Using Gravitational Wave Parallax to Measure the Hubble Parameter with Pulsar Timing Arrays

Abstract

We demonstrate how pulsar timing arrays (PTAs) can, in principle, yield a purely gravitational wave (GW) measurement of the luminosity distance and comoving distance to a supermassive black hole binary source, hence providing an estimate of the source redshift and the Hubble constant. The luminosity distance is derived through standard measurement of the chirp mass, which for the slowly evolving binary sources in the PTA band can be found by comparing the frequency of GW-timing residuals at the Earth compared to those at distant pulsars in the array. The comoving distance can be measured from GW-timing parallax caused by the curvature of the GW wavefronts. This can be detected for single sources at the high-frequency end of the PTA band out to Gpc distances with a future PTA containing well-timed pulsars out to $\mathcal{O}(10)$ kpc, when the pulsar distance is constrained to less than a GW wavelength. Such a future PTA, with $\gtrsim 30$ pulsars with precise distance measurements between 1 and 20~kpc, could measure the Hubble constant at the tens of percent level for a single source at $0.1\lesssim z\lesssim 1.5$. At $z\lesssim 0.1$, the luminosity and comoving distances are too similar to disentangle, unless the fractional error in the luminosity distance measurement is decreased below 10%. At $z\gtrsim 1.5$, this measurement will likely be restricted by a signal-to-noise ratio threshold. Generally, clarification of the different types of cosmological distances that can be probed by PTAs, and their relation to pulsar distance measurements is important for ongoing PTA experiments aimed at detecting and characterizing GWs.

arXiv commentSubmitted to Physical Review D. Comments welcome

References in corpus (41)

• Planck 2015 results. XIII. Cosmological parameters
• A 2.4% Determination of the Local Value of the Hubble Constant
• Large Magellanic Cloud Cepheid Standards Provide a 1% Foundation for the Determination of the Hubble Constant and Stronger Evidence for Physics Beyond LambdaCDM
• Laser Interferometer Space Antenna
• A gravitational-wave standard siren measurement of the Hubble constant
• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• Using gravitational-wave standard sirens
• The Parkes multibeam pulsar survey: VI. Discovery and timing of 142 pulsars and a Galactic population analysis
• A 2 per cent Hubble constant measurement from standard sirens within 5 years
• The Astrophysics of Nanohertz Gravitational Waves
• Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays
• Ultra-high precision cosmology from gravitational waves
• Optimal strategies for gravitational wave stochastic background searches in pulsar timing data
• Expected properties of the first gravitational wave signal detected with pulsar timing arrays
• The stochastic background: scaling laws and time to detection for pulsar timing arrays
• Cosmology with the lights off: Standard sirens in the Einstein Telescope era
• Pulsar searches and timing with the SKA
• Gravitational wave astronomy of single sources with a pulsar timing array
• Strong Dependence of Type Ia Supernova Standardization on the Local Specific Star Formation Rate
• Astrometric Effects of a Stochastic Gravitational Wave Background
• Measuring the parameters of massive black hole binary systems with Pulsar Timing Array observations of gravitational waves
• Microarcsecond VLBI pulsar astrometry with PSR$\pi$ II. parallax distances for 57 pulsars
• Single Sources in the Low-Frequency Gravitational Wave Sky: properties and time to detection by pulsar timing arrays
• Discovery of 14 radio pulsars in a survey of the Magellanic Clouds
• Are we there yet? Time to detection of nanohertz gravitational waves based on pulsar-timing array limits
• Binary super-massive black hole environments diminish the gravitational-wave signal in the pulsar timing band
• Detection, Localization and Characterization of Gravitational Wave Bursts in a Pulsar Timing Array
• Precise radio astrometry and new developments for the next generation of instruments
• Prospects for accurate distance measurements of pulsars with the SKA: enabling fundamental physics
• Detecting eccentric supermassive black hole binaries with pulsar timing arrays: Resolvable source strategies
• Detection and localization of single-source gravitational waves with pulsar timing arrays
• A Bayesian analysis pipeline for continuous GW sources in the PTA band
• Radio Pulsars in the Magellanic Clouds
• Repeated Gravitational Lensing of Gravitational Waves in Hierarchical Black Hole Triples
• Eight New Radio Pulsars in the Large Magellanic Cloud
• Accelerated Bayesian model-selection and parameter-estimation in continuous gravitational-wave searches with pulsar-timing arrays
• VLBI astrometry of PSR J2222-0137: a pulsar distance measured to 0.4% accuracy
• Pulsar timing array observations of gravitational wave source timing parallax
• Pulsar Timing Arrays: No longer a Blunt Instrument for Gravitational Wave Detection
• The radio pulsar population of the Small Magellanic Cloud
• Geometrical vs wave optics under gravitational waves

Cited by in corpus (11)

• The Gravitational-Wave Physics II: Progress
• Extending the frequency reach of pulsar timing array based gravitational wave search without high cadence observations
• On Detecting Nearby Nano-Hertz Gravitational Wave Sources via Pulsar Timing Arrays
• Solar System-scale interferometry on fast radio bursts could measure cosmic distances with sub-percent precision
• Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms
• Measuring the Hubble Constant with Double Gravitational Wave Sources in Pulsar Timing
• Fresnel Models for Gravitational Wave Effects on Pulsar Timing
• Pulsar Timing Response to Gravitational Waves with Spherical Wavefronts from a Massive Compact Source in the Quadrupole Approximation
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• Can we hear beats with pulsar timing arrays?
• Full analytic expressions of overlap reduction functions for anisotropies of the stochastic gravitational-wave background with pulsar timing arrays