Constraining the Black Hole Mass Spectrum with Gravitational Wave Observations I: The Error Kernel

TL;DR

This paper introduces an 'error kernel' method to incorporate gravitational wave measurement uncertainties into population models, enabling better discrimination of supermassive black hole formation scenarios with LISA data.

Contribution

The paper presents a novel error kernel approach to account for measurement errors in gravitational wave data analysis of black hole populations.

Findings

The error kernel effectively integrates LISA measurement uncertainties into population models.

Applying the method to various models shows LISA's potential to distinguish black hole formation scenarios.

Tentative conclusions suggest LISA can test SMBH origin hypotheses despite measurement errors.

Abstract

Many scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many of these formation scenarios predict a high-redshift population of intermediate-mass black holes (IMBHs), with masses in the range 100 to 100000 times that of the Sun. A powerful way to observe these IMBHs is via gravitational waves the black holes emit as they merge. The statistics of the observed black hole population should, in principle, allow us to discriminate between competing astrophysical scenarios for the origin and formation of SMBHs. However, gravitational wave detectors such as LISA will not be able to detect all such mergers nor assign precise black hole parameters to the merger, due to weak gravitational wave signal strengths. In order to use LISA observations to infer the statistics of the underlying population, these errors must be taken into account. We describe here a method for folding the LISA gravitational wave parameter error estimates into an `error kernel' designed for use at the population model level. The effects of this error function are demonstrated by applying it to several recent models of black hole mergers, and some tentative conclusions are made about LISA's ability to test scenarios of the origin and formation of supermassive black holes.