Measuring the parameters of massive black hole binary systems with Pulsar Timing Array observations of gravitational waves

Abstract

The observation of massive black hole binaries (MBHBs) with Pulsar Timing Arrays (PTAs) is one of the goals of gravitational wave astronomy in the coming years. Massive (>10^8 solar masses) and low-redshift (< 1.5) sources are expected to be individually resolved by up-coming PTAs, and our ability to use them as astrophysical probes will depend on the accuracy with which their parameters can be measured. In this paper we estimate the precision of such measurements using the Fisher-information-matrix formalism. We restrict to "monochromatic" sources. In this approximation, the system is described by seven parameters and we determine their expected statistical errors as a function of the number of pulsars in the array, the array sky coverage, and the signal-to-noise ratio (SNR) of the signal. At fixed SNR, the gravitational wave astronomy capability of a PTA is achieved with ~20 pulsars; adding more pulsars (up to 1000) to the array reduces the source error-box in the sky ΔΩby a factor ~5 and has negligible consequences on the statistical errors on the other parameters. ΔΩimproves as 1/SNR^2 and the other parameters as 1/SNR. For a fiducial PTA of 100 pulsars uniformly distributed in the sky and a coherent SNR = 10, we find ΔΩ~40 deg^2, a fractional error on the signal amplitude of ~30% (which constraints only very poorly the chirp mass - luminosity distance combination M_c^{5/3}/D_L), and the source inclination and polarization angles are recovered at the ~0.3 rad level. The ongoing Parkes PTA is particularly sensitive to systems located in the southern hemisphere, where at SNR = 10 the source position can be determined with ΔΩ~10 deg^2, but has poorer performance for sources in the northern hemisphere. (Abridged)

20 pages, 12 figures, 2 color figures, submitted to Phys. Rev. D

References in corpus (35)

• The Assembly and Merging History of Supermassive Black Holes in Hierarchical Models of Galaxy Formation
• Coalescing binary systems of compact objects to (post)$^{5/2}-Newtonian order. V. Spin Effects
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Angular Resolution of the LISA Gravitational Wave Detector
• Gravitational-Radiation Damping of Compact Binary Systems to Second Post-Newtonian order
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
• Low-Frequency Gravitational Waves from Massive Black Hole Binaries: Predictions for LISA and Pulsar Timing Arrays
• The distribution and cosmic evolution of massive black hole spins
• Upper bounds on the low-frequency stochastic gravitational wave background from pulsar timing observations: current limits and future prospects
• Cosmological black hole spin evolution by mergers and accretion
• The Population of Viscosity- and Gravitational Wave-Driven Supermassive Black Hole Binaries Among Luminous AGN
• Low-frequency gravitational radiation from coalescing massive black hole binaries in hierarchical cosmologies
• Long Term Evolution of Massive Black Hole Binaries
• Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays
• Supermassive black hole binaries in gaseous and stellar circumnuclear discs: orbital dynamics and gas accretion
• Ultra-Low Frequency Gravitational Radiation from Massive Black Hole Binaries
• Detecting the stochastic gravitational wave background using pulsar timing
• An excess power statistic for detection of burst sources of gravitational radiation
• Timing stability of millisecond pulsars and prospects for gravitational-wave detection
• Black hole mass and spin coevolution by mergers
• LISA observations of rapidly spinning massive black hole binary systems
• The imprint of massive black hole formation models on the LISA data stream
• The gravitational wave signal from massive black hole binaries and its contribution to the LISA data stream
• Low-frequency gravitational waves from supermassive black holes
• Black Hole Growth in Hierarchical Galaxy Formation
• Models for jet power in elliptical galaxies: A case for rapidly spinning black holes
• Localizing coalescing massive black hole binaries with gravitational waves
• Bayesian Bounds on Parameter Estimation Accuracy for Compact Coalescing Binary Gravitational Wave Signals
• The Parkes Pulsar Timing Array
• Testing models of supermassive black hole seed formation through gravity waves
• Pre-Merger Localization of Gravitational-Wave Standard Sirens With LISA I: Harmonic Mode Decomposition
• Probing white dwarf interiors with LISA: periastron precession in double white dwarfs
• The Most Massive Black Holes in the Universe: Effects of Mergers in Massive Galaxy Clusters
• Estimation of parameters of gravitational waves from coalescing binaries

Cited by in corpus (86)

• Black holes, gravitational waves and fundamental physics: a roadmap
• The International Pulsar Timing Array: Second data release
• The Quest for Dual and Binary Supermassive Black Holes: A Multi-Messenger View
• Assessing the Role of Spin Noise in the Precision Timing of Millisecond Pulsars
• Expected properties of the first gravitational wave signal detected with pulsar timing arrays
• European Pulsar Timing Array Limits on Continuous Gravitational Waves from Individual Supermassive Black Hole Binaries
• The stochastic background: scaling laws and time to detection for pulsar timing arrays
• Gravitational wave astronomy of single sources with a pulsar timing array
• Gas driven massive black hole binaries: signatures in the nHz gravitational wave background
• Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays
• The NANOGrav 11-Year Data Set: Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
• Detection of gravitational waves from the QCD phase transition with pulsar timing arrays
• Self consistent model for the evolution of eccentric massive black hole binaries in stellar environments: implications for gravitational wave observations
• An all-sky search for continuous gravitational waves in the Parkes Pulsar Timing Array data set
• Multimessenger astronomy with pulsar timing and X-ray observations of massive black hole binaries
• Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays
• Observational Signatures of Binary Supermassive Black Holes
• New advances in the Gaussian-process approach to pulsar-timing data analysis
• Resolving multiple supermassive black hole binaries with pulsar timing arrays
• Optimal strategies for continuous gravitational wave detection in pulsar timing arrays
• Time-domain Implementation of the Optimal Cross-Correlation Statistic for Stochastic Gravitational-Wave Background Searches in Pulsar Timing Data
• From Bright Binaries To Bumpy Backgrounds: Mapping Realistic Gravitational Wave Skies With Pulsar-Timing Arrays
• Detection of eccentric supermassive black hole binaries with pulsar timing arrays: Signal-to-noise ratio calculations
• Electromagnetic counterparts of supermassive black hole binaries resolved by pulsar timing arrays
• Prompt Tidal Disruption of Stars as an Electromagnetic Signature of Supermassive Black Hole Coalescence
• Searching for continuous Gravitational Waves in the second data release of the International Pulsar Timing Array
• Limits on anisotropy in the nanohertz stochastic gravitational-wave background
• Detecting eccentric supermassive black hole binaries with pulsar timing arrays: Resolvable source strategies
• The NANOGrav 12.5-year data set: Search for Non-Einsteinian Polarization Modes in theGravitational-Wave Background
• Detection and localization of single-source gravitational waves with pulsar timing arrays
• A Bayesian analysis pipeline for continuous GW sources in the PTA band
• Electromagnetic Counterparts to Black Hole Mergers
• Gravitational wave emission from binary supermassive black holes
• Ripple effects & oscillations in the broad FeKa line as a probe of massive black hole mergers
• Multi-messenger Time-domain Signatures Of Supermassive Black Hole Binaries
• Pulsars as gravitational wave detectors
• Astrophysics of Super-massive Black Hole Mergers
• Observing the dynamics of super-massive black hole binaries with Pulsar Timing Arrays
• Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms
• Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays
• Resolving multiple supermassive black hole binaries with pulsar timing arrays II: genetic algorithm implementation
• The most powerful astrophysical events: Gravitational-wave peak luminosity of binary black holes as predicted by numerical relativity
• Practical Methods for Continuous Gravitational Wave Detection using Pulsar Timing Data
• The NANOGrav 12.5-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries
• A coherent method for the detection and estimation of continuous gravitational wave signals using a pulsar timing array
• Gravitational Wave Detection with Photometric Surveys
• Harmonic space analysis of pulsar timing array redshift maps
• The Nanohertz Gravitational Wave Astronomer
• Improving timing sensitivity in the microhertz frequency regime: limits from PSR J1713$+$0747 on gravitational waves produced by super-massive black-hole binaries
• Optimizing Pulsar Timing Arrays to Maximize Gravitational Wave Single Source Detection: a First Cut
• On the Amplitude and Stokes Parameters of a Stochastic Gravitational-Wave Background
• The Gravitational Wave Universe Toolbox: A software package to simulate observation of the Gravitational Wave Universe with different detectors
• Multi-messenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation: Implications for Nanohertz Gravitational Wave Searches with Pulsar Timing Arrays
• Imprints of Supermassive Black Hole Evolution on the Spectral and Spatial Anisotropy of Nano-Hertz Stochastic Gravitational-Wave Background
• Associating Host Galaxy Candidates to Massive Black Hole Binaries resolved by Pulsar Timing Arrays
• Electromagnetic signatures of supermassive black hole binaries resolved by PTAs
• Detectability of Gravitational Waves from High-Redshift Binaries
• Gravitational Wave Hotspots: Ranking Potential Locations of Single-Source Gravitational Wave Emission
• Pulsar timing arrays and the challenge of massive black hole binary astrophysics
• Neutron Star Physics in the Square Kilometer Array Era : An Indian Perspective
• Limits on the strength of individual gravitational wave sources using high-cadence observations of PSR B1937+21
• Blindly detecting orbital modulations of jets from merging supermassive black holes
• Gravitational Wave Timing Array
• Identifying Host Galaxies of Supermassive Black Hole Binaries Found by PTAs
• On using inspiralling supermassive binary black holes in the PTA frequency band as standard sirens to constrain dark energy
• Extending the frequency reach of pulsar timing array based gravitational wave search without high cadence observations
• Null stream analysis of Pulsar Timing Array data: localisation of resolvable gravitational wave sources
• Pulsar Timing Array Experiments
• Radio pulsars: testing gravity and detecting gravitational waves
• Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays
• Differential Interferometric Signatures of Close Binaries of Supermassive Black Holes in Active Galactic Nuclei
• Multimessenger Approaches to Supermassive Black Hole Binary Detection and Parameter Estimation II: Optimal Strategies for a Pulsar Timing Array
• Resolving the nano-Hz gravitational wave sky: the detectability of eccentric binaries with PTA experiments
• Signatures of Massive Black Hole Merger Host Galaxies from Cosmological Simulations I: Unique Galaxy Morphologies in Imaging
• Precision of localization of single gravitational-wave source with pulsar timing array
• Iterative time-domain method for resolving multiple gravitational wave sources in Pulsar Timing Array data
• Separating deterministic and stochastic gravitational wave signals in realistic pulsar timing array datasets
• Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms
• Sensitivity of new detection method for ultra-low frequency gravitational waves with pulsar spin-down rate statistics
• Host Galaxy Demographics Of Individually Detectable Supermassive Black-hole Binaries with Pulsar Timing Arrays
• Damping of long wavelength gravitational waves by the intergalactic medium
• Realistic assessment of a single gravitational wave source localization taking into account precise pulsar distances with pulsar timing arrays
• Gravitational wave science with laser interferometers and pulsar timing
• Binary black hole signatures in polarized light curves
• Solar-System Studies with Pulsar Timing Arrays
• Description and Application of the Surfing Effect