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

TL;DR

This paper systematically studies the stochastic gravitational-wave background from massive black hole binaries, assessing its detectability with Pulsar Timing Arrays and LISA, and explores implications for understanding black hole cosmic evolution.

Contribution

It provides the first comprehensive analysis of the gravitational-wave background from massive black hole binaries across various assembly scenarios and evaluates detection prospects with current and future observatories.

Findings

Predicted background amplitude ranges from 5x10^-16 to 8x10^-15 at 10^-8 Hz.

The background spectrum follows a steeper power-law than f^-2/3 at frequencies above 10^-8 Hz.

Detection of both stochastic background and individual sources will fully characterize black hole cosmic history.

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.