Parameter-Estimation Biases for Eccentric Supermassive Binary Black Holes in Pulsar Timing Arrays: Biases Caused by Ignored Pulsar Terms

Abstract

The continuous nanohertz gravitational waves (GWs) from individual supermassive binary black holes (SMBBHs) can be encoded in the timing residuals of pulsar timing arrays (PTAs). For each pulsar, the residuals actually contain an Earth term and a pulsar term, but usually only the Earth term is considered as signal and the pulsar term is dropped, which leads to parameter-estimation biases (PEBs) for the SMBBHs, and currently there are no convenient evaluations of the PEBs. In this article, we formulate the PEBs for a SMBBH with an eccentric orbit. In our analyses, the unknown phases of pulsar terms are treated as random variables obeying the uniform distribution $U[0,2\pi )$, due to the fact that pulsar distances are generally poorly measured. Our analytical results are in accordance with the numerical work by Zhu et. al. (2016) at $1.5\sigma$ level, implying that our formulae are effective in estimating magnitudes of the PEBs. Additionally, we find that for two parameters -- Earth term phase ${\phi }^E$ and orbital eccentricity $e$, their biases $\Delta {\phi }^E$ and $\Delta e/e$ monotonically decrease as $e$ increases, which partly confirms a hypothesis in our previous work Chen & Zhang (2018). Furthermore, we also calculate the PEBs caused by the recently observed common-spectrum process (CSP), finding that if the strain amplitude of the continuous GW is significantly stronger ($3$ times larger, in our cases) than the stochastic GW background, the PEBs from pulsar terms are larger than those from the CSP. Our formulae of the PEBs can be conveniently applied in the future PTA data analyses.

29 pages, 4 figure, accepted by ApJ

References in corpus (17)

• The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) Project
• The International Pulsar Timing Array second data release: Search for an isotropic Gravitational Wave Background
• On the evidence for a common-spectrum process in the search for the nanohertz gravitational-wave background with the Parkes Pulsar Timing Array
• Common-red-signal analysis with 24-yr high-precision timing of the European Pulsar Timing Array: Inferences in the stochastic gravitational-wave background search
• Expected properties of the first gravitational wave signal detected with pulsar timing arrays
• On Pulsar Distance Measurements and their Uncertainties
• The Local Nanohertz Gravitational-Wave Landscape From Supermassive Black Hole Binaries
• Measuring the parameters of massive black hole binary systems with Pulsar Timing Array observations of gravitational waves
• An all-sky search for continuous gravitational waves in the Parkes Pulsar Timing Array data set
• The First Spectroscopically Resolved Sub-parsec Orbit of a Supermassive Binary Black Hole
• The NANOGrav 11-Year Data Set: Limits on Gravitational Wave Memory
• Observing the dynamics of super-massive black hole binaries with Pulsar Timing Arrays
• Detection and localization of continuous gravitational waves with pulsar timing arrays: the role of pulsar terms
• Subtraction-noise projection in gravitational-wave detector networks
• A coherent method for the detection and estimation of continuous gravitational wave signals using a pulsar timing array
• Extending the frequency reach of pulsar timing array based gravitational wave search without high cadence observations
• Supermassive Binary Black Hole Evolution can be traced by a small SKA Pulsar Timing Array