Fisher vs. Bayes : A comparison of parameter estimation techniques for massive black hole binaries to high redshifts with eLISA

Abstract

Massive black hole binaries are the primary source of gravitational waves (GW) for the future eLISA observatory. The detection and parameter estimation of these sources to high redshift would provide invaluable information on the formation mechanisms of seed black holes, and on the evolution of massive black holes and their host galaxies through cosmic time. The Fisher information matrix has been the standard tool for GW parameter estimation in the last two decades. However, recent studies have questioned the validity of using the Fisher matrix approach. For example, the Fisher matrix approach sometimes predicts errors of $\ge 100\%$ in the estimation of parameters such as the luminosity distance and sky position. With advances in computing power, Bayesian inference is beginning to replace the Fisher matrix approximation in parameter estimation studies. In this work, we conduct a Bayesian inference analysis for 120 sources situated at redshifts of between $0.1\le z\le 13.2$, and compare the results with those from a Fisher matrix analysis. The Fisher matrix results suggest that for this particular selection of sources, eLISA would be unable to localize sources at redshifts of $z\lesssim 6$. In contrast, Bayesian inference provides finite error estimations for all sources in the study, and shows that we can establish minimum closest distances for all sources. The study further predicts that we should be capable with eLISA, out to a redshift of at least $z\le 13$, of predicting a maximum error in the chirp mass of $\lesssim 1\%$, the reduced mass of $\lesssim 20\%$, the time to coalescence of 2 hours, and to a redshift of $z\sim 5$, the inclination of the source with a maximum error of $\sim 60$ degrees.

15 pages

References in corpus (26)

• A luminous quasar at a redshift of z = 7.085
• Formation of Supermassive Black Holes by Direct Collapse in Pregalactic Halos
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Supermassive black hole formation during the assembly of pre-galactic discs
• A Compact Supermassive Binary Black Hole System
• A massive binary black-hole system in OJ287 and a test of general relativity
• Formation of the first nuclear clusters and massive black holes at high redshift
• Supermassive black hole binaries in gaseous and stellar circumnuclear discs: orbital dynamics and gas accretion
• Reconstructing the massive black hole cosmic history through gravitational waves
• Self consistent model for the evolution of eccentric massive black hole binaries in stellar environments: implications for gravitational wave observations
• Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy
• Constraining the high redshift formation of black hole seeds in nuclear star clusters with gas inflows
• A milliparsec supermassive black hole binary candidate in the galaxy SDSS J120136.02+300305.5
• A Bayesian Approach to the Detection Problem in Gravitational Wave Astronomy
• LISA observations of supermassive black holes: parameter estimation using full post-Newtonian inspiral waveforms
• The Effect of Higher Harmonic Corrections on the Detection of massive black hole binaries with LISA
• A Bayesian approach to the follow-up of candidate gravitational wave signals
• MCMC Exploration of Supermassive Black Hole Binary Inspirals
• Catching Super Massive Black Hole Binaries Without a Net
• Constraining properties of the black hole population using LISA
• Supermassive Black Hole Binaries: The Search Continues
• Inference on inspiral signals using LISA MLDC data
• Inference on white dwarf binary systems using the first round Mock LISA Data Challenges data sets
• Automatic Bayesian inference for LISA data analysis strategies
• Supermassive Black Hole Tests of General Relativity with eLISA
• Markov chain Monte Carlo searches for Galactic binaries in Mock LISA Data Challenge 1B data sets

Cited by in corpus (2)

• Preliminary study on parameter estimation accuracy of supermassive black hole binary inspirals for TianQin
• GPU-accelerated massive black hole binary parameter estimation with LISA