including confusion noise and a 4–10 year mission duration, the inference remains reliable.
• The study confirms that LISA observations can provide strong constraints on the physics of MBH seeding and the last parsec problem by analyzing the statistical properties of the MBHB population.
• The pipeline demonstrates that population inference via hierarchical Bayesian methods is a viable path to reverse-engineer the formation history of massive black holes from gravitational wave data.