Cosmic variance in the nanohertz gravitational wave background

Abstract

We use large N-body simulations and empirical scaling relations between dark matter halos, galaxies, and supermassive black holes to estimate the formation rates of supermassive black hole binaries and the resulting low-frequency stochastic gravitational wave background (GWB). We find this GWB to be relatively insensitive ($\lesssim 10\%$) to cosmological parameters, with only slight variation between WMAP5 and Planck cosmologies. We find that uncertainty in the astrophysical scaling relations changes the amplitude of the GWB by a factor of $\sim 2$. Current observational limits are already constraining this predicted range of models. We investigate the Poisson variance in the amplitude of the GWB for randomly-generated populations of supermassive black holes, finding a scatter of order unity per frequency bin below 10 nHz, and increasing to a factor of $\sim 10$ near 100 nHz. This variance is a result of the rarity of the most massive binaries, which dominate the signal, and acts as a fundamental uncertainty on the amplitude of the underlying power law spectrum. This Poisson uncertainty dominates at $\gtrsim 20$ nHz, while at lower frequencies the dominant uncertainty is related to our poor understanding of the astrophysical scaling relations, although very low frequencies may be dominated by uncertainties related to the final parsec problem and the processes which drive binaries to the gravitational wave dominated regime. Cosmological effects are negligible at all frequencies.

12 pages, 7 figures. Accepted by ApJ

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• Single Sources in the Low-Frequency Gravitational Wave Sky: properties and time to detection by pulsar timing arrays
• The Need For Speed: Rapid Refitting Techniques for Bayesian Spectral Characterization of the Gravitational Wave Background Using PTAs
• Massive black hole evolution models confronting the n-Hz amplitude of the stochastic gravitational wave background
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• Harmonic space analysis of pulsar timing array redshift maps
• Spectral Variance in a Stochastic Gravitational-Wave Background From a Binary Population
• Ephemeris Errors and the Gravitational Wave Signal: Harmonic Mode Coupling in Pulsar Timing Array Searches
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• The NANOGrav 15 yr Data Set: Looking for Signs of Discreteness in the Gravitational-wave Background
• A High Fraction of Double-peaked Narrow Emission Lines in Powerful Active Galactic Nuclei
• Toward a test of Gaussianity of a gravitational wave background
• Reading signatures of supermassive binary black holes in pulsar timing array observations