English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The continuous nanohertz gravitational waves (GWs) from individualsupermassive binary black holes (SMBBHs) can be encoded in the timing residualsof pulsar timing arrays (PTAs). For each pulsar, the residuals actually containan Earth term and a pulsar term, but usually only the Earth term is consideredas signal and the pulsar term is dropped, which leads to parameter-estimationbiases (PEBs) for the SMBBHs, and currently there are no convenient evaluationsof the PEBs. In this article, we formulate the PEBs for a SMBBH with aneccentric orbit. In our analyses, the unknown phases of pulsar terms aretreated as random variables obeying the uniform distribution $U[0,2\pi)$, dueto the fact that pulsar distances are generally poorly measured. Our analyticalresults are in accordance with the numerical work by Zhu et. al. (2016) at$1.5\sigma$ level, implying that our formulae are effective in estimatingmagnitudes of the PEBs. Additionally, we find that for two parameters -- Earthterm phase $\varphi^E$ and orbital eccentricity $e$, their biases $\Delta\varphi^E$ and $\Delta e/e$ monotonically decrease as $e$ increases, whichpartly confirms a hypothesis in our previous work Chen & Zhang (2018).Furthermore, we also calculate the PEBs caused by the recently observedcommon-spectrum process (CSP), finding that if the strain amplitude of thecontinuous GW is significantly stronger ($3$ times larger, in our cases) thanthe stochastic GW background, the PEBs from pulsar terms are larger than thosefrom the CSP. Our formulae of the PEBs can be conveniently applied in thefuture PTA data analyses.

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