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 M⊙, 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 regardless of the specific model of massive black hole binaries formation and evolution, the characteristic amplitude hc of the gravitational wave stochastic background at 10 −8 Hz varies by less than a factor of 2. However, taking into account the uncertainties surrounding the actual key model parameters, the amplitude lies in the interval hc(f = 10 −8 Hz) ≈ 5 ×10 −16 −8×10 −15. The most optimistic predictions place the signal level at a factor of ≈ 3 below the current sensitivity of Pulsar Timing