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

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.

22 pages, 4 figures. There have been various clarifications, typos corrected, and so on, partly in response to referee comments. This second arXiv version has been switched to AASTeX preprint format for better compatibility with the arXiv. Accepted for publication in MNRAS

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• Probing Massive Black Hole Binary Populations with LISA
• Systematic biases in parameter estimation of binary black-hole mergers
• Constraining properties of the black hole population using LISA
• Characterizing Spinning Black Hole Binaries in Eccentric Orbits with LISA
• Cosmological simulations of massive black hole seeds: predictions for next generation electromagnetic and gravitational wave observations
• Constraining the Black Hole Mass Spectrum with LISA Observations II: Direct comparison of detailed models
• Gravitational Waves from Direct Collapse Black Holes Formation
• Orbital effects of a monochromatic plane gravitational wave with ultra-low frequency incident on a gravitationally bound two-body system