Choosing Suitable Noise Models for Nanohertz Gravitational-wave Astrophysics

Accurately estimating the parameters of the nanohertz gravitational-wave background is essential for understanding its origin. The background is typically modeled with a power-law spectrum, parameterized with an amplitude A , which describes its intensity, and a spectral index γ , which describes how the background varies with frequency. Different collaborations have produced varied estimates of γ , some in tension with the value of γ = 13/3 expected for circular, gravitational-wave-driven binary black holes. However, estimates of A and γ can be affected by systematic errors and misspecified noise models. We investigate how systematic errors—which may plausibly be present in pulsar timing analyses—can shift inferences about A , γ . We demonstrate that conservatively incorporating noise sources into the model that are not actually present in the data does not produce bias inferences in practice. This addresses concerns that an overly complex noise model might lead to bias from a needlessly conservative prior. Our results highlight the importance of using comprehensive noise models in pulsar timing analyses to ensure accurate and reliable parameter estimation of the gravitational-wave background.