Black hole mass function and its evolution -- the first prediction for the Einstein Telescope

Abstract

The knowledge about the black hole mass function (BHMF) and its evolution would help to understand the origin of the BHs and how BH binaries formed at different stages of the history of the Universe. We demonstrate the ability of future third generation gravitational wave (GW) detector -- the Einstein Telescope (ET) to infer the slope of the BHMF and its evolution with redshift. We perform the Monte Carlo simulation of the measurements of chirp signals from binary BH systems (BBH) that could be detected by ET, including the BH masses and their luminosity distances ($d_L$). We use the mass of a primary black hole in each binary system to infer the BHMF as a power-law function with slope parameter as $\alpha$. Taking into account the bias that could be introduced by the uncertainty of measurements and by the selection effect, we carried out the numerical tests and find that only one thousand of GW events registered by ET ($\sim 1\%$ amount of its yearly detection rate) could accurately infer the $\alpha$ with a precision of $\alpha \sim 0.1$. Furthermore, we investigate the validity of our method to recover a scenario where $\alpha$ evolves with redshift as $\alpha (z)={\alpha }_0+{\alpha }_1\frac{z}{1+z}$. Taking a thousand of GW events and using $d_L$ as the redshift estimator, our tests show that one could infer the value of evolving parameter ${\alpha }_1$ accurately with the uncertainty level of $\sim 0.5$. Our numerical tests verify the reliability of our method. The uncertainty levels of the inferred parameters can be trusted directly for the several sets of the parameter we assumed, yet shouldn't be treated as a universal level for the general case.

arXiv comment9 pages, 4 figures, 1 table; Accepted by ApJ

References in corpus (28)

• Observation of Gravitational Waves from a Binary Black Hole Merger
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• Binary Black Hole Mergers in the first Advanced LIGO Observing Run
• Binary Black Hole Population Properties Inferred from the First and Second Observing Runs of Advanced LIGO and Advanced Virgo
• Observing binary inspiral in gravitational radiation: One interferometer
• Pulsational Pair-Instability Supernovae
• Black hole mergers in the universe
• A new route towards merging massive black holes
• Mass Limits For Black Hole Formation
• Theoretical Black Hole Mass Distributions
• Double Compact Objects II: Cosmological Merger Rates
• The chemically homogeneous evolutionary channel for binary black hole mergers: rates and properties of gravitational-wave events detectable by advanced LIGO
• Evolution of Binary Compact Objects Which Merge
• Does the Black Hole Merger Rate Evolve with Redshift?
• Cosmology with the lights off: Standard sirens in the Einstein Telescope era
• Estimating cosmological parameters by the simulated data of gravitational waves from the Einstein Telescope
• Speed of Gravitational Waves from Strongly Lensed Gravitational Waves and Electromagnetic Signals
• The Black Hole Mass Function from Gravitational Wave Measurements
• Testing the speed of gravitational waves over cosmological distances with strong gravitational lensing
• The basic physics of the binary black hole merger GW150914
• Strong gravitational lensing of gravitational waves from double compact binaries - perspectives for the Einstein Telescope
• Populations of stellar mass Black holes from binary systems
• Strongly lensed gravitational waves from intrinsically faint double compact binaries - prediction for the Einstein Telescope
• Strong gravitational lensing of gravitational waves in Einstein Telescope
• The Formation of Stellar Black Holes
• Cosmological inference from standard sirens without redshift measurements
• Estimating parameters of binary black holes from gravitational-wave observations of their inspiral, merger and ringdown
• How does the Earth's rotation affect predictions of gravitational wave strong lensing rates?

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• A flexible Gaussian process reconstruction method and the mass function of the coalescing binary black hole systems
• The Black Hole Mass Function Across Cosmic Times I. Stellar Black Holes and Light Seed Distribution
• Impact of gravitational lensing on black hole mass function inference with third-generation gravitational wave detectors