Spectral Variance in a Stochastic Gravitational-Wave Background From a Binary Population

Abstract

A population of compact object binaries emitting gravitational waves that are not individually resolvable will form a stochastic gravitational wave signal. While the expected spectrum over population realizations is well known from Phinney (2001), its higher order moments have not been fully studied before or computed in the case of arbitrary binary evolution. We calculate analytic scaling relationships as a function of gravitational-wave frequency for the statistical variance, skewness, and kurtosis of a stochastic gravitational-wave signal over population realizations due to finite source effects. If the time derivative of the binary orbital frequency can be expressed as a power-law in frequency, we find that these moment quantities also take the form of power-law relationships. We also develop a numerical population synthesis framework against which we compare our analytic results, finding excellent agreement. These new scaling relationships provide physical context to understanding spectral fluctuations in a gravitational-wave background signal and may provide additional information that can aid in explaining the origin of the nanohertz-frequency signal observed by pulsar timing array campaigns.

arXiv comment8 pages, 3 figures. Published in ApJL

References in corpus (26)

• Array Programming with NumPy
• The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
• Search for an isotropic gravitational-wave background with the Parkes Pulsar Timing Array
• Searching for the nano-Hertz stochastic gravitational wave background with the Chinese Pulsar Timing Array Data Release I
• The second data release from the European Pulsar Timing Array III. Search for gravitational wave signals
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• Upper Limits on the Isotropic Gravitational-Wave Background from Advanced LIGO's and Advanced Virgo's Third Observing Run
• Gravitational Waves Probe the Coalescence Rate of Massive Black Hole Binaries
• The NANOGrav 15-year Data Set: Constraints on Supermassive Black Hole Binaries from the Gravitational Wave Background
• The Gravitational Wave Background from Cosmological Compact Binaries
• Gas driven massive black hole binaries: signatures in the nHz gravitational wave background
• Characterising gravitational wave stochastic background anisotropy with Pulsar Timing Arrays
• The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
• Constraining the Solution to the Last Parsec Problem with Pulsar Timing
• Variance of the Hellings-Downs Correlation
• The second data release from the European Pulsar Timing Array: VI. Challenging the ultralight dark matter paradigm
• Constraints On The Dynamical Environments Of Supermassive Black-hole Binaries Using Pulsar-timing Arrays
• Solar Wind Charge Exchange: An Astrophysical Nuisance
• Astrophysical constraints on massive black hole binary evolution from Pulsar Timing Arrays
• Cosmic variance in the nanohertz gravitational wave background
• Disentangling Multiple Stochastic Gravitational Wave Background Sources in PTA Datasets
• Pulsar timing array source ensembles
• The Probability Distribution of Astrophysical Gravitational-Wave Background Fluctuations
• Neural Networks unveiling the properties of gravitational wave background from massive black hole binaries
• Frequency-Domain Distribution of Astrophysical Gravitational-Wave Backgrounds

Cited by in corpus (10)

• The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background
• Toward a test of Gaussianity of a gravitational wave background
• Projections of the uncertainty on the compact binary population background using popstock
• Reading signatures of supermassive binary black holes in pulsar timing array observations
• Measuring anisotropies in the PTA band with cross-correlations
• Polarization Properties of the Electromagnetic Response to High-frequency Gravitational Wave
• Accelerated inference of binary black-hole populations from the stochastic gravitational-wave background
• Reconciling PTA and JWST and preparing for LISA with POMPOCO: a Parametrisation Of the Massive black hole POpulation for Comparison to Observations
• Accurate pulsar timing array residual variances and correlation of the stochastic gravitational wave background
• Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background