Hierarchical Bayesian method for detecting continuous gravitational waves from an ensemble of pulsars

Abstract

When looking for gravitational wave signals from known pulsars, targets have been treated using independent searches. Here we use a hierarchical Bayesian framework to combine observations from individual sources for two purposes: to produce a detection statistic for the whole ensemble of sources within a search, and to estimate the hyperparameters of the underlying distribution of pulsar ellipticities. Both purposes require us to assume some functional form of the ellipticity distribution, and as a proof of principle we take two toy distributions. One is an exponential distribution, defined by its mean, and the other is a half-Gaussian distribution defined by its width. We show that by incorporating a common parameterized prior ellipticity distribution we can be more efficient at detecting gravitational waves from the whole ensemble of sources than trying to combine observations with a simpler non-hierarchical method. This may allow us to detect gravitational waves from the ensemble before there is confident detection of any single source. We also apply this method using data for 92 pulsars from LIGO's sixth science run. No evidence for a signal was seen, but 90\% upper limits of $3.9\ee{-8}$ and $4.7\ee{-8}$ were set on the mean of an assumed exponential ellipticity distribution and the width of an assumed half-Gaussian ellipticity distribution, respectively.

18 pages, 8 figures, published in PRD

References in corpus (19)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Advanced Virgo: a 2nd generation interferometric gravitational wave detector
• Advanced LIGO
• The ATNF Pulsar Catalogue
• LIGO: The Laser Interferometer Gravitational-Wave Observatory
• A New Electron Density Model for Estimation of Pulsar and FRB Distances
• Robust parameter estimation for compact binaries with ground-based gravitational-wave observations using the LALInference software library
• The LIGO Open Science Center
• A statistical test for Nested Sampling algorithms
• Inferring the eccentricity distribution
• Upper limits on gravitational wave emission from 78 radio pulsars
• Evidence for a minimum ellipticity in millisecond pulsars
• The optimal search for an astrophysical gravitational-wave background
• First narrow-band search for continuous gravitational waves from known pulsars in advanced detector data
• psrqpy: a python interface for querying the ATNF pulsar catalogue
• Dirichlet Process Gaussian-mixture model: An application to localizing coalescing binary neutron stars with gravitational-wave observations
• Prospects of observing continuous gravitational waves from known pulsars
• Results of the deepest all-sky survey for continuous gravitational waves on LIGO S6 data running on the Einstein@Home volunteer distributed computing project
• Method to detect gravitational waves from an ensemble of known pulsars

Cited by in corpus (11)

• Searches for Gravitational Waves from Known Pulsars at Two Harmonics in 2015-2017 LIGO Data
• Lunar Gravitational-Wave Antenna
• Mining Gravitational-wave Catalogs To Understand Binary Stellar Evolution: A New Hierarchical Bayesian Framework
• Status and perspectives of Continuous Gravitational Wave searches
• Gravitational Waves from Double White Dwarfs as probes of the Milky Way
• Gravitational wave detection without boot straps: a Bayesian approach
• Density estimation with Gaussian processes for gravitational-wave posteriors
• Stochastic gravitational-wave background searches and constraints on neutron-star ellipticity
• Targeted search for the stochastic gravitational-wave background from the galactic millisecond pulsar population
• Search for gravitational wave signals from known pulsars in LIGO-Virgo O3 data using the 5n-vector ensemble method
• Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches