The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays

Abstract

Massive black hole binary systems, with masses in the range ~10^4-10^10 \msun, are among the primary sources of gravitational waves in the frequency window ~10^-9 Hz - 0.1 Hz. Pulsar Timing Arrays (PTAs) and the Laser Interferometer Space Antenna (LISA) are the observational means by which we will be able to observe gravitational radiation from these systems. We carry out a systematic study of the generation of the stochastic gravitational-wave background from the cosmic population of massive black hole binaries. We consider a wide variety of assembly scenarios and we estimate the range of signal strength in the frequency band accessible to PTAs. We show that, taking into account the uncertainties surrounding the actual key model parameters, the amplitude lies in the interval h_c(f = 10^-8 Hz)~5x10^-16 - 8x10^-15. The most optimistic predictions place the signal level at a factor of ~3 below the current sensitivity of Pulsar Timing Arrays, but within the detection range of the complete Parkes PTA for a wide variety of models, and of the future Square-Kilometer-Array PTA for all the models considered here. We also show that at frequencies >10^-8 Hz the frequency dependency of the generated background follows a power-law significantly steeper than f^-2/3, that has been considered so far. Finally we show that LISA observations of individual resolvable massive black hole binaries are complementary and orthogonal to PTA observations of a stochastic background from the whole population in the Universe. In fact, the detection of gravitational radiation in both frequency windows will enable us to fully characterise the cosmic history of massive black holes.

21 pages, 14 figures, minor revisions, accepted for publication in MNRAS

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• Nano-Hertz Gravitational Waves Searches with Interferometric Pulsar Timing Experiments
• High-Redshift Merger Model for Low-Frequency Gravitational Wave Background
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• The impact of outliers on pulsar timing arrays
• Gravitational wave astronomy: astrophysical and cosmological inferences
• Exploring realistic nanohertz gravitational-wave backgrounds
• A Parallelized Bayesian Approach To Accelerated Gravitational-Wave Background Characterization
• Time-dependent deflection reconstruction: new technique to search for gravitational waves with the cosmic microwave background
• Searching for A Generic Gravitational Wave Background via Bayesian Nonparametric Analysis with Pulsar Timing Arrays
• Assessing the performance of future space-based detectors: Astrophysical foregrounds and individual sources
• Pulsar timing array projects
• Full analytic expressions of overlap reduction functions for anisotropies of the stochastic gravitational-wave background with pulsar timing arrays
• Stochastic gravitational wave background from the collisions of dark matter halos