Reading signatures of supermassive binary black holes in pulsar timing array observations

Constraining the origin of the nanohertz gravitational-wave background necessitates precise noise modelling to avoid parameter estimation biases. In this work, we find the inferred properties of the putative gravitational wave background in the second data release of the European Pulsar Timing Array to be in better agreement with theoretical expectations under the improved noise model. In particular, our improved noise models show consistency of the background's strain spectral index with the value of  -2/3, favoring the population of supermassive black hole binaries as the origin of the background. Our results further suggest that the observed gravitational wave emission is the dominant source of the binary energy loss, with no evidence of environmental effects or eccentric orbits. At the reference gravitational wave frequency of yr^-1, we also find a lower power-law strain amplitude of the background than in previous data analyses. This mitigates some of the tensions of the strain amplitude with the expected number density and mass scale of binaries discussed in the literature. Our analysis demonstrates the importance of accurate modelling of radio pulsar pulse profile variations, hierarchical properties of noise across pulsars, as well as noise model averaging, when inferring properties of the gravitational wave background.